Biology A path through The Default Library ======================================== How life works, from molecules to cells to bodies to ecosystems, and how evolution ties it all together. Step 1. General Chemistry: Electrons Decide Everything ------------------------------------------------------ Why: Atoms and bonds come first. Every substance, from salt to proteins, is a pattern of electrons deciding to share, steal or keep their distance. Learn the pattern and the table, the shapes and the reactions start to look inevitable. Drop a pinch of salt into water and it vanishes. Drop a spoon of sugar in and it vanishes too. Yet the salt water conducts electricity and the sugar water does not, the salt can be pulled back out only by boiling the water away, and the two behave nothing alike in your cooking. Strike a match, and a stick of wood and a little powder become heat, light and smoke. Charge a phone, and something inside it moves from one side to the other and back again. A chemist looks at all of these and asks the same two questions. What are the atoms doing with their outer electrons? And where is the energy going? General Chemistry is the course that teaches you to ask those questions in your sleep. Almost every later chemistry course, and most of biology, is these two ideas applied to a bigger puzzle. The course in one box Who takes itChemistry, biology, chemical and materials engineering and pre-medical students, in year 1, almost everywhere in the world. Programmes shaped by the American Chemical Society, MIT's Course 5 or the Royal Society of Chemistry all start here. What it is forReading a formula as a picture of electrons, and predicting what will react, how much, and how much energy changes hands. Comes afterSchool algebra and physics. Calculus I (34/01) and Physics I: Mechanics (34/06) run alongside it. Leads toEquilibrium & Kinetics (35/37), Organic Chemistry: Structure & Mechanism (35/38), and through them Biochemistry (35/43) and Cell Biology (35/44). What this piece gives youYou will not be able to balance a hard redox equation under exam pressure. You will see why the periodic table has the shape it has, why a water molecule is bent, and how to turn grams into moles into energy. A kitchen-flavoured first read is The Science of Bread (14/07); for the chemistry of a battery see Batteries (29/08). This piece goes further. Atoms: the electrons are what chemistry sees An atom is a tiny nucleus of protons and neutrons with electrons around it. The nucleus almost never changes in a chemical reaction. That is the difference between chemistry and nuclear physics: chemistry is what happens when atoms trade, share or lend electrons and the nuclei stay put. (Radioactivity is the other business; Marie Curie won the 1903 Nobel Prize in Physics and the 1911 prize in Chemistry, the second for discovering radium and polonium, and her work sits on the border between them.) Electrons are not little planets. Quantum mechanics (see Quantum Mechanics, 34/83, for the real thing) says each electron occupies an orbital, a cloud-shaped region where it is likely to be found, and each orbital has a fixed energy. Orbitals come in shells numbered 1, 2, 3 and so on, and in shapes called s, p, d and f. An orbital holds at most two electrons. Fill them from the lowest energy up, and you get the atom's electron configuration. fill 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p …lowest energy first · s holds 2, p holds 6, d holds 10 · only the outermost shell takes part in most chemistry Try it. Slide to carbon (6): 1s² 2s² 2p², so four electrons in the outer shell. Oxygen (8) has six. Sodium (11) has one, alone in a third shell. Sodium's single lonely outer electron and chlorine's seven, one short of a full eight, are why the two meet so eagerly. At 24 (chromium) and 29 (copper) you will see the table's first small exceptions: a half-full or full 3d subshell is slightly more stable than the tidy filling order predicts. Interactive · Build an atom, electron by electron Element (atomic number Z) Configurations by the Madelung filling order (1s 2s 2p 3s 3p 4s 3d 4p) with the chromium and copper exceptions; shell counts are the sum over subshells. Shells are drawn as rings for counting, not as orbits. The periodic table is a map of shell-filling In 1869 Dmitri Mendeleev presented a table that arranged the known elements by atomic weight and, crucially, left gaps where the pattern said an element should exist, and described what the missing ones would be like. The gaps were later filled by gallium, scandium and germanium. The modern table is the same idea, ordered by atomic number, and now we know what the rows are: each row is a shell filling up, and each column holds atoms with the same number of outer electrons, which is why they behave alike. (Mendeleev was not the only person to see the pattern; Lothar Meyer published a similar one around the same time. Mendeleev's gift was trusting the pattern enough to predict.) Three trends do most of the work, and one picture explains all three. An outer electron feels the nucleus's pull, partly cancelled by the electrons between. Move across a row and the nuclear charge grows while the new electrons go into the same shell, so the pull gets stronger and the atom shrinks. Move down a column and a whole new shell is added, so the atom is bigger and its outer electron is easier to remove. Interactive · Periodic trends from real data Ionisation energy Electronegativity Covalent radius Highlight element Data: first ionisation energies in kJ/mol from the NIST Atomic Spectra Database values (via Wikipedia's data page); Pauling electronegativities; covalent radii from Cordero et al., Dalton Trans. 2008 (carbon sp3; Mn, Fe, Co low-spin). Noble gases He, Ne and Ar have no Pauling value. Look at the ionisation energy plot: a sawtooth. Each peak is a noble gas, whose shell is full and which holds its electrons tightly; each trough is the alkali metal that follows, with one electron far out in a new shell. Sodium needs about 496 kJ per mole of electrons to lose one, neon needs 2081. That sawtooth is why sodium is violently reactive and neon is not reactive at all. Everything about metals, nonmetals and the families in between falls out of it. Bonds: a tug-of-war for electrons Atoms bond because the shared or transferred arrangement has lower energy than separate atoms. Which kind of bond forms depends on how unevenly the atoms pull. Electronegativity is a number for an atom's pull on the electrons it shares; Linus Pauling's scale runs from 0.82 for potassium to 3.98 for fluorine. If two atoms pull almost equally (hydrogen with hydrogen), the electrons are shared: a covalent bond. If one pulls vastly harder (chlorine versus sodium), it takes the electron outright, and the two resulting ions, one plus and one minus, stick together by plain electrical attraction: an ionic bond. In between lies the common case, the polar covalent bond, where the electrons are shared but sit closer to one atom. Water's O–H bond is the standard example. Δ(electronegativity) small → covalent · middling → polar covalent · large → ionic-likerough textbook cut-offs near 0.4 and 1.7. They are a guide, not a law: bonding is a continuum Interactive · What kind of bond? Na–Cl H–Cl O–H C–H H–H Na/Mg Atom A Atom B Pauling values (Z = 1 to 36, noble gases He, Ne and Ar omitted). Two metals are labelled metallic instead. The result matters outside the lab. Salt dissolves in water because water's polar O–H bonds make its oxygen end slightly negative and its hydrogen ends slightly positive, and those poles pry ions out of the crystal. Oil and water do not mix because oil has no poles to grip. "Like dissolves like" is bond polarity in one sentence. Shape: electron pairs repel, and that sets the geometry A molecule is not a flat diagram. Water is bent, not straight; ammonia is a little pyramid. One rule predicts most of it, the VSEPR rule (valence-shell electron-pair repulsion). Count the electron domains on the central atom, meaning each bond (single, double or triple counts as one) and each lone pair, since each domain is a cloud of negative charge. They repel, so they spread as far apart as they can on a sphere: two domains sit 180° apart, three at 120°, four at 109.5°, five and six in the arrangements below. The molecule's shape is then the arrangement of the atoms only; the lone pairs are invisible in the name but they still take up room. That is why water is bent: oxygen has four domains (two bonds and two lone pairs), arranged like a tetrahedron, but only two corners hold atoms. Lone pairs are slightly bulkier than bonds, so they squeeze the angle: 109.5° in methane, about 107° in ammonia, about 104.5° in water. Water's bend is why it is polar and why ice floats, which is why lakes freeze from the top down. Interactive · Build a molecule's shape CH₄ NH₃ H₂O CO₂ SF₆ XeF₄ Bonded atoms Lone pairs on the centre Directions are the ideal geometry for each number of domains; lone pairs fill the equatorial positions first in the five-domain case and opposite positions in the six-domain case, as VSEPR prescribes. Angles are textbook values; real molecules deviate by a few degrees. The tool stops at six domains (the common textbook range). The mole: counting atoms by weighing You cannot count atoms, but you can weigh them, and the mole turns one into the other. A mole is a fixed number of things, exactly 6.02214076 × 10²³ since the 2019 redefinition of the SI. The point of choosing that number is that one mole of any element weighs, in grams, its atomic weight: carbon about 12.011 g, oxygen 15.999 g (the IUPAC standard atomic weights, rounded). So grams become moles by dividing by the atomic or molar weight, and a balanced equation is a recipe in moles. C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂Oone mole of propane needs five moles of oxygen · the equation balances atoms, so mass in = mass out A worked number. One mole of propane (the gas in a camping stove) weighs 3 × 12.011 + 8 × 1.008 = 44.097 g. It needs five moles of oxygen, 159.99 g, and produces three moles of carbon dioxide (132.03 g) and four of water (72.06 g). In: 204.09 g. Out: 204.09 g. Nothing is lost. If there is less oxygen than five to one, the oxygen is the limiting reagent: the reaction stops when it runs out, some propane is left, and (in a real stove) you get soot and poisonous carbon monoxide, the reason you never burn a stove indoors without ventilation. Because air is about 21% oxygen, burning a volume of propane needs roughly 24 volumes of air. Interactive · Who runs out first? Propane Oxygen Molar masses from the IUPAC abridged standard atomic weights (C 12.011, H 1.008, O 15.999). Assumes complete combustion to CO₂ and H₂O. Energy in reactions: breaking costs, making pays Why does propane burn and release heat? Because the products' bonds are stronger than the reactants'. Breaking a bond always costs energy, since you pull two atoms against their attraction. Making a bond always releases it. A reaction's energy change is the bill for breaking all the old bonds minus the payment for making all the new ones. If you get paid more than you spent, heat comes out: exothermic. Otherwise it must be supplied: endothermic. ΔH ≈ (energy to break bonds) − (energy released making bonds)average bond enthalpies are estimates: they differ a little between tables and between molecules Methane burning: break four C–H and two O=O (2648 kJ), make two C=O and four O–H (3450 kJ), net −802 kJ per mole: exothermic. The measured value is −802.5. That match is partly luck, since the numbers are averages over many molecules, as the hydrogenation of ethene (−123 estimated against −136 measured) shows. Interactive · Bond ledger H₂ + Cl₂ CH₄ burning N₂ + H₂ Ethene + H₂ Average bond enthalpies in kJ/mol as in common textbook tables (the LibreTexts table lists e.g. C–H 415, H–Cl 432; C=O is the value for CO₂). Measured ΔH from standard enthalpies of formation, gaseous water. N₂ + 3H₂ → 2NH₃ is the Haber reaction (measured −92.28 kJ per mole of N₂ is the quoted standard value). Acids and bases: who gives up a proton An acid, at this level, is a molecule that hands a hydrogen ion (a proton) to water; a base takes one. The strength of an acid is not about how concentrated it is but about how readily it lets go. A strong acid such as hydrochloric acid gives up essentially all its protons. A weak one such as the acetic acid in vinegar gives up only a small fraction, which is why vinegar is safe to put on a salad and the same concentration of hydrochloric acid is not. The pH is minus the base-10 logarithm of the hydrogen-ion concentration, so each step down in pH is ten times more acidic. Worked number: 0.1 M hydrochloric acid has pH 1.00. 0.1 M acetic acid, with an acid constant of 1.75 × 10⁻⁵ (pKa 4.76), has pH 2.88, and only about 1.3% of its molecules have let go. Dilute it a thousand times and the fraction rises to roughly a third, an early hint of the equilibrium ideas of Equilibrium & Kinetics (35/37). And dilute even a strong acid to 10⁻⁸ M and the pH is 6.98, not 8: water itself supplies hydrogen ions, and you cannot make an acid into a base by adding water. Interactive · Strong versus weak Strong acid Acetic acid (vinegar) Concentration Solved exactly from the charge balance [H+] = [A-] + [OH-] with Kw = 10-14 and Ka = 10-4.756 for acetic acid at 25 °C. Ideal solution (activities ignored). What a graduate just sees A formula is an electron story: count the outer electrons first and the bonding follows. Position on the periodic table predicts size, reactivity and bond type; you rarely need to look anything up. Atoms bond to lower their energy, and unequal pulls make polar bonds, which make water, soap and proteins behave as they do. Count the electron pairs around an atom and you know the shape of the molecule. Equations are recipes in moles, not grams; the limiting reagent decides what you get. Atoms are neither created nor destroyed: if the equation does not balance, something is missing. Breaking bonds costs, making bonds pays, and the difference is the heat of the reaction. Strong is not concentrated: strength is how readily an acid lets go, concentration is how much you have. Where it shows up next Equilibrium & Kinetics (35/37): the weak acid you just met is the first reaction that does not go to completion, and the next course asks how far and how fast. Organic Chemistry (35/38): carbon's four bonds, the shapes above and electronegativity are the whole starting kit for curly arrows. Biochemistry (35/43): proteins fold because of polar bonds, water and pH; DNA holds together by hydrogen bonds you can now name. In the world: the lithium-ion battery in your phone (see Batteries, 29/08), fertiliser made from the Haber reaction, the reason a camping stove must be ventilated, and the pH label on a shampoo bottle. If you want to go deeper 📘 Free textbook. OpenStax, Chemistry 2e (Flowers, Theopold, Langley, Robinson et al.; free to read online, 2019). A full first-year course with worked problems. openstax.org 📘 Textbook. Brown, LeMay, Bursten, Murphy, Woodward and Stoltzfus, Chemistry: The Central Science (Pearson). One of the two or three books most universities assign, strong on the visuals. 📘 Gentler. Primo Levi, The Periodic Table (1975): twenty-one memoir chapters, each named for an element, by a chemist who survived Auschwitz. No equations, much meaning. 🌐 Free course. MIT OpenCourseWare 5.111 Principles of Chemical Science (Fall 2008): lectures on atoms, bonding, equilibrium and acids. The takeaway Chemistry is electron bookkeeping and energy bookkeeping. An atom's outer electrons set its place on the table, how it bonds and what shape its molecules take; the mole lets you weigh your way into those counts; and the balance between breaking and making bonds says whether a reaction gives heat or takes it. Try this: this week, look at the back of a food label or a bottle of vinegar and find one chemical name. Write its formula and count its outer electrons. (Kitchen-safe, and no mixing needed: just a pen.) Sources & Further Reading Sources. Electron configurations, VSEPR, the mole, bond enthalpies and pH are standard first-year textbook chemistry (OpenStax Chemistry 2e). Pauling electronegativities, first ionisation energies (NIST Atomic Spectra Database) and Cordero covalent radii (Dalton Trans. 2008, 2832) as tabulated on Wikipedia's data pages. Mendeleev presented his table to the Russian Chemical Society in 1869 (Wikipedia, Dmitri Mendeleev). Marie Curie: Nobel Prizes in Physics 1903 and Chemistry 1911 (nobelprize.org via Wikipedia). SI mole redefinition 2019 (BIPM). This is a textbook summary, not laboratory instruction. Go deeper. 🌐 OpenStax Chemistry 2e 🌐 MIT OCW 5.111 Principles of Chemical Science 📘 Primo Levi, The Periodic Table Step 2. Organic Chemistry: Structure & Mechanism ------------------------------------------------ Why: Life is carbon chemistry. A few shapes, a few small groups of atoms and one rule about where electrons want to go explain more of carbon chemistry than any list of reactions could. Smell a freshly peeled orange and then a handful of caraway seeds. Two different smells, from two molecules that have exactly the same atoms connected in exactly the same order. The only difference is that one is the mirror image of the other, like a left and right hand, and your nose can tell them apart. Spearmint and caraway are the same way: one handed form of carvone smells of spearmint, its mirror image of caraway. Organic chemistry is the chemistry of carbon compounds, and it is the subject people fear most. It shouldn't be. It looks like thousands of reactions to memorise, but graduates carry something much smaller: a handful of shapes, a handful of small groups of atoms, and one idea about where electrons want to go. With those, reactions that look new are variations on ones you already know. The course in one box Who takes itChemistry, biochemistry, biology, pharmacy, medicine and chemical engineering students; usually year 2, typically a full year in the US and UK, sometimes split across years. Programmes shaped by the American Chemical Society, MIT's Course 5 or the Royal Society of Chemistry all require it. What it is forPredicting what a carbon compound will do from how its atoms are arranged and where its electrons are, and drawing the steps with curly arrows. Comes afterGeneral Chemistry (35/36); Equilibrium & Kinetics (35/37) helps for rates and acidity. Leads toOrganic Synthesis (35/39), Physical Chemistry (35/40) and Biochemistry (35/43). What this piece gives youYou will not be able to plan a multi-step synthesis. You will be able to look at a molecule, say what its atoms' shapes are, spot which end is electron-rich, and draw why a reaction goes where it goes. This piece describes mechanisms only: no procedures. A kitchen-flavoured first read is How Taste Actually Works (14/10); for the molecules of life see Biochemistry (35/43). Carbon makes four bonds, and the shape depends on the hybrid Carbon has four outer electrons and wants four bonds. In the molecule methane, CH₄, the four bonds point to the corners of a tetrahedron, 109.5° apart. That puzzled early chemists, because carbon's outer orbitals are one s and three p, which should not give four equal bonds. The fix is hybridisation: mix the s and p orbitals into four identical sp³ hybrids that point to the tetrahedron's corners. Jacobus van 't Hoff, in a pamphlet of 1874, proposed this tetrahedral carbon; Joseph Le Bel is credited with the same idea at the same time. Mix fewer orbitals and you get different shapes. In ethene, each carbon uses one s and two p orbitals to make three sp² hybrids in a plane, 120° apart, and the leftover p orbital sticks up and down to form a pi bond over the top. In ethyne (acetylene) each carbon makes two sp hybrids in a line, 180° apart, and keeps two p orbitals for two pi bonds. The bond length and strength follow: single C–C about 153 pm and 347 kJ/mol; C=C about 133 pm and 611 kJ/mol; C≡C about 118 pm and 839 kJ/mol. Shorter and stronger as more electrons are shared, but not in simple proportion: a pi bond is weaker than a sigma bond. Interactive · One carbon, three shapes Ethane Ethene Ethyne Benzene Bond lengths and strengths as quoted for alkanes, alkenes and alkynes in Wikipedia's Alkene and Alkyne articles (citing March's Advanced Organic Chemistry); benzene's 140 pm from neutron diffraction. s character is 1 part in the number of orbitals mixed (25, 33, 50 %). Drawn schematically; the dashed bond points away from you. In 1865 August Kekulé proposed that benzene is a ring; later work showed that all six bonds are the same length, 140 pm, between a single and a double bond. We will see why in the resonance section. Functional groups: a few small groups do almost all the chemistry A big organic molecule is a skeleton of carbon and hydrogen, which is mostly inert, hung with a few small clusters of other atoms: a functional group. The skeleton sets the size and shape; the groups do the chemistry. An alcohol (–OH), a carboxylic acid (–COOH), an ester (–COO–), an amine (–NH₂), a ketone (C=O between carbons), an alkene (C=C): each behaves the same way wherever it appears. Learn about a dozen and you can read the structure of aspirin, a fruit flavour or a protein and know where the reactive spots are. Interactive · Find the group Alcohol Phenol Ether Aldehyde Ketone Acid Ester Amide Amine Alkene Aromatic A small, illustrative list of familiar molecules, each tagged with the groups it contains (aspirin: acid, ester, aromatic ring; vanillin: aldehyde, phenol, ether, ring; paracetamol: amide, phenol, ring). The groups and their rough behaviour are standard textbook content. The same group in a new molecule gives the same behaviour. An ester links the vinegar-like acid and the alcohol in a banana-smelling flavour. The amide link joins amino acids into proteins, and it is the same link that holds nylon together: a cousin in your jacket and in your muscle. Isomers and handedness: same atoms, different molecules Two molecules can share a formula and be different substances. Structural isomers have their atoms connected in a different order: butane and isobutane are both C₄H₁₀. The numbers explode. There are 2 alkanes with 4 carbons, 5 with 6, 75 with 10, 366,319 with 20. That is why chemists need a system to name and draw structures. Stereoisomers have the same connections but a different arrangement in space. The classic case is a carbon with four different groups: a stereocentre. It has two forms that are mirror images that cannot be stacked, like your hands: enantiomers. Chemically they behave identically in a symmetric world, but not inside a living cell, where enzymes and receptors are themselves handed. The two carvones smell different (R is spearmint, S is caraway), and a drug's two hands can act differently. The thalidomide story is often told too simply. Marketed from 1957 in West Germany, thalidomide caused severe birth defects, and was withdrawn in Europe in 1961; estimates are of more than 10,000 children seriously harmed. The popular version says one mirror image cured morning sickness and the other caused the damage, so a pure sample would have been safe. In fact the two forms interconvert in the body through an acidic hydrogen on the stereocentre, so separating them would not have prevented it. The real lessons were about testing and regulation: the 1962 Kefauver-Harris Amendment in the United States and tougher drug rules in many countries. Frances Kelsey at the US FDA had held up its approval there. (This is chemistry history, not medical advice.) Interactive · Count isomers, test a carbon Carbons in the alkane Stereocentres Click each position to change the group on one carbon HHHH Isomer counts for CnH2n+2 are the standard values (Wikipedia, Alkane). The maximum is 2n stereoisomers for n stereocentres; molecules with internal symmetry (meso compounds) have fewer. Resonance: when one drawing is not enough Some molecules cannot be drawn correctly with one picture. Acetate (the ion left when acetic acid loses its proton) has two oxygens. One drawing puts the double bond to the first oxygen; another puts it on the second. Neither is real. The truth is a single structure in which the electrons are spread over both oxygens, and both C–O bonds are identical, in between a single and a double bond. The drawings are resonance contributors, and the real molecule, the resonance hybrid, is more stable than any of them. Benzene is the same: six carbons sharing six pi electrons, with all bonds equal. The practical effect is acidity. A molecule is a stronger acid when its anion is more stable. The ethoxide anion from ethanol has its negative charge stuck on one oxygen. Acetate spreads it over two. Phenoxide spreads it into the ring. The result is that acetic acid (pKa 4.76) is about 10¹¹ times stronger than ethanol (15.9), with phenol (9.95) in between. Interactive · Who gives up its proton? Solution pH Fraction ionised = 1 / (1 + 10pKa − pH), pKa in water at 25 °C: ethanol 15.9 (Wikipedia, Ethanol), phenol 9.95 (Phenol), acetic acid 4.756 (Acid dissociation constant). Ethanol's pKa is quoted between about 15.5 and 16 in different sources. Curly arrows: following the electrons Organic mechanisms are drawn with curly arrows, an idea usually credited to Robert Robinson in 1922. The rule is short. An arrow starts where electrons are (a lone pair or a bond) and ends where they are going (a new bond or an atom taking a lone pair). A reaction is a sequence of such arrows. It reduces memorisation to a question you can ask of any molecule: where are the electrons, and where is the electron-poor spot they would like to go to? Take the simplest case, SN2: a nucleophile (Nu⁻, electron-rich) replaces a leaving group (X) on a carbon. One arrow goes from Nu's lone pair to carbon; another goes from the C–X bond to X. The carbon cannot hold five bonds, so the second arrow must happen as the first does. It all occurs in a single step, with Nu arriving on the side opposite X, and the carbon's three other groups flip like an umbrella in the wind. This is the Walden inversion. Because both reactants are in the one step, the rate depends on both. Hughes and Ingold, working on kinetics in the 1930s, used this signature to separate the two classic pathways and gave them the names SN1 (first order) and SN2 (second order). Interactive · Slide through an SN2 reaction Reaction coordinate Schematic: the geometry and the energy curve are idealised (an exothermic reaction with a single barrier), not computed from quantum chemistry. The H–C–X angle runs from 109.5° (tetrahedral) through 90° (planar transition state) to 70.5° (the inverted tetrahedron). Substitution or elimination: reading the substrate A nucleophile can also act as a base: instead of attacking the carbon, it can pluck off a hydrogen from the neighbouring carbon, pushing electrons to form a C=C bond and kicking out X. That is elimination, E2 (one step, second order) or E1 (two steps, after ionisation). Which wins? The standard rules read the carbon holding X. A methyl or primary carbon is open; SN2 can get in. A tertiary carbon is crowded, so the nucleophile cannot reach it, but it can ionise into a stable tertiary carbocation (SN1 and E1) or let a strong base pick off a hydrogen (E2). Secondary carbons sit in between, and the answer depends on the reagent. A bulky base cannot get close to the carbon but can reach the outer hydrogens, so it eliminates. Heat favours elimination, because it makes more molecules. Polar protic solvents help the ionising paths; polar aprotic ones help SN2. Interactive · Which path? Substrate Methyl Primary Secondary Tertiary Reagent Good Nu, weak base Strong small base Strong bulky base Weak Nu, weak base Temperature Mild Warm A lookup of the textbook decision rules (e.g. Clayden et al., Organic Chemistry), for understanding which factor matters, not a prediction tool for real syntheses. Examples of the reagent types are given in the labels. Addition: where the electrons go first An alkene's pi bond is a rich, exposed cloud of electrons sitting above and below the plane, easy to reach. So alkenes act as nucleophiles and react with electrophiles: acids, bromine. In the addition of H–Br to an alkene, the pi electrons attack the hydrogen (curly arrow 1), H–Br breaks (arrow 2), and a carbocation forms on the carbon that did not get the hydrogen. Then bromide attacks the cation (arrow 3). The hydrogen can land on either carbon of an unsymmetrical alkene, and the choice decides the product. It goes where it leaves the more stable cation, and a cation is more stable the more alkyl groups are attached to its carbon, since they donate electrons toward its empty orbital (hyperconjugation and induction). Tertiary beats secondary beats primary. This is Markovnikov's rule, formulated by Vladimir Markovnikov around 1870 from observations, and explained by the cation a century later. It is an example of the series' big idea: reactions go where the intermediate is most stable. Interactive · HBr meets an alkene Ethene Propene 1-Butene 2-Butene 2-Methylpropene 1 · Meet 2 · Cation forms 3 · Product Primary, secondary and tertiary refer to the number of alkyl groups on the cationic carbon (1, 2, 3). Stability order tertiary > secondary > primary is the textbook result. Under the conditions assumed here (no peroxides). What a graduate just sees Four sigma bonds means a tetrahedron, three means a flat triangle, two means a line. A pi bond is an exposed electron cloud: a place where things attack, and a reason a double bond cannot twist. A big molecule is a skeleton plus a few groups; the groups do the chemistry. Four different groups on a carbon means a handed molecule, and living systems care which hand. Spread-out charge is stable charge: that is why carboxylic acids are acids and benzene is calm. Every mechanism is a story of electrons moving from where they are rich to where they are poor. Crowding decides: open carbons get substituted, crowded ones eliminate or ionise. When there is a choice, reactions go through the more stable intermediate. Where it shows up next Organic Synthesis (35/39): the same arrows, strung into multi-step plans to build a target molecule from simple starting points. Physical Chemistry (35/40): the quantum picture of why hybrids, resonance and transition states have the energies they do. Biochemistry (35/43): every biological reaction is a mechanism with curly arrows, catalysed by an enzyme. In 2022, Carolyn Bertozzi shared the Chemistry Nobel with Morten Meldal and K. Barry Sharpless for click and bioorthogonal chemistry: reactions designed with these ideas to run inside living cells. In the world: drugs (aspirin, paracetamol), plastics and nylon, flavours and fragrances, fuels, soap. It also underlies green chemistry, the effort to design reactions that waste less and avoid hazardous solvents. If you want to go deeper 📘 Textbook. Jonathan Clayden, Nick Greeves and Stuart Warren, Organic Chemistry (Oxford, 2nd edition, 2012). Mechanism first, very widely used in the UK and Europe. 📘 Textbook. John McMurry, Organic Chemistry (Cengage) or David Klein, Organic Chemistry (Wiley): the common US choices, with many practice problems. 📘 Free textbook. OpenStax, Organic Chemistry. openstax.org 📘 Gentler. Penny Le Couteur and Jay Burreson, Napoleon's Buttons (2003): seventeen molecules that changed history, from spices to nylon. 🌐 Free course. MIT OpenCourseWare 5.12 Organic Chemistry I (Spring 2005); also Khan Academy's Organic chemistry. The takeaway Organic chemistry is shape, groups and electrons. Carbon's hybrids set the shape; a few functional groups set the behaviour; and curly arrows track electrons from rich spots to poor ones. When a reaction has a choice, it goes through the more stable intermediate, the less crowded path, or the lower barrier. Try this: this week, read the ingredient list on a food or medicine package and pick one name ending in -ate, -ol or -amine. Say which functional group it names and what that group tends to do. (Nothing to mix or heat; a pen is enough.) Sources & Further Reading Sources. Hybridisation, functional groups, resonance, SN1/SN2/E1/E2 and Markovnikov are standard textbook organic chemistry (Clayden et al.; OpenStax Organic Chemistry). van 't Hoff's 1874 pamphlet on tetrahedral carbon (Wikipedia, Jacobus Henricus van 't Hoff). Kekulé's benzene paper, 1865 (Wikipedia, Benzene). Curly arrows by Robert Robinson, 1922 (Wikipedia, Arrow pushing). Hughes and Ingold kinetic work, 1937 (Wikipedia, SN2 reaction). Carvone: R is spearmint, S is caraway (Wikipedia, Carvone). Thalidomide: marketed 1957 in West Germany, withdrawn in Europe 1961, over 10,000 children severely harmed, enantiomers interconvert in the body (Wikipedia, Thalidomide). Alkane isomer counts (Wikipedia, Alkane). Bertozzi, Meldal and Sharpless, Nobel Prize in Chemistry 2022. Mechanisms only; no procedures. Go deeper. 🌐 MIT OCW 5.12 Organic Chemistry I 🌐 OpenStax Organic Chemistry 📘 Le Couteur & Burreson, Napoleon's Buttons Step 3. Cell Biology: The Smallest Unit That Is Alive ----------------------------------------------------- Why: The cell: life's smallest whole unit. Every living thing from a bacterium to a blue whale is made of cells, and no cell is very large. The course shows why, what is inside them, how they talk, how they divide, and how that division goes wrong in cancer. .chips button{min-width:0} .row2{display:flex;gap:8px;flex-wrap:wrap} .row2 button{flex:1 1 90px;min-width:0} A drop of pond water under a simple microscope teems with things that were not visible a moment ago: one swims, one divides, one eats another. In 1665 Robert Hooke looked at thin slices of cork and drew little chambers he called "cells", and a few years later Antonie van Leeuwenhoek saw living ones swim. By 1838 and 1839 Matthias Schleiden and Theodor Schwann had proposed that all plants and animals are built of cells, and cell theory was born. Later, in 1855, Rudolf Virchow popularised the idea that new cells come only from existing ones (the phrase is often credited to him, and Robert Remak's earlier work is part of that story). Cell biology is the course that takes that idea seriously. Whatever a living thing does, a cell does it: it keeps an inside different from the outside, it turns food into work, it makes copies of itself, and it listens to its neighbours. A graduate keeps a mental picture of that small, crowded, busy room. The course in one box Who takes itEvery biology major, usually in year 1 or 2; biochemistry, neuroscience, nursing and medical students too. Programmes shaped by Vision and Change (the AAAS and NSF framework for undergraduate biology), MIT's Course 7 and Cambridge's Natural Sciences all place the cell at the base of biology, early. What it is forSeeing life as a collection of small, self-maintaining units, and learning what is inside each. Comes afterGeneral Chemistry (35/36). Leads toMolecular Biology (35/45), then Physiology (35/49), Plant Biology (35/53) and, through those, Genetics (35/46) and Microbiology (35/50). Biochemistry (35/43) is its chemical companion. What this piece gives youYou will not be able to draw every organelle from memory. You will see why cells are as small as they are, what a membrane's voltage means, how transport inside a cell is solved, why cancer is a disease of the cell cycle, and what a microscope can and cannot show. Easier first reads: Your Immune System, Day by Day (01/10) and Biological Psychology (35/20), where the neuron's voltage is a cell-biology story. This describes how biology works and is not medical advice. Why cells are small Cells span a huge range, from a bacterium about a micrometre long (a thousandth of a millimetre) to a human cell near ten, to an egg that is visible to the naked eye. Yet there is a ceiling, and the reason is geometry. A cell takes in food and oxygen through its surface, but burns it throughout its volume. Double a cell's radius and its surface grows 4 times, its volume 8 times: the supply line grows more slowly than the demand. For a sphere, surface-to-volume ratio is 3 divided by the radius, so smaller is better. The second limit is time. Inside a cell, many molecules move by diffusion, a random walk, and the time it takes to cross a distance grows with the square of the distance. A small molecule diffusing at about 100 µm² per second (an illustrative value for the cytoplasm) crosses a 1 µm bacterium in about a thousandth of a second, a 10 µm cell in about a sixth of a second, and a giant cell 1 mm in radius in around half an hour. t ≈ r² / (6D), and surface-to-volume = 3 / rfor a sphere of radius r; D is the diffusion coefficient. Time grows as the square of distance Interactive · How big can a cell be? Cell radius Bacterium Typical animal cell Large egg (0.5 mm) Slider is logarithmic. Spherical cell; D = 100 µm²/s is an illustrative value for a small molecule in cytoplasm (proteins diffuse more slowly). Real big cells avoid the limit by pumping fluid, streaming, or sitting still. Big cells exist, but they work around the limit. A large egg is mostly stored food and does little until it divides. Plant cells keep most of their volume as a watery vacuole, so the working cytoplasm is a thin layer. Large animals are not made of large cells but of more cells: an elephant's cells are about the size of yours. The rule of thumb is that growing up means dividing. Membranes and transport: the cell's voltage A cell is defined by its membrane, the double layer of lipids described in Biochemistry (35/43). It keeps water-soluble things out, and so every cell needs pores, channels and pumps in it for what must pass. Some molecules cross by simple diffusion, some through channels that open and close, some by carriers, and some are pumped uphill, against their concentration, using ATP. The sodium–potassium pump sends 3 sodium ions out for each 2 potassium ions in, so cells end up with high potassium inside and high sodium outside. That imbalance is a store of energy and a source of voltage. If a membrane lets one kind of ion through, that ion drifts down its concentration gradient until the electrical force pushes back with equal strength. The voltage at which this balance happens is the Nernst potential: Eion = (RT / zF) · ln([ion]out / [ion]in)at 37 °C, RT/F is about 26.7 mV; z is the ion's charge For potassium at 5 mM outside and 140 mM inside, E = −89 mV. A real nerve cell at rest sits near −70 mV, close to potassium's value because its resting membrane leaks mostly potassium; open sodium channels and the voltage moves toward sodium's +67 mV, which is how a neuron fires (see Biological Psychology, 35/20). Interactive · What voltage does each ion want? Potassium Sodium Chloride Calcium Outside concentration vs normal Typical mammalian concentrations (mM, out / in): K 5 / 140; Na 145 / 12; Cl 110 / 10; Ca 1.8 / 0.0001. Textbook values at 37 °C; they vary by cell type. Not a medical tool. Notice calcium: a 18,000-fold gradient. That is why a small leak of calcium into a cell is a loud signal, and why cells spend so much energy keeping it out of the cytoplasm. Organelles and the merger that built them Cells come in two broad plans. Bacteria and archaea (prokaryotes) are small, have no nucleus and few internal compartments, and carry their DNA in a loop in the cytoplasm. Eukaryotes, which include animals, plants, fungi and single-celled protists, are typically ten to a hundred times wider, keep their DNA in a nucleus, and have internal compartments called organelles: the endoplasmic reticulum and Golgi apparatus that process proteins, lysosomes that digest, and mitochondria, which make most of the cell's ATP. Plants and algae add chloroplasts. FeatureBacteriumAnimal cell Typical size1 to 5 µm10 to 100 µm DNAmostly one ring, in the cytoplasmseveral chromosomes, in a nucleus Energyacross the cell's own membranemostly inside mitochondria Compartmentsfew or nonemany membrane-bound Why do mitochondria look like small bacteria? Because, in the best-supported account, they were. Lynn Margulis (then Lynn Sagan) argued in a 1967 paper, rejected by many journals before it was published, that mitochondria and chloroplasts descend from free-living bacteria that were taken up by another cell and stayed. Evidence since has made this the textbook view: mitochondria have two membranes, their own small circular DNA (the human one has 37 genes), ribosomes more like bacterial ones, and they divide by pinching in two. Their closest bacterial relatives are in a group called the alphaproteobacteria; chloroplasts descend from cyanobacteria. The host was an archaeon, probably related to a group called the Asgard archaea, and in 2020 a Japanese team reported growing one such organism in the lab. How and in what order it all happened is still debated. It matters because it explains why eukaryotes could grow large and complex: each cell carries hundreds of internal power stations, so the surface-to-volume limit above no longer applies to energy production in the same way. It also explains why a cell's powerhouse has its own tiny genome. The cytoskeleton: roads, ropes and motors A cell is not a bag of soup. Three kinds of protein filaments run through it: actin (about 7 nm across) forms the cell's cortex and drives crawling; intermediate filaments (about 10 nm) are ropes that resist stretching; microtubules (about 25 nm, hollow tubes) are roads. Motor proteins walk along them carrying cargo. Kinesin takes steps about 8 nanometres long toward the end where a microtubule grows; dynein walks the other way. Each step uses one ATP. The reason cells need roads is the same diffusion law as before. Over short distances, diffusion is fine. Over long ones it is hopeless: a nerve cell in your leg can be a metre long, and its far end is made of proteins built in the cell body. Diffusion would take centuries; a motor carrying a vesicle at about a micrometre per second takes days. The crossover is where the distance equals 2D / v, which here is about 20 µm. Interactive · Diffuse or ride? Distance to deliver Across a cell, 20 µm Motor neuron, 1 cm Giraffe nerve, 1 m Diffusion in one dimension, t = L² / 2D with D = 10 µm²/s for a vesicle-sized cargo; motor at a steady 1 µm/s (the order of magnitude of fast axonal transport). Illustrative values; log scale. A metre-long nerve is a human leg or a large animal. Cell signalling: switches, not dimmers Cells also listen. A signal molecule, such as a hormone or growth factor, binds a receptor on the surface (or inside) and sets off a chain of events that ends in a change: a gene switched on, a muscle contracting, a cell deciding to divide. The largest family of receptors in humans, the G-protein-coupled receptors, number around 800 genes and are the targets of roughly a third of approved drugs. Robert Lefkowitz and Brian Kobilka won the 2012 Nobel Prize in Chemistry for them. The key idea is that cells often need yes-or-no answers, not gradual ones. One way to get a sharp response is cooperativity: when binding sites help one another, the response to a rising signal becomes steeper. The standard description is the Hill equation, where the exponent n measures steepness. With n = 1 it takes an 81-fold rise in signal to go from a 10% to a 90% response; with n = 4 only a 3-fold rise does. Haemoglobin, binding oxygen at about n ≈ 3, is the classic case, and signalling cascades can sharpen a response far more. response = [L]n / (Kn + [L]n)Hill equation; K is the signal level giving a half response; 10% to 90% takes 811/n-fold Interactive · Dimmer or switch? Steepness n Signal level, in units of K Computed from the Hill equation; the log axis runs from 0.01 K to 100 K. Cell responses have more complex mechanisms; this is the standard first model. The cell cycle, and cancer as its breakdown A dividing cell moves through a cycle: G1 (growth), S (copying DNA), G2 (checking and preparing) and M (mitosis, the division itself). Between phases are checkpoints that ask: is the DNA intact, is it fully copied, are the chromosomes attached correctly? A family of proteins, the cyclins and the kinases they activate, act as the clock. Leland Hartwell, Paul Nurse and Tim Hunt shared the 2001 Nobel Prize in Physiology or Medicine for finding these controls. Normal human cells in a dish stop after roughly 40 to 60 divisions (the Hayflick limit, Leonard Hayflick 1961), partly because their chromosome ends shorten. Cancer is what happens when a cell line escapes those controls: it ignores stop signals, divides without growth signals, avoids its own death programme and eventually can spread. It is a disease of the cell cycle, and, since each cell division copies DNA with rare errors, of accumulated mutations. A tumour of a billion cells, about a cubic centimetre, is 30 doublings from one cell (230 is just over a billion); 40 doublings give about a trillion, around a kilogram. Tumours grow far more slowly than cells cycle, because many cells die or rest. Why does cancer risk rise so steeply with age? In 1954 Peter Armitage and Richard Doll proposed that if a cell needs k separate rare changes in sequence, the incidence should rise with age raised to the power k − 1. Many adult cancers rise about like the 4th to 6th power of age, and genome sequencing later found that a typical tumour carries only a handful of "driver" mutations, often cited as two to eight. The model is simple, and later work has added others (stem-cell division counts, the immune system, the role of the tissue neighbourhood), but it explains a basic pattern. Interactive · Steps to cancer and the age curve Rate-limiting steps k Armitage–Doll: incidence ∝ agek−1. Illustrative: the curve is scaled to equal 1 at age 80. It does not diagnose, predict or compare any individual's risk. Seeing it as a breakdown of the cell cycle explains the main kinds of cancer gene. Oncogenes are accelerators stuck on; tumour suppressors are brakes that fail. The best known suppressor, p53, a protein that halts the cycle or triggers cell death after DNA damage, is mutated in about half of human cancers. Microscopy: seeing the cell Everything above was discovered by looking. A light microscope bends visible light through glass lenses, and the finest detail it can separate is set by diffraction. Ernst Abbe worked this out in 1873: the smallest resolvable distance is about the wavelength divided by twice the lens's numerical aperture (NA, the cone of light it gathers). d ≈ λ / (2 · NA)Abbe limit for light; with green light (550 nm) and the best oil lens (NA 1.4), d ≈ 196 nm About 200 nm is a hard wall for ordinary optics: mitochondria (about 0.5 to 1 µm wide) are visible, ribosomes (about 25 nm) are not. To see smaller things you need a shorter wavelength. Electrons have a wavelength of about 3.7 picometres at 100 kV, roughly 150,000 times shorter than green light, and electron microscopes have been used since the 1930s. In practice lenses limit the detail more than wavelength does, but the best reach atoms. Cryo-electron microscopy, which freezes samples in glassy ice, earned Jacques Dubochet, Joachim Frank and Richard Henderson the 2017 Nobel Prize in Chemistry. The Abbe limit was then beaten by cleverness, not by shorter waves: fluorescent labels that blink or are switched on one at a time, in techniques that earned Eric Betzig, Stefan Hell and W. E. Moerner the 2014 Chemistry Nobel. Green fluorescent protein, from a jellyfish and used to tag proteins in living cells (Shimomura, Chalfie and Tsien, Nobel 2008), turned microscopes into movie cameras for molecules. Interactive · What can this microscope resolve? Light Electrons Wavelength Numerical aperture Light: d = λ/(2 NA). Electrons: relativistic de Broglie wavelength from CODATA constants; in practice lens aberrations limit detail to about 0.1 to 0.2 nm in the best instruments, far above the wavelength. Sizes are typical values. What a graduate just sees Cells are small because surface grows as r², demand as r³, and diffusion time as r². Bigger animals have more cells, not bigger ones. A membrane with a pump and a leaky channel is a battery, and its voltage is set by concentration ratios (Nernst). Mitochondria and chloroplasts are the descendants of bacteria that moved in. Over long distances cells use motors on tracks; over short distances, diffusion is enough. Cells need switch-like responses, and cooperativity makes them. Cancer is a cell-cycle disease, built from a handful of mutations in accelerators and brakes. A microscope's resolution is limited by wavelength, and the limit can be dodged. Where it shows up next Molecular Biology (35/45): the cell's information system: DNA, RNA, protein and control of genes. Physiology (35/49): how cell voltages become nerve signals, muscle contractions and hormone responses. Plant Biology (35/53): chloroplasts, cell walls and why plants are built as they are. Microbiology (35/50): the cells that do not have a nucleus, and the world they live in. In the world: cancer screening and drugs, vaccines, stem-cell therapy, biotechnology that grows medicine in cells, and the ethics of cell lines such as HeLa, whose source, Henrietta Lacks, was treated in 1951 and whose cells were taken without her knowledge or consent. If you want to go deeper 📘 Textbook. Bruce Alberts and colleagues, Molecular Biology of the Cell (W. W. Norton, 7th edition). The standard text, thorough and beautifully illustrated. 📘 Textbook. Gerald Karp, Janet Iwasa and Wallace Marshall, Karp's Cell and Molecular Biology (Wiley, 9th edition). A more compact undergraduate alternative. 📘 Gentler. Nick Lane, Power, Sex, Suicide: Mitochondria and the Meaning of Life (Oxford University Press). The best popular account of the endosymbiosis story. Also Siddhartha Mukherjee, The Emperor of All Maladies (2010), a history of cancer. 🌐 Free course. OpenStax Biology 2e, chapters on cell structure. And MIT OpenCourseWare 7.016 Introductory Biology (Fall 2018). The takeaway A cell is a small room kept different from the outside, and its size is set by geometry and diffusion. It runs on voltage across a membrane, got its power stations by merger, moves cargo on tracks, answers signals with switches, and divides under checkpoints whose failure is cancer. Try this: look at the surface of a leaf, a thin onion skin or a spoonful of yeast in sugar-water under a magnifier or a phone lens (a cheap clip-on lens is enough). Notice the repeating units, and ask what keeps each one small. Sources & Further Reading Sources. Hooke, Micrographia (1665); Schleiden (1838) and Schwann (1839); Virchow (1855), with Remak's earlier work. Nernst potentials: standard physiology textbooks; ion concentrations as typical mammalian values. Sodium–potassium pump stoichiometry (3 Na+ out, 2 K+ in). Endosymbiosis: Margulis (as Sagan), Journal of Theoretical Biology (1967); human mitochondrial genome of 16,569 base pairs and 37 genes; Imachi et al., Nature (2020), on cultured Asgard archaea. Kinesin steps of about 8 nm: Schnitzer and Block, Nature (1997). Fast axonal transport of the order of 1 µm/s: standard neuroscience texts. GPCRs: Nobel Prize in Chemistry 2012 (Lefkowitz and Kobilka); about a third of approved drugs: Hauser et al., Nature Reviews Drug Discovery (2017). Hill equation and cooperativity: standard biochemistry texts. Cell cycle: Nobel Prize in Physiology or Medicine 2001 (Hartwell, Nurse, Hunt). Hayflick (1961). Armitage and Doll, British Journal of Cancer (1954); driver mutations: Vogelstein et al., Science (2013). p53 mutated in about half of cancers: standard reviews. Abbe (1873); electron wavelength from CODATA constants; Nobel Prizes in Chemistry for cryo-EM (2017), super-resolution (2014) and GFP (2008). HeLa: Henrietta Lacks, 1951. The diffusion numbers in the interactives are illustrative and labelled. This is not medical advice. 🌐 OpenStax Biology 2e: Cell Structure 🌐 MIT OCW 7.016 Introductory Biology 📘 Alberts et al., Molecular Biology of the Cell 📘 Lane, Power, Sex, Suicide Step 4. Probability & Statistics: Reasoning with Uncertainty ------------------------------------------------------------ Why: Biology is a science of variation and statistics. Nothing you measure is exact, and no part comes out the same twice. Statistics is the discipline of knowing how much to trust a number. A machinist turns a hundred steel shafts to "10 millimetres". Measure them with a good micrometer and no two are the same: 9.981, 10.012, 10.004. Nothing is wrong. That scatter is a fact of every process, every material and every sensor. Now stack five of those parts end to end in a gearbox. Will the stack still fit the housing? A pollster calls a thousand people and says 52% will vote yes, give or take three. A drug trial says "significant". A forecast says 30% chance of rain. Every one of these is the same question: given scatter, how much should I trust this number? A graduate of probability and statistics doesn't see a single number any more. They see the shape of the scatter behind it. This piece builds that sight with eight things you can run: dice, tolerances, polls, a drug-trial trap, a belief that updates, and a gearbox stack. The course in one box Who takes it: almost every engineering and science student, usually in the second year; computer scientists meet it again before machine learning. What it's for: deciding what to believe, and how far to trust a measurement, when outcomes are uncertain. Comes after: Calculus I (34/01), which helps with continuous distributions, though the ideas here need little more than arithmetic. Leads to: Machine Learning (34/32) needs it directly. It also shows up in Materials Science & Manufacturing (34/13: process control and defects), Systems Engineering (34/22: reliability) and Computer Security (34/33: randomness and guessing). Honest line: you won't be able to design a clinical trial after this. You will see why "significant" doesn't mean "important", why a bigger sample beats a cleverer guess, and why most real quantities look like a bell curve. For easier first reads, see the library's Probability: How to Not Fool Yourself (12/03), Statistics for Reading the World (12/05) and Bayes' Theorem (12/17); this piece goes further into the engineering side. Random variables: a shape with a centre and a spread A random variable is a number that comes out of a process you can't predict one run at a time. The key move is to stop asking "what will it be?" and ask "what is the shape of what it could be?" Roll two dice and add them: 7 is six times as likely as 2 or 12, so the shape is a tent. Roll many times and the tent appears. Interactive · Roll dice, grow a shape Dice added together Roll 10 timesRoll 1,000 timesClear Without JavaScript: two dice add to 7 with probability 6/36 and to 2 or 12 with probability 1/36 each. The mean total is 7 and the standard deviation is about 2.42. Two numbers summarise a shape. The mean is its balance point: 7 for two dice. The standard deviation (the "spread") says how far values typically stray from the mean: about 2.4 for two dice, which means totals usually land between roughly 5 and 9. The variance is the standard deviation squared, and it is the one that adds up neatly when you combine independent things. standard deviation = √( average of (value − mean)² ) Now the shape that matters most. Measured quantities (shaft diameters, heights, sensor noise) tend to form the normal curve, the bell. Its great convenience is a fixed rule: about 68.3% of values fall within one standard deviation of the mean, 95.4% within two, and 99.7% within three. Engineers use it every day. Say the shaft's spec is 10.00 mm ± 0.05 mm. Slide the process around and see what share of parts get thrown away. Interactive · How many parts fail the spec? Average diameter Spread (standard deviation) Without JavaScript: a centred process with standard deviation 0.025 mm (the spec limits are exactly ±2 standard deviations) scraps about 4.55% of parts. Cut the spread to 0.01 mm and about 0.00006% are scrapped. Shift the average 0.02 mm off-centre with spread 0.02 mm and about 6.7% are scrapped. Two lessons graduates keep. First, spread, not average, decides quality: a process centred perfectly but wide still scraps parts. Second, being off-centre costs a lot even when the spread is fine. That is why factories track both. The central limit theorem: why the bell keeps appearing Why should so many things be bell-shaped? The answer is one of the most useful theorems in mathematics. Take almost any random process, however lopsided, and average a few dozen independent draws. The averages pile up in a bell, centred on the true mean, with spread shrinking like 1/√n. Early forms are due to de Moivre in 1733 (for coin flips) and Laplace, whose general version dates from about 1810. Pick a lopsided source and drag the sample size. Interactive · Average anything, get a bell Flat (0 to 1) Very lopsided Coin (0 or 1) Draws averaged together: n Without JavaScript: for the lopsided source (mean 1, standard deviation 1) the average of n = 30 draws has standard deviation 1/√30 = 0.183, and the 3,000 averages form a close-to-normal bell around 1. At n = 1 you see the raw source. By n = 30 even the lopsided one is a near-bell. The prediction (the curve) uses only two numbers from the source, its mean and its standard deviation. The shape of the source is forgotten. That is why a measurement made of many small independent errors is normal, and why so much of statistics can pretend things are bell-shaped. standard error of an average = σ / √n In words: the average of n draws wobbles less than one draw, by the square root of n. To halve the wobble you need four times the data, not twice. It is the quietest expensive fact in all of experimental science. Sampling and confidence intervals: how sure is a poll? You can't ask everyone, so you ask n people and treat the share saying yes as an estimate. How far off might it be? The standard error from the last section gives the answer. For a share p the wobble is √(p(1−p)/n), and a 95% confidence interval is the estimate plus and minus about two of those. For n = 1,000 and a share near half, that is ±3.1 percentage points: the familiar "margin of error". The wording is subtle, and the interactive makes it concrete. "95% confidence" is a statement about the method, not about one interval: if you ran the procedure again and again, about 95 intervals in 100 would capture the true value. Here the truth is secretly 52%. Run 100 polls. Interactive · 100 polls, one truth People asked in each poll Run 100 polls Without JavaScript: with 1,000 people per poll the margin of error is about 3.1 points; run 100 polls and about 95 of the intervals cover the true value. With 4,000 people the margin halves to about 1.5 points. Watch two things. Roughly five in a hundred intervals miss the truth even when everything is done correctly. And quadrupling the sample from 1,000 to 4,000 only halves the interval. A poll of a country and a poll of a town need the same sample size for the same precision, as long as the sample is random. The real danger is not the margin of error; it is a sample that isn't random at all, which no formula fixes. P-values and Bayes: two ways to weigh evidence A hypothesis test asks whether data are surprising if nothing is going on. The p-value is the probability, assuming nothing is going on, of seeing a result at least as extreme as yours. Flip a coin 100 times and get 60 heads: for a fair coin the chance of a split at least that lopsided in either direction is about 5.7%. It is not the probability that the coin is fair, and it is not the probability that the result was "due to chance". The American Statistical Association issued a rare formal statement on this in 2016, with six principles. Two of them: p-values do not measure the probability that a hypothesis is true, and a p-value does not measure the size or importance of an effect. The classic trap is testing many things. At the usual cut-off of 0.05, a test of a true "nothing" comes out "significant" one time in 20 by luck. Test twenty unrelated things and the chance that at least one lights up is 1 − 0.9520, about 64%. Try it: each press tests twenty effects that are, by construction, nothing. Interactive · Test twenty things that do nothing Run 20 testsReset the tally Without JavaScript: twenty tests of pure noise at the 0.05 level give at least one false "discovery" about 64% of the time, and one in 20 tests on average. If you report only the one that lit up, you have a headline and no finding. This is part of why many published results fail to repeat: in the Open Science Collaboration's 2015 attempt to replicate 100 psychology studies, 97% of the originals had statistically significant results but only 36% of the replications did. Bayes' rule answers a different question: given the data, how should my belief move? Start with a prior belief, multiply by how well each possibility explains the data, and renormalise. Say you test parts and want the defect rate. Know nothing at first (any rate from 0% to 100% equally likely) and add parts one at a time. Interactive · Learn a defect rate from parts Add a good partAdd 10 good partsAdd a defective partReset Without JavaScript: after 20 good parts and no defects, a flat starting belief gives a most-plausible defect rate near 0%, an average of 4.5%, and a 90% credible range of roughly a quarter of a percent to 13%. Twenty clean parts cannot rule out a defect rate near one in eight. Frequentists and Bayesians disagree about the philosophy: one treats probability as long-run frequency and never assigns it to a hypothesis, the other as degrees of belief that data update. In practice both are used, often on the same project, and on big data sets they usually agree. The Bayesian version has one practical advantage here: after twenty clean parts it honestly says "we still can't rule out one in eight". Correlation, regression and the trap of causation Correlation (called r) measures how tightly two quantities move together along a straight line, from −1 to +1. Regression fits the best line through the cloud (by least squares, as in Linear Algebra, 34/04). Both are summaries, and any summary can hide the story. In 1973 the statistician Francis Anscombe made four data sets with, to two decimals, the same mean, the same spread, the same r (0.82) and the same line (y = 3 + 0.5x). Look at each. Interactive · Four data sets, one set of numbers Set 1Set 2Set 3Set 4 Without JavaScript: all four Anscombe sets have mean x = 9, mean y = 7.50, correlation 0.816 and line y = 3.00 + 0.50x. Set 1 is a noisy line, set 2 a curve, set 3 a line with one outlier, and set 4 a single far point that creates the whole slope. The numbers agree and the stories do not: one noisy line, one curve, one line with a rogue point, one vertical stack held up by a single point. Always plot first. The other trap is the famous one. Ice-cream sales and drownings rise together, because summer heat drives both. A confounder (a hidden third factor) makes two things move together without either causing the other. The remedy graduates know is randomised assignment: if a coin decides who gets the treatment, nothing else can be systematically linked to it. Where you can't randomise, causal claims need much more than a line through a cloud. Engineering: tolerance stacks, reliability and Monte Carlo Five parts, each 10 mm ± 0.1 mm, line up in an assembly. What is the worst the total can be out? Worst-case stacking adds the tolerances: ±0.5 mm. It is safe and expensive, because it assumes every part is at its extreme in the same direction at once. If the parts vary independently, variances add, so the standard deviations add in quadrature: root-sum-square, √5 × 0.1 = ±0.224 mm. For five parts that is under half the worst-case figure. When the formulas get hard, engineers use Monte Carlo: let the computer build the assembly ten thousand times with random parts and count how often it fails. Here each part's tolerance is treated as three standard deviations. Choose how many parts are stacked. Interactive · Monte Carlo tolerance stack Parts in the stack Build 10,000 assemblies again Without JavaScript: five parts at ±0.1 mm (three standard deviations) give a worst-case limit of ±0.5 mm, a root-sum-square limit of ±0.224 mm, and in simulation only about 0.3% of assemblies exceed the root-sum-square limit; none come close to 0.5 mm. The honest caveat is that root-sum-square assumes the parts vary independently and are centred. A tool wearing in the same direction on every part breaks that assumption, and so does one supplier's batch. Engineers disagree about when to trust statistical stacking over worst-case; safety-critical designs often insist on worst-case. Reliability follows the same arithmetic. A system that needs all of its parts is a series system, and probabilities multiply: ten components that each work 99% of the time give 0.9910 ≈ 90.4% for the whole. Add a backup in parallel and failure needs both to fail: two units that each work 90% of the time give 1 − 0.1² = 99%. The two rules drive why aircraft duplicate systems and why complicated machines need very reliable components. What a graduate just sees Every number has a spread behind it; the first question is "how scattered?", not "what is it?". Spread, not the average, decides how many parts are scrapped, and centring matters too. Averages of many independent things are bell-shaped, whatever the source looked like. Halving the uncertainty costs four times the data. A 95% interval is a claim about a method: it misses one time in twenty by design. A p-value is "how surprising is this if nothing is going on", not "how likely is it true". Test twenty things and one will look significant; ask how many were tried. Plot the data; correlation is not causation, and only randomising breaks a confounder. Independent errors add in quadrature; series reliabilities multiply. Where it shows up next Machine Learning (34/32): training is fitting a model to noisy data; ideas of overfitting, error bars and Bayes are this course made bigger. Materials Science & Manufacturing (34/13): process capability and scrap rates are the normal curve against a spec limit. Mechanics of Materials (34/11) and Machine Design (34/19): safety factors exist because loads and strengths are distributions, not numbers. Systems Engineering (34/22): reliability budgets multiply series probabilities and add redundancy to push them back up. Computer Security (34/33) and Algorithms (34/24): good random numbers, randomised algorithms, and the odds of guessing a secret. If you want to go deeper 📘 Douglas Montgomery and George Runger, Applied Statistics and Probability for Engineers (Wiley; 7th edition). The standard engineering course text, with plenty of tolerance, quality and reliability problems. 📘 Joseph Blitzstein and Jessica Hwang, Introduction to Probability (CRC Press; 2nd edition, 2019). Best for deep intuition about probability itself, from Harvard's Stat 110. 📖 David Spiegelhalter, The Art of Statistics (2019): the most readable route for learning alone, built around real cases and honest about uncertainty. 🌐 MIT OpenCourseWare 18.05, Introduction to Probability and Statistics (Spring 2022): free notes and problem sets, with Bayesian and classical statistics side by side. The takeaway Nothing you measure is exact, so every number is a shape. Summarise a shape by its centre and its spread, trust averages more as the square root of the sample, read a confidence interval as a promise about a method, treat a p-value as a measure of surprise, and plot before you believe a correlation. Try this: next time you see a poll or a "significant" headline, find the sample size and ask how many things were tested. Then, in the dice widget above, add four dice and watch the tent turn into a bell. Sources & Further Reading Sources. The normal-curve rule (68.3%, 95.4%, 99.7%), the central limit theorem, confidence intervals, the binomial test, the Beta posterior, root-sum-square stacking and series/parallel reliability are standard textbook results (Montgomery and Runger; MIT 18.05); every number shown was recomputed in code. Wasserstein and Lazar, "The ASA's Statement on p-Values: Context, Process, and Purpose", The American Statistician (2016). Open Science Collaboration, "Estimating the reproducibility of psychological science", Science (2015): 97% of originals significant against 36% of replications. Anscombe, "Graphs in Statistical Analysis", The American Statistician (1973). Early forms of the central limit theorem: de Moivre (1733) and Laplace (c. 1810), as surveyed in recent histories such as Ulyanov, "From classical to modern central limit theorems" (arXiv 2405.19828). Go deeper. The books and course above; Wasserstein and Lazar's statement is free and short (doi.org/10.1080/00031305.2016.1154108). Step 5. Biochemistry: The Chemistry That Keeps Itself Going ----------------------------------------------------------- Why: Enzymes, energy and the molecules of life. A chain of amino acids folds itself, an enzyme speeds a reaction a million-fold, and a cell runs on a rechargeable molecule it turns over every minute. Biochemistry is the course where the molecules of life are treated as chemistry, with a ledger. .chips button{min-width:0} .row2{display:flex;gap:8px;flex-wrap:wrap} .row2 button{flex:1 1 90px;min-width:0} Eat a piece of bread and, a few hours later, its glucose is a trickle of electrons moving along proteins inside your mitochondria. A single genetic typo in a haemoglobin gene turns one amino acid into another, and red cells bend into sickles. A medicine blocks one enzyme and a symptom eases. In each case the story can be told in molecules, in numbers, and in energy bookkeeping. Biochemistry asks what those molecules are, how they fold and catalyse, and how a cell pays for everything. It is the bridge between the chemistry of carbon and the biology of cells, and it sits on both routes: chemists take it to see where their subject leads, and biologists take it to see what their subject is made of. The course in one box Who takes itChemistry majors, usually in year 3 or 4; biology, biomedical and nutrition majors, usually in year 2 or 3; and, as a prerequisite, most students heading for medicine, pharmacy or dentistry. Programmes shaped by the American Chemical Society guidelines list it among the foundations of a chemistry degree, and the Vision and Change framework puts "structure and function", "energy and matter" and "information flow" at the centre of undergraduate biology, which is exactly its territory. What it is forExplaining how the large molecules of life are built, how they speed up and steer reactions, and how cells store and spend energy. Comes afterOrganic Chemistry: Structure & Mechanism (35/38). Leads toMolecular Biology (35/45), then Physiology (35/49) and Microbiology (35/50), plus Cell Biology (35/44) as its companion. It is also the chemistry under Genetics (35/46) and Plant Biology (35/53). What this piece gives youYou will not be able to balance a metabolic pathway from memory. You will see why shape is everything for a protein, what Michaelis–Menten kinetics predict, how a cell can pull energy from sugar in steps, why fat stores more energy than starch, and what AlphaFold did and did not solve. Easier first reads: Fermentation: Letting Microbes Do the Cooking (14/08), The Science of Bread (14/07), and Entropy: Why You Can't Unstir Your Coffee (13/12) for the idea of free energy. This describes how science works; it is not medical advice. Twenty amino acids, one folded shape Proteins are chains of amino acids, twenty kinds in the standard genetic code, joined by peptide bonds. Each kind has a different side chain: some are oily and avoid water (leucine, valine), some carry a charge (lysine is positive, aspartate negative), some can form hydrogen bonds (serine). A chain of a few hundred of these is a protein. The sequence is written in DNA, but what does the work is the shape: oily side chains bury themselves in the core, charged ones face the water, and the chain settles into helices and sheets that pack into a compact fold. In 1961 Christian Anfinsen showed that the enzyme ribonuclease, unfolded with chemicals, refolded by itself into an active form when the chemicals were removed. The information for the shape is therefore in the sequence. He shared the 1972 Nobel Prize in Chemistry (with Stanford Moore and William Stein). It has caveats: some proteins need helper "chaperones", and some work while floppy. But it set the problem. The sharp question is Levinthal's. A chain cannot find its shape by trying them all. Cyrus Levinthal estimated in 1969 on the order of 10300 possible shapes for a typical protein, yet real ones fold in milliseconds to seconds. The slider counts it your way: if each of n residues has just 3 positions, there are 3n shapes, and at a trillion tries a second the search for a 100-residue chain would last about 1027 years. Proteins do not search; they slide downhill on an energy landscape shaped like a funnel. Interactive · Why a protein cannot search Residues in the chain Shapes per residue A thought experiment, not a model of folding: kn shapes, one tried every 10−13 s (a bond vibration), against the universe's age of 13.8 billion years. Real proteins fold in about 10−3 to 10 s. Log scale. A single change can matter enormously. In sickle-cell disease, glutamic acid at position 6 of the β-globin chain of haemoglobin is replaced by valine. That oily side chain on the surface makes haemoglobin molecules stick into fibres when they let go of oxygen, and bend the red cell. Carriers of one copy are partly protected against severe malaria, which is why the variant is common where malaria has been. Genes and environment are in conversation here, a theme of Genetics (35/46). Enzymes: catalysts that set the pace of life Most reactions that a cell needs would take years at body temperature. Enzymes make them take milliseconds. An enzyme does not change where a reaction ends up (the equilibrium); it lowers the barrier on the way, by holding the substrate in a pocket shaped to stabilise the transition state. Carbonic anhydrase, which interconverts carbon dioxide and bicarbonate in your blood, can turn over about a million substrate molecules per second per enzyme, among the fastest known. In 1913 Leonor Michaelis and Maud Menten wrote down the simplest model that explains how rate depends on substrate concentration. At low [S] the enzyme is mostly empty, so the rate rises in proportion. At high [S] every enzyme is busy and the rate saturates at Vmax. The Km is the substrate concentration at which the rate is half of Vmax: a small Km means the enzyme grabs its substrate even when it is scarce. v = Vmax · [S] / (Km + [S])rate rises with substrate, then saturates; Km is the [S] where v = Vmax/2 A competitive inhibitor resembles the substrate and occupies the pocket. It does not change Vmax (flood the system with substrate and you win), but it raises the apparent Km by a factor (1 + [I]/Ki). Many drugs are inhibitors of enzymes: ibuprofen reversibly blocks the cyclooxygenase enzymes, and aspirin does it by chemically modifying them. Try the sliders. Interactive · Michaelis–Menten, with an inhibitor Substrate [S] Km Competitive inhibitor, [I] / Ki Illustrative units: Vmax = 100 µM/s. Solid: with the inhibitor; dashed: without. Curves computed from v = Vmax[S]/(Km,app + [S]). Notice what the readout says: at [S] = Km the rate is exactly half of maximum, and at 10 × Km it is already 91%, so doubling the substrate again barely helps. That saturation is why a cell regulates enzymes by controlling the enzyme, not the substrate. ATP: the energy ledger's currency A cell cannot burn sugar like a flame; the heat would cook it. Instead it moves energy in small, controlled steps, and the common change is ATP (adenosine triphosphate). Splitting its last phosphate off to give ADP and phosphate releases energy that other reactions can borrow when they are coupled to it. Under standard biochemical conditions (1 M of everything, pH 7) the free energy change is −30.5 kJ per mole. In a living cell the concentrations are far from standard, and the free energy depends on them: ΔG = ΔG°′ + RT ln([ADP][Pi] / [ATP])free energy of ATP hydrolysis; R = 8.314 J/(mol·K), T = 310 K at body temperature, so RT ≈ 2.58 kJ/mol Textbooks quote about −50 to −65 kJ/mol inside cells. The reason is striking: at equilibrium ATP would be almost entirely broken down, and a cell keeps its ATP/ADP ratio many orders of magnitude above that. It is held there by constant work, and a human turns over roughly their own body weight in ATP in a day (an estimate), recycling it between ATP and ADP, not accumulating it. Interactive · How far from equilibrium? Resting cell Exhausted [ATP] [ADP] [Pi] Illustrative concentrations in mM, 37 °C, ΔG°′ = −30.5 kJ/mol. Real cells vary by tissue and state, and free Mg2+ matters; this is the textbook estimate. Metabolism as bookkeeping: glucose to ATP Metabolism is a set of linked reactions, and the neat way to hold it in your head is a ledger with three columns: ATP, and two electron carriers, NADH and FADH2, which carry electrons to the cell's power plant. Glycolysis, in the cytosol, splits one glucose into two pyruvate, and pays a net 2 ATP and 2 NADH. With oxygen, pyruvate goes into the mitochondrion, giving 2 more NADH (as it becomes acetyl-CoA), and the citric acid cycle (Hans Krebs, 1937) turns the rest into carbon dioxide, with 6 NADH, 2 FADH2 and 2 more ATP-equivalents. All that is the "earnings"; the real payout comes when the carriers deposit their electrons into the respiratory chain, which pumps protons across the inner membrane. Peter Mitchell proposed in 1961 that the resulting proton gradient, not a chemical intermediate, drives ATP synthase, a tiny rotary motor; his chemiosmotic theory won the 1978 Nobel Prize in Chemistry. The old textbooks said one glucose gives 36 to 38 ATP. Newer measurements put it at about 30 to 32, because a proton-driven motor does not pay in whole molecules. The ledger lets you see why the range exists. Interactive · The ATP ledger, step by step Next stage Reset Malate shuttle Glycerol-phosphate shuttle Modern (2.5 and 1.5) Old textbook (3 and 2) Per glucose. The ATP yield per NADH (about 2.5) and FADH2 (about 1.5) are modern estimates; older textbooks used 3 and 2. Cytosolic NADH enters through a shuttle, which costs a little in some tissues. All numbers are textbook estimates. Without oxygen, the cell stops after glycolysis and must recycle its NADH by making lactate or, in yeast, ethanol: two ATP per glucose instead of about thirty. That is the arithmetic behind a sprinter's burning legs and a baker's rising dough, and it is why oxygen matters. Lipids, sugars and membranes: fuel, walls and labels Three more families fill out the picture. FamilyBuilt fromRoles Carbohydratessugars (glucose, fructose) joined in chainsquick fuel (starch, glycogen); structure (cellulose); labels on cell surfaces Lipidsfatty acids, glycerol, cholesteroldense energy store; membranes; signals (steroid hormones) Proteinsamino acidscatalysis, structure, transport, signalling The small difference in how sugar units are joined has large effects: starch and cellulose are both glucose polymers, but the link is shaped differently in each, so humans digest starch and cannot digest cellulose. Fats carry about 37 kJ per gram (9 kcal) against about 17 kJ (4 kcal) for carbohydrate and protein, because a fat is more reduced, with more electrons to hand to the respiratory chain. That is why animals store energy as fat. Membranes come from a simpler fact: a phospholipid has a water-loving head and two oily tails. In water such molecules assemble themselves into a double layer, tails inward, about 5 nanometres thick, which is the same physics that lets soap form droplets around grease. Proteins embedded in that layer do the transport and sensing; see Cell Biology (35/44). Nucleic acids as molecules DNA and RNA are chains of nucleotides: a sugar, a phosphate and a base. The backbone is sugar–phosphate; the bases (A, C, G, T in DNA; U replaces T in RNA) stick out. In 1953 James Watson and Francis Crick proposed the double helix, using X-ray data from Rosalind Franklin's group and Maurice Wilkins's; the 1962 Nobel Prize went to Watson, Crick and Wilkins. The key chemistry is complementary pairing: A binds T with two hydrogen bonds, and G binds C with three. Erwin Chargaff had found the matching counts of A with T, and G with C, years earlier. How the code is read is the job of Molecular Biology (35/45); here the point is simpler: a G–C pair holds more tightly than an A–T pair. For a short DNA piece, a rule of thumb (the Wallace rule) puts the melting temperature at about 2 °C for each A or T and 4 °C for each G or C. Longer pieces and real salt conditions need more careful models, which is why labs use calculators. Interactive · How tightly does a short duplex hold? Length G–C share Wallace rule, valid only for short pieces (about 14 bases or fewer): Tm ≈ 2(A+T) + 4(G+C), in °C. Dark = G–C (three hydrogen bonds), light = A–T (two). AlphaFold and the protein-structure problem Knowing a protein's sequence is not the same as knowing its shape. For decades the only way to get a shape was experiment: X-ray crystallography, NMR, and more recently cryo-electron microscopy, each a long project. The Protein Data Bank, started in 1971, now holds well over 200,000 experimental structures, but known protein sequences number in the hundreds of millions. Predicting the shape from the sequence became a competition, CASP, held every two years. In November 2020 DeepMind's AlphaFold 2 reached accuracy in CASP14 that was comparable to experimental structures for many targets, a result the organisers called a breakthrough. The method was published in 2021 (Jumper and colleagues) and in 2022 predictions for about 200 million proteins were released in a public database. The 2024 Nobel Prize in Chemistry went half to David Baker for computational protein design and half to Demis Hassabis and John Jumper for structure prediction. What it did not do is end the subject. A prediction is a model with a confidence score, not a measurement. It does not by itself explain how a chain folds (Levinthal's question), how a protein moves or how it behaves when it binds a drug or another protein, and it is less certain for floppy regions and rare folds. Experimental structures still check it, and they train it. Treat it as a very good map, drawn from the territory that experiments surveyed. What a graduate just sees A protein's job is set by its shape, and its shape is set by its sequence and by water. One amino acid out of hundreds can change everything, and effects depend on environment. Enzymes lower barriers and never move the equilibrium; rates saturate at Vmax. Cells keep ATP enormously far from equilibrium, and that distance is the energy they spend. Metabolism is a ledger: sugar becomes carriers (NADH, FADH2), carriers become a proton gradient, the gradient becomes ATP. Fat is dense fuel because it is more reduced than sugar. Membranes assemble themselves from molecules with a wet head and an oily tail. G–C pairs are stronger than A–T pairs: three hydrogen bonds against two. A predicted structure is a model with a confidence level, not a measurement. Where it shows up next Molecular Biology (35/45): how DNA is copied and read, and how cells control which genes are on. Physiology (35/49): hormones, muscle and the fuel switches between fed and fasting states. Microbiology (35/50): bacteria differ chiefly in which metabolism they run, with or without oxygen. Plant Biology (35/53): photosynthesis is respiration in reverse, with light paying the bill. In the world: drug design, enzyme-based detergents and diagnostics, brewing and baking, sports science and diabetes care. If you want to go deeper 📘 Textbook. David Nelson and Michael Cox, Lehninger Principles of Biochemistry (Macmillan / W. H. Freeman, 8th edition). The standard in many courses; strong on energetics. 📘 Textbook. Jeremy Berg, John Tymoczko, Gregory Gatto and Lubert Stryer, Biochemistry (Macmillan / W. H. Freeman, 9th edition). Known for clear diagrams and for connecting to medicine. 📘 Gentler. Nick Lane, Power, Sex, Suicide: Mitochondria and the Meaning of Life (Oxford University Press, 2005; 2nd ed. 2018). A popular account of energy in cells. 🌐 Free course. MIT OpenCourseWare 7.05 General Biochemistry. Also the free OpenStax Biology 2e. The takeaway Life's molecules obey the same chemistry as everything else; what is special is how they are arranged. Shape follows from sequence, enzymes set the pace, ATP is held far from equilibrium and spent in small steps, and a good ledger tells you where the energy of a sugar goes. Try this: chew an unsweetened cracker for a full minute and notice when it starts to taste sweet. An enzyme in your saliva is snipping starch into sugars, and you are tasting the product. Sources & Further Reading Sources. Anfinsen (1961), Nobel Prize in Chemistry 1972 (with Moore and Stein). Levinthal (1969), "How to fold graciously": estimate of about 10300 conformations. Sickle-cell: Glu6Val in β-globin; carriers' partial protection against malaria (established in the 1950s). Carbonic anhydrase turnover about 106 per second: Lindskog, Pharmacology & Therapeutics (1997). Michaelis and Menten (1913). ATP hydrolysis ΔG°′ = −30.5 kJ/mol and cellular values near −50 to −65 kJ/mol: Nelson and Cox, Lehninger. Krebs (1937); Mitchell, chemiosmotic hypothesis (1961), Nobel Prize in Chemistry 1978. ATP yield of about 30 to 32 per glucose: Lehninger and other recent textbooks (older editions 36 to 38). Fat and carbohydrate energy: Atwater factors (9 and 4 kcal/g). Watson and Crick (1953); Nobel Prize in Physiology or Medicine 1962; Chargaff's rules; Wallace rule for short oligonucleotides. Protein Data Bank (announced 1971, Nature New Biology). AlphaFold: CASP14 (November 2020); Jumper et al., Nature 596 (2021); AlphaFold Database release of about 200 million structures (July 2022); Nobel Prize in Chemistry 2024 (Baker; Hassabis and Jumper). Numbers in the interactives are illustrative or textbook estimates and are labelled. This is not medical advice. 🌐 MIT OCW 7.05 General Biochemistry 🌐 OpenStax Biology 2e 📘 Nelson and Cox, Lehninger Principles of Biochemistry 📘 Lane, Power, Sex, Suicide Step 6. Molecular Biology: How a Sequence Becomes a Cell -------------------------------------------------------- Why: DNA to RNA to protein, and how it's controlled. The cell copies a three-billion-letter text with almost no typos, reads it three letters at a time, and keeps most of it switched off. That one idea explains your cells, a bacterium's lunch, and the tools of modern biology. A skin cell and a nerve cell in your body carry the same three billion letters of DNA, and they could hardly be less alike. One sheds and renews every few weeks; the other can last a lifetime and sends signals over a metre. Neither has lost a page of the manual. They differ in which pages are open. Pour a cup of milk for a bacterium and something similar happens. A bacterium that has been living on glucose will switch on a handful of genes for digesting milk sugar, but only when the sugar is there and the better food is gone. Nobody told it. The switch is a molecule that sticks to a stretch of DNA. A molecular biologist sees all of this as one story: information stored in DNA is copied, read, and switched on and off, by machines made of the very molecules they read. Everything in later biology, from inheritance to development to cancer, is a variation on that story. The course in one box Who takes itBiology, biochemistry, biomedical and pre-medical students, usually in year 2, once the cell and some organic chemistry are in place. Programmes shaped by the AAAS and NSF Vision and Change report (2011), and courses such as MIT's Course 7 or Cambridge's Natural Sciences, treat "information flow" as one of the core ideas of biology. What it is forExplaining how the sequence of a gene becomes a working protein, how it is copied faithfully, and how a cell decides which genes to use. Comes afterCell Biology (35/44) and Biochemistry (35/43). Leads toGenetics (35/46), Microbiology (35/50), Developmental Biology (35/51) and Bioinformatics & Genomics (35/52). What this piece gives youYou will not be able to design an experiment. You will be able to read a DNA sequence into a protein by hand, explain why copying errors are so rare, say why one genome makes many cell types, and understand PCR and CRISPR as ideas. Easier first reads: Nature, Nurture, and You (02/04) and Your Immune System, Day by Day (01/10). This is not medical advice. The central dogma, and what it never said In 1958 Francis Crick stated an idea about sequence information: it can pass from nucleic acids to protein, but once it is in a protein it cannot get back out. In a 1970 paper in Nature he restated it carefully, and the version he wrote is stricter and more interesting than the textbook cartoon "DNA makes RNA makes protein". He listed which transfers are general (DNA to DNA, DNA to RNA, RNA to protein), which are special (RNA to RNA, RNA to DNA, and DNA straight to protein), and which are unknown (from a protein to anything). Some "special" cases turned out to be everywhere. Retroviruses such as HIV carry RNA and copy it into DNA using reverse transcriptase, found independently by Howard Temin and David Baltimore in 1970 (Nobel Prize in Physiology or Medicine, 1975). Many RNA viruses copy RNA straight into RNA. And RNA is not only a messenger: Thomas Cech and Sidney Altman showed that some RNAs are catalysts, enzymes made of RNA (Nobel Prize in Chemistry, 1989). Prions are the case people think breaks the dogma. A misfolded protein makes other copies of the same protein misfold. Stanley Prusiner won the 1997 Nobel Prize for the idea. But no sequence is copied from protein to anything; the amino-acid order is still written in the host's gene. The dogma is about sequence, and prions pass on a shape. Interactive · Which way can information flow? Categories follow Crick (1970). "Seen" means observed in nature or, for the special DNA-to-protein case, in a test tube. Replication: copying three billion letters DNA is two strands, each the template for the other. Matthew Meselson and Franklin Stahl showed in 1958 that copying is semi-conservative: each new double helix keeps one old strand and builds one new one. The enzyme that builds is DNA polymerase, which only adds letters to an existing end, in one direction, using the old strand as the pattern: A pairs with T, and C with G. The remarkable part is how rarely it slips. A polymerase choosing letters gets roughly one in 105 wrong. Many polymerases also carry a proofreading arm that backs up and removes the last letter if it is wrong, which cuts errors by a factor of about a hundred. After the copy, a separate mismatch repair system scans the new strand for the bumps where a wrong letter sits, and fixes most of what is left, by roughly another hundred-fold. Those are textbook orders of magnitude, not exact constants, but the structure is the point: three filters in a row, each cheap. errors per copy = letters copied × error rate per letterthe three stages multiply: 10−5 × 10−2 × 10−2 = 10−9 Interactive · The error budget Proofreading arm of the polymerase (÷100) Mismatch repair after copying (÷100) Illustrative orders of magnitude (10−5 raw, ÷100, ÷100). Genome sizes are approximate: phage lambda 48.5 kb, E. coli K-12 4.6 Mb, baker's yeast 12 Mb, human about 3.1 Gb per haploid set, so 6.2 Gb in a body cell. With all three filters on, copying a human body cell's roughly 6.2 billion letters leaves about six mistakes. With none, about sixty thousand. The mistakes that remain are the raw material of mutation (see Genetics, 35/46, and Evolution, 35/47). Perfect copying would be a trap too: a species that never changed could not adapt. Transcription and translation: the real code To use a gene, the cell does not read DNA directly. RNA polymerase copies one strand of the gene into a messenger RNA, the same letters but with U instead of T. In bacteria the message goes straight to a ribosome. In humans and other eukaryotes it is first edited: non-coding stretches (introns) are cut out and the coding stretches (exons) joined, and cutting in different ways, alternative splicing, lets one gene make several proteins. Humans have roughly 20,000 protein-coding genes, a number that surprised people in 2001 and 2004 when the genome was sequenced, because the real richness is in splicing and regulation. The ribosome reads the message three letters at a time. Each triplet, a codon, is matched by a transfer RNA carrying one amino acid, and the ribosome links them into a chain that folds into a protein. With four letters there are 43 = 64 codons for 20 amino acids: 61 codons code for an amino acid, and three (UAA, UAG, UGA) say stop. AUG both codes for methionine and is the usual start signal. The code is redundant but not ambiguous: leucine, serine and arginine each have six codons, while methionine and tryptophan have one each. Marshall Nirenberg and Heinrich Matthaei cracked the first word in 1961: an RNA made only of U's produced a chain of phenylalanine. The code is almost universal across life; a few exceptions exist, such as mitochondria reading UGA as tryptophan. The worked example is the most famous single-letter change in medicine. Haemoglobin's beta chain begins with the codons GTG, CAC, CTG, ACT, CCT, GAG (after the opening ATG). The sixth is GAG, which gives glutamic acid. In sickle cell disease it is GTG, which gives valine. One letter, one amino acid, a protein that sticks to its neighbours when oxygen is low. Try it, and try breaking it other ways. Interactive · Read the code Coding-strand DNA (A, C, G, T only; starts at the first ATG) Sequence: the start of the human HBB gene, bases 51 to 92 of RefSeq NM_000518.5, plus a stop codon added for the example. The mRNA matches the coding strand with U for T; the template strand is its reverse complement. Standard genetic code, NCBI table 1. Notice what the third preset does. Deleting one letter does not change one amino acid; it shifts every codon after it. That is a frameshift, and it usually ends in an early stop. The reading frame is why insertions and deletions of one or two letters are so much more damaging than one swapped letter. Gene regulation: the same genome, different genes on François Jacob and Jacques Monod worked out the first complete switch in the early 1960s, in E. coli (Nobel Prize, 1965, shared with André Lwoff). The lac operon is a cluster of genes for taking up and digesting lactose, under two controls. A repressor protein sits on a stretch of DNA called the operator and blocks RNA polymerase. When lactose is around, a lactose by-product binds the repressor and it lets go. That is the first control, a "don't make the enzymes when there is nothing to digest" switch. The second is an activator, CAP, that helps the polymerase but only when glucose is scarce, which the cell senses through a small molecule called cyclic AMP. So the logic is an AND gate with a twist: full expression needs lactose present and glucose absent. The cell does not waste effort on milk sugar while its preferred food is in the dish. Interactive · The lac operon Lactose is present Glucose is present Expression numbers are illustrative relative levels (induced = 100), not measurements. Mutant strains as in the classic experiments: a broken repressor gene, or an operator the repressor cannot recognise. Humans use the same ideas with far more parts. Instead of one operator, a gene may be controlled by many transcription factors that bind enhancers, DNA switches that can sit thousands, even a million letters from the gene. A limb enhancer for the gene Sonic hedgehog lies about a million letters away, and a single-letter change in it can cause extra fingers. A cell type is a particular pattern of factors turned on: the genome is a library, and the factors choose the books. Epigenetics without the hype "Epigenetic" originally meant everything that makes a cell become what it is. Today it usually means chemical marks on DNA and on the histone proteins that DNA winds around, mainly DNA methylation and histone modifications, that change how readable a gene is without changing its letters. These marks can be copied when a cell divides, which is how a liver cell's daughters stay liver cells. What is solid: marks hold cell identity; in females one X chromosome in each cell is silenced by marking (Mary Lyon, 1961); some genes are switched on from only the mother's or only the father's copy (imprinting); cancers carry abnormal methylation; and methylation patterns drift with age so reliably that "epigenetic clocks" (Steve Horvath, 2013) estimate age from a blood or tissue sample. Identical twins are more different epigenetically when they are older (Fraga and colleagues, 2005). What is oversold: the claim that your grandparents' hunger or trauma is written into your genes. Epigenetic inheritance across generations is documented in plants and in some animals, including worms, but in mammals most marks are wiped in the early embryo and germ cells. Studies of people born around the Dutch Hunger Winter (1944 to 1945) found differences in methylation decades later, a real finding, but it shows the womb environment leaves marks, not that marks are passed to grandchildren. Whether and how much this happens in people is open. If a headline says "trauma inherited in DNA", read the study. PCR and CRISPR as ideas PCR, the polymerase chain reaction, was conceived by Kary Mullis in 1983 (Nobel Prize in Chemistry, 1993). It is replication, repeated: heat splits the double strand; short primers stick to the two ends of the stretch you want; polymerase builds new copies; repeat. Each cycle roughly doubles the number of copies of that stretch, so n cycles give about 2n times more. Thirty cycles is about a billion-fold. A heat-tolerant polymerase from a hot-spring bacterium, Thermus aquaticus, is what made the cycling practical. PCR is behind most infectious disease tests, forensic profiles and ancient DNA work. Interactive · Doubling, and why it is never perfect Cycles Efficiency per cycle Starting copies copies = start × (1 + efficiency)cycles. Real reactions run out of ingredients and plateau; this page caps at an illustrative 1012. CRISPR began as a puzzle in bacterial genomes: strange repeated stretches, noticed in 1987 by Yoshizumi Ishino's group in Osaka and characterised from the 1990s by Francisco Mojica in Alicante. In 2007 Rodolphe Barrangou, Philippe Horvath and colleagues showed it is an immune system: bacteria keep snippets of virus DNA as a "most wanted" list, and a protein (Cas9) guided by a matching RNA cuts any DNA that matches. In 2012 Jennifer Doudna, Emmanuelle Charpentier and colleagues showed it could be programmed, by changing the guide, to cut a chosen site; the pair shared the 2020 Nobel Prize in Chemistry. In 2013 teams including those of Feng Zhang and George Church made it work in human cells. As an idea it is a search-and-cut tool: a guide of about 20 letters finds the one place in the genome it matches. Why does 20 work? The number of possible 20-letter strings is 420, about 1.1 trillion, much larger than the genome, so a random match is rare. Slide the guide length and see. Interactive · How long a guide? Guide length (letters) Expected chance matches = 2 × 3.1×109 ÷ 4L (both strands), assuming random sequence. Real genomes are not random and the tool tolerates some mismatches, which is why off-target cuts are a real engineering problem. The first CRISPR-based medicine, exa-cel (Casgevy), received conditional approval in the UK in November 2023 and US approval in December 2023 for sickle cell disease and a related blood disorder. It edits a patient's own blood stem cells outside the body. A very different case: in 2018 the Chinese researcher He Jiankui announced that he had edited human embryos that became babies. It was condemned worldwide as premature and unethical, and he was later sentenced to prison in China. Editing eggs, sperm or embryos, which would pass changes on, is a policy debate, not a routine technique. None of this is a guide to doing it, and none of it is medical advice. What a graduate just sees A sequence is a message with a reading frame: the same letters in a different frame are a different protein, or none. Information flows DNA to RNA to protein, but the dogma is about sequence: reverse transcription, RNA catalysts and prions are all consistent with it. Copying accuracy comes from layers, not from one perfect enzyme: select, proofread, repair. The code has 64 words for 20 meanings; most single-letter changes in the third position of a codon change nothing. A cell type is a gene-regulation pattern, not a different genome. Regulation is logic: repressors and activators combine like AND and NOT gates. Epigenetic marks are real and useful, and "inherited trauma" headlines usually run ahead of the evidence. Exponentials explain PCR; sequence uniqueness explains CRISPR targeting. Where it shows up next Genetics (35/46): mutation is a copying error that survives, and the codon table tells you whether it matters. Microbiology (35/50): bacteria, phages and CRISPR; antibiotics that target the bacterial ribosome or the replication machinery. Developmental Biology (35/51): an embryo is gene regulation unfolding in space, with enhancers and transcription factors as the instructions. Bioinformatics & Genomics (35/52): everything above, read as strings, aligned and searched at scale. In the world: diagnostic tests, mRNA vaccines (which use the cell's own ribosomes), forensic and ancestry DNA, gene therapies and crop breeding. If you want to go deeper 📘 Textbook. Bruce Alberts and others, Molecular Biology of the Cell (W. W. Norton, 7th edition, 2022). The standard reference for the cell and gene expression, with outstanding figures. 📘 Textbook. James Watson and others, Molecular Biology of the Gene (Pearson, 7th edition, 2014). A tighter, gene-centred course text. 📘 Gentler. Siddhartha Mukherjee, The Gene: An Intimate History (Scribner, 2016), for the story from Mendel to editing, and Horace Freeland Judson's The Eighth Day of Creation (1979) for how the code was cracked. 🌐 Free course. MIT OpenCourseWare 7.01SC Fundamentals of Biology (Fall 2011), and the free Biology 2e textbook from OpenStax. The takeaway Information in DNA is copied with layered accuracy, read three letters at a time into proteins, and switched on and off by regulators that behave like logic gates. One genome, many cell types; a few strange cases such as prions and reverse transcription fit once the dogma is read as being about sequence. PCR and CRISPR are what you get when you turn replication and bacterial immunity into tools. Try this: take any short word and read it in the wrong frame, moving the spaces by one letter. That is a frameshift, and it is why a one-letter deletion is worse than a swap. Sources & Further Reading Sources. Crick, "Central dogma of molecular biology", Nature 227 (1970); Meselson and Stahl, PNAS (1958); the Nobel Prizes of 1965, 1968, 1975, 1989, 1993, 1997 and 2020 (nobelprize.org); Jacob and Monod, J Mol Biol (1961); Jinek and others, Science (2012); Barrangou and others, Science (2007); NCBI RefSeq NM_000518.5 and the standard genetic code (NCBI table 1); Mullis, Nobel lecture (1993); Fraga and others, PNAS (2005); Horvath, Genome Biology (2013); Heijmans and others, PNAS (2008); UK MHRA (16 November 2023) and US FDA (December 2023) on Casgevy. Error rates are textbook orders of magnitude (Alberts, Molecular Biology of the Cell). Describes, and is not medical advice. 🌐 MIT OCW 7.01SC Fundamentals of Biology 🌐 OpenStax Biology 2e 📘 Alberts and others, Molecular Biology of the Cell 📘 Mukherjee, The Gene Step 7. Genetics: Inheritance, Chance and What Genes Can't Tell You ------------------------------------------------------------------- Why: Inheritance, from Mendel to genomes. From Mendel's peas to millions of genomes: how traits pass on, why carriers hide, what a polygenic score really predicts, and the history we should not repeat. Your eyes are not exactly your mother's or your father's. Your sister, with the same two parents, looks different from you again. Some families carry a rare illness across generations that skips whole branches. And yet a pea plant, a fruit fly and a person all obey the same few rules of inheritance, written down first by a monk with a garden. Genetics is the science of that regularity and of what breaks it. It began as arithmetic on counted plants, grew into a map of chromosomes, and is now the statistics of millions of people's genomes. It is also the subject whose misuse has done real harm, so this piece tells that history too. The course in one box Who takes itEvery biology, biochemistry and pre-medical student, usually in year 2. Medical courses reuse it for inherited disease and risk. Programmes in the Vision and Change tradition (AAAS and NSF, 2011) and courses such as MIT's 7.03 teach it as the link between molecules and populations. What it is forPredicting how traits pass between generations, and telling what a gene can and cannot explain. Comes afterMolecular Biology (35/45) and Statistics (34/05). Leads toEvolution (35/47), Developmental Biology (35/51) and Bioinformatics & Genomics (35/52). What this piece gives youYou will not be able to run a genetic analysis. You will be able to work a Punnett square, explain why carriers vastly outnumber the affected, say what a polygenic score does and does not tell you, and recognise bad arguments about human groups. Easier first reads: Nature, Nurture, and You (02/04), Personality & Individual Differences (35/26) for what heritability means, and Probability: How to Not Fool Yourself (12/03). It describes how things work and is not medical advice. Mendel, and why he was lucky Gregor Mendel, an Augustinian friar in Brno (then Brünn, now in the Czech Republic), crossed pea plants for years and counted the offspring. He presented the results in 1865 and published them in 1866. His key choice was to look at single, clear-cut traits: round or wrinkled seed, yellow or green. Cross a pure round line with a pure wrinkled one and every child is round. Cross those children with each other and about a quarter of the grandchildren are wrinkled again. His counts for seed shape were 5,474 round and 1,850 wrinkled, a ratio of 2.96 to 1. From such counts came two ideas. Segregation: each plant carries two copies of each factor (we say alleles of a gene), and each pollen or egg cell gets just one. Independent assortment: factors for different traits are shuffled separately. A dominant allele shows when present; a recessive one shows only with two copies. Dominant does not mean common or healthy. It is a statement about how the two copies combine. He was lucky in ways that are worth knowing. Each trait he chose depends mostly on one gene, with one allele fully dominant, which is rare for traits in general. He started from pure-breeding lines. And the trait pairs he crossed were not tightly linked on a chromosome, which would have blurred his ratios. Nobody read the work: it was rediscovered in 1900 by Hugo de Vries, Carl Correns and Erich von Tschermak. In 1936 the statistician R. A. Fisher noted that Mendel's counts sit closer to the ideal ratios than chance usually allows. Historians still argue about why (stopping a count at a convenient point, rounding, an overeager helper). Nobody has shown the laws are wrong; thousands of later crosses confirm them. Sampling noise is the lesson: try it. Interactive · Draw offspring Number of offspring Draw againUse Mendel's 7,324 A random draw from the expected probabilities (a seeded generator, so results repeat until you press Draw again). χ² compares observed with expected; the p-value is how often chance alone would look at least this far from the ideal. At 8 offspring a "3 to 1" cross often looks like 5 to 3 or 7 to 1. At several thousand it settles close to 3 to 1. A p-value near 1 means suspiciously perfect, a very low one means something other than chance is going on, and most real crosses sit in the middle. That is also the first lesson of Statistics (34/05): a ratio from a small sample is a rumour. Chromosomes and linkage Genes live on chromosomes. In 1902 and 1903 Walter Sutton and Theodor Boveri noticed that chromosomes pair and split in the same pattern as Mendel's factors. In 1910 Thomas Hunt Morgan, at Columbia, found a white-eyed male fruit fly among red-eyed ones, and traced the trait to the X chromosome. Humans have 23 pairs: 22 pairs of autosomes and the sex chromosomes (XX or XY). Shuffling whole chromosomes alone can give one person about 223, over 8 million, different gametes. Genes on the same chromosome travel together, except when crossing over swaps stretches between the two copies. The further apart two genes are, the likelier a swap between them. In 1913 Alfred Sturtevant, then a student in Morgan's lab, turned that into the first genetic map: 1% recombinant offspring means 1 map unit, now called a centimorgan. Genes 50 or more centimorgans apart look unlinked, as if on different chromosomes. That is the situation Mendel stumbled into. r = ½ (1 − e−2d)Haldane's map function: recombinant fraction r from map distance d in morgans · small d gives r ≈ d · large d gives r → ½ Interactive · Linked or not? Distance between two genes For a parent with alleles AB on one chromosome and ab on the other. Parental types AB and ab are equally common; recombinants Ab and aB share the rest. Mutation: where new variants come from Every allele began as a copy that went slightly wrong (see Molecular Biology, 35/45). A mutation can swap one letter, delete or insert some, or repeat a stretch many times. It matters in the germline (eggs and sperm, so it can be inherited) or in a somatic cell (which affects only that body, as in a cancer). In humans the rate is about 1.1 to 1.2 × 10−8 per letter per generation, so a child has roughly 60 to 70 new mutations that neither parent carried. Most come from the father, and the count rises with his age, by about two for every extra year. Since only some 1 to 2% of the genome codes for protein, a typical child has on the order of one new mutation in the coding part, and most of those are harmless. Examples show the range. Sickle cell disease is one letter changed (Glu6Val). The commonest cause of cystic fibrosis is a three-letter deletion that removes one amino acid, F508del. Huntington's disease is a stretch of CAG repeats that has grown too long. The ability to digest milk as an adult, lactase persistence, comes from changes next to the lactase gene that stop it switching off, and it arose independently several times, in Europe and in East Africa. And mutation is random with respect to need. In 1943 Salvador Luria and Max Delbrück showed that resistance in bacteria appears before the bacteria meet the virus that selects it, not because of it (Nobel Prize, 1969). That is the foundation of Evolution (35/47). Interactive · New mutations in one child Mutation rate per letter per generation New mutations = rate × 2 × 3.1 billion letters. Coding share taken as 1.5% of the genome (an approximate round figure). Measured counts are a little lower (60 to 70) because some regions cannot be read reliably. Hardy–Weinberg: why carriers vastly outnumber the affected In 1908 the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg independently pointed out something simple. If mating is random and nothing pushes allele frequencies around, they stay put, and the three genotypes appear in fixed proportions. For two alleles with frequencies p and q (p + q = 1): p² + 2pq + q² = 1two copies of the common allele · one of each (carriers) · two copies of the rare allele (affected, if recessive) Take a recessive condition seen in 1 birth in 2,500. Then q² = 1/2,500, so q = 0.02. Carriers are 2pq = 2 × 0.98 × 0.02, about 3.9%, roughly 1 person in 25. A rare recessive allele hides almost entirely in healthy carriers, which is why such conditions seem to "come out of nowhere" in families with no history. (Cystic fibrosis in some European-ancestry populations is close to this; figures vary by population.) Sickle cell shows the opposite lesson: where malaria is common, carrying one copy protects against severe malaria (A. C. Allison, 1954), so the allele stays frequent in parts of Africa, the Mediterranean, the Middle East and India. When relatives have children, rare alleles meet more often. With an inbreeding coefficient F, affected children are q² + Fpq. First cousins' children have F = 1/16, which here raises the risk from 1 in 2,500 to about 1 in 615. Interactive · Hardy–Weinberg Frequency of the rare allele, q Inbreeding coefficient, F Genotypes: AA = p² + Fpq, Aa = 2pq(1 − F), aa = q² + Fpq. Assumes a simple recessive trait; illustrative. The same arithmetic undid an old idea. In 1917 R. C. Punnett pointed out that preventing carriers of a rare recessive from breeding changes the allele frequency very slowly: removing every affected person's genes each generation takes the frequency from q to q/(1 + q), so the time to halve a frequency of 1% is about a hundred generations. Slow, and costly in human lives. We will meet the consequences in a moment. Complex traits and polygenic scores Most traits people care about, such as height, blood pressure and risk of common illnesses, are not Mendelian. In 1918 Fisher showed that many genes each adding a small effect make a smooth bell curve, as dice do when you add up many. This is the polygenic picture, and sequencing has confirmed it. The largest study of height (Yengo and colleagues, 2022, in Nature, with about 5.4 million people) found 12,111 common variants linked to height. Together they predict about 40% of the variation in people of European ancestry. Twin studies put the heritability of height around 80%, so there is still a gap, and it is partly rare variants and effects not yet measured. A polygenic score adds up a person's copies of the variants, each weighted by its estimated effect. It is a statistic about populations, with four limits. First, it predicts a range, not a destiny: even with a good score, many individuals fall far from the prediction. Second, it works much less well in people whose ancestry differs from the studied group: studies of this transfer problem (Martin and colleagues, 2019) found scores several times less accurate in people of African ancestry than in Europeans, because most data come from Europe. Third, scores for behavioural traits such as years of schooling pick up family environment as well as direct genetic effects, and shrink when siblings are compared. Fourth, genes work through environments: the same score predicts different outcomes in different places and times. Interactive · Many small effects, one imperfect score Number of genes shaping the trait Heritability (share of variation from genes) Share of the genes your score includes 2,000 simulated people with a fixed random seed. Each gene has two equally common alleles of equal size. Trait = genes + environment, scaled so that the genes' share of variance is your heritability. An invented model for intuition, not data. Notice what the numbers say. Set heritability to 100% and one gene gives three lumps; 40 genes give a bell. At 60% heritability and a score holding half the genes, the score explains about 30% of the variation, a correlation near 0.55, and the top tenth by score are only moderately enriched for the top tenth by trait. That is the best case in a model with no ancestry gap. Human genetic variation, told correctly Any two people share about 99.9% of their DNA; a typical genome differs from the reference at roughly four to five million sites (1000 Genomes Project, 2015). Where does the difference sit? In 1972 Richard Lewontin analysed protein markers across populations and found that about 85% of the variation lay within local populations, and only a small remainder between groups. Later work with hundreds to hundreds of thousands of markers, from Noah Rosenberg and colleagues in 2002 (377 markers) onwards, found the same broad pattern: most variation, in the region of 85 to 95% depending on the markers and populations, is within populations. Two further facts keep this honest. First, A. W. F. Edwards pointed out in 2003 that combining many markers lets you place a person's ancestry accurately, which is why ancestry tests work. Both statements are true: groups can be told apart statistically, and individuals within a group differ far more than the group averages do. Second, variation is mostly continuous and geographic, not boxed. Africa holds more genetic diversity than the rest of the world, because modern humans spent longest there; people elsewhere descend from smaller groups that left, and diversity falls with distance from Africa. Traits that look like clear categories often are not. Light skin evolved more than once, with different genes in Europe and East Asia. Sickle trait follows malaria, not "race". Lactase persistence arose several times. Genes also depend on environment: phenylketonuria is a recessive inherited condition whose harm can be prevented by diet, found by newborn screening. Heritability, as Personality & Individual Differences (35/26) explains, is a population statistic in one environment; it does not measure how fixed anything is, and it cannot be compared between groups living in different conditions. Interactive · Predict, then reveal Your guess: share of all human genetic variation that lies within a single local population Reveal Measured: about 85% (Lewontin 1972); later genome-wide studies roughly 85 to 95%, depending on markers and populations. The history of eugenics Francis Galton, Darwin's cousin, coined eugenics in 1883 for the idea that society should improve its heredity by encouraging some people to have children and discouraging others. It spread around the world in the early twentieth century, across the United States, Britain, Germany, the Nordic countries, Latin America, Japan and beyond, and respectable scientists and reformers backed it. It rested on three mistakes: it treated complex traits as simple Mendelian ones, it read social disadvantage as inherited defect, and it assumed some people's lives were worth less. It was also racist in practice. Where and whenWhat happened United States, from 1907Indiana passed the first sterilisation law in 1907; many states followed. Buck v. Bell (1927) upheld Virginia's law, with Justice Holmes writing that "three generations of imbeciles are enough." Estimates of people sterilised under such laws are in the tens of thousands. Nazi Germany, 1933 to 1945A 1933 law led to the sterilisation of over 400,000 people. The "euthanasia" programmes killed many thousands of disabled people, and the same personnel and methods fed into the Holocaust. Sweden, 1934 to 1976A government inquiry in 2000 estimated about 21,000 people forcibly and about 6,000 coercively sterilised, mostly women. Alberta, Canada, 1928 to 1972About 2,800 sterilisations under the province's Sexual Sterilization Act. Japan, 1948 to 1996The Eugenic Protection Law led to about 25,000 forced sterilisations; Japan's Supreme Court held it unconstitutional in July 2024. Peru, 1995 to 2000A national family-planning programme sterilised about 25,000 men and some 330,000 women according to a 2002 report; coercion of poor and Indigenous women was alleged and investigated. India, 1975 to 1977During the Emergency, millions of vasectomies were carried out, many under pressure. Many early critics were geneticists, as the Punnett argument above shows. The practice fell out of favour after 1945, though states went on sterilising for decades. Today's questions are subtler: prenatal screening, which is a choice, but one made in a society that treats some lives as lesser; and companies offering embryo selection using polygenic scores, which the European Society of Human Genetics has called unproven. Disability-rights writers and geneticists alike warn that the old logic can return in softer forms. The lesson of the history is not that genetics is dangerous. It is that a statistic about populations is not a verdict on a person. What a graduate just sees Ratios from small samples are noisy. A "3 to 1" cross of 8 offspring is not a failed law. Dominant describes how alleles combine, not how common or healthy they are. Genes close together travel together; genes far apart behave as if on different chromosomes. Most new mutations are neutral, and they arise without regard to need. Rare recessive alleles hide in carriers, who are far more common than the affected. Most traits are polygenic: many small effects, a bell curve, and a score that predicts a range for a population, not an outcome for a person. Most human genetic variation is within populations, and it is geographic and continuous, not boxed. Heritability is about variation in a population in an environment; it is not fate and not a ranking of groups. Eugenics was mainstream science plus prejudice, and it is a reason to be careful with every new use of genetic prediction. Where it shows up next Evolution (35/47): Hardy–Weinberg is the null model; selection, drift, migration and mutation are the forces that break it. Developmental Biology (35/51): the same genes act at different times and places; mutations that change regulation change bodies. Bioinformatics & Genomics (35/52): genome-wide studies, polygenic scores and ancestry inference are statistics on exactly these ideas. Medicine and the clinic: carrier screening, newborn screening, inherited cancer risk, pharmacogenetics and genetic counselling. Agriculture: crop and livestock breeding, from Mendel's peas to marker-assisted selection. If you want to go deeper 📘 Textbook. Anthony Griffiths and others, Introduction to Genetic Analysis (Macmillan/W. H. Freeman, 12th edition, 2020). A standard course text, strong on problem-solving. 📘 Textbook. Benjamin Pierce, Genetics: A Conceptual Approach (Macmillan, 7th edition, 2020). Clearer on the concepts, with many worked problems. 📘 Gentler. Adam Rutherford, A Brief History of Everyone Who Ever Lived (2016) and Control: The Dark History and Troubling Present of Eugenics (2022); Kathryn Paige Harden, The Genetic Lottery (Princeton, 2021); Siddhartha Mukherjee, The Gene (2016). 🌐 Free course. MIT OpenCourseWare 7.03 Genetics (Fall 2004), and the genetics chapters of OpenStax Biology 2e. The takeaway Inheritance is arithmetic on pairs of alleles: segregation, assortment, linkage and sampling noise. New alleles arise by random mutation; rare recessives hide in carriers; most traits come from many genes of small effect plus environment, so predictions are statistics about groups. People differ genetically, but mostly within populations and along gradients, and the story of eugenics shows what happens when a statistic is mistaken for a verdict. Try this: next time you read "X% heritable" or "the gene for Y", ask what population, what environment, and whether the finding is about one person or about a group. Sources & Further Reading Sources. Mendel, Versuche über Pflanzen-Hybriden (1866), seed-shape counts 5,474 and 1,850; Fisher, Annals of Science (1936); Hardy (1908) and Weinberg (1908); Sturtevant (1913); Haldane (1919) map function; Luria and Delbrück (1943); Allison (1954); Punnett (1917); Yengo and others, Nature 610 (2022); Martin and others, Nature Genetics (2019); Lewontin (1972); Edwards (2003, on "Lewontin's fallacy"); Rosenberg and others, Science (2002); 1000 Genomes Project, Nature (2015); Kong and others, Nature (2012) on mutation rates and father's age; Galton (1883); Buck v. Bell, 274 U.S. 200 (1927); Swedish government inquiry (2000) and other counts as summarised in encyclopaedic overviews, with estimates varying; Japan Supreme Court ruling, July 2024. Describes how things work and is not medical advice. 🌐 MIT OCW 7.03 Genetics 📘 Griffiths and others, Introduction to Genetic Analysis 📘 Harden, The Genetic Lottery 📘 Rutherford, Control Step 8. Evolution: The Idea That Makes Sense of Biology ------------------------------------------------------- Why: The idea that makes sense of all of biology. Variation, inheritance and unequal success are enough to change a population, and the evidence from fossils, genes and the lab says it has. What the idea is, what it is not, and where scientists still argue. A hospital treats a patient's infection with an antibiotic. Within days the bacteria are gone, then a few survivors regrow, and the next dose does nothing. Nobody designed that resistance. A farmer in Mexico saves the biggest kernels of corn each year for nine thousand years, and a grass with a handful of hard seeds turns into maize. Nobody designed that either, and the farmer never knew a gene was involved. Both are the same process, and it is the one Darwin and Wallace described in 1858: living things vary, some of the variation is inherited, and some variants leave more offspring than others. Given enough time, that is enough to produce eyes, wings and rainforests. As Theodosius Dobzhansky titled a 1973 essay, "nothing in biology makes sense except in the light of evolution". This piece is about why a biologist says that, and what the idea is not. The course in one box Who takes itBiology majors, usually in year 2 or 3, and increasingly pre-medical students, since pathogens and cancers evolve. In the Vision and Change framework (AAAS and NSF, 2011) evolution is the first of the five core concepts. Cambridge Natural Sciences and MIT's Course 7 teach it alongside genetics and ecology. What it is forExplaining why organisms are the way they are, and predicting how populations change. Comes afterGenetics (35/46). Leads toEcology (35/48), and the evolutionary side of Microbiology (35/50), Developmental Biology (35/51) and Bioinformatics & Genomics (35/52). What this piece gives youYou will not be able to build a phylogeny. You will be able to say what evolution is and is not, predict a response to selection with one equation, see why small populations drift, and recognise the evidence and the misconceptions. It respects readers of every belief: it describes what the science says and how it is tested, and does not argue about anything else. Easier first reads: Nature, Nurture, and You (02/04), Why Exponential Growth Rules Everything (12/02) and Game Theory: Cooperation & Conflict (12/06); see also Game Theory (34/45) in this series. This is not medical advice. Three ingredients: variation, inheritance, selection Charles Darwin spent twenty years collecting evidence, and in 1858 learned that Alfred Russel Wallace, working in the Malay Archipelago, had reached the same idea. Their joint papers were read at the Linnean Society of London that July. Darwin's On the Origin of Species followed in November 1859. The logic needs three things, and if all three are present, change follows: Variation: individuals in a population differ in some trait. Heredity: part of that difference is passed to offspring. Differential success: individuals with some variants leave more offspring. This is selection, and it needs no foresight. Darwin did not know how heredity worked; Mendel's laws and DNA supplied it. The size of the response can be predicted. Breeders and biologists use the breeder's equation: R = h² × Sresponse to selection = heritability × selection differential (how far the survivors' average is from the whole population's average) Heritability here means what Personality & Individual Differences (35/26) says it does: the share of variation in this population that tracks genes. If it is zero, selecting changes nothing next generation, however strong the selection. Take a trait with standard deviation 1 and let only the top 20% reproduce. Then S is about 1.4 standard deviations, and with h² = 0.5 the next generation's average moves up about 0.7. Try it. Interactive · Breeding for a trait Share of the population that reproduces Heritability, h² Run again Simulation of 1,000 individuals over 10 generations, with a seeded random generator: the trait is genes plus environment, parents are chosen by their trait value, and offspring inherit the midparent value plus shuffling. Units are standard deviations of the starting population. Predicted line: R = h² × S, with S from the normal curve. The simulation usually falls a little short over many generations, because selection itself uses up some of the variation it works on. Every crop and farm animal is the result: maize from the Mexican grass teosinte (domesticated roughly nine thousand years ago), rice in the Yangtze valley, wheat in the Fertile Crescent, potatoes in the Andes, sorghum in Africa; cabbage, kale and broccoli are one species. Darwin opened the Origin with pigeon breeders for the same reason: artificial selection is natural selection with a person choosing. Real populations do not move in straight lines. On the small Galápagos island of Daphne Major, Peter and Rosemary Grant and their students measured every finch for decades. In the 1977 drought, small, soft seeds ran out and mostly large, hard ones were left, and birds with deeper beaks survived better; their offspring had deeper beaks. Selection plus heredity, watched in a lifetime. Drift: change without a reason Not all change is selection. When a population is small, which alleles get passed on is partly luck, like a coin flipped few times. This is genetic drift. In the Wright–Fisher model each new generation is drawn by sampling the previous one, and a variant at frequency p will, over time, either vanish or take over (fixation). A neutral variant's chance of eventually fixing is just its starting frequency, p. What differs is how fast: in a population of 2N gene copies, genetic variety shrinks each generation by a factor of (1 − 1/2N). The bigger the population, the weaker drift. That is why small populations lose variety, why cheetahs and island species are fragile, and why founders matter in human history: a few people who leave a population carry only part of its diversity. Mutation, selection, drift and migration are the four forces. Try a coin-flip population. Interactive · Ten populations, same start Population size N Starting frequency of the variant Run again Wright–Fisher model: N diploid individuals, so 2N gene copies sampled with replacement each generation; no selection. Ten replicate populations, 100 generations, seeded. Expected variety left after t generations: (1 − 1/2N)t. Speciation: how one lineage becomes two A species is, in Ernst Mayr's classic 1942 definition, a group of interbreeding natural populations reproductively isolated from others. It works well for birds and badly for bacteria, plants that hybridise, and fossils, so biologists use several definitions. What matters is the process: when two populations stop exchanging genes, they drift apart. The commonest route is geographic. A mountain, a sea or a river splits a population (allopatric speciation). Each side meets different environments and different mutations. Over time, changes accumulate that do not work together when the groups meet again: the Dobzhansky–Muller picture, in which each side's new alleles are fine at home but clash in hybrids. Closure of the Isthmus of Panama, a few million years ago, split marine populations into Atlantic and Pacific halves that are now related species. Salamanders in California form a ring around the Central Valley in which neighbours interbreed but the two ends, where the ring closes, do not. And hundreds of cichlid fish species in Africa's Great Lakes arose in lakes that are young in geological terms. It can also happen without a barrier. Plants often double their chromosome number in a hybrid, which isolates them in a single generation; bread wheat is such a hybrid of three grasses, formed in the Fertile Crescent roughly eight to ten thousand years ago. Boundaries stay fuzzy: modern humans outside Africa carry roughly 1 to 2% of DNA from Neanderthals, a sign that populations long separated still interbred when they met. The evidence: fossils, homology and molecular clocks The case for common descent comes from independent lines that agree. A few: Fossils with predicted features. In 2004 a team led by Edward Daeschler, Neil Shubin and Farish Jenkins went to Ellesmere Island in Arctic Canada because the rock there was the right age (about 375 million years) and kind to hold fish becoming land animals. They found Tiktaalik, a fish with a neck, a flat head and bones in its fins like a limb. In Pakistan and India, a sequence of fossils shows whale ancestors with legs, and DNA places whales inside the even-toed hoofed mammals, with hippos closest. Homology. A human arm, a bat wing, a whale flipper and a horse leg are built from the same bones, adapted to different jobs. Embryos of many vertebrates share structures that vanish or change later. Shared genetic errors. Humans cannot make vitamin C because a gene needed for it is broken, and the same gene is broken, with matching damage, in other apes and monkeys. A design reused for no reason is odd; an inherited error is expected. Human chromosome 2 is a fusion of two chromosomes that remain separate in other apes. Geography. Wallace noticed that the animals of Bali and of neighbouring Lombok differ strikingly, because deep water divides the Asian and Australian faunas (the "Wallace Line"). Many trees agree. Family trees built from anatomy and from DNA, made independently, match to a degree chance cannot explain. DNA also gives a clock. In 1962 Emile Zuckerkandl and Linus Pauling saw that the differences between species' haemoglobins grew with the time since the species split. Motoo Kimura's neutral theory (1968) explained why: most changes that persist at the DNA level are neutral, and for neutral changes the rate of substitution equals the mutation rate, whatever the population size. Then the time since two species split is the genetic difference divided by twice the rate (both lineages change). t = d ÷ (2μ)time since the split = fraction of sites that differ ÷ (2 × substitution rate per site per year) Interactive · A molecular clock Substitution rate (per site per year) Approximate single-letter differences: human–chimpanzee about 1.2% (Chimpanzee Sequencing Consortium, 2005), human–gorilla about 1.6%, human–orangutan about 3%. The rate must be calibrated from fossils or from pedigrees, and the two methods disagree: that is why published human–chimp split dates range from roughly 6 to 13 million years. Moving the rate slider is the honest lesson. A molecular clock is a ratio, and its answer depends on a calibration. Fossils and DNA must agree across hundreds of cases, and they do; at the edges, they argue. Evolution you can watch: antibiotic resistance Evolution is not only about the past. In 1988 Richard Lenski began growing twelve populations of E. coli in his Michigan lab, transferring a sample to fresh food every day. By 2020 the populations had passed 70,000 generations. All twelve got faster at growing in the flask. In one, around generation 31,500, bacteria arose that could use citrate, a molecule in the broth that E. coli normally cannot eat: a new ability, noticed and traced. The frozen samples let the team replay history. Resistance is the same story with higher stakes. Alexander Fleming warned in his 1945 Nobel lecture that careless use could breed resistant microbes. Within a few years of methicillin's introduction, resistant staphylococci (MRSA) were reported, in Britain in 1961. A 2022 analysis in The Lancet (Murray and colleagues) estimated 1.27 million deaths in 2019 directly attributable to bacterial resistance, and 4.95 million associated with it. How does it happen? There is a small number of resistant mutants in any large bacterial population before the drug arrives; the drug kills the rest. Resistance usually carries a cost, which is why resistant strains fade when the drug is absent. Interactive · Who is left after the drug? Resistant share before treatment Drug kills susceptible cells by a factor of Growth speed of resistant cells (cost of resistance) Illustrative expected-value model, not a clinical one: 109 bacteria regrow to the same total between eight treatments; resistant cells survive each drug exposure and grow at the stated relative speed. Real resistance varies by drug, species and patient; follow a clinician's advice on antibiotics. What evolution is not: common misconceptions Common ideaWhat the science says "Survival of the fittest" means the strongest win.Herbert Spencer coined the phrase (1864); Darwin adopted it from 1869. Fitness means how many offspring that survive to reproduce, which can favour small, quiet or cooperative. Evolution is "only a theory".In science a theory is a tested, explanatory framework, like germ theory or plate tectonics. It is not a guess. Humans came from monkeys.Humans and living apes share common ancestors; we are apes, not descended from any living species. Evolution is random.Mutation is random with respect to need; selection is not. The combination is not a lottery. Individuals evolve to meet needs.Individuals do not change their genes. Populations change over generations as variants spread. Evolution is a ladder toward us.It is a branching tree with no goal. Bacteria alive today have as long a history as we do. Evolution explains how life began.Evolution explains change in living populations; the origin of the first life is a separate research question. Beliefs matter here. Many scientists are religious, and many religious communities accept evolution. The Catholic Church, for example: Pope John Paul II told the Pontifical Academy of Sciences in 1996 that evolution is "more than a hypothesis". Others disagree, and that is their right. What science can offer is the evidence and the method, and anyone can check both. The modern synthesis and where scientists still argue In the 1930s and 1940s, R. A. Fisher, J. B. S. Haldane and Sewall Wright showed mathematically that Mendelian genes and gradual selection fit together, and Dobzhansky, Mayr, Simpson and others tied this to experiments, species and fossils. This modern synthesis is the base. Since then, DNA, development and genomes have added to it, and real arguments continue: Selection or drift? Neutralists following Kimura say most molecular differences are neutral; selectionists point to widespread signs of adaptation. Most now accept both, and argue about the mix. Slow or in bursts? Niles Eldredge and Stephen Jay Gould argued in 1972 that species often stay the same for long periods and change in short episodes (punctuated equilibrium). Gradualists respond that the fossil record is incomplete and the bursts are still gradual on human timescales. Both patterns appear. Does the theory need extending? In 2014 Kevin Laland and colleagues argued in Nature for an "extended evolutionary synthesis" including niche construction, developmental plasticity and non-genetic inheritance. Gregory Wray and colleagues replied in the same journal that the standard theory already accommodates these. The disagreement is partly about emphasis. Which level does selection act on? Genes, individuals, groups, species. Kin selection (William Hamilton, 1964) explains much cooperation; "group selection" remains contested, and the two camps often describe the same maths differently. A tree or a web? Among bacteria, genes pass sideways; and complex cells arose when one cell took up another (Lynn Margulis, 1967), so the early tree of life has tangles. What a graduate just sees Change needs variation, heredity and differential success. Take any one away and nothing happens. Response to selection is heritability times selection differential. High pressure with no heritable variation does nothing. Populations evolve; individuals do not. Selection acts on individuals, and what changes is the population. Luck matters in small populations. Not every change is an adaptation. Species are fuzzy: a process, not a box. Separation plus time makes new ones. The strongest evidence is agreement between independent lines: fossils, anatomy, genes, geography. "Fittest" means most offspring, not strongest. Evolution has no goal and no ladder. Resistance in bacteria, pests and cancers is evolution at work, and is predictable. Where it shows up next Ecology (35/48): populations, competition and predation are the selection pressures; communities are shaped by their evolutionary histories. Microbiology (35/50): resistance, virulence and the evolution of pathogens, including why vaccines and drugs need updating. Developmental Biology (35/51): body plans evolve by changing when and where genes act. Bioinformatics & Genomics (35/52): phylogenetic trees, alignments and tests for selection are applied evolution. In the world: crop and livestock breeding, antibiotic stewardship, conservation of small populations, cancer therapy, and tracing outbreaks from sequences. If you want to go deeper 📘 Textbook. Douglas Futuyma and Mark Kirkpatrick, Evolution (Oxford University Press, 5th edition, 2023). The standard upper-level text. 📘 Textbook. Carl Zimmer and Douglas Emlen, Evolution: Making Sense of Life (Macmillan, 3rd edition, 2020). More readable, with strong examples. 📘 Gentler. Jonathan Weiner, The Beak of the Finch (1994), on the Grants' work; Neil Shubin, Your Inner Fish (2008), on fossils and anatomy. 🌐 Free course. UC Berkeley's Understanding Evolution, with lessons for self-study; and MIT OpenCourseWare 7.014 Introductory Biology (Spring 2005), which places evolution in the wider course. The takeaway Variation, inheritance and unequal success are enough for populations to change; the breeder's equation says how fast. Drift adds luck, isolation makes new species, and fossils, anatomy, DNA and geography all agree on common descent. Resistance shows it in real time. The arguments that remain, between neutral and adaptive, slow and fast, narrow and extended, are among scientists who agree on the core. Try this: next time you hear "survival of the fittest" or "evolved to", ask whose offspring, in what environment, and over how many generations. Sources & Further Reading Sources. Darwin and Wallace, Linnean Society (1 July 1858); Darwin, On the Origin of Species (1859); Dobzhansky, American Biology Teacher (1973); Fisher (1930), Haldane (1932), Wright (1931) and the modern synthesis; Mayr, Systematics and the Origin of Species (1942); Kimura (1968); Zuckerkandl and Pauling (1962); Eldredge and Gould (1972); Laland and others, Nature 514 (2014) and Wray and others, same issue; Hamilton (1964); Margulis (1967); Daeschler, Shubin and Jenkins, Nature (2006) on Tiktaalik; Boag and Grant, Science (1981) on the 1977 drought; Blount, Borland and Lenski, PNAS (2008); Murray and others, Lancet 399 (2022); Jevons (1961) on MRSA; Fleming, Nobel lecture (1945); Chimpanzee Sequencing Consortium, Nature (2005); Green and others, Science (2010) on Neanderthal DNA; John Paul II, address to the Pontifical Academy of Sciences (22 October 1996). Dates for domestication and speciation events are approximate. Describes the science and is not medical advice. 🌐 Understanding Evolution (UC Berkeley) 🌐 MIT OCW 7.014 Introductory Biology 📘 Futuyma and Kirkpatrick, Evolution 📘 Weiner, The Beak of the Finch Step 9. Physiology: How Bodies Keep Themselves Alive ---------------------------------------------------- Why: How bodies keep themselves alive. A body is not a machine that runs; it is a collection of thermostats, all holding numbers steady while the world pushes. Physiology is the course that learns the set points, the sensors and the muscles of each loop. Run up a flight of stairs and four things happen without a decision. Your heart speeds up, you breathe harder, you start to feel warm, and soon you sweat. Walk back down, stand still, and all four drift back to where they began. Nothing is reading a dial; each is a loop that senses a number and pushes it back. Physiology asks how a living animal does this, organ by organ. A physiologist looks at a body and sees a set of regulated quantities (blood pressure, blood oxygen, temperature, water, sugar) and the plumbing, muscles and chemical messengers that hold them in range. This piece takes the eight ideas that stay with people who have studied it. It describes how bodies work; it is not medical advice, and nothing here replaces a clinician who knows you. The course in one box Who takes itBiology, nursing, medicine, physiotherapy, sport science and biomedical engineering students, typically in year 2 or 3. Medical schools teach it in the first year or two, often with anatomy. What it is forExplaining how organs work and what they regulate, so that what goes wrong can be understood. Comes afterCell Biology (35/44), because every organ is cells doing a job. Leads toDevelopmental Biology (35/51) and Biological Psychology (35/20) in this series, and, for medicine, pharmacology, pathology and clinical medicine. What this piece gives youYou will not be able to interpret a blood test or diagnose anyone. You will see feedback as the master idea, why a narrow vessel matters so much, why altitude is hard, how the kidney does its sum, how muscle trades force for speed, and why a mouse and an elephant live at different tempos. Easier first reads: Why You Feel Before You Think (01/01), What Exercise Actually Does (01/07) and Your Immune System, Day by Day (01/10). Homeostasis: hold the number, accept the cost In the nineteenth century Claude Bernard wrote that a complex animal lives in a stable "internal environment" even as the outside changes. Walter Cannon named the idea homeostasis in the 1920s and gave it a popular book, The Wisdom of the Body (1932). The mechanism is almost always negative feedback: a sensor measures the quantity, a control centre compares it with a set point, and an effector pushes it back toward the set point. correction = gain × (set point − measured value)bigger gain, smaller error left over; but add a delay and a big gain makes the loop swing Two things follow, and they are the heart of control theory (see Control Systems, 34/20). A loop with finite gain never removes the error completely: a body in a cold room settles slightly below its set point. And a loop with a delay between sensing and acting overshoots; push the gain too high and it oscillates, like a shower where the hot tap answers ten seconds late. Interactive · Your own thermostat Loop gainDelay (steps) A toy model, not a body: xt+1 = xt + 0.1·(Tenv − xt) + 0.1·gain·(37 − xt−delay). The environment drops from 37 to 17 at step 10. Arbitrary time units, illustrative. With gain 4 and no delay the model settles near 33, short of 37, and it settles smoothly (the exact answer is (17 + 4 × 37) ÷ 5 = 33.0). Raise the gain to 15 and the target moves to (17 + 15 × 37) ÷ 16 = 35.75, a dip of only 1.25 degrees. Add a delay of just 2 steps and gain 15 runs away completely; even gain 4 keeps ringing with a delay of 4. Real regulation keeps gain high, stacks several loops and uses fast sensors, which is why healthy bodies are steady and why tired or sick ones can overshoot. The heart and circulation: flow equals push over resistance The heart is two pumps in series. The right sends blood through the lungs; the left sends it round the body. In each beat a ventricle ejects a stroke volume; times the number of beats a minute, that is the cardiac output. At rest a healthy adult is typically around 5 litres a minute, for example 70 beats of about 70 mL. Pushing blood round the body is like pushing water through pipes: the pressure you need is flow times resistance. MAP ≈ CO × TPR  ·  resistance ∝ 1 / radius4mean arterial pressure ≈ cardiac output × total peripheral resistance · Poiseuille's law for a tube The fourth power is the striking part. Halve a tube's radius and resistance rises sixteen-fold. That is why the body steers blood by making small vessels a little narrower or wider (after a meal, more to the gut; in the cold, less to the skin), and why a small narrowing of an artery matters so much. Real vessels are elastic and blood is not a simple fluid, so Poiseuille's law is a guide, not a prediction. Interactive · Pump and pipes Heart rate (beats/min)Stroke volume (mL)Small-vessel radius vs resting (%) Resting total peripheral resistance taken as 18 mmHg per L/min (illustrative round number). Central venous pressure ignored. Resistance scales with radius−4. Not a clinical calculator. At 70 beats × 70 mL the output is 4.9 L/min and pressure comes out near 88 mmHg. Narrow the small vessels by 10% and resistance rises by about 52% (1 ÷ 0.94), pressure follows, unless the heart compensates. A fit person at rest has a bigger stroke volume and a slower rate for the same output. Lungs and gas exchange: diffusion needs area and a gradient Oxygen crosses from air to blood by diffusion alone. Fick's law says that flow of gas through a membrane is proportional to the area, the pressure difference of that gas, and inversely to thickness. So the lung is built as a huge surface a few cells thin: some 300 million tiny air sacs (alveoli) give a gas-exchange surface of tens of square metres (often quoted as about 70; estimates differ) wrapped in blood capillaries. What drives the flow is the partial pressure of oxygen. Air is 20.95% oxygen at every altitude; what changes is the total pressure. Climb and the push to get oxygen into blood shrinks. The oxygen pressure in the lung's air sacs is lower than in the air you breathe, because you subtract carbon dioxide, which is why breathing harder helps: PAO2 ≈ PIO2 − PACO2 ÷ 0.8alveolar oxygen ≈ inspired oxygen − CO₂ ÷ respiratory ratio · PIO2 = 0.2095 × (Ptotal − 6.3 kPa water vapour) Interactive · Climb a mountain Altitude (m)Alveolar CO₂ (mmHg) Standard-atmosphere pressure P = 101.325·(1 − 2.25577×10−5h)5.256 kPa; 1 kPa = 7.5 mmHg. Real pressure varies with weather, latitude and season (Everest is higher than the standard atmosphere gives). At sea level the model gives an inspired oxygen pressure of about 19.9 kPa (149 mmHg) and an air-sac value near 100 mmHg. On a 4,000 m pass the inspired oxygen pressure is about 58% of sea level. At the height of Everest, standard-atmosphere pressure leaves an inspired value about 26% of sea level, and with normal breathing the air-sac value is below zero in this model: the only way to have any oxygen at all is to breathe much harder and blow off CO2, which climbers do. Kidneys: filter everything, take back almost all The kidneys do not look for waste and pull it out. They do the opposite: about a million tiny filters in each kidney (nephrons) push a large share of blood plasma, water and small molecules, into a tube, and then the tube takes nearly all of it back. What is not taken back is urine. Normal filtration is around 125 mL a minute, about 180 litres a day, from a plasma volume of only about 3 litres: the blood is filtered some 60 times a day. urine = filtered × (1 − fraction reabsorbed)about 180 L filtered a day · about 99% reabsorbed · about 1.5 L left Because the filter is so large, a tiny change in the fraction taken back makes a large change in the output. A hormone from the pituitary, ADH (vasopressin), tells the collecting ducts how many water channels to open, and the nephron's loop, a hairpin that concentrates the fluid around it, sets how concentrated urine can get. Animals of dry habitats, such as desert rodents, have long loops and make far more concentrated urine than we can. When kidneys fail, dialysis imitates the filter; it is a hard job, which shows how much the kidney does. Interactive · A sum with a huge multiplier Normal dayDehydratedDrank a lotFiltration rate (mL/min)Fraction reabsorbed (%) Presets set illustrative reabsorbed fractions (99.2, 99.6 and 98.5%). Urine = rate × 1440 min × (1 − fraction). A healthy kidney varies this by the hour; this is not a diagnostic tool. At 125 mL/min and 99.2% reabsorbed, urine is 1.44 L a day. Move the fraction to 98.5% and it doubles to 2.7 L; to 99.6% and it halves to 0.72 L. A swing of half a percentage point in what is taken back is the whole difference between a thirsty day and a wet one. Hormones: slow messages through the blood Nerves are for speed, in milliseconds. Hormones are for broadcast and persistence: a gland releases a chemical into blood, which reaches every cell, and only cells with the right receptor respond. Ernest Starling coined the word in 1905; the hormone insulin was isolated in Toronto in 1921, and the 1923 Nobel Prize went to Banting and Macleod, who shared their money with Best and Collip. The loops are the same negative feedback as before, just slower. The hypothalamus tells the pituitary, the pituitary tells the thyroid or adrenal gland, and the hormone released tells the hypothalamus to ease off. Blood sugar is a two-hormone loop: insulin from the pancreas helps cells take up glucose after a meal, and glucagon raises it between meals. A few loops run positive, so that one event feeds itself to a conclusion: the surge of luteinizing hormone that triggers ovulation, or oxytocin in labour. How long a hormone acts is set by how fast it is cleared. Adrenaline is gone in minutes, which suits an emergency; thyroid hormone (thyroxine) has a half-life of about a week, so its level takes weeks to move and it is a slow tuner of metabolism. In general a level reaches 90% of a new steady value after about 3.3 half-lives, so a hormone with a long half-life cannot be quickly "reset" by anything. Popular "hormone balancing" claims in wellness ads usually ignore all of this: hormones are tied to feedback loops, so pushing one tends to be answered by the others. Muscle: force and speed trade off A muscle fibre is a stack of overlapping thick (myosin) and thin (actin) filaments. In 1954 two teams, Andrew Huxley with Rolf Niedergerke and Hugh Huxley with Jean Hanson, independently proposed the sliding filament model: the filaments keep their length, and myosin heads grab the actin and pull it past in repeated strokes, each powered by ATP and triggered by calcium. Muscle shortens because many tiny ratchets act in parallel and in series. Because each stroke takes time, a fast shortening muscle has fewer heads attached at once: it can pull hard or fast, not both. A. V. Hill described the curve in 1938: (F + a)(v + b) = (F0 + a) bF = load, v = shortening speed, F₀ = maximum force, a and b = constants of the muscle Power is force times speed, so it is zero at both ends (no speed when holding a maximal load, no force when moving freely) and peaks at about a third of the maximal force for typical constants. That is why a bicycle has gears: they let your legs work near the power peak. Interactive · The force–velocity trade Load (% of maximum force) Hill's equation with a = 0.25·F0 (a common textbook value; real muscles differ). Speed shown as a fraction of its no-load maximum, power as a fraction of its peak. With those constants, power peaks when the load is 31% of the maximum and the muscle is shortening at 31% of its fastest speed; the peak is about 9.5% of F0 × vmax. Raise the load to 80% and speed falls to 5% of maximum. Temperature control: a thermostat with a heater, a fan and a pipe Mammals and birds hold the core near 37 °C (set points differ by species) by balancing heat made against heat lost. The hypothalamus compares the signals from the skin and core with a set point and drives the effectors: shivering and brown fat make heat; narrowing skin vessels keeps it in; widening them and sweating let it out. Sweat cools by evaporation, which needs the air to take up more water. Fever is not a failure of the thermostat but a raised set point: you feel cold until the body reaches it. That cooling has a limit when the air is hot and wet. In 2010 Steven Sherwood and Matthew Huber argued that a sustained wet-bulb temperature of 35 °C is a theoretical limit for human survival. In 2022 laboratory work on young, healthy adults found people hitting their limit well below that, and the value depends on both temperature and humidity. The honest summary is: there is no single threshold, and older and ill people are at risk at lower values. Scaling: Kleiber's law and the pace of small animals If you double an animal's length, its mass goes up eight-fold, but the surface it loses heat through goes up only four-fold. Small animals lose heat faster for their weight, so they burn more per kilogram. In 1932 Max Kleiber compared animals from rats to cattle and found that basal metabolic rate rises not as the mass nor the surface (the 2/3 power) but about as the three-quarter power of mass. BMR ≈ 3.4 × M0.75 wattsM in kilograms · same as 70 × M0.75 kcal a day A 70 kg person comes out near 82 W (about 1,700 kcal a day), a 25 g mouse about 0.2 W, an elephant of 4 tonnes about 1.7 kW. Per kilogram, the mouse burns around twenty times what an elephant does, and its heart races at several hundred beats a minute where the elephant's beats about thirty. West, Brown and Enquist proposed in 1997 that the exponent comes from the branching of the circulatory network; others (Kozłowski, Konarzewski) disagree, and data for small birds and insects often fit 2/3 better. Whether the exponent is exactly 3/4 is still argued over. Interactive · A mouse, a person, an elephant 3/4 (Kleiber)2/3 (surface)Body mass (log scale) Both lines are anchored to 82 W at 70 kg. Heart-rate rule of thumb HR ≈ 240 × M−1/4 beats/min; real species scatter widely around it. Slider is log10 of mass in kg. Slide to a 25 g mouse: about 0.2 W under the 3/4 law, against 0.4 W on the 2/3 line, and 8.6 W per kg against 1.2 for a person. Often-repeated claims that every mammal gets the same number of heartbeats in a lifetime are only roughly true; people, with a heart rate of about 70, clearly exceed it. What a graduate just sees Everything regulated has a sensor, a set point and an effector; read any disease as a loop that has broken or been overloaded. Feedback with a delay and a lot of gain oscillates; the body needs fast sensors and several loops. Flow equals pressure over resistance, and resistance goes with radius to the fourth power, so a slightly narrower artery is a big deal. Oxygen delivery is diffusion down a pressure gradient across a very large, thin surface. The kidney filters everything and reabsorbs almost all, so tiny percentage changes make big volume changes. Hormones are slow because they are broadcast and cleared slowly; half-life sets the tempo. Muscle is a force–speed trade; maximum power sits at a modest load. Metabolic rate rises more slowly than mass, so small animals live fast. Where it shows up next Biochemistry (35/43) and Cell Biology (35/44) sit below it: ATP, receptors and ion pumps are the parts of every loop. Biological Psychology (35/20) and Control Systems (34/20) use the same feedback logic for brains and machines. Microbiology (35/50): infection is a challenge physiology answers with fever, immunity and inflammation. In the world: sport and training, medicine and nursing, high-altitude expeditions, heat-wave planning, drug dosing, and wearables that track heart rate and sleep. If you want to go deeper 📘 Textbook. Dee Unglaub Silverthorn, Human Physiology: An Integrated Approach (Pearson). A widely assigned textbook built around homeostasis and feedback. 📘 Textbook. Arthur Guyton and John Hall, Textbook of Medical Physiology (Elsevier). The classic medical-school reference, heavy on quantitative reasoning. 📘 Gentler. Bill Bryson, The Body: A Guide for Occupants (2019). A very readable tour with almost no maths. 🌐 Free course. OpenStax Anatomy and Physiology 2e, a free full textbook, and Khan Academy's Human anatomy and physiology videos. The takeaway A body stays alive by holding a few numbers steady with feedback loops, and each organ is a sensor, a pump or a filter in one of them. The equations are small (flow = pressure ÷ resistance, diffusion needs area and a gradient, force trades against speed, rate scales as mass to the three-quarters), and they explain surprisingly much of what you feel. Try this: this week, take your resting pulse for 30 seconds, then climb two flights of stairs and take it again. Then watch how long it takes to settle. That recovery time is a feedback loop made visible. (This is curiosity, not a fitness test.) Sources & Further Reading Sources. Feedback, Poiseuille's law, Fick's law, the alveolar gas equation, renal handling, the force–velocity curve (A. V. Hill, 1938) and the sliding-filament model (Huxley and Niedergerke; Huxley and Hanson, Nature, 1954) are standard textbook physiology (Silverthorn; Guyton and Hall). Kleiber (1932) and the West–Brown–Enquist (1997) debate were checked against an encyclopaedia summary. Cardiac output and GFR typical values from encyclopaedia summaries of textbook figures. The wet-bulb limit: Sherwood and Huber (2010) and Vecellio et al. (2022). Not medical advice. All interactive numbers were computed in node. 🌐 OpenStax Anatomy and Physiology 2e (free) 🌐 Khan Academy: Human anatomy and physiology 📘 Silverthorn, Human Physiology: An Integrated Approach 📘 Bryson, The Body: A Guide for Occupants Step 10. Microbiology: The Invisible Majority --------------------------------------------- Why: Bacteria, viruses and the invisible majority of life. Most of the life on Earth, and most of what has ever lived on you, is too small to see. Microbiology learns how fast it grows, what it does, and how we have learned to live beside it, use it and fight it. A teaspoon of garden soil holds more bacterial cells than there are people on Earth. The bread you ate this week was raised by a fungus. The yogurt, the cheese, the pickle and the soy sauce were made by microbes, and so was the insulin in many a pharmacy fridge. And a cut that goes red, a cold that goes round a classroom, a hospital infection that no antibiotic touches: also microbes. Microbiology is the study of all of these: bacteria, archaea, viruses, fungi and a few other tiny things. It is where biology gets quantitative fast, because microbes multiply in minutes. This piece covers concepts only (what the groups are, how populations grow, how drugs and vaccines work in principle), not how to grow anything. It is not medical advice; if you are unwell, or worried about an infection, see a health professional. The course in one box Who takes itBiology, biomedical, nursing, food science, pharmacy, veterinary and medical students, usually in year 2 or 3, often with a lab. Medical schools teach a clinical version. What it is forKnowing the microbes that cause disease, keep us well and run the planet's chemistry, and the principles for living with them. Comes afterMolecular Biology (35/45), because most of the course is about microbial genes and cell machinery. Leads toGenetics (35/46) and Evolution (35/47) use microbes as the test case, Ecology (35/48) uses microbial communities, and a Medicine major goes on to immunology and infectious disease. What this piece gives youYou will not be able to identify a bacterium or treat an infection. You will see the size of the microbial world, why growth is exponential, what the microbiome evidence does and does not show, why resistance is evolution in a flask, and what a vaccination threshold means. Easier first reads: The Science of Bread (14/07), Fermentation: Letting Microbes Cook (14/08) and Your Immune System, Day by Day (01/10). Three domains and the viruses beside them Antonie van Leeuwenhoek looked at pond water through hand-ground lenses in the 1670s and saw "animalcules". Two centuries later Pasteur and Koch tied particular microbes to particular diseases. For a long time everything without a nucleus was called a bacterium. In 1977 Carl Woese and George Fox used ribosomal RNA to show that a group of odd microbes from swamps, hot springs and salt lakes were not bacteria at all. The living world has three domains: Bacteria, Archaea (single cells that look like bacteria but are in some of their molecular machinery nearer to us), and Eukarya (cells with a nucleus: animals, plants, fungi and protists). Fungi are eukaryotes, closer to animals than to plants: yeasts, moulds and mushrooms, with cell walls of chitin that digest food outside the body. Viruses are a different kind of thing: a strand of DNA or RNA in a protein coat that cannot copy itself without a host cell's machinery. Whether to call them alive is a definition argument, not a measurement; what is clear is that they are enormously abundant, and the most numerous kind, the bacteriophages that infect bacteria, are estimated at around 1031 particles on Earth. A quick, non-clinical way to sort bacteria is the Gram stain, invented by Hans Christian Gram in 1884: a thick wall of peptidoglycan keeps the purple dye (Gram-positive), a thin one lets it wash out (Gram-negative, which also have an outer membrane). It matters later, because it shapes which drugs reach which cells. Interactive · Zoom into the invisible Field of view (log scale) Typical diameters (they vary a lot): hair 70 µm, skin cell 30 µm, yeast 8 µm, E. coli about 2 µm long, a typical virus 0.1 µm (100 nm). Circles are drawn at true relative size; anything under one pixel is shown as a dot. Set the field to 1 mm (1,000 µm) and a human hair is a 7% sliver of the view while a bacterium would need 500 side-by-side to cross it. Set it to a hair's width and you can fit 35 E. coli end to end. A typical virus is about twenty times smaller than the bacterium it can infect, which is why ordinary light microscopes cannot see one. Growth curves: doubling is the whole game A bacterium grows, then divides in two. If conditions are good, each cell of a fast species such as Escherichia coli can divide about every 20 minutes. That is three doublings an hour, and 230 after ten hours: one cell becomes more than a billion (1.07 billion). Left unchecked for two days, the mass would exceed the Earth's. Nature never allows that, because food runs out, waste builds up and the culture stops. N(t) = N0 × 2t / tdcells now = cells at the start × 2 to the power (time ÷ doubling time) · growth stops near the carrying capacity A culture's life in a closed container has four phases. A lag phase while cells adjust and make the right enzymes; an exponential phase, a straight line on a log plot; a stationary phase, as food runs out; and a death phase. Biologists therefore plot on a log scale: constant doubling then looks like a straight line, and the slope is the growth rate. What Ecology (35/48) says about logistic growth holds here too, since a flask is a population with a ceiling. Interactive · A culture, as a model Doubling time (minutes)Lag phase (hours) Model, not an experiment: start at 1,000 cells/mL, capacity 109 cells/mL (illustrative), N = 1 / (1/Nexp + 1/K) with Nexp = N0·2(t − lag)/td. Not a protocol. With a 30-minute doubling time and a one-hour lag, the model reaches half of its capacity at about 11 hours and is flat soon after. Slow the doubling to 3 hours and in 24 hours it has grown only about 200-fold, nowhere near the ceiling. A small change in doubling time is a huge change in numbers: that is why food left warm goes off so much faster than food left cold. The microbiome without the hype Your gut, skin and mouth are inhabited by communities of microbes, most of them harmless and many of them useful. The old claim that microbes outnumber your own cells ten to one has been revised: a 2016 estimate by Ron Sender, Shai Fuchs and Ron Milo puts it at roughly one to one, about 38 trillion bacteria and 30 trillion human cells in a typical adult, with large uncertainty. The genes are a different story: the microbial genes in a gut outnumber human genes by something like a hundred to one. What is well supported: gut microbes help break down fibre and make some vitamins and short-chain fatty acids; they train the immune system, especially early in life; and a stable community resists invaders. The clearest medical use is also the most dramatic: for repeated Clostridioides difficile infections, which can follow antibiotics, restoring a healthy community has worked well enough that microbiome-based treatments have been approved by regulators in recent years. What is less well supported are the sweeping claims: that your microbiome "causes" obesity, mood or autism in people, that a probiotic yogurt will "rebalance" a healthy gut, or that a single stool test can score your health. Many links come from mouse studies or correlations in small human samples, and cause and effect are hard to separate. A community's diversity is the idea that holds up best, and ecologists already have a number for it. H = − Σ pi ln piShannon diversity: p = share of each species · higher when there are more species and when they are more even Interactive · Counting a community EvenFour, unevenOne dominatesSpecies A (relative abundance)Species BSpecies CSpecies D Invented abundances for illustration, not data from any real gut. Shannon H uses natural logs; evenness J = H / ln(richness); Simpson index = 1 − Σp². Four species at 40, 30, 20 and 10% give H = 1.28; four equal species give the maximum, ln 4 = 1.39; a community that is 97% one species is about 0.17. The same number can be raised by adding species or by evening them out. Antibiotics tend to reduce diversity in the gut, which usually recovers, though not always fully; and the question of which diversity matters for health is open. Antibiotics and resistance: evolution in a flask An antibiotic is a poison chosen to hit something bacteria have and we do not. Penicillin, found by Alexander Fleming in 1928 and made into a medicine in the 1940s by Howard Florey, Ernst Chain and colleagues, blocks the building of the bacterial cell wall, a structure human cells lack. Other classes target the bacterial ribosome (which differs from ours), the enzymes that copy bacterial DNA, or the pathway for making folate. They do nothing against viruses, which have none of these targets. Resistance is natural selection in plain view. In 1943 Salvador Luria and Max Delbrück showed that bacterial resistance mutations arise at random before the drug is added, not in response to it. Among a billion cells there are a few that happen to survive; the drug removes their competitors; they take over. Bacteria can also swap resistance genes between species on small DNA circles called plasmids. A 2022 analysis in The Lancet estimated that in 2019 resistant bacterial infections were directly responsible for about 1.27 million deaths worldwide and associated with 4.95 million. f′ = R / (R + S × (1 − kill))after one round of drug: new resistant share = resistant ÷ (resistant + surviving susceptible) · the population then regrows Interactive · Selection, round by round Resistant fraction before the drug (log₁₀)Drug kill of susceptible cells (log₁₀)Rounds of drug Expected values for 109 cells that regrow to the same size between rounds, with no cost of resistance. Illustrative: a real infection also has the immune system, drug levels that vary, and chance. Not guidance on treatment. With one resistant cell in ten million (10−7) among a billion, 100 cells are resistant at the start. A drug that kills 99.9% of the susceptible cells leaves their share at 10−4 after round one, about 0.09 after round two and 99% after round three. A stronger kill (more nines) hastens the takeover of the survivors, since competitors are removed. That is why microbiologists talk about slowing resistance and not stopping it: stewardship means using drugs only where they will work, and matching the drug to the target, and why you take a prescription as your clinician directs. Viruses and vaccines: the threshold idea A virus is at heart a copy instruction. It enters a cell, hijacks its machinery, and the cell makes thousands of new particles. For public health the key number is the basic reproduction number R0: how many people one case infects in a fully susceptible population. If it is above 1, an outbreak grows; below 1, it fades. R0 is not a fixed constant of a virus: it depends on contacts, climate and behaviour. Measles is commonly quoted at 12 to 18, among the highest known; seasonal influenza is far lower, nearer 1 to 2. A vaccine, in concept, shows the immune system a harmless version or piece of a pathogen (a weakened or inactivated virus, a purified protein, or the instructions to make one) so that memory cells are ready when the real one arrives. Edward Jenner's 1796 experiment with cowpox began it; smallpox was declared eradicated in 1980, and rinderpest, a cattle virus, in 2011. If each case infects R0 people but a fraction of contacts are protected, the effective number falls: Reff = R0 × (1 − coverage × effectiveness)  ·  threshold = (1 − 1/R0) ÷ effectivenessoutbreaks fade when Reff < 1 · "herd" protection is when enough are immune that chains break Interactive · How much is enough? Flu-like (1.5)3Measles-like (15)Basic reproduction number R₀Vaccine effectiveness (%)Coverage (%) R₀ values are illustrative and vary by place and time. Simple well-mixed model: no waning immunity, no clustering of the unvaccinated, which in real life lowers protection. Describes how the idea works; not advice about any vaccine. At R0 = 3 and a vaccine that is 90% effective, you need 74% coverage (0.667 ÷ 0.9). At 15 you need 1 − 1/15 = 93.3% immune, so about 104% coverage with a 90% vaccine: not reachable, which is why a measles-like virus returns when coverage slips even a few points, and why immunity from earlier infection or a second dose counts. Real populations are lumpy: unvaccinated people cluster in families and schools, so the average can hide pockets that sustain outbreaks. Microbes at work: bread, soil, medicine and industry Most microbes do chemistry we depend on. Yeasts ferment sugars to carbon dioxide and alcohol: the bubbles in bread, the base of beer and wine. The East Asian mould Aspergillus oryzae (koji) makes soy sauce, miso and sake; lactic acid bacteria sour yogurt, kimchi, sauerkraut and Ethiopia's injera batter; bacteria raise cassava gari in West Africa. In soil, Rhizobium bacteria in the roots of beans, peas and clover turn nitrogen from the air into a form plants can use, and fungi called mycorrhizae trade nutrients with roots (the popular "wood wide web" story of trees talking through them has been criticised in a 2023 review as going beyond the evidence). Sewage plants are managed microbial communities. Industry uses them as factories. In 1978 a team at Genentech and City of Hope made human insulin in engineered E. coli, and human insulin made that way reached patients in 1982. The heat-stable DNA-copying enzyme in PCR, Taq polymerase, comes from Thermus aquaticus, a microbe from a Yellowstone hot spring. Fungi cause trouble too: a chytrid fungus has driven declines in hundreds of amphibian species worldwide, which links the subject back to ecology. Interactive · A rising loaf: how much sugar? Dough volume (mL)Rise wanted (× original volume)Share of the gas the dough holds (%) Ideal gas at 25 °C and 1 atm (24.46 L per mole). Yeast fermentation C₆H₁₂O₆ → 2 C₂H₅OH + 2 CO₂ (glucose 180.16 g/mol). Real dough also dissolves some CO₂, and flour supplies sugar from its starch. A back-of-envelope, not a recipe. To double a 500 mL lump of dough, you need 500 mL of new gas, which is 0.0204 mole of CO2 and so 0.0102 mole of glucose, about 1.8 g of sugar, if the dough holds every bubble. If the dough holds only 60% of the gas, the figure is 3.1 g. A few grams of sugar will raise a loaf; flour starch, broken down by enzymes, supplies it. Fermentation is a few lines of chemistry run by millions of cells. What a graduate just sees The microbial world is the majority of living things; animals and plants are a small branch. Bacteria, archaea and eukaryotes are three domains; viruses sit outside the tree, dependent on a host. Growth is a doubling; a small change in doubling time is a huge change in numbers. Log scales turn exponential growth into a straight line. The microbiome is real and important; most dramatic health claims about it are ahead of the evidence. Antibiotics aim at structures bacteria have and we do not, which is why they do nothing to viruses. Resistance is selection: the variants are there first, and the drug picks them. Vaccination works by pushing the reproduction number below 1; the threshold rises steeply with R0. Many foods, medicines and materials are by-products of microbial chemistry. Where it shows up next Genetics (35/46) and Molecular Biology (35/45): bacteria and phages are where most of the molecular toolkit was found, from restriction enzymes to Taq. Evolution (35/47): a flask of bacteria is evolution you can watch in days. Ecology (35/48): soil and ocean microbes run the carbon and nitrogen cycles. Physiology (35/49) and, in a medicine major, immunology and infectious disease: fever, inflammation and the immune response are the body's side of the story. In the world: hospital infection control, food safety, vaccination programmes, brewing and dairies, water treatment, biotech, and antimicrobial stewardship. If you want to go deeper 📘 Textbook. Michael Madigan and colleagues, Brock Biology of Microorganisms (Pearson). The standard university text, the one MIT's microbiology course lists. 📘 Textbook. Joanne Willey, Kathleen Sandman and Dorothy Wood, Prescott's Microbiology (McGraw Hill). The other widely assigned general text. 📘 Gentler. Ed Yong, I Contain Multitudes (2016). A readable, balanced tour of the microbiome. 🌐 Free course. MIT OpenCourseWare 20.106J Systems Microbiology (Fall 2006), and the free OpenStax Microbiology textbook. The takeaway Microbes are small, abundant and fast. They divide exponentially until something stops them, they swap genes, they are the first chemists of the planet, and they evolve in front of us. That one picture explains why infections grow, why drugs lose power, why vaccines have thresholds, and why bread rises. Try this: this week, find three foods in your kitchen that microbes made (bread, yogurt, cheese, vinegar, soy sauce, pickles). Ask which kind: yeast, bacterium or mould, and what it did to the food. (Observation only; do not taste anything that looks or smells off.) Sources & Further Reading Sources. Domains (Woese and Fox, 1977), the Gram stain (1884), growth phases, antibiotic targets, plasmids, R0 and the vaccination threshold are standard textbook microbiology (Madigan; Willey). The Luria–Delbrück experiment (1943), and the microbial cell counts of Sender, Fuchs and Milo (2016), were checked against encyclopaedia summaries. The antimicrobial-resistance burden is Murray et al., The Lancet (2022). Smallpox eradication (WHO, 1980), rinderpest (2011), recombinant insulin (1978, 1982) and Taq polymerase are standard history, given in outline. Not medical advice. All interactive numbers were computed in node. 🌐 MIT OCW 20.106J Systems Microbiology 🌐 OpenStax Microbiology (free) 📘 Madigan et al., Brock Biology of Microorganisms 📘 Yong, I Contain Multitudes Step 11. Developmental Biology: How One Cell Becomes a Body ----------------------------------------------------------- Why: How one cell becomes a body. Every cell in your body carries the same genome, yet one becomes a neuron and another a bone cell. The trick is not different instructions but different places: cells read their position from chemical gradients, and a shared toolkit older than the animals themselves turns that position into a body. Look at your hand. Five fingers, each with the right number of bones, the thumb on the correct side, the whole thing the right size for the arm it hangs from. Nobody drew a plan and nobody supervised the building. It began as a single fertilised egg, a cell about a tenth of a millimetre across, and the egg divided, and the descendants somehow worked out what to become. Now look at a different puzzle: a sliced-up flatworm. Cut a planarian into pieces and each piece grows back the missing end, head where a head belongs, tail where a tail belongs. Cut a salamander's leg off and it builds a new one, bones, muscle and nerves in the right order. Something in the tissue knows where it is, and what is missing. A developmental biologist looks at both and sees one question: how does a cell find out where it is, and what does it do with the answer? The answers turned out to be few, surprisingly general, and shared between a fruit fly and you. That shared set of answers is what a graduate of this course still just sees. The course in one box Who takes itBiology, biomedical science and pre-medical students, usually in year 3 or 4, as a core course or a popular elective. Programmes in the vein of MIT's Course 7 and Cambridge's Natural Sciences teach it after genetics and molecular biology, and increasingly pair it with stem-cell and regeneration units. What it is forExplaining how one cell becomes an organism, so you can reason about birth defects, stem-cell medicine, regeneration and how animal body plans evolved. Comes afterGenetics (35/46), and behind it Molecular Biology (35/45) and Cell Biology (35/44). Leads toNo later subject in this series depends on it, but it feeds Evolution (35/47) (evo-devo), Physiology (35/49) and, outside this series, embryology, regenerative medicine and cancer biology. What this piece gives youConcepts only. You will not be able to run an embryo experiment. You will see why a gradient can draw stripes, why a fly and a mouse share a body-plan code, and what "reprogramming a cell" means. Easier first reads: Nervous System & Body (01) for the finished body. One genome, many cells: the egg already knows The first thing to get straight is what does not change. A skin cell and a neuron hold the same DNA. In 1962 John Gurdon showed this in frogs: he took the nucleus out of an intestinal cell of a Xenopus tadpole, put it into an egg whose own nucleus had been destroyed, and sometimes got a whole new tadpole. The "specialised" nucleus still held every instruction. Gurdon shared the 2012 Nobel Prize in Physiology or Medicine for this, with Shinya Yamanaka. In 1996 the same logic produced Dolly the sheep, cloned from a mammary-gland cell. So cells differ not by what they contain but by which genes are on. Development is a long sequence of switches. A cell that finds itself in one place switches on one set of transcription factors (proteins that read DNA); those switch on others; and each choice narrows what the cell can later become. The question becomes: what tells the first switch which way to go? Gradients: a cell reads its position from a concentration The classic answer was set out by Lewis Wolpert in 1969, in a paper on positional information. Imagine a row of identical cells. At one end, a source releases a chemical, a morphogen, that spreads and is slowly broken down, so its concentration falls smoothly with distance. Every cell can measure the local concentration. Give the cells two threshold rules ("above level 1 become blue; between levels 1 and 2 become white; below level 2 become red") and a smooth slope turns into three sharp bands, like the French tricolour. Wolpert's "French flag model" is the shortest possible account of how a pattern comes from nothing but a slope and a few thresholds. The real example is the fly. The mother deposits the messenger RNA for a protein called Bicoid at the front end of the egg; it is translated and the protein spreads backward, forming a gradient. Nobel-winning work by Christiane Nüsslein-Volhard and Eric Wieschaus (1995 prize, shared with Edward Lewis) showed that this gradient switches on different genes at different positions. The mathematics is simple: a steady source and steady decay give an exponential, c(x) = c0 · e−x/λconcentration at distance x from the source = source level × exp(−distance ÷ decay length λ) Every λ of distance divides the concentration by e (about 2.7). Try it. Below, the embryo is 500 µm long (about the size of a fly embryo; the decay length λ and the thresholds are illustrative numbers in the right range, not measured values for any one gene). Interactive · Draw a French flag with a slope Source strength c₀ Decay length λ Embryo length Cells above 0.5 become "blue", between 0.2 and 0.5 "white", below 0.2 "red". Boundaries solve c₀·e−x/λ = threshold, so x = λ·ln(c₀ ÷ threshold). At the defaults the blue band ends at 69 µm, the white at 161 µm, and the rest of the 500 µm is red. Notice two things the sliders teach. Double the source and every boundary slides back by λ·ln 2 (about 69 µm): the pattern moves. Shorten the embryo and the bands keep their absolute size but the red region shrinks, so the proportions are wrong. Real embryos are often properly proportioned at different sizes, so something must scale the gradient; how remains an active research question, and not every system solves it the same way. A smooth slope plus a few thresholds is enough to draw sharp stripes. The cell only has to measure and compare. Gradients are not the only pattern-maker. Alan Turing proposed in 1952 that two chemicals which diffuse at different speeds and react with each other can create spots and stripes spontaneously (reaction-diffusion). Real tissues usually mix the two: gradients set coarse positions, and local interactions sharpen and repeat them. A clock and a wavefront: building a spine segment by segment Your backbone is a repeat: vertebra after vertebra, each from a block of tissue called a somite. Somites form one pair at a time, head to tail, like a conveyor belt that stamps out beads. The leading model, the clock and wavefront, is neat. Cells in the tail-bud oscillate, switching key genes on and off with a fixed period, like a ticking clock. As the embryo extends, a wavefront moves backwards through the tissue at some speed. Each time the clock completes a cycle a stripe of cells gets "locked in" as one somite. The segment length is therefore: segment length = wavefront speed × clock perioda faster clock means more, smaller segments for the same speed Species set the period. A somite pair forms about every 30 minutes in zebrafish, every 90 in a chick and every 100 in a snake; in the mouse it is around two hours, and in human cells grown in a dish the clock period comes out near five hours (two 2020 studies, Matsuda et al. and Diaz-Cuadros et al.). A snake makes hundreds of vertebrae because its clock runs fast compared with its body growth. Interactive · Tune the segmentation clock Zebrafish Chick Mouse Human cells Clock period Wavefront speed Wavefront speeds here are illustrative. The periods for zebrafish, chick, snake, mouse and human are the ones in the text; the real front speed differs per species and over time. At 90 minutes and 2 µm/min, one somite is 180 µm and 16 form in a day. Slow the clock to a human's 300 minutes at the same speed and each segment is 600 µm, with only 4.8 per day. Change the period and the number of segments changes; change the speed and the size changes. Both are things evolution can tune. Hox genes: one toolkit for every animal's body plan A gradient says where. Something else must say what lives here. In the fruit fly, Edward Lewis found mutants in which a whole body part was built in the wrong place: a fly with a second pair of wings where its small balancing organs (haltere) should be, or legs growing where antennae belong. These were not broken parts; they were correct parts in the wrong segment. The genes responsible are the Hox genes, a family of transcription factors that tell each segment its identity. Two facts make them remarkable. First, in a fly the eight Hox genes sit on the chromosome in the same order as the body regions they control, head to tail (a property called colinearity). Second, mice and humans have the same kind of genes: 39 Hox genes in four clusters, which also pattern the head-to-tail axis, including our spine. Mammals duplicated the clusters; the logic survived. A fly and a mouse last shared an ancestor over 500 million years ago, and both still build their long axis with a related code. Use the tool below to see how the code reads out in the fly. Interactive · Read the fly's Hox code Normal fly Lose Ubx Antp misplaced to the head Body region (head to tail) A simplified teaching map: each region is shown with the main Hox gene that defines it. Real expression domains overlap and the details are subtle. In Drosophila the genes are lab, pb, Dfd, Scr (Antennapedia complex) and Antp, Ubx, abd-A, Abd-B (Bithorax complex). Look at what the "Lose Ubx" button does: without Ubx, the third thoracic segment behaves like the second, and the haltere becomes a wing, the four-winged fly of Lewis's famous bithorax mutants. The body parts were all in the genome; Hox genes only choose which program runs where. Stem cells and reprogramming: rolling downhill in a landscape The embryologist Conrad Waddington gave the picture that still organises the subject. In 1957 he described an "epigenetic landscape": a ball (a cell) starts high on a hillside and rolls down through branching valleys. Each valley is a fate; the ridges between them keep a cell that has chosen from drifting back. Noise and signals decide which valley an undecided cell enters. Cells at the top, with many options, are stem cells. Cells at the valley floors are specialised. For fifty years that landscape was a one-way street. Gurdon's frogs showed it could be reversed by the egg's cytoplasm. In 2006 Shinya Yamanaka and Kazutoshi Takahashi in Kyoto showed that adding just four genes (Oct4, Sox2, Klf4, c-Myc) to mouse skin cells could push them all the way back up to an embryonic-like state. These are induced pluripotent stem cells (iPSCs); human ones followed in 2007 from Yamanaka's lab and, with a slightly different set of factors, from James Thomson's. In effect the cell flattens its own ridges and climbs back out of its valley. The simulation below uses a simple mathematical landscape; real reprogramming is far messier and slow. Interactive · Roll 300 cells through a landscape Ridge height (commitment) Noise Signal tilting toward fate A Start undecided (on the ridge) Start as a specialised A cell Specialised A cell + flatten the ridge for a while Each cell obeys dx = −(x³ − a·x − b)dt + σ dW, a double-well with valleys near ±√a (fate B on the left, A on the right). 300 simulated cells, fixed random seed. A toy model, not a gene network. With a mid-height ridge and a little noise, undecided cells split roughly evenly; a small tilt biases the split. A specialised A cell stays A. Press the third button and the ridge is flattened temporarily: at the default settings the cells scatter and about half end up as B once the ridge is rebuilt. That is the picture of reprogramming: not erasing the genome, but reshaping the landscape the cell sits in. iPSC-derived cells are used to model diseases in a dish and are in early clinical studies; this describes the science and isn't medical advice. Regeneration: development you can restart If a cell can read its position, a damaged body can reread it. Planarians are the extreme case: Thomas Hunt Morgan studied them around 1900, and fragments estimated at as little as 1/279 of the worm can rebuild a whole one, because a reservoir of stem cells is spread through the body and gradients tell each stump which end is missing. Salamanders such as the axolotl regrow whole limbs by forming a blastema, a bud of cells that reverts to a more flexible state and repeats limb development. Zebrafish regrow fins and, in an influential 2002 study, about a fifth of the heart's main chamber. Mammals do far less. Human fingertips can regrow in young children if the cut is near the tip and clean, and the liver can rebuild much of its mass, but a lost limb does not return. Why mammals lost the ability, and whether it can be coaxed back, is open. Interactive · Predict, then reveal Planarian Axolotl Zebrafish Adult human Your guess: can it regrow most of a lost limb or a large piece of its body? Yes, it can No, it can't Pick an animal, then make your guess. Evo-devo: change when and where, not what If the toolkit is shared, then bodies must differ mostly by when and where the same genes are used, not by having different genes. Evidence has piled up. The gene Pax6 is needed for eyes in flies and mice, though the eyes are built differently; in 1995 Walter Gehring's lab showed that mouse Pax6 switched on in a fly's leg triggers a fly-type eye there. Stickleback fish in lakes repeatedly lost their pelvic spines; Chan and colleagues (2010) traced this in several populations to deletions in the control region of the gene Pitx1, which switched off the gene in the pelvis only, leaving it working elsewhere. And in Darwin's finches in the Galápagos, deeper, broader beaks go with more expression of the signalling gene Bmp4 in the beak (Abzhanov and colleagues, 2004). Evolution works by editing switches, which is why this subject is the other half of Evolution (35/47). What a graduate just sees Every cell has the whole genome; cell types are the pattern of what is switched on. A smooth gradient plus thresholds turns into sharp bands: the cell measures and compares. Shift a source or a threshold and the boundary moves by λ·ln of the ratio; pattern is tunable. Repeats like vertebrae and fingers come from clocks, waves and spacing rules, not from a blueprint of each part. Hox genes say "what is here", and the same code runs in flies and in you; a wrong address makes a right part in the wrong place. A cell's fate is a valley in a landscape: noise and signals choose, ridges lock the choice, and reprogramming reshapes the landscape. Regeneration is development replayed from an injury; animals differ in how much they kept. Evolution of form is mostly evolution of switches, not of the genes themselves. Where it shows up next Evolution (35/47): every example of evo-devo, from stickleback to finches, is the mechanism that gives selection something to choose from. Genetics (35/46) and Molecular Biology (35/45): transcription factors and enhancers are the machinery behind each switch. Physiology (35/49): organs are the product of development; many adult diseases, and cancer, involve development programs running in the wrong place or time. In the world: birth-defect research (many arise from errors in gradients and Hox-type genes), organoids and iPSC disease models, regenerative-medicine trials, and animal breeding. If you want to go deeper 📘 Textbook. Scott Gilbert and Michael Barresi, Developmental Biology (Oxford University Press / Sinauer, 12th edition, 2019). The standard course text, broad and well illustrated. 📘 Textbook. Lewis Wolpert and colleagues, Principles of Development (Oxford University Press, 6th edition, 2019). Shorter and more concept-driven, by the author of the French flag model. 📘 Gentler. Sean B. Carroll, Endless Forms Most Beautiful (2005). The story of the toolkit and evo-devo for a general reader. 🌐 Free course. MIT OpenCourseWare 7.013 Introductory Biology (Spring 2018) includes development and stem cells among its topics. For short films and animations, HHMI BioInteractive is free. The takeaway One genome builds every cell type because cells read where they are, from gradients and neighbours, and answer by switching genes on and off. A shared toolkit, including the Hox code, does this across animals, and evolution changes bodies mainly by editing when and where its switches fire. Cell fates are valleys that can sometimes be climbed out of, which is what reprogramming and regeneration exploit. Try this: this week, look at the repeated parts around you (your fingers, a centipede in the garden, the ribs of a leaf, the stripes of a zebra photo) and ask what a gradient, a clock or a spacing rule could have made it. Then count: is it always the same number? Sources & Further Reading Sources. Wolpert, Positional information and the spatial pattern of cellular differentiation, J. Theor. Biol. 25 (1969). Gurdon's 1962 nuclear transfer and the 2012 Nobel Prize in Physiology or Medicine (Gurdon and Yamanaka): nobelprize.org. Takahashi & Yamanaka, Cell 126 (2006); Takahashi et al., Cell (2007); Yu et al., Science (2007). Lewis, Nüsslein-Volhard and Wieschaus, Nobel Prize 1995. Hox genes: 8 in Drosophila, 39 in humans in four clusters. Somite periods: zebrafish 30 min, chick 90 min, snake 100 min (Gomez et al., Nature 2008); human about 5 h and mouse about 2 to 2.5 h (Matsuda et al. and Diaz-Cuadros et al., 2020). Planarian 1/279 estimate and Morgan's early work. Pax6: Halder, Callaerts & Gehring, Science 1995. Stickleback Pitx1: Chan et al., Science 2010. Finch beaks and Bmp4: Abzhanov et al., Nature 2004. Waddington, The Strategy of the Genes (1957). Turing, 1952. The sliders' numbers are teaching models computed in the page. This describes science and isn't medical advice. 📘 Gilbert & Barresi, Developmental Biology 📘 Wolpert et al., Principles of Development 📘 Carroll, Endless Forms Most Beautiful 🌐 MIT OCW 7.013 Introductory Biology 🌐 HHMI BioInteractive Step 12. Plant Biology: Sunlight, Water and the Food We Eat ----------------------------------------------------------- Why: Photosynthesis, plants and the food we eat. Plants run the planet's food supply on sunlight, air and water pulled up through dead pipes. Learn the light curve, the three ways to fix carbon, the tension in the xylem and a handful of hormones, and a field of wheat turns from scenery into machinery. A single redwood in northern California can stand about 116 metres tall. Its topmost leaves are a football pitch's length above the soil, and each one is making sugar from air and light while a column of water, pulled from the roots with no pump anywhere in the tree, climbs to reach them. A cactus beside a desert road does something different: it keeps its pores shut all day and opens them only in the cool of the night. A field of maize in Mexico keeps its pores open in heat that makes a wheat plant in the next field struggle. These are all answers to the same trade-off, and a plant biologist sees it everywhere: to take in carbon dioxide you have to open a hole, and every open hole lets water out. A graduate of this course still just sees plants as organisms solving that problem with light, pipes, chemistry and hormones, and still sees every grain on the table as the result of a long human argument with the same plants. The course in one box Who takes itBiology, agriculture, environmental-science and plant-science students, usually in year 3. Programmes in the vein of MIT's Course 7 and Cambridge's Natural Sciences cover plants within a cell and organism course; agriculture degrees spend far longer on crops and soils. What it is forExplaining how plants capture energy, move water, grow, sense their world and become crops, so you can reason about food, forests and climate. Comes afterCell Biology (35/44), which gives chloroplasts and cell walls. Leads toIt feeds Ecology (35/48) (primary production), Evolution (35/47) (domestication is evolution run by people) and, outside this series, agronomy, forestry and food security. What this piece gives youYou will not be able to design a crop trial. You will see why leaves saturate in bright light, why a few warm-climate grasses feed much of the world, how a tree lifts water 100 metres, how two hormones decide root or shoot, and what the Green Revolution did and cost. Easier first reads: The Science of Bread (14/07) for wheat on the plate and Entropy (13/12) for why sunlight is such a good energy source. Photosynthesis and its light curve Photosynthesis turns carbon dioxide and water into sugar and oxygen, using light. Light first knocks electrons loose in the thylakoid membranes of the chloroplast and charges up two carriers (ATP and NADPH); then an enzyme called Rubisco in the Calvin cycle uses that energy to attach CO₂ to a five-carbon sugar. The two stages limit each other, and that gives the signature shape every course draws: the light-response curve. In dim light, every extra photon adds a little more fixed carbon, so the curve rises steeply and almost straight. In strong light the machinery downstream cannot keep up and the curve flattens at a ceiling, Pmax. In the dark the plant still respires, so net uptake is negative. The light level where uptake exactly cancels respiration is the compensation point. A common textbook formula for the curve is a "non-rectangular hyperbola", a smooth bend between the steep start and the flat top: θP² − (αI + Pmax)P + αI·Pmax = 0P = gross photosynthesis, I = light, α = initial slope, Pmax = ceiling, θ = how sharp the bend is. Net uptake = P − respiration. Interactive · A sun leaf and a shade leaf Sun leaf Shade leaf Light (photons per m² per second) Units: µmol CO₂ fixed per m² of leaf per second; light in µmol photons per m² per second (full midday sun is roughly 2,000). Parameters are typical-looking illustrative values (sun: Pmax 25, α 0.05, respiration 1.5, θ 0.8; shade: 6, 0.055, 0.5, 0.8), not measurements of a species. The two curves teach opposite lessons. The sun leaf has a high ceiling, but pays for its machinery with higher respiration, so it needs more light just to break even (about 30 here). The shade leaf is cheap to run, breaks even in dim light (about 9), but tops out near a quarter of the sun leaf. At 600 the sun leaf nets about 17.3 and the shade leaf about 5.3; double the light to 1,200 and the sun leaf gains to about 20.9 while the shade leaf barely moves (5.4). That is why a forest-floor plant scorches in a clearing, and why a house plant that "likes bright indirect light" is not lying. C3, C4 and CAM: three ways around Rubisco's flaw Rubisco is the most abundant enzyme on Earth and has a flaw: it also grabs oxygen. Oxygen is about 500 times more plentiful than CO₂ in air, so in the model below Rubisco picks oxygen instead of CO₂ roughly one time in four at 25 °C, producing a toxic by-product that the cell must expensively recycle (photorespiration, which releases some of the carbon again). The share lost grows with temperature, because the enzyme's preference shifts and because warm leaves close pores and starve the inside of CO₂. Most plants (rice, wheat, potatoes, trees) simply pay this cost; they are C3 plants, named for the three-carbon molecule that is their first product. Two other strategies evolved, in many separate lineages, to get around it. C4 plants (maize, sugarcane, sorghum, millet) first fix CO₂ in the outer mesophyll cells into a four-carbon acid using an enzyme that ignores oxygen, then pump that acid into inner bundle-sheath cells (the ring of cells called Kranz anatomy), where it releases CO₂ right next to Rubisco at high concentration. It costs extra energy but nearly stops photorespiration. CAM plants (cacti, agaves, pineapple, many orchids) do the same pumping in time rather than in space: pores open at night, CO₂ is stored as malic acid, and by day the pores are shut while the stored acid supplies Rubisco, which saves a lot of water. C4 species are about 3% of plant species but account for roughly a quarter of the carbon fixed on land. Which wins depends on temperature and CO₂. Below, C3 is modelled with the standard Farquhar expression for photon efficiency, using a temperature-dependent photorespiratory compensation point; C4 is held at a flat efficiency, as measured in the lab, because its CO₂ concentrating pump masks photorespiration. C3 efficiency ∝ (Ci − Γ*) ÷ (4Ci + 8Γ*)Ci = CO₂ inside the leaf; Γ* = the CO₂ level where photorespiration cancels uptake, rising steeply with temperature Interactive · When does C4 beat C3? Leaf temperature Atmospheric CO₂ Model: Γ*(T) = exp(19.02 − 37.83 ÷ (0.008314·TK)) µmol/mol (Bernacchi et al. 2001); Ci = 0.7 × CO₂; C3 efficiency = 0.35 × (Ci − Γ*) ÷ (4Ci + 8Γ*) with the 0.35 factor chosen so C3 matches the roughly 0.05 measured near 30 °C; C4 flat at 0.053 mol CO₂ per mol photons. A teaching model; real crossovers vary with species, light and water. At today's roughly 420 ppm the lines cross near 29 °C: cooler, C3 is more efficient; hotter, C4 wins. At 180 ppm, like the ice ages, the crossover drops to about 13 °C, so C4 wins in almost any warm place; at 800 ppm it rises to about 42 °C. That is one reason researchers link the spread of C4 grasslands to low-CO₂ ages, and why some predict shifts as CO₂ rises (though water and nitrogen matter too). It is also why teams try to engineer C4 traits into rice. Water: pulled, not pushed Where does the pull come from? Evaporation. Water leaves through pores (stomata) in the leaf, and the sticky cohesion of water molecules means the loss tugs on the whole column of water in the xylem, the dead hollow pipes of wood, down to the roots. This is the cohesion–tension idea, argued by Dixon and Joly in 1894. The water is under negative pressure: stretched, like a rope. That is odd, because a suction pump can only lift water about 10 metres, when the column breaks. Tree xylem is narrow and lined with water-loving walls, so the stretched water stays together, but it is fragile: air bubbles (embolisms) can snap a pipe. Gravity alone costs 0.0098 MPa for every metre of height (about 0.1 atmosphere per metre, so roughly one atmosphere for every 10 m). Friction in the narrow pipes adds more. The water potential at the top is the soil's potential minus both: ψleaf = ψsoil − 0.0098·h − r·hψ in MPa, h = height in metres, r = flow resistance per metre (MPa/m) Interactive · How hard is it to lift water to the top? Tree height Flow resistance r Soil water potential Illustrative. Real leaves also adjust their salt content, close pores, and vary in resistance over the day. At 100 m with the default sliders the top leaf sits at −1.78 MPa, a suction of about 17.6 atmospheres, far past what a pump manages. In a 2004 study of coast redwoods, George Koch and colleagues measured leaf water stress rising with height and estimated that gravity and path resistance could limit trees to about 122 to 130 m, though they said they were not predicting that trees would reach it; the tallest then known was 112.7 m. The stomata decide the water bill: a leaf typically loses several hundred water molecules for every CO₂ it takes in, which is why C4 and CAM, and every drought-adapted plant, are in the end water-saving stories. Hormones and senses: how a plant that cannot move decides A plant cannot run, so it grows toward what it needs. Charles Darwin and his son Francis showed in 1880 that grass seedlings bend toward light only if the tip is uncovered, so the tip must send a signal. In the 1920s Frits Went caught that signal in agar blocks: auxin, which moves to the shaded side of the stem and makes cells there elongate, so the stem curves toward the light. Auxin also drives gravity responses and organises roots. Others complement it: cytokinins promote cell division and shoots; gibberellins lengthen stems; ethylene, a gas, ripens fruit; abscisic acid closes stomata in drought. Plants also sense light colour through phytochromes (red versus far-red decides whether to stretch or branch, and when to flower), so a plant "sees" a neighbour's shadow before touching it. The mix matters more than any one hormone. Skoog and Miller showed in 1957 that in tissue culture the ratio of auxin to cytokinin steers a lump of undifferentiated cells: lots of auxin gives roots, lots of cytokinin gives shoots, and a middle ratio gives unorganised callus. Interactive · Auxin to cytokinin ratio Auxin : cytokinin (log scale) Thresholds (roots above about 3:1, shoots below about 1:3) are illustrative: they differ between species and between the specific hormones. The same system explains why pinching off the tip of a shrub makes it bushy: the tip's auxin was suppressing side shoots. Plants also react to touch and injury. The Venus flytrap closes only if two touches arrive within about twenty seconds, which acts as a short memory, so a raindrop does not trigger it. Domestication: crops from every continent About 10,000 years ago people in several regions, independently, began saving and sowing seed. The wild plants had traits that suit them and not farmers: seeds that shatter and scatter, dormancy, bitter chemicals, many branches. Selection for the opposite (seeds that stay on the plant, big grains, uniform sprouting) is domestication, evolution run by people. It happened in separate places: CropWhereWhen (approx.)What changed WheatFertile Crescent (Southwest Asia)~11,500 years ago (first cultivation c. 9600 BC)Tough rachis, free-threshing grain; bread wheat is a hexaploid with three genomes from hybridisation with goatgrass RiceYangtze basin, China~9,000 years ago (estimates span about 8,000 to 13,500)Non-shattering, larger grain MaizeSouthwestern Mexico (Balsas River valley)~9,000 years agoFrom teosinte: one ear, naked kernels, one main stalk PotatoAndes of southern Peru and Bolivia, near Lake Titicaca7,000 to 10,000 years agoTubers, with toxins bred down; thousands of Andean varieties SorghumEastern Sudan, Africa>5,000 years agoLarger grain, free-threshing; drought tolerant, a Sahel staple Look at maize. Teosinte has tiny, hard-cased seeds and many side branches; maize has a huge cob on a single stalk. Surprisingly, a few genes with large effect, such as teosinte branched 1 (tb1, which suppresses side branches), account for much of the difference, which is what makes rapid domestication plausible. Monoculture brings a risk that the Andes avoided by growing thousands of potato varieties: in the 1840s Europe, and especially Ireland, relied on very few potato types; the late-blight pathogen Phytophthora infestans struck in 1845 and, together with economic and political conditions under British rule, helped cause a famine that killed an estimated 775,000 to 1.5 million people. Genetic diversity is crop insurance, and the wild relatives in the Andes now supply blight-resistance genes to breeders. The Green Revolution and its critics By the 1950s the old wheat varieties had a problem. Feed them more nitrogen and they grew taller, and fell over (lodging) before the harvest. The fix was height: a Japanese dwarf cultivar, Norin 10 (bred by Gonjiro Inazuka), was crossed into wheat by Orville Vogel in the US and used by Norman Borlaug in Mexico from the 1940s, and in 1966 the International Rice Research Institute in the Philippines released the semi-dwarf rice IR8. Shorter, stiffer plants put more of their growth into grain: harvest index, the grain share of the whole plant, rose. The dwarfing genes turned out to be mutations in gibberellin synthesis or response, so the Green Revolution was a hormone story: a plant that sees less gibberellin makes a shorter stem. Borlaug won the Nobel Peace Prize in 1970. Interactive · Fertiliser, height and grain Nitrogen fertiliser Stylised model with invented numbers: biomass = 14·(1 − e−N/70) t/ha; tall wheat has harvest index 0.35 and loses yield by lodging above 60 kg N/ha; semi-dwarf has harvest index 0.45 and lodges only above 180 kg. Shows the logic, not real field data. The logic holds: the tall variety peaks at a modest dose and then falls, while the semi-dwarf keeps responding up to about 180 kg of nitrogen. In the real world the results were large. Annual rice production in the Philippines rose from 3.7 to 7.7 million tonnes in about two decades after IR8 was released, and Mexico moved from importing about half its wheat in 1943 to exporting by 1964. Supporters, such as the economists Evenson and Gollin, argue that modern varieties raised yields across Asia and Latin America, held down food prices, and spared land that would otherwise have been ploughed. The critics are serious too. Because the new varieties needed fertiliser, irrigation and credit, benefits went first to farmers with all three, and widening inequality followed in some regions. Heavy use of nitrogen and pesticides polluted water; irrigation drew down groundwater in places such as India's Punjab; replacing many local varieties with a few risked diversity. The Indian physicist and activist Vandana Shiva, in The Violence of the Green Revolution (1991), argues it damaged soils, traditions and farmers' autonomy. Defenders reply that without the higher yields, famines would have been worse or more land would have been cleared. Neither side is wrong about the facts it cites; the fight is over what to count. Africa, where sorghum, millet and cassava dominate, saw far less of the first Green Revolution, and later initiatives have tried different approaches. Genetic engineering and gene editing are debated in the same terms. What a graduate just sees Every open pore trades water for carbon. Nearly every plant adaptation is about that exchange. A leaf's light curve rises, bends and flattens: sun leaves have high ceilings and high running costs, shade leaves the reverse. Rubisco also binds oxygen; C4 and CAM are two solutions, one in space, one in time. C4 wins hot and low-CO₂. Trees pull water under tension; gravity costs about a tenth of an atmosphere per metre of height, and tall trees are near a hydraulic limit. Growth is steered by hormone balance: auxin to the shade side; the auxin-to-cytokinin ratio decides root versus shoot. Domesticated crops are products of selection on a few key genes, independently on every farming continent. Monocultures are brittle; diversity is insurance. The Green Revolution was a harvest-index story with real gains and real costs, both countable. Where it shows up next Ecology (35/48): a leaf's carbon budget scales up to forest and ocean productivity and the carbon cycle. Evolution (35/47): domestication is the best-documented case of selection, and C4 shows convergent evolution. Cell Biology (35/44) and Biochemistry (35/43): the chloroplast, the thylakoid and Rubisco kinetics reappear in detail. In the world: crop breeding and food policy, forestry, drought and heat research, biofuel and carbon-capture debates, urban greening and gardening. If you want to go deeper 📘 Textbook. Lincoln Taiz, Eduardo Zeiger, Ian Møller and Angus Murphy, Plant Physiology and Development (Sinauer / Oxford University Press; use the latest edition). The standard upper-level text on photosynthesis, water and hormones. 📘 Textbook. Ray Evert and Susan Eichhorn, Raven Biology of Plants (Freeman / Macmillan, 8th edition). Broader: structure, diversity and evolution. 📘 Gentler. Michael Pollan, The Botany of Desire (2001), a human-eye view of apples, tulips, cannabis and potatoes; or Zoë Schlanger, The Light Eaters (2022), on how plants sense and respond. 🌐 Free course. OpenStax Biology 2e, free online, with chapters on photosynthesis and on plant structure, transport and sensing; plus HHMI BioInteractive films. The takeaway A plant is a solar machine that must keep its pores open to eat and shut them to avoid drying out. Light curves, the three carbon-fixing strategies, tension in the xylem and a few hormones are how that bargain is struck, and farmers have spent ten thousand years choosing the plants that struck it best. The Green Revolution used the same logic at scale, with benefits and costs worth keeping in the same sentence. Try this: this week, find a plant growing toward a window and one growing in deep shade, and compare their leaves: size, thickness, colour. Then rotate the first plant a half turn and see how many days it takes to bend back. Sources & Further Reading Sources. Light curve, Farquhar-type model and C3/C4/CAM biochemistry: standard plant-physiology texts (Taiz and Zeiger; Raven). Γ* temperature dependence: Bernacchi et al., Plant, Cell & Environment 2001. C4: Hatch and Slack, 1966; about 3% of plant species and about 23% of terrestrial carbon fixation (Wikipedia, citing the review literature). Cohesion–tension: Dixon & Joly 1894. Redwood height limit 122 to 130 m: Koch, Sillett, Jennings & Davis, Nature 2004, tallest then known tree 112.7 m; Hyperion, about 116 m (Wikipedia). Darwin & Darwin, The Power of Movement in Plants (1880); Went, 1920s (auxin); Skoog & Miller, 1957. Domestication dates: maize (southern Mexico, about 9,000 years ago, Balsas teosinte, Doebley 2004), rice (Yangtze, 13,500 to 8,200 years, japonica 6,000 to 9,000), potato (7,000 to 10,000 years, Titicaca region), sorghum (eastern Sudan, more than 5,000 years), wheat (Fertile Crescent, about 9600 BC), from Wikipedia summaries of the archaeological and genetic literature; dates are ranges. Irish famine 1845 to 1852 with excess deaths 775,000 to 1.5 million (range). Green Revolution: Borlaug Nobel Peace Prize 1970; Norin 10, Inazuka and Vogel; IR8 1966 and Philippine rice output 3.7 to 7.7 million tonnes (Wikipedia); the dwarfing genes sd1 and Rht are gibberellin pathway genes; Evenson & Gollin, Science 2003; Shiva 1991. The charts are teaching models computed in the page with illustrative numbers. 📘 Taiz, Zeiger, Møller & Murphy, Plant Physiology and Development 📘 Pollan, The Botany of Desire 🌐 OpenStax Biology 2e 🌐 HHMI BioInteractive Step 13. Ecology: Why Populations Boom, Crash and Balance --------------------------------------------------------- Why: Populations, communities and ecosystems. Every species is a bank account with deposits (births) and withdrawals (deaths). Ecology is the course that learns what happens when thousands of accounts are tied together, and what people are doing to the whole ledger. In 1944 the US Coast Guard put 29 reindeer on St. Matthew Island, a treeless island in the Bering Sea with no predators, as an emergency food source. By summer 1963 there were about 6,000. The next winter or two the herd collapsed to 42 animals, and by the 1980s there were none. Nobody shot them. The island simply could not feed the number that compounding growth had produced. A wolf pack, a coral reef, a cornfield and a cod fishery are all the same kind of puzzle: living things that multiply, eat each other, compete for the same food, and pass the same atoms around. Ecology is the course that gives you the few equations that explain why numbers boom, why they crash, and why they sometimes balance for centuries. The course in one box Who takes itBiology, environmental science, forestry, fisheries and conservation students, usually in year 3 or 4. Medical and public-health students meet its population maths again in epidemiology. What it is forPredicting how populations and communities change, and which levers (harvest, habitat, predators, nutrients) move them. Comes afterEvolution (35/47) and Differential Equations (34/03). The models here are rates of change. Leads toConservation biology, fisheries science, epidemiology, climate and Earth-system science. In this series it sits beside Evolutionary Game Theory (34/45) and Bioinformatics & Genomics (35/52). What this piece gives youYou will not be able to manage a fishery. You will see why growth has a ceiling, why predator and prey chase each other round, why a food chain has about five links, and how to read a headline about wildlife decline. Easier first read: Entropy (13/12), for why energy only flows through. Growth compounds, then meets a ceiling A population grows the way money does at compound interest. If each individual leaves on average more than one surviving offspring, the next generation is bigger, and every extra individual adds to the next increase. Ecologists write the per-capita growth rate as r. With nothing in the way, the population follows a curve that doubles every ln 2 / r time units, about 0.69 / r. dN/dt = r Ngrowth per unit time = growth rate × number present  ·  doubling time = 0.693 ÷ r But food, space and disease do not scale up. Add a brake that gets stronger as the population nears what the place can support, the carrying capacity K, and you have the logistic equation, written by Pierre-François Verhulst in 1838. dN/dt = r N (1 − N/K)growth is fastest at N = K/2, and stops at N = K The curve is an S. Growth looks exponential at first, then slows, then flattens at K. The fastest absolute growth is at half of K, where the population adds r K / 4 individuals per unit time. That one fact runs fisheries, which we meet below. The St. Matthew reindeer show the limit of the model: they overshot K and crashed, because food recovers slowly. A study by Klein linked the crash to scarce food combined with an exceptionally severe winter. Real populations lag behind their own brakes. Interactive · Boom, brake, overshoot Growth rate r (per year)Carrying capacity KStarting number N00"> Illustrative numbers, not a species. Logistic closed form N(t) = K / (1 + ((K − N0)/N0) e−rt). The dashed line is unchecked exponential growth, clipped at the top of the chart. With r = 0.8 per year, K = 1,000 and a start of 10, the population takes about 5.7 years to reach half of K (ln 99 ÷ 0.8) and adds about 200 individuals a year at that moment. The same animals with no brake would pass 1,000 in about 5.8 years, then keep going. The two lines are almost indistinguishable at first. Early growth tells you nothing about the ceiling. Predators and prey chase each other Add a second species that eats the first. Prey multiply when predators are few; predators multiply when prey are plentiful; then predators over-eat, prey crash, predators starve, and prey recover. Alfred Lotka (1925) and Vito Volterra (1926) wrote this down independently, Volterra after fish-catch records from the Adriatic during the First World War. dx/dt = αx − βxy    dy/dt = δxy − γyprey x grow at α and are eaten at βxy · predators y grow by eating (δxy) and die at γ The model predicts something odd and testable: endless loops, with the predator peak lagging the prey peak by about a quarter cycle. Near equilibrium the period is about 2π / √(αγ). The famous real-world match is the Hudson's Bay Company's fur returns for snowshoe hare and Canada lynx, which cycle every ten years or so. But the model is a cartoon. It lets prey grow without limit and predators eat without limit, and its loops are fragile: small random dips can wipe a species out (the "atto-fox problem"). Ecologists still argue how much of the hare cycle is predators and how much is food and other factors. Interactive · Wolves and deer, simulated Prey growth αPredator death γStarting prey Lotka–Volterra with β = 0.04, δ = 0.02, solved by fourth-order Runge–Kutta for 40 time units; starting predators 9. Illustrative units. With α = 0.8 and γ = 0.6 the equilibrium is 30 prey and 20 predators, the loops orbit it, and a full cycle takes 9 to 10 time units (the small-loop formula gives 9.1; big loops run a little longer). Raise the predator death rate to 0.9, for instance by culling them, and the prey equilibrium climbs from 30 to 45 while the predator equilibrium stays at 20. The counter-intuitive lesson: in this model, the average number of predators depends on the prey's growth rate, and the average number of prey on the predators' death rate. Competition and niches Two species that need the same limited thing cannot both stay for ever. In the early 1930s Georgii Gause grew two Paramecium species, alone and together, in steady conditions: together, P. aurelia eventually drove P. caudatum out, though changing the conditions let the loser survive. The idea became the competitive exclusion principle: complete competitors cannot coexist. What lets many species share a forest is niches: each uses the resource differently enough that it limits itself more than it limits the others. Extend the logistic with competition coefficients: α12 is how much one individual of species 2 counts against species 1's room, and the reverse for α21. The rule falls out of the algebra: coexist if α12 < K1/K2 and α21 < K2/K1each species must hurt itself more than it hurts the other Interactive · Who stays? Different nichesSpecies 1 winsNeither can invadeα12 (species 2's effect on 1)12 (species 2's effect on 1)">α21 (species 1's effect on 2)21 (species 1's effect on 2)"> K1 = 100, K2 = 80, r = 0.5 for both, starting at 10 each; Euler steps of 0.05 to time 100. Illustrative. With the starting values the two settle at about 90 and 17: the weaker competitor survives only because each species crowds itself more than the other. Push either coefficient above its limit and one disappears. Push both over and the winner depends on who got there first. Food webs and energy pyramids Sunlight enters through plants, algae and some bacteria. Each time something is eaten, most of the energy is spent on living (respiration, heat), left as waste, or lies uneaten. The fraction passed from one level to the next is the trophic transfer efficiency. The textbook figure is "about 10%", from Raymond Lindeman's 1942 study of a Minnesota lake. Real values vary widely, from well under 1% to about 37% in his data, and marine plankton systems are often higher, near 15 to 20%. energy at level k = energy at the base × eke = transfer efficiency per step (about 0.1 as a rule of thumb) Because the energy shrinks geometrically, a food chain runs out after only a handful of links, and top predators are rare and need large territories. Webs are tangled, not chains, and removing one species can ripple: sea otters eat sea urchins that eat kelp (Estes and Palmisano, 1974), so otter loss opened the way for urchin-grazed kelp loss. The Yellowstone wolf story is famous but contested: wolves returned in 1995 and 1996, browsing of some trees fell in places, but bears, cougars, hunting and a changed stream channel also matter, and "wolves changed the rivers" overstates what the evidence shows. Interactive · The pyramid Transfer efficiency per stepEnergy fixed by plants (units) Illustrative units. A level counts as viable if it gets at least 1 unit. Bar width is on a log scale, the labels give the true energy. At 10% and 10,000 units from plants, herbivores get 1,000, small carnivores 100, bigger predators 10 and a top predator 1: five levels. At 5% the chain loses a level. That is the arithmetic behind "why are there no predators the size of a house". Nutrient cycles: the atoms go round, the energy does not Energy flows through an ecosystem once and leaves as heat. Atoms of carbon, nitrogen, phosphorus and water go round and round. Every cycle has pools (the atmosphere, plants, soil, ocean) and fluxes (photosynthesis, respiration, decay, runoff). The average time an atom stays in a pool, its residence time, is simply pool ÷ flux. A pool that is small compared with the flux through it turns over fast: the carbon in the atmosphere cycles through plants and oceans within a few years, while carbon in deep sediments and fossil fuels sits for millions. Humans are now a big flux. Burning fossil carbon moves carbon from a slow pool to a fast one; that is the climate story. Nitrogen is the other: the Haber process (met in Equilibrium & Kinetics, 35/37) lets factories turn atmospheric N2 into fertiliser, feeding billions, while the excess washes into rivers and coasts and fuels algal blooms that leave low-oxygen "dead zones". Which pool, which flux, and which way the arrow points answers most questions about a cycle. Biodiversity, islands and why species numbers matter Biodiversity is the variety of life at three levels: genes, species and ecosystems. About 8.7 million species is one estimate for all eukaryotes, most still unnamed, and diversity peaks in the tropics, which hold about half of species on less than a fifth of the land. Why does it matter? Three reasons, and a careful ecologist separates them. Function: long-running grassland experiments such as those at Cedar Creek, Minnesota, found that more diverse plots tend to be more productive and steadier, an "insurance" effect because different species do well in different years. Services: pollination, water filtering, fisheries. Value in itself: a claim about ethics, not data. How many species live somewhere depends strongly on area. Plotted on log axes, species number rises as a power of area, S = c Az, with z in textbooks usually quoted between about 0.15 and 0.35. A tenfold area gives 10z times the species: with z = 0.25, about 1.8 times. Run it backwards and cutting habitat to a tenth eventually loses about 44% of species. Some ecologists argue this method overstates extinctions from habitat loss, and extinctions lag behind the loss, an "extinction debt". In 1967 Robert MacArthur and E. O. Wilson explained islands with a balance: immigration of new species falls as an island fills up (fewer newcomers are new), extinction rises as it fills (more species, each with fewer individuals). Where the lines cross is the equilibrium number, and it is not static: species keep arriving and vanishing. Near islands get more immigrants; small islands lose species faster. Simberloff and Wilson tested it on tiny Florida Keys mangrove islands in 1969. Interactive · An island's balance, and what habitat loss costs Distance from mainland (km)Island area (km²)Species–area exponent zHabitat lost (%) Mainland pool P = 100 species; immigration rate 1·e−d/400·(1 − S/P) per year and extinction rate 0.25·(A/100)−0.5·S/P per year: illustrative shapes, not measured. Habitat lost uses Safter/Sbefore = (1 − lost)z. Try the preset-free defaults: a 100 km² island 200 km out settles near 70 of 100 mainland species; shrink it or move it far and the equilibrium falls. And with z = 0.25, losing 90% of the habitat leaves (0.1)0.25 = 56% of the species in the end. Human impact, measured honestly Headlines about nature are full of enormous numbers, so read the denominator. The WWF and the Zoological Society of London's Living Planet Report 2024 says monitored wildlife populations fell on average 73% between 1970 and 2020. That is an average change across a sample of vertebrate populations, not 73% of animals or species gone, and critics note the data lean toward birds and Europe and that a few populations with huge changes can drive the average. The direction is not in doubt; the exact size is. Insects are similar: a 2017 German study of 63 nature reserves found about three-quarters less flying-insect biomass over 27 years, and it is a real and alarming result for one region, not a global count. PlaceWhat happened North AmericaPassenger pigeons, once in the billions, were hunted out; the last one died in 1914. Atlantic cod off Newfoundland collapsed and Canada closed the fishery in 1992. South AmericaAmazon forest clearing is measured every year by Brazil's satellite programme (INPE); the rate has swung with policy. EuropeFarmland birds and insects have fallen; the Krefeld result above. AfricaThe Nile perch, introduced to Lake Victoria in the 1950s, was followed by the loss or collapse of many of the lake's cichlid fish species; the numbers are debated. AsiaThe Aral Sea shrank from the 1960s as rivers feeding it were diverted to irrigate cotton. OceaniaThe Great Barrier Reef has had repeated mass coral bleaching since 2016 as ocean heat waves hit. Antarctica20th-century whaling cut Southern Ocean whale populations to small fractions of their original size; some are slowly recovering. It is not all one-way. The 1987 Montreal Protocol cut ozone-damaging chemicals, and several whale populations are rebuilding. Management works when the model is right. The simplest case is a harvest: if you take a fraction h of the population each year from a logistic population, it settles at N = K (1 − h/r) and you take h N a year. That yield is highest at h = r/2, which gives the maximum sustainable yield r K / 4. Fish harder than r and the population falls to zero. Interactive · Harvest a fishery Growth rate rHarvest rate h (fraction taken per year) Schaefer-style surplus-production model with K = 1000 (illustrative). Equilibrium N = K(1 − h/r) and catch = h·N, valid for h < r; above r the stock goes to zero. Real fisheries add noise, age structure and uncertain stock estimates. At r = 0.5 and h = 0.25 the stock sits at 500 and the catch is 125 a year, the maximum. Push h to 0.4 and the catch is 80 while the stock is only 200: you work harder for less, and a bad year could tip it over. That is why managers target below the peak. Numbers here describe how ecologists think; they are not a forecast for any real place. What a graduate just sees Growth is multiplicative; every population is exponential until something pushes back. The fastest growth is half-way to the ceiling, which is also where harvest is most productive. Predator and prey numbers cycle; removing predators can make prey boom and crash instead of simply rise. Two species with the same needs cannot stay together; coexistence means different niches. About a tenth of energy passes up each step, so food chains are short and top predators are few. Atoms cycle, energy flows through once; check pools, fluxes and residence times. More area means more species, in a power law; losing habitat costs species slowly and then for good. Any decline statistic needs its denominator: what was counted, where, and over what years. Where it shows up next Evolution (35/47) feeds in: niches and competition are the selection pressures. Evolutionary Game Theory (34/45): cooperation and conflict in populations use the same coupled equations. Microbiology (35/50): a flask of bacteria is a population with exactly these curves. In the world: fishery quotas, wildlife reserves, invasive-species control, pest management, climate models and disease ecology (predator and prey become host and pathogen). If you want to go deeper 📘 Textbook. Michael Begon, Colin Townsend and John Harper, Ecology: From Individuals to Ecosystems (Wiley, 5th edition 2021). The standard upper-level text. 📘 Textbook. Robert Ricklefs and Rick Relyea, The Economy of Nature (W. H. Freeman). The widely assigned survey with a broad range of examples. 📘 Gentler. David Quammen, The Song of the Dodo (1996). Island biogeography as a travel story, from Wallace to modern extinction. 🌐 Free course. MIT OpenCourseWare 1.018J Ecology I: The Earth System (Fall 2009), covering cycles, populations and food webs. Also free: the ecology chapters of OpenStax Biology 2e. The takeaway Numbers of living things are set by a few ratios: how fast they can grow, how much room there is, who eats whom, and how much energy gets passed up. Learn those and you can read most ecological news. It also explains why saving a species is mostly about habitat and harvest, not good intentions. Try this: this week, find one population near you (pigeons, ants on a path, weeds in a crack) and ask what its ceiling K is and what sets it. You will usually find the answer is food, space or something that eats it. Sources & Further Reading Sources. Exponential and logistic growth (Verhulst, 1838), Lotka–Volterra (Lotka 1925, Volterra 1926), competition (Gause, early 1930s) and island biogeography (MacArthur and Wilson, 1967) are standard textbook ecology (Begon et al.; Ricklefs). St. Matthew Island reindeer, trophic transfer efficiency (Lindeman 1942), the Yellowstone dispute, the Living Planet Report 2024 figure and its criticisms, and the Krefeld insect study were checked against encyclopaedia summaries of the primary papers. Regional examples are well-documented cases given in outline. All interactive numbers were computed in node; model parameters are illustrative. 🌐 MIT OCW 1.018J Ecology I 🌐 OpenStax Biology 2e (free) 📘 Begon, Townsend & Harper, Ecology: From Individuals to Ecosystems 📘 Quammen, The Song of the Dodo Step 14. Bioinformatics & Genomics: Biology as Data --------------------------------------------------- Why: Biology as data: sequences, genomes and trees. A genome is a text of three billion letters that nobody can read in one piece. Biology now works by reading it in fragments, aligning the fragments, comparing them across species and people, and asking a computer what the pattern means. In April 2003 a headline said the human genome was finished. In March 2022 another said it was finished, again. Both were true. The first was a reference with gaps that held about 92% of the sequence; the second, 19 years later, filled in the rest. How can a text be "complete" twice? And how do you read three billion letters when your machine can only read a few hundred at a time? The answers are the core of bioinformatics: biology treated as information. A graduate sees a genome as a very long text with typos, repeats, copies and relatives, and sees biology questions as questions about strings: where does this read go, how similar are these two, which letters travel with a disease, and what shape does this sequence fold into? This piece walks through the five ideas that every course in the subject builds on. The course in one box Who takes itBiology, biochemistry, biomedical and computational-biology students, usually in year 3 or 4; computer-science and statistics students take it as an application. Some programmes teach it as a core course, others as a computing module inside genetics. What it is forTurning raw sequence data into biological statements: where a gene is, how two species are related, which variants are linked with a trait. Comes afterGenetics (35/46) and Programming Fundamentals (34/09). Leads toNothing later in this series, but it feeds modern Evolution (35/47), Microbiology (35/50), personalised medicine and any biology job that involves code. What this piece gives youYou will not be able to run a sequencing pipeline. You will see why reads must overlap, how an alignment is scored, how a tree comes out of a table of distances, why a hit in a genome-wide study is not a cause, and what AlphaFold does. Easier first reads: Entropy (13/12) for information ideas and LLMs (29/02) for pattern-finding by machine. A genome is a text read in scraps DNA is a four-letter text (A, C, G, T). A human haploid genome is about 3.1 billion letters, all copied in nearly every cell. No machine reads it end to end. Instead it is broken into pieces, every piece is read, and a computer stitches them back together by finding overlaps. This is shotgun sequencing, the method behind the genomes since the 1990s: in 1977 Frederick Sanger's group read the 5,386 letters of a small virus, phiX174; in 1995 the 1.8 million letters of the bacterium Haemophilus influenzae were the first free-living organism's genome; the Human Genome Project ran from 1990 to 2003, cost around $3 billion, and delivered a rough draft in 2000 and 2001 and a declared finish in April 2003. Since then the cost of sequencing has fallen far faster than the cost of computing did under Moore's law, which is why genomes of thousands of species and millions of people exist. Two numbers decide whether the assembly works. Coverage c is the average number of times each letter is read: reads × read length ÷ genome length. Reads land at random, so by the Lander–Waterman argument the fraction of the genome that nothing ever hit is e−c. uncovered fraction = e−cat 1× about 37% is missed; at 10× about 0.005%; at 30× essentially nothing The second number is the read length against the length of repeats. A read can only place itself if it contains something unique. The human genome is full of repeated stretches, some thousands of letters long and some, like the centromeres, millions long. A 150-letter read inside a 6,000-letter repeat has no way to know where it is. Long reads that reach out of the repeat can. Interactive · Shotgun sequencing: coverage and repeats Coverage c Read length (100 to 100,000 letters) Length of one repeat in the genome Genome 3,100 million letters. Reads = c × genome ÷ read length. Uncovered = e−c (idealised random reads, no errors). At 30× with 150-letter reads you need about 620 million reads, around 93 billion letters, and almost nothing is missed. But a 6,000-letter repeat is still unresolved. That is exactly why the 2003 "complete" genome kept holes, and why the 2022 genome needed reads tens of thousands of letters long. Alignment: finding the best way to line two texts up Once you have a sequence, the first thing you ask is: what does it resemble? Two similar sequences are rarely identical: letters are swapped, and some are inserted or deleted. An alignment lines two sequences up, with gaps, so that matching letters sit in the same column. Which alignment is best? Give points for matches, take points for mismatches, and take more for opening a gap, then find the arrangement with the highest total. In 1970 Saul Needleman and Christian Wunsch showed how to do that exactly, by filling in a table: S(i,j) = max( S(i−1,j−1) + score(aᵢ,bⱼ), S(i−1,j) + gap, S(i,j−1) + gap )best score for the first i letters of one and the first j of the other, built from three smaller answers This is dynamic programming: don't search every possible alignment (there are astronomically many), solve small prefixes once and reuse them. Smith and Waterman (1981) adapted it to find the best local match, and BLAST (1990) made a fast approximate version that searches databases of billions of letters in seconds. Try your own sequences below. Interactive · Needleman–Wunsch alignment Sequence 1 (letters A, C, G, T; up to 12) Sequence 2 GATTACA / GCATGCA One deletion Unrelated Match score Mismatch score Gap score Notice what the scores mean. Make gaps cheap and the program inserts gaps freely to force matches; make them dear and it prefers mismatches. There is no "true" alignment from the scores alone: the numbers encode a belief about how often evolution inserts, deletes and substitutes. Real tools use substitution matrices (BLOSUM, PAM) built from observed protein changes. Trees from distances: reading relatedness off a table Align many species and count the differences between each pair: you get a table of distances. Humans and chimpanzees differ at roughly 1 to 1.5% of aligned letters, humans and orangutans at about 3%, humans and macaques at about 6 to 7%. A tree is a way to draw such a table. The oldest recipe is UPGMA (Sokal and Michener, 1958): repeatedly join the two closest groups and average the distances. It is simple, and it quietly assumes a molecular clock: every lineage changes at the same rate. When rates differ, it goes wrong. In 1987 Naruya Saitou and Masatoshi Nei introduced neighbor-joining, which corrects each distance by how far each taxon is from all the others, so a fast-evolving "long branch" does not fool it. Interactive · The long-branch trap Four species A, B, C, D. The true tree pairs A with B and C with D. A and C evolve fast (long branches of length L); B and D are slow (length 1); the middle branch has length 1. (Illustrative lengths.) Length L of the fast branches With L=5 the table has AB=6, CD=6, AC=11, AD=7, BC=7, BD=3. The closest pair is B and D, at 3. UPGMA joins them, which is wrong: they are not each other's closest relatives at all, they only evolved slowly. Neighbor-joining recovers the true grouping. Below L=2 both agree. Modern methods (maximum likelihood, Bayesian inference) model rates explicitly, but the lesson stays: a method's assumptions are part of its answer. Genome-wide association: a million small bets If genomes differ by about one letter in a thousand between two people, which differences go with a trait? A genome-wide association study (GWAS) takes thousands to millions of people, records millions of variants (SNPs) and tests each one against the trait. The first big success was age-related macular degeneration in 2005. The statistics have a trap built in: test a million variants at p<0.05 and about 50,000 will "pass" by luck. The accepted threshold is therefore p<5×10−8 (roughly 0.05 divided by a million tests). A real association appears as a tall tower on a "Manhattan plot". Interactive · A simulated GWAS People in the study Variance each causal variant explains Naive threshold p < 0.05 Genome-wide p < 5×10⁻⁸ Simulation: 1,000 variants, 5 truly causal (marked ring), the rest null. Test statistic z ~ Normal(√(n·v/(1−v)), 1) for causal and Normal(0,1) otherwise. Fixed seed. Slide the sample size up and causal towers rise out of the noise; with the naive threshold the null variants light up too. Three cautions every course repeats. A hit is an association, often with a neighbouring variant that is inherited with it (linkage disequilibrium), not a proven cause. Most traits are polygenic: thousands of variants each with a tiny effect, so single hits explain little. And the studies have historically been dominated by people of European ancestry, so scores built from them predict less well elsewhere: a 2019 analysis of UK Biobank-based scores found them roughly two-fold less accurate in East Asian and several-fold (about 4.5 times in one summary) less accurate in African-ancestry samples. Biobanks in Japan, China, Mexico and Africa (BioBank Japan, China Kadoorie, the Mexico City Prospective Study, H3Africa) exist partly to fix this. What "heritability" does and does not mean is in Personality and Individual Differences (35/26). Also remember the human-variation fact: most genetic variation lies within populations, not between them (Lewontin, 1972, confirmed by later genomic work). This describes research and isn't medical advice. From sequence to shape: reading co-evolution, and what AlphaFold did A protein's function depends on its folded shape, and the shape is, in principle, written in its sequence. For decades predicting it was a grand challenge. One clue is old: if two positions in a protein touch in 3-D, a mutation at one is often compensated by a change at the other, so their letters change together across species. Align hundreds of relatives and look for columns that vary in step: that is co-evolution, and you can score it with mutual information. Interactive · Find the touching pair Sequences in the alignment Toy alignment: 10 columns, 4-letter alphabet. Columns 3 and 8 co-evolve (each value of one fixes the other); the rest vary independently. Fixed seed, first n rows used. With four or five sequences the pair you want is not even first: small samples make unrelated columns look linked. With about eight it leads, but rivals are still strong; with dozens or hundreds they fade and the true pair stands alone. That is why deep alignments mattered, and why DeepMind's AlphaFold 2 won the CASP14 competition in November 2020, scoring above 90 on the global-distance test for roughly two-thirds of targets, a level that experimentalists described as a stunning advance. It combines these alignment signals with a neural network trained on known structures (Jumper and colleagues, Nature, 2021). A public database of predictions launched in July 2021 with EMBL-EBI and grew to about 200 million structures in 2022. Demis Hassabis and John Jumper shared half of the 2024 Nobel Prize in Chemistry for it; David Baker took the other half for computational protein design. Limits matter. A predicted structure is a hypothesis with its own confidence score, not an experiment; the model does little for proteins that move, for disordered regions, or for how a mutation changes stability. Structural biologists still do the experiments, now with a far better starting guess. Privacy: your genome is also your family's Genetic data are unlike a password. You cannot change them, and they are shared with relatives who never agreed. In 2013 Gymrek and colleagues showed that surnames could be inferred from anonymous research genomes by matching Y-chromosome patterns against public genealogy databases. In 2018 investigators identified the Golden State Killer suspect by finding distant cousins in a public genealogy database; later that year Erlich and colleagues estimated that about 60% of searches for people of European descent in the US would already find a third cousin or closer in the consumer databases of the day, and that coverage would soon be near-universal. Genetic data are protected differently around the world: the EU's GDPR classes them as a special category needing stronger grounds; the US Genetic Information Nondiscrimination Act of 2008 covers health insurance and employment but not, for example, life insurance. When a testing company went into bankruptcy in 2025, many customers asked what happens to their data in a sale, which is a good question to ask of any provider. Indigenous communities have pressed for data sovereignty after cases such as the Havasupai blood samples, used for research they had not agreed to and settled in 2010. A genome is not just yours. Whoever holds your cousin's data holds a fuzzy copy of yours. What a graduate just sees A genome is a text; sequencing reads scraps and assembly depends on overlap, coverage (1 − e−c) and unique anchors. Repeats longer than the read are what stay unresolved, which is why "complete" took until 2022. Every alignment is a scoring choice. The numbers encode a belief about evolution. A tree is a model with assumptions. A clock assumption that fails puts the wrong species together. A million tests means a stricter threshold; a hit is a pointer, not a cause. A genome-wide result carries the ancestry of the people in it, so scores travel poorly. Sequence → shape works because shape is conserved and positions co-evolve. A prediction is a hypothesis. Genetic data identify relatives as well as you. Where it shows up next Genetics (35/46) and Evolution (35/47): variants, selection and phylogeny are now measured by exactly these tools. Microbiology (35/50): outbreaks and antibiotic-resistance genes are tracked by sequencing and tree-building, and metagenomics reads whole communities of microbes at once. Probability & Statistics (34/05): multiple testing, false discovery and confounding are the daily problems of a GWAS. In the world: rare-disease diagnosis, tumour sequencing, ancestry kits, forensic genealogy, crop and livestock breeding, and drug-target discovery. If you want to go deeper 📘 Textbook. Phillip Compeau and Pavel Pevzner, Bioinformatics Algorithms: An Active Learning Approach (Active Learning Publishers). Each chapter starts from a real biological puzzle and builds the algorithm. 📘 Textbook. Richard Durbin, Sean Eddy, Anders Krogh and Graeme Mitchison, Biological Sequence Analysis (Cambridge University Press, 1998). The classic on alignment and probabilistic models, still read. 📘 Gentler. Rosalind, a free site that teaches bioinformatics by short programming problems, from counting DNA letters up to assembly and alignment. 🌐 Free course. MIT OpenCourseWare 7.91J Foundations of Computational and Systems Biology (Spring 2014): sequence alignment, genomes and networks. The takeaway Biology is now also an information science: genomes are texts read in scraps, aligned by scoring, compared as distances, searched for associations and folded by learned patterns. Each step has a model with assumptions you should be able to name, and each step involves data about real people who are related to other real people. Try this: this week, take any word and a misspelling of it (for example "separate" and "seperate") and align them by hand: mark matches, a mismatch, and find where a gap would help. You have just run Needleman–Wunsch. Sources & Further Reading Sources. Human Genome Project: declared complete 14 April 2003, about 92% of the sequence, cost roughly $3 billion (Wikipedia summary of NHGRI and DOE records; NHGRI's sequencing-cost series, last updated 2023, graphs costs against a Moore's-law line). Telomere-to-telomere genome: Nurk et al., The complete sequence of a human genome, Science 376, 44–53 (31 March 2022; DOI 10.1126/science.abj6987), 3.055 billion letters and nearly 200 million new; the Y chromosome followed in 2023. Needleman & Wunsch 1970; Smith & Waterman 1981; Altschul et al. 1990 (BLAST); Sokal & Michener 1958 (UPGMA); Saitou & Nei 1987 (neighbor-joining); Lander & Waterman 1988 coverage argument. GWAS threshold 5×10⁻⁸ is standard; Martin et al., Nature Genetics 2019 (polygenic score accuracy by ancestry; secondary coverage gives slightly different African-ancestry ratios, so the figure here is approximate). AlphaFold: CASP14 (November 2020), Jumper et al., Nature 2021, database expansion to about 200 million structures (July 2022), 2024 Nobel Prize in Chemistry. Privacy: Gymrek et al., Science 2013; Erlich et al., Science 362, 690–694 (2018); GINA 2008; GDPR. The sequence tools and charts are teaching models computed in the page; the species distances are rounded and illustrative. This describes science and isn't medical or legal advice. 📘 Compeau & Pevzner, Bioinformatics Algorithms 📘 Durbin, Eddy, Krogh & Mitchison, Biological Sequence Analysis 🌐 Rosalind 🌐 MIT OCW 7.91J Step 15. Programming Fundamentals: Instructions, State and Taking Things Apart ------------------------------------------------------------------------------ Why: Biologists now program. A computer can't guess what you meant. Everything in a first programming course is a way of saying it exactly enough, and of working out why you didn't. Tap "sort by price" and a list of a thousand items rearranges before you've lifted your finger. Somewhere, a person wrote down steps so exact that a machine with no judgment, no memory of yesterday and no idea what a "price" is could do it perfectly, a thousand times over. That is the whole trade. A programmer isn't someone who knows a language, they're someone who can state a task so precisely that nothing is left to guess. And since people are bad at being precise on the first try, the other half of the skill is finding out what you actually said, as opposed to what you meant. Mechanical and aerospace engineers use the same habits to simulate a wing before it's built; computer scientists use them to build every other subject on the degree. Python and MATLAB are the common first languages for engineers, and this piece uses Python-style code. The ideas carry to every language. The course in one box Who takes it: first-year students of Computer Science (usually their very first course) and Mechanical & Aerospace Engineering (often in MATLAB or Python). What it's for: telling a machine what to do exactly, and finding out when you didn't. Comes after: nothing; it has no prerequisites. Leads to: Data Structures (34/23), Computer Architecture (34/25) and Software Engineering (34/31) on the computing side; Differential Equations (34/03), Dynamics (34/12) and Control Systems (34/20) on the engineering side, all of which are solved on a computer in practice. Honest line: you won't be able to ship an app after this. You will be able to read ten lines of code, predict what they do, and make a physics model in a loop. A program is instructions plus state Strip away the syntax and a program is two things: a list of instructions, and the state, the current values of all its named boxes. Each instruction reads the state and changes it a little. Running the program is just that, one step after another, and the answer is whatever state is left (or printed) at the end. The graduate habit is to run the program in their head: keep a small table of variable values and update it line by line. Below is a tiny interpreter that does it visibly. Press Step. Then edit the program: change the 6 in the Collatz example, or write your own with =, +=, if/else, while, for … in range(…) and print. Interactive · Step through a program Add 1 to 5 Collatz steps Count down by 3 The program (edit me) StepRun to the endStart again A real mini-interpreter, written for this page. It stops after 400 steps, in case you write a loop that never ends. The first program adds 1 + 2 + 3 + 4 + 5 and prints 15. The Collatz one halves even numbers and triples-plus-one odd ones until it reaches 1: starting from 6 it takes 8 steps. Nobody knows if every starting number reaches 1, and yet the program is five lines long. That's what "simple instructions, deep behaviour" feels like. Variables and types: what a number is made of A variable is a name for a box in memory. A type says what kind of thing is in the box, and therefore what you may do with it: you can add two numbers, join two pieces of text, but adding "3" and 4 is an error or a surprise. Types exist because the machine stores everything as patterns of bits, and the pattern means nothing without the type. The box has a size too. A signed 16-bit integer holds −32,768 to 32,767, and nothing more. Decimals are stored as floating point, binary fractions of limited precision, so 0.1 can't be stored exactly and 0.1 + 0.2 gives 0.30000000000000004. On 4 June 1996 the first Ariane 5 rocket veered off course and broke up about 37 seconds after lift-off, a loss of more than US$370 million. The investigation traced it to the guidance software, reused from Ariane 4: a 64-bit floating-point value (the horizontal bias) was converted to a 16-bit signed integer, and on the faster rocket it didn't fit. The failure shut down both inertial units. A number too big for its box was enough. Interactive · Does it fit? 8 bits 16 bits 32 bits Number to store Ariane's code reportedly raised an error on overflow; some systems wrap silently instead, which is shown here. Conditionals and loops: choosing and repeating With state and instructions, only two more ideas are needed to compute anything: choose (if something is true, do this, else that) and repeat (while something is true, or for each value in a range). Together they let ten lines do work that would take ten million lines written out. The classic trap is in the edges. In Python's range(1, 10) the loop starts at 1 and stops before 10, so it runs 9 times, not 10. Off-by-one errors are the "fencepost" mistake: a fence of 10 sections needs 11 posts. Try the bounds yourself. Interactive · Edit the loop Add up i Add up i² Just count Start Stop (never reached) Step With the defaults, range(1, 11) runs 10 times and adds up to 55. Make the step negative and the start bigger than the stop to count down. Set the start above the stop with a positive step and the body never runs at all, which is perfectly legal and a common source of silent bugs. Functions and recursion: naming a piece, then calling it again A function packages some instructions under a name, takes inputs, and gives back an output. That is decomposition, the central skill of engineering of any kind: break a big problem into pieces small enough to understand and test alone, give each a name, then build on the names. The tracer above could be one function; so could braking distance. Recursion is a function that calls itself on a smaller version of its problem, until it reaches a case it can answer directly. The Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, …, each the sum of the previous two) have a one-line recursive definition. Run it naively and the machine re-solves the same sub-problems again and again. Interactive · Count the calls Naive Remember answers (memo) Compute fib(n), n = Time it on this device Naively, fib(5) makes 15 calls, fib(20) makes 21,891, and fib(30), whose answer is just 832,040, makes 2,692,537. Remembering answers brings fib(30) down to 59 calls. Same answer, a different algorithm, and the course after this one (Algorithms, 34/24) is the study of exactly that difference. Data: lists and dictionaries Most programs aren't about single numbers but collections. A list is an ordered row of values, found by position (the third item). A dictionary maps a key to a value (a word to its count, a student ID to a name) and finds an entry by key without scanning. Choosing the right container is the first lesson of Data Structures (34/23). The difference is speed. To find a word in a list of n you may have to look at all n. A dictionary (usually built as a hash table) jumps almost straight to it, in roughly constant time on average, however large it is. Paste some text below and look a word up. Interactive · Count the words Textthe cat sat on the mat and the dog sat on the cat Look up a word Debugging is the scientific method Programs don't do what you meant; they do what you wrote. Finding the gap is science: look at the result, form a hypothesis ("the loop is skipping the last item"), make a prediction ("if I print the count here it will be one short"), run the experiment (print it), and revise. Guessing and changing things at random is the opposite, and it's how you add new bugs. The strongest move is bisection. If the code is a chain of steps and the result is wrong, check the value halfway along. If it's right, the fault is in the second half; if wrong, the first. Each check halves the suspects. In 1947 operators of Harvard's Mark II computer taped a moth found stuck in a relay into the logbook with the note "First actual case of bug being found" — a joke that only works because engineers already called faults "bugs". Interactive · Find the bug in as few probes as you can Start with x = 5. Slide to a step and probe the value there against what you'd get by hand. Look at x Probe hereBlame this stepNew bug Twelve suspect lines need at most four probes when you halve each time, because 2⁴ = 16 is at least 12. Checking from the top, one line at a time, can take twelve. Modelling: a physics simulation in a dozen lines Engineers model long before they build. Most physical laws give a rate of change (acceleration from forces, as in Physics I), and a computer can follow a rate forward in small steps: update the position using the velocity, update the velocity using the acceleration, repeat. That is the Euler method, and the loop is the whole simulation. x, y = 0.0, 0.0 vx, vy = 21.2, 21.2 # 30 m/s at 45 degrees dt = 0.1 # time step in seconds while y >= 0: x = x + vx * dt y = y + vy * dt vy = vy - 9.81 * dt # gravity changes vy only print(x) # about 93.9 metres Smaller time steps are more accurate and cost more. For the cannonball at 30 m/s and 45°, the exact range without air is 91.7 m. With a step of 0.5 s the simulation says 102.1 m, 0.1 s gives 93.9 m, and 0.001 s gives 91.8. Now add air drag, for which no tidy formula exists: the same loop still works, which is why engineers simulate. Interactive · A cannonball in code No air With air drag Launch speed Launch angle Time step Drag is modelled as a quadratic term with a baseball-like coefficient (0.007 per metre); a model, not a measurement. Readable code is a letter to a person A program is run by a machine once and read by people many times: the next engineer, the reviewer, you in six months. The well-known line from the preface of Structure and Interpretation of Computer Programs is: "Programs must be written for people to read, and only incidentally for machines to execute." The machine will accept either version below. Only one of them can be checked by a human. def f(a, b): return (a / 3.6) ** 2 / (2 * b * 9.81) def braking_distance(speed_kmh, friction): speed = speed_kmh / 3.6 # convert to metres per second return speed ** 2 / (2 * friction * 9.81) Both give 14.05 m for 50 km/h and a friction of 0.7, the braking distance of Physics I. Only the second tells you what it means, and so lets a reader spot a wrong constant. Good names, small functions and comments that say why are the cheapest debugging tools there are. People disagree on how much structure is enough: some teams favour heavy up-front design, others short cycles of build, test and revise; Software Engineering (34/31) covers both camps. What a graduate just sees A program is instructions plus state; to understand it, track the variables line by line. Every value has a type and a size, and a number too large for its box is a real way to lose a rocket. Loops run until their stop value, not through it: watch the edges. Break a problem into named functions you can test one at a time. A function that calls itself can be elegant and wildly wasteful; counting calls shows which. The right container (list or dictionary) can be the difference between instant and never. Debugging means hypotheses and experiments; halve the suspects each time. Simulation is a rate of change plus a loop, and smaller steps cost more for less error. Code is read far more often than it is written. Where it shows up next Data Structures (34/23) and Algorithms (34/24): the list-versus-dictionary and naive-versus-memo contrasts above, measured properly. Computer Architecture (34/25): the fixed-size boxes and overflow are the hardware's registers; instructions plus state is literally how a processor works. Software Engineering (34/31): decomposition, testing and readable code, scaled to teams and years. Differential Equations (34/03), Dynamics (34/12), Control Systems (34/20): the Euler loop is the starting point of numerical solvers, vehicle simulators and the code that runs a controller. Machine Learning (34/32): training is a loop that nudges numbers until the error falls. If you want to go deeper 📘 Standard textbook. John Guttag, Introduction to Computation and Programming Using Python (3rd ed., MIT Press, 2021), the text behind MIT's introductory course, written for engineers and scientists, with modelling and data. 📘 Gentler, free. Allen Downey, Think Python (3rd ed., Green Tea Press / O'Reilly), free to read online at greenteapress.com. For the deeper "why", Structure and Interpretation of Computer Programs by Abelson and Sussman is free online from MIT Press. 🌐 Free course. MIT OpenCourseWare 6.0001 Introduction to Computer Science and Programming in Python (Fall 2016), or Harvard's CS50x (starts in C, then Python and SQL) and CS50P (Python only), free on OpenCourseWare. The takeaway A program is instructions acting on state. Variables, types, choices, loops and functions are how you say it exactly; lists and dictionaries are how you hold data; debugging is hypothesis and experiment; and a simulation is a rate of change inside a loop. The graduate's real skill is reading code, predicting it, and taking a big problem apart. Try this: take any small thing you do by hand, like splitting a bill or converting recipe units, and write it as exact steps for a friend to follow without any judgment. Then watch where they get stuck: those are your bugs. Sources & Further Reading Sources. Ariane 5 flight 501 (4 June 1996; 64-bit floating-point to 16-bit signed integer conversion overflow; about 37 seconds; more than US$370 million): Wikipedia, "Ariane flight V88", which summarises the Inquiry Board's report. The Mark II moth (9 September 1947, logbook note "First actual case of bug being found", now at the Smithsonian) from the Computer History Museum and JSTOR Daily, "The bug in the computer bug story", which notes the term was already in use. The SICP quotation from the preface of Abelson & Sussman, Structure and Interpretation of Computer Programs (MIT Press, 1985). CS50x language order from cs50.harvard.edu/x; Think Python 3rd ed. from greenteapress.com. Computed and checked in node, including by running the page's own interpreter on its example programs: 15; 8 Collatz steps; −2; 40,000 wraps to −25,536 in 16 bits; fib call counts 15, 177, 21,891 and 2,692,537 (and 2n−1 with a memo); projectile ranges 91.74 m exact and 102.1, 93.9, 91.8 m for steps of 0.5, 0.1 and 0.001 s; 14.05 m braking distance. 🌐 MIT OpenCourseWare: 6.0001 🌐 Harvard CS50x and CS50P 📘 Think Python, 3rd edition (free online) 📘 Guttag, Introduction to Computation and Programming Using Python, 3rd ed. (MIT Press) 🌐 JSTOR Daily: the bug in the computer bug story Step 16. Game Theory: When Your Best Move Depends on Mine --------------------------------------------------------- Why: Evolutionary game theory: why cooperation evolves. Two shops pick prices, two countries pick tariffs, a hundred bidders pick bids. Game theory is the maths of choosing when everyone else is choosing too, and it explains why smart people can trap themselves. Two petrol stations face each other across a road. If both charge a fair price, both make a decent profit. If one cuts its price, it steals the customers and makes more, for a while. So each is tempted to cut. Both cut. Both now earn less than before, and neither can raise prices alone without losing everyone. Nobody was stupid. Each did the sensible thing given what the other might do. That pattern, a trap built entirely out of sensible choices, is the first thing game theory teaches you to see. It then teaches how to get out of the trap: by repeating the game, by changing who moves first, by changing the rules. The same toolkit explains the design of radio-spectrum auctions and the matching of kidney donors. The course in one box Who takes itEconomics majors in year 2, straight after microeconomics. Business schools teach it inside strategy courses, and computer science and political science programmes teach it too, because algorithms and elections are games. What it is forPredicting what rational, self-interested players will do when each one's best move depends on the others, and designing rules so the result is a good one. Comes afterMicroeconomics (34/42). Leads toStrategy & Competition (34/54); it also underlies the auctions and pricing in Pricing (34/61) and the rules-of-the-game thinking in Public Economics (34/49). What this piece gives youYou will not be able to solve a multi-stage game with incomplete information. You will see why a dominant strategy can leave everyone worse off, why a threat only works if carrying it out is in your interest, and why an auction format changes how people bid. Easier first reads: the library's The Social Contract (18/14) asks why we accept rules and a state at all, and Anarchism (31/04) covers the commons problem in words. This piece puts numbers on that kind of trap. Players, strategies, payoffs, and the Nash equilibrium A game has three ingredients: the players (who decides), the strategies (what each can do) and the payoffs (what each gets for every combination of choices, in whatever they care about: money, time, votes, survival). Two players with two options each fit in a small grid, the payoff matrix. One player picks the row, the other the column, and each cell holds two numbers: the row player's payoff first, the column player's second. Two ideas solve most such grids. A dominant strategy is one that is best for you whatever the other does: if it exists, play it. When neither player has one, look for a Nash equilibrium: a pair of choices where neither player could do better by changing their own choice alone. John Nash proved in 1950 that every finite game has at least one, possibly in mixed strategies (rolling dice between options). Nash shared the 1994 economics Nobel prize with John Harsanyi and Reinhard Selten for it. Nash equilibrium: each player's choice is a best response to the other'snobody gains by switching alone; it says nothing about whether the outcome is good Interactive · The payoff-matrix workbench Prisoner's dilemma Stag hunt Chicken Matching pennies Which side to drive Each cell: your payoff (row player), then the column player's. Edit the numbers; the analysis updates. Shaded = a best response for that player; outlined cell = Nash equilibrium. Without JavaScript: in the prisoner's dilemma (5, 3, 1, 0), defecting is dominant for both players, the only Nash equilibrium is both defecting for 1 each, and both cooperating would give 3 each. Try the presets and read the verdicts. Chicken and the driving game have two pure equilibria and a mixed one at 50:50; matching pennies has no pure equilibrium at all, only the mixed one, which is why a goalkeeper and a penalty-taker must be unpredictable. In matching pennies, if the row player leans even slightly toward heads, the column player exploits it. The prisoner's dilemma: why smart players choose badly Merrill Flood and Melvin Dresher devised it at the RAND Corporation in 1950, and Albert Tucker gave it its story: two suspects, questioned separately. Stay silent (cooperate) and both get a light sentence. Betray the other (defect) and you walk free while he gets the worst. Both betray and both get a heavy sentence. With points instead of years, the standard payoffs are: temptation 5, mutual cooperation 3, mutual defection 1, being betrayed 0. Whatever the other does, defecting pays you more: 5 beats 3 if she cooperates, 1 beats 0 if she defects. So both defect and both get 1, when both cooperating would have given 3 each. The equilibrium is stable and bad. That is the logic of arms races, overfishing, price wars and the two petrol stations. Now play it. Ten rounds against a computer opponent whose rule you can pick; you know the game is exactly ten rounds long. Interactive · Play ten rounds Tit for tat Always defect Always cooperate Grudger Coin flip CooperateDefectRestart Payoffs per round: both cooperate 3 each; you defect on a cooperator 5 to 0; both defect 1 each. Tit for tat copies your last move; the grudger cooperates until you defect once, then never again. Against tit for tat, the best ten-round total is 32: cooperate nine times, defect on the last round when it can no longer be punished. Against always-defect, nothing beats 10. Against always-cooperate you can take 50. The right play depends on who is on the other side, which is the whole subject in one sentence. Repeated games: when tomorrow changes today Meet the same person again and again and the logic changes: defecting today invites revenge tomorrow. In 1980 the political scientist Robert Axelrod invited game theorists to send in programs for a repeated prisoner's dilemma, each program playing every other for 200 moves. The winner, in this tournament and in a second, larger one, was the simplest entry: tit for tat, sent by the psychologist and game theorist Anatol Rapoport. It cooperates first, then copies the opponent's last move. Axelrod's 1984 book The Evolution of Cooperation drew the lesson: successful strategies were nice (never defect first), provocable (punish defection at once), forgiving (return to cooperation) and clear (easy to read). Tit for tat never beats the partner it faces; the best it can do in a single match is tie. It won by getting good scores out of nearly everyone. Run your own small tournament. Six kinds of players meet in a 200-round round robin; add copies of Always-defect and see whether the winner changes. Interactive · A round-robin tournament (a toy field) Always-defect entrants No mistakes 5% of moves slip Entrants: Always cooperate, Tit for tat, Grudger, Pavlov (cooperate only if both did the same last round), Coin flip, plus the Always-defect copies. Everyone meets everyone else for 200 rounds; bars show the average points per round. Payoffs 5, 3, 1, 0. A toy field, far smaller than Axelrod's. With no Always-defect, the nice, retaliating strategies fill the top. Add more defectors and the field gets harsher: the defectors climb to the top once enough naive cooperators and coin-flippers are there to be exploited, while their scores against each other stay at 1. Success in a repeated game depends on who else is playing. Turn on the 5% slips and tit for tat loses ground too: after one accidental defection two tit-for-tat players can lock into a spiral of mutual retaliation. Later work found more forgiving variants, such as generous tit for tat, and the Pavlov rule do better in noisy worlds. Cooperation without a referee needs a future worth protecting, which is why long-term relationships, reputations and repeated dealings support trust that one-off meetings cannot. Coordination games: when you just need to match Not every game is a conflict. In the driving game, both of you want to pick the same side; which side hardly matters. Load "Which side to drive" above: two equilibria, both good, and nothing in the payoffs says which. Conventions (driving on the left in the UK, Japan and India, on the right in most of the rest of the world) are equilibria picked by history. The stag hunt adds risk: both hunting stag gives 4 each, but hunting hare alone is safe at 3. Two equilibria again, one better but riskier. Thomas Schelling, in The Strategy of Conflict (1960), noticed that when payoffs cannot choose, players use focal points: the obvious, salient option, like meeting "at the clock" in a station. Many real-world failures, from bank runs to standards wars, are coordination games stuck on the bad equilibrium. Sequential games: the credible threat When players move in turn, you solve the game backwards: start at the end, see what the last mover would do, and work back. Take a company deciding whether to enter a market held by an incumbent. The incumbent says: "If you enter, I'll start a price war." Should the entrant believe it? Only if fighting is actually best for the incumbent after entry happens. If, once the entrant is in, the war would cost the incumbent more than sharing the market, the threat is empty. A rational entrant sees that and enters. Reinhard Selten's refinement of Nash equilibrium, subgame-perfect equilibrium, rules such empty threats out. Interactive · Entry, threats and commitment Incumbent's profit if it fights after entry No commitment Commit to fight (contract penalty) Payoffs (entrant, incumbent): stay out (0, 10); enter and incumbent accommodates (4, 5); enter and incumbent fights (−2, your slider). The commitment option makes accommodating cost the incumbent 3 (so it pays only 2). The slider has a threshold. With a war worth less than 5 to the incumbent, the threat is empty and the entrant walks in. Raise the war's payoff above 5, or use the commitment button, and the threat becomes credible, the entrant stays out, and the incumbent never has to fight. Commitment devices (spare factory capacity already built, a contract that punishes backing down, a reputation) have this strange property: by taking away your own options they can make you better off. Auctions: bid your value, or shave it An auction is a game where the rules decide the payoffs. In a sealed-bid second-price auction, the highest bidder wins but pays only the second-highest bid. William Vickrey analysed it in 1961 (it had been used by stamp collectors since 1893). Here, bidding exactly your true value is a dominant strategy: bidding more risks paying above your value, bidding less risks losing an item you would have profited from. In a first-price auction you pay what you bid, so you shave your bid below your value, trading a bigger profit if you win against a smaller chance of winning. With four bidders whose values are equally likely to be anywhere in a range, the equilibrium bid is three-quarters of your value (in general, (n−1)/n of it). Interactive · Four bidders, two formats (3,000 simulated auctions) Your bid as a share of your value second-price   first-price Values for all four bidders are drawn uniformly between 0 and 100. The three rivals bid their full value in the second-price format and three-quarters of it in the first-price format. Your average profit is per auction, including those you lose. Slide the share. In the second-price format your profit peaks at 100% of your value; in the first-price format it peaks near 74%. Also watch the seller's average revenue: it is about 60 in both formats, a first glimpse of the revenue equivalence theorem. Real auctions differ from this textbook case. When bidders are unsure of the item's true value (oil leases, spectrum) the winner tends to be the one who overestimated most, the winner's curse. Mechanism design: design the game, then let people play it Game theory asks: given the rules, what will players do? Mechanism design turns it around: what rules would make self-interested players do what we want? Two famous cases. Spectrum auctions. Governments own radio frequencies and need to hand them to phone companies. For decades they used beauty contests and lotteries. From July 1994 the US Federal Communications Commission instead ran a "simultaneous multiple round" auction, where many related licences are sold together over many rounds and bidders see each other's bids. Theorists including Paul Milgrom and Robert Wilson helped shape the design, and they shared the 2020 economics Nobel prize for improvements to auction theory and new auction formats. In 2000 the UK's 3G auction raised £22.5 billion from five licences. Kidney exchange. Many people who need a kidney have a willing donor who is the wrong blood type. Selling kidneys is illegal almost everywhere, so prices cannot match people. Alvin Roth, Tayfun Sönmez and Utku Ünver designed algorithms (their 2004 paper in the Quarterly Journal of Economics) in which pair A's donor gives to pair B's patient while B's donor gives to A's: a swap, extended to longer cycles and to chains started by an altruistic donor. The first paired exchange recorded was in South Korea in 1991 and the first in the US in 2000; by 2012 the US National Kidney Registry had organised a 60-surgery chain, and by 2014 one of 70. Roth shared the 2012 economics Nobel prize with Lloyd Shapley for the theory of stable allocations and the practice of market design. Game theory predicts what people do under the rules. Mechanism design chooses the rules. What a graduate just sees Before asking what someone will do, ask what they would do if they expected you to do each of your options. A dominant strategy needs no guess about the other player. If it exists, it settles the game. A Nash equilibrium is stable, not good. The prisoner's dilemma's equilibrium leaves both worse off than cooperating. Repetition changes the game: cooperation can be rational when the future is long enough and defection is punishable. A threat counts only if carrying it out is in your interest when the time comes. Otherwise build a commitment or expect to be called. When payoffs do not choose between equilibria, the focal point does: salience, convention, a shared story. In a second-price auction, bid your value. In a first-price auction, shave your bid. The rules decide how people behave. When a market cannot use prices, you can still design the rules. Where it shows up next Strategy & Competition (34/54): firms setting prices, building capacity and deciding whether to enter are playing the games above. Pricing (34/61): discounts, price matching and surge pricing are games with customers and competitors. Behavioral Economics (34/46): the next piece asks when real people do not play the equilibrium, as in the ultimatum game. Machine Learning (34/32) and Computer Networks (34/27): game-playing AIs and congestion control both apply these ideas. In the world: online-advertising auctions, spectrum sales, school and hospital matching, climate treaties, arms control. If you want to go deeper 📘 Textbook. Robert Gibbons, Game Theory for Applied Economists (Princeton, 1992). Short and widely used in economics programmes. 📘 Textbook. Martin Osborne, An Introduction to Game Theory (Oxford). A fuller undergraduate treatment with many worked games. 📘 Gentler. Avinash Dixit and Barry Nalebuff, The Art of Strategy (Norton, 2008), and Robert Axelrod, The Evolution of Cooperation (1984). Real cases, almost no algebra. 🌐 Free course. Open Yale Courses ECON 159: Game Theory (Ben Polak, 24 lectures, recorded Fall 2007), covering Nash equilibrium, backward induction and signalling. The takeaway When your best move depends on others' moves, look for dominant strategies, then for equilibria, and remember that a stable outcome can be a bad one. Repetition, commitment and well-designed rules are the three ways out, and each is a way of changing the game rather than the players. Try this: this week, spot a situation where you and someone else are each waiting for the other to move first or to give in, and ask what the payoff grid looks like and whether it is a game you can change. Sources & Further Reading Sources. Dominance, Nash equilibrium, mixed strategies, backward induction and the second-price result are standard textbook game theory (Gibbons; Osborne; Polak's Yale lectures). The prisoner's dilemma was devised by Flood and Dresher at RAND in 1950 and named by Tucker (Wikipedia, "Prisoner's dilemma"). Nash, "Equilibrium points in n-person games," PNAS 36, 1950; the 1994 economics Nobel prize went to Nash, Harsanyi and Selten. Axelrod's tournaments (c. 1980) and 1984 book: tit for tat, by Anatol Rapoport, won both; matches were 200 moves; the death-spiral under noise and generous tit for tat are as described in Wikipedia's "Tit for tat". Schelling, The Strategy of Conflict (1960). The second-price auction was described by Vickrey in 1961 and used by stamp collectors from 1893. The FCC has held spectrum auctions since July 1994 using a simultaneous multiple round design; the UK's 2000 auction raised £22.5 billion from five 3G licences (Wikipedia, "Spectrum auction"). The 2020 prize went to Milgrom and Wilson, the 2012 prize to Roth and Shapley. Kidney exchange history from Wikipedia's "Kidney paired donation"; Roth, Sönmez & Ünver, "Kidney Exchange," QJE 2004. Every number an interactive shows was computed in node from the code on this page: ten-round best score against tit for tat 32, against always-defect 10, against always-cooperate 50; the four-bidder first-price optimum is near 0.74 (theory 0.75); the average winning price is near 60 in both formats; the toy tournament's ranking depends on the chosen field and is not Axelrod's result. 🌐 Open Yale Courses ECON 159 Game Theory 📘 Dixit & Nalebuff, The Art of Strategy 📘 Axelrod, The Evolution of Cooperation Step 17. Biological Psychology: The Wet Machine Behind the Mind --------------------------------------------------------------- Why: The nervous system, from the psychology side. Every thought, mood and night's sleep is made of cells that fire or stay quiet, chemicals that drift across a gap twenty nanometres wide, and blood flow that scanners can see. The course teaches what that does and does not explain. .chips button{min-width:0} .row2{display:flex;gap:8px;flex-wrap:wrap} .row2 button{flex:1 1 90px;min-width:0} .legend{font-family:-apple-system,sans-serif;font-size:.8rem;color:var(--muted)} .brainmap circle{cursor:pointer;stroke:var(--ink);stroke-width:1} Strike a funny bone and your arm jerks before you decide anything. Drink a coffee at four in the afternoon and you lie awake at midnight. A blow to the head changes a person's memory or temper. Someone stops taking a medicine and their mood shifts. In each case something happened in tissue, and something happened in experience, and the two cannot be pulled apart. Biological psychology is the course where psychologists meet that fact. Its job is not to explain the mind by pointing at the brain. It is to learn what the tissue does, in what units, at what speed, and, just as important, which popular stories about "the chemical for love" or "the part of the brain for fear" are too neat to be true. The course in one box Who takes itEvery psychology major, usually in year 1 or 2. Neuroscience, nursing, medicine, biology and pharmacy students take a deeper cousin. The British Psychological Society lists biological psychology among its core areas, and the APA guidelines expect undergraduates to link behaviour to its biological basis. What it is forConnecting what people do and feel to the signalling of nerve cells, hormones, and the body that carries them. Comes afterNo psychology prerequisite; school biology helps. Leads toSensation & Perception (35/21), then Cognitive Psychology (35/22), and Clinical Psychology (35/27), where the chemistry of disorders and drugs comes back. What this piece gives youYou will not be able to read a brain scan. You will see how a neuron decides, why "dopamine is the pleasure chemical" is wrong, what a brain image can claim, and how sleep and learning work. Easier first reads: Why You Feel Before You Think (01/01), Sleep Is a Skill (01/04) and Dopamine Is Not the Pleasure Chemical (01/08). This one goes further. Descriptive only, not medical advice. The neuron: a cell that fires or stays quiet The human brain holds about 86 billion neurons, according to a careful 2009 count that replaced the round "100 billion", along with a roughly equal number of supporting cells. A neuron is a cell that collects inputs and, when enough arrive, sends a brief electrical pulse down its fibre. At rest its inside sits about 70 millivolts below the outside. If inputs push it up to about −55 mV, the threshold, channels open, sodium rushes in, and the voltage swings to roughly +30 mV for about a millisecond before resetting. That pulse is the action potential. Alan Hodgkin and Andrew Huxley worked out its mechanism in 1952 on the giant axon of a squid, and shared a Nobel Prize for it in 1963. Two facts matter more than the details. First, it is all or none: a neuron cannot fire a weak spike. A stronger input does not make a bigger pulse, it makes pulses come more often. The rate is the message. Second, the spike travels along the fibre, and fatty myelin wrapped around it makes the signal jump, so speeds reach roughly 100 metres per second in the fastest fibres, against about a metre per second in thin unwrapped ones. C dV/dt = −(V − Vrest)/R + I, and fire when V reaches thresholdthe leaky integrate-and-fire neuron: input charges it, it leaks back, and a spike resets it Interactive · One neuron deciding Steady input (voltage it would reach) A textbook model, not a real cell: time constant 20 ms, rest −70 mV, threshold −55 mV, 2 ms refractory period. Input is the voltage above rest that the cell would reach if it never fired. Below 15 mV of drive, nothing happens, however long you wait. At 20 mV the cell fires about 34 times a second; at 40, nearly 90. The size of every spike is identical. This is the brain's coding trick: not louder, but faster. The synapse: chemical messages, and the myths about them Neurons do not touch. They are separated by a gap about 20 nanometres wide, the synapse, and the signal crosses it as chemistry. Otto Loewi showed in 1921, with two frog hearts, that a nerve releases a substance rather than just a current. When a spike arrives, the cell releases a neurotransmitter, which binds receptors on the next cell and nudges it toward firing (excitation) or away from it (inhibition). Then the leftover is cleared: pumped back (reuptake) or broken down. In the brain, glutamate is the main excitatory transmitter and GABA the main inhibitory one. Pop psychology turns each transmitter into a mood: dopamine is pleasure, serotonin is happiness, oxytocin is love. The truth is messier. Dopamine neurons fire strongly for unexpected rewards and cues, a "better than expected" signal, which is why they matter for learning and wanting, and not simply for enjoying. Most of the body's serotonin sits in the gut, not the brain. Oxytocin does affect social behaviour, but results from squirting it up the nose have been inconsistent, and many early findings shrank as samples grew. One transmitter plays many roles in different circuits; one behaviour uses many transmitters. Interactive · Release, clearing and a reuptake blocker Normal clearing Reuptake blocked (SSRI-style) Presynaptic firing rate Reuptake activity A toy model in arbitrary units: each spike adds one unit; the gap clears at a rate of 10 + 50 × reuptake per second. With full reuptake, a 10 Hz neuron keeps the gap at about 0.16 units; block 80% of reuptake and the level triples to 0.5. That is, roughly, what drugs like SSRIs do within hours. Yet their effect on mood takes weeks, and the slogan "depression is a chemical imbalance" is a simplification that psychiatrists themselves avoid. A 2022 review argued there is no consistent evidence that low serotonin causes depression; others replied that this was never the standard claim and that the drugs still beat placebo on average (a large 2018 comparison of 21 antidepressants found all outperformed placebo, with modest average effects). What can be said: transmitters matter, the story is not one chemical, and no one should change a medicine because of a diagram. Talk to a prescriber. Hormones are the slow cousin. Glands release them into the blood and they act over minutes to days: cortisol, from a chain called the HPA axis, prepares the body for demands; adrenaline acts in seconds. A nerve impulse reaches your foot in a few hundredths of a second; a hormone takes minutes. Two systems, two timescales. The brain's map: what parts do, and what they do not Where things happen in the brain is one of the oldest questions. In 1848 railway foreman Phineas Gage survived an iron bar through the front of his skull, and accounts say his behaviour changed (the details were exaggerated in retelling). In 1861 Paul Broca examined a man who could understand speech but say almost only one syllable; the damage was in the left frontal lobe. In 1953 surgeons removed parts of Henry Molaison's temporal lobes to treat epilepsy; he could no longer form new lasting memories of events, yet he could still learn a new motor skill. Cases like these show that some functions depend on particular tissue. Do not conclude that each part has one job. Functions are networks: damage to one place can break a skill that many places share. Three myths to drop. We do not use 10% of the brain; imaging shows activity throughout, and the brain, about 2% of body weight, uses around a fifth of the body's resting energy. "Left-brained" and "right-brained" people do not exist; a 2013 analysis of over 1,000 scans found no person-wide dominance, although the two halves do specialise a little (language is usually left). And the neuron count is lopsided: the cerebellum, tucked under the back of the brain and often thought of as just for coordination, holds roughly 80% of the neurons. Interactive · If this part is damaged… A cartoon, not an atlas. Pick a region or tap its circle. Deficits are textbook summaries of famous cases and vary by person. Brain imaging: what a scan can and cannot show A scan of the brain is not a photograph of thinking. MRI shows structure. fMRI measures the blood-oxygen signal (BOLD): active neurons use oxygen, blood flow rises a few seconds later, and the scanner sees the change. So it is indirect, slow (seconds) and blurry (millimetres), whereas EEG catches the brain's electrical rhythms in milliseconds but cannot say precisely where they come from. Neither shows a thought, and neither shows cause. For that you need a lesion, a drug, or brain stimulation. The classic warning is a dead Atlantic salmon. In 2009 Craig Bennett and colleagues put one in a scanner, "showed" it photographs of people, and found voxels (3D pixels) that lit up, because with tens of thousands of voxels, each tested at p < .05, some pass by chance. They used it to argue for corrections for multiple comparisons, and it won an Ig Nobel Prize in 2012. Two related traps: "reverse inference" (the amygdala was active, therefore the person felt fear: it is active in many states) and tiny samples. A 2022 study by Scott Marek and colleagues found that linking brain scans to behaviour in the general population needs thousands of people, not the dozens typical of older studies. Interactive · A scan of nothing p < .05p < .01p < .001 No correctionCorrected for all voxels Voxels in the scan Every voxel is pure noise. The grid shows 2,000 of the voxels; the readout counts them all. Bonferroni correction divides the threshold by the number of tests. With 50,000 voxels at p < .05 you expect 2,500 false "activations". Uncorrected, a scan of nothing finds a brain at work. Correcting the threshold for 50,000 tests keeps the chance of any false alarm near 5%. Modern studies correct, share data and replicate; but an old headline of the "this region lights up when…" kind deserves the same suspicion as any small study (see Research Methods in Psychology, 35/19). Sleep: a pressure that builds and a clock that ticks Sleep is not the brain switching off. Over a night it cycles about every 90 minutes through lighter and deeper stages and REM sleep, discovered in 1953 by Eugene Aserinsky and Nathaniel Kleitman, when the brain is highly active and most vivid dreams occur. A 2015 expert consensus recommended that adults regularly sleep at least seven hours; needs vary between people and across life, and no single "right" number fits everyone. The standard picture, proposed by Alexander Borbély in 1982, is the two-process model. Process S is a sleep pressure that rises the longer you are awake and drops during sleep (adenosine is a leading candidate for part of it, which is why caffeine, an adenosine blocker, delays sleepiness without removing the debt). Process C is the circadian clock, set mainly by a tiny region called the suprachiasmatic nucleus and by light, which makes you more alert at some hours than others. You feel sleepy when S is high and C is low. Jet lag and shift work are C and S out of step. Interactive · Pressure against the clock Sleep each night Bedtime Schematic model after Borbély, with rise time 18.2 h and fall time 4.2 h as in early human fits, scale 0 to 1. The circadian curve is a simple wave peaking at 18:00. Illustrative, not a prediction for any person. With 8 hours' sleep and bed at 23:00, pressure at waking falls to about 0.09 of the scale and ends the day near 0.62. Cut sleep to 5 hours and the morning level only gets down to about 0.22: you begin each day with leftover debt, and it does not clear itself overnight. Plasticity: the brain is rewired by use In 1949 Donald Hebb proposed that when one cell repeatedly helps to fire another, the connection between them strengthens. The slogan "cells that fire together wire together" is a later paraphrase. The effect, called long-term potentiation, was shown in rabbit hippocampus by Tim Bliss and Terje Lømo in 1973. It is the leading model of learning: experience changes connection strengths, not the number of cells. Interactive · A Hebbian cell Input A already drives the cell. Input B is too weak alone. Present them together and watch B's connection grow. Present A + BB aloneA aloneReset Rule: when the cell fires, each active input's weight w grows by 0.2 × (1 − w). The cell fires when the summed active weights reach 0.5. Cartoon of the Hebb rule, not a cell model. After three pairings B alone crosses the threshold. The adult brain stays plastic in far larger ways: in a 2000 study, London taxi drivers who had passed the demanding street test had a larger posterior hippocampus than controls, in proportion to years of driving. But claims that new neurons keep forming in adult humans are disputed. Two 2018 papers, one finding almost no new cells in adult hippocampus and one finding plenty, are still argued over. What is solid is that the brain changes with use throughout life, more in youth, and less than the popular word "rewiring" suggests. What a graduate just sees A neuron's message is a rate of identical spikes, not a loudness. Transmitters have many jobs. "The pleasure chemical" and "the chemical imbalance" are slogans. Nerve signals are fast and local; hormones are slow and body-wide. Functions run on networks, so a lesion shows what a region is needed for, not that it holds the skill alone. A brain scan is an indirect, slow, noisy measure and needs statistical care before it says anything. "We use 10% of the brain" and "left-brained people" are myths. Sleep pressure and the body clock are separate and add up to how awake you feel. Learning changes connection strengths, and use shapes the brain across life. Where it shows up next Sensation & Perception (35/21): how receptors turn light and sound into those spikes, and what the cortex does with them. Cognitive Psychology (35/22): memory and attention, and where the lesion cases above matter again. Clinical Psychology (35/27): mood, anxiety and psychosis, medication and therapy, where the transmitter story and its limits come back. Machine learning (34/32): artificial networks borrow the idea of weights strengthened by experience, loosely. In the world: caffeine and shift work, sleep clinics, brain-imaging headlines, anaesthesia, rehabilitation after stroke, and the question of how far any drug can explain a mood. If you want to go deeper 📘 Textbook. James Kalat, Biological Psychology (Cengage, 14th edition). Written for psychology majors; the common choice. 📘 Textbook. Mark Bear, Barry Connors and Michael Paradiso, Neuroscience: Exploring the Brain (Jones & Bartlett / Wolters Kluwer). More depth for neuroscience-leaning readers. 📘 Gentler. Oliver Sacks, The Man Who Mistook His Wife for a Hat (1985): case histories that make the lesion cases human. 🌐 Free course. MIT OpenCourseWare 9.01 Introduction to Neuroscience (Fall 2007). Also the introduction in 9.00SC Introduction to Psychology. The takeaway The mind runs on cells that signal by firing rate, chemicals that cross a gap, hormones that travel slowly, and connections that change with use. That is a powerful picture and a limited one: slogans about single chemicals or single brain regions, and strong claims from small brain scans, need the same scepticism as any psychological finding. Try this: this week, notice a mood shift (after poor sleep, a late coffee or a skipped meal) and think of the two layers: what the tissue is doing, and what you are feeling. Neither explains the other alone. Sources & Further Reading Sources. Action potential and leaky integrate-and-fire model: standard textbook (Kalat; Bear et al.); Hodgkin & Huxley (1952), Nobel 1963. Neuron count: Azevedo et al., Journal of Comparative Neurology (2009): about 86 billion neurons, about 80% in the cerebellum. Loewi (1921). Reward prediction error: Schultz, Dayan & Montague, Science (1997). Antidepressants: Cipriani et al., The Lancet (2018); Moncrieff et al., Molecular Psychiatry (2022), with published replies. Gage (1848), Broca (1861), Molaison (1953, Scoville and Milner). Left/right brain: Nielsen et al., PLoS ONE (2013). Dead salmon: Bennett et al. (2009); Ig Nobel 2012. Marek et al., Nature (2022). REM: Aserinsky & Kleitman (1953). Sleep duration: Watson et al., consensus statement, Sleep (2015). Two-process model: Borbély (1982); Daan, Beersma & Borbély (1984). Hebb (1949); Bliss & Lømo (1973). Maguire et al., PNAS (2000). Adult neurogenesis: Sorrells et al. and Boldrini et al., both 2018. Simulated numbers are toy models computed live. This is descriptive, not medical advice. If you are struggling, a doctor or local helpline (findahelpline.com) can help. 🌐 MIT OCW 9.01 Introduction to Neuroscience 🌐 MIT OCW 9.00SC Introduction to Psychology 📘 Kalat, Biological Psychology 📘 Sacks, The Man Who Mistook His Wife for a Hat