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.
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.
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.
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:
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).
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.
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.
| Feature | Bacterium | Animal cell |
|---|---|---|
| Typical size | 1 to 5 µm | 10 to 100 µm |
| DNA | mostly one ring, in the cytoplasm | several chromosomes, in a nucleus |
| Energy | across the cell's own membrane | mostly inside mitochondria |
| Compartments | few or none | many 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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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. 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.