Everything alive is built from cells, and the interesting part of that sentence is that it is a discovery rather than a definition.
This subject assumes nothing beyond ordinary school science: that matter is made of atoms, that a chemical reaction rearranges them, and that energy is conserved. Everything else is built here. Where a piece of chemistry or physics is needed, it is derived at the point of use rather than assumed.
Three claims, each of which had to be earned
Robert Hooke put a shaving of cork under a compound microscope in 1665 and saw a honeycomb of empty boxes. He called them cells, after the small rooms of a monastery, and he counted them: sixty across a span of one eighteenth of an inch, which makes each box a thousand and eightieth of an inch across, which makes a cubic inch of cork contain of them. He was looking at the dead cell walls of a plant, not at anything living, but the number is the first honest measurement in the subject.
Antonie van Leeuwenhoek, grinding single lenses in Delft, went further in the 1670s and saw things that moved. His letters to the Royal Society describe bacteria from his own dental plaque, protists in pond water, and sperm cells. Nobody could reproduce his lenses for a century, which is why his observations were doubted, and it is worth noticing that the first person to see a living cell was believed largely on the strength of his reputation for care.
The generalisation took another one hundred and sixty years and arrived in three parts. Matthias Schleiden argued in 1838 that all plant tissue is cellular, and Theodor Schwann extended it to animals in 1839, which is the claim that everything alive is made of cells. Schwann then got the second part badly wrong: he thought cells crystallised out of a formless fluid. Rudolf Virchow supplied the correction in 1855 with the slogan omnis cellula e cellula, every cell from a cell, and Louis Pasteur turned it from a slogan into an experiment. His swan-necked flasks, reported from 1859, held sterile broth open to the air indefinitely, because dust settled in the bend of the neck and never reached the liquid. Tip the flask so that the broth touched the dust and it clouded within a day.
So the cell theory is three separate empirical claims: living things are made of cells, the cell is the smallest unit that is itself alive, and cells arise only by the division of existing cells. None follows from the others. The third is the one that matters most for this course, because it means that the machinery inside a cell is never built from scratch. It is always inherited, running, from a cell that was already running.
Why life is packaged at all
A cell is a bag, and it is worth asking what the bag buys. The answer is that every living thing maintains a chemical composition different from its surroundings, and a difference in composition is only meaningful if there is a boundary across which it exists.
The numbers are not subtle. Human blood plasma carries about 5 mM potassium and 145 mM sodium. The inside of a human cell runs the ratio backwards, roughly 140 mM potassium and 12 mM sodium. Seawater is about 10 mM potassium. A cell is not in equilibrium with anything, and a system that is not in equilibrium with its surroundings is either being held there or is relaxing towards it. Life is the first case, permanently, which means it costs something permanently.
That is the whole architecture of the subject in one sentence. A boundary makes the difference possible, machinery in the boundary maintains it, and the maintenance has to be paid for. The next five lessons are the boundary and the payment.
The physics that sets the size
Nothing so far says how big a cell can be. That is set by diffusion, and diffusion has a property that is easy to state and easy to underestimate: the time it takes grows as the square of the distance.
A molecule in solution is knocked about by collisions and performs a random walk. The mean square displacement after time in one dimension is , where is the diffusion coefficient, so the time to cover a distance is
For a small metabolite in water is about m²/s, and cytoplasm is a few times slower than water because it is crowded. Put numbers in. Over 1 µm, the length of a bacterium, s, one millisecond. Over 100 µm, a large animal cell, it is 10 s. Over 1 mm it is 1000 s, about seventeen minutes. Over 1 m it is s, which is thirty-two years.
That is the constraint. A bacterium can run its entire chemistry on diffusion alone, with no transport system at all, because everything inside it meets everything else a thousand times a second. A millimetre of undifferentiated tissue cannot. The quadratic term means the penalty for growing is not proportional but brutal: ten times the radius is a hundred times the mixing time, while the volume that has to be supplied has gone up a thousandfold and the surface available to supply it only a hundredfold. The ratio of surface to volume for a sphere is , so a cell of radius 1 µm has ten times the membrane per unit of contents that a cell of radius 10 µm has.
Example. A ball of cells 1 mm across grows in culture with no blood supply. Using the diffusion law above, argue from the numbers whether its centre can be fed, and say what you would expect to find there.
The centre is 0.5 mm from the surface, so a small nutrient molecule needs s to arrive, about four minutes. That does not sound fatal, and taken alone it is not: diffusion delivers, slowly. The killer is that every cell on the way consumes as the molecule passes, so the concentration falls with depth and the supply reaching the centre is what is left over. Real tumour spheroids show exactly this: a proliferating outer shell about 100 to 200 µm thick, a quiescent layer beneath it, and a necrotic core. The threshold sits near the distance oxygen can travel while being consumed, which is why capillaries in tissue are spaced tens of micrometres apart rather than millimetres. The general lesson is that diffusion sets a supply radius, and any organism that wants to be bigger than that radius has to invent plumbing.
Now you. A motor neuron in your spinal cord has an axon reaching a metre to your foot. The diffusion law says a protein made in the cell body would take decades to arrive. What must be true for such a cell to work at all?
Answer
Two things, and both are real. First, the cell cannot rely on diffusion for delivery, so it must move material actively: motor proteins walk cargo down microtubule tracks at roughly 1 µm/s, which covers a metre in about twelve days rather than thirty years, and that is exactly what axonal transport is. The eventual mechanism, kinesin taking eight nanometre steps for one ATP each, is the subject of a later lesson. Second, the cell cannot signal by diffusion either, which is why a nerve impulse is not a chemical travelling down the axon but a voltage change propagating at up to 100 m/s, using ion gradients the next two lessons build. The neuron is not an exception to the diffusion limit. It is an object built entirely out of ways around it.
One bacterium, counted
Take Escherichia coli, the best-quantified organism on the planet. A cell is a rod about 2 µm long and 0.8 µm across, so its volume is µm³, which is litres, one femtolitre. Roughly seventy per cent of that is water.
Inside it are about three million protein molecules of some four thousand different kinds, with a mean mass near 40 kDa. Check that against the volume: daltons, at g per dalton, is g in litres, which is 200 g per litre. That is a strikingly high figure. Cytoplasm is not a dilute solution, it is closer in consistency to a thick syrup, and the crowding is dense enough to change reaction rates and to be one reason diffusion inside a cell is slower than in water.
The genome is a single circular DNA molecule of 4,641,652 base pairs in the standard K-12 strain. At 0.34 nm per base pair that is nm mm of DNA, packed into a cell 2 µm long, a ratio of about 790 to 1. A human cell is worse: 6.4 billion base pairs is 2.2 m of DNA folded into a nucleus around 6 µm across. Any account of how DNA works has to explain how a molecule that long is stored, and how a polymerase finds one specific spot on it.
Example. An E. coli cell in rich medium divides every 20 minutes. Using the three million proteins above, work out how fast it builds protein, and then estimate how many ribosomes that requires if each one adds twenty amino acids per second.
To double, the cell must make three million proteins in 1200 s, which is complete proteins per second. At a mean length of 300 amino acids that is peptide bonds per second. A ribosome working flat out at twenty residues per second therefore supports of them, so the cell needs something like forty thousand ribosomes. Measured counts for fast-growing E. coli run from about 45,000 to 70,000, so an estimate built from two textbook numbers lands within a factor of two of the real thing. That agreement is worth more than either number alone: it says the picture is roughly right, and it says translation is not a minor activity of a cell but its single largest construction project.
Now you. The same cell contains about 4,000 kinds of protein but only one copy of its genome. What does that force to be true about how genes are used?
Answer
A single template has to serve every copy, so the gene cannot be consumed by being read. Reading must be non-destructive and repeatable, which rules out any scheme where the gene is converted into the product. It also means the gene is a bottleneck: with three million protein molecules and one copy of each gene, the average gene has been read out into hundreds or thousands of products, so there must be an amplifying intermediate between the gene and the protein rather than a one-to-one correspondence. That intermediate is messenger RNA, and the fact that its existence can be argued for from a counting argument, before any experiment, is a good sign that the eventual experiment was looking for something real.
Two ways of building a cell, and one thing they share
Cells come in two architectures. A bacterial cell has its DNA loose in the cytoplasm and no internal membranes to speak of. A eukaryotic cell keeps its DNA inside a nucleus and is filled with membrane-bounded compartments: mitochondria, endoplasmic reticulum, Golgi, lysosomes. It is also far larger. A typical animal cell of 15 µm diameter has a volume near 1800 µm³, roughly two thousand times a bacterium, and a plant or fungal cell larger still.
The old division into prokaryote and eukaryote hides something important. Carl Woese, comparing ribosomal RNA sequences in 1977, found that the organisms lumped together as bacteria are two groups as different from each other as either is from us. Bacteria and archaea look alike under a microscope and are not close relatives. "Prokaryote" is therefore a statement about what a cell lacks, which is a poor basis for a category, and it survives because it is useful shorthand rather than because it names a natural group.
What all three domains share is the striking part, and it is the reason this subject exists. Every cell yet examined is bounded by a lipid bilayer, stores its inheritance as double-stranded DNA, reads it into RNA and then into protein by ribosomes built of RNA, uses very nearly the same genetic code, and pays for its chemistry with adenosine triphosphate. That common core is why one course can be about "the cell" rather than about a catalogue of organisms.
Where the theory frays
An honest course names the exceptions early. A mature human red blood cell has ejected its nucleus and contains no DNA at all, so it cannot divide and cannot be the origin of another cell; it is a cell by descent rather than by capacity. A skeletal muscle fibre is a single cell up to 30 cm long containing hundreds of nuclei, formed by cells fusing, which makes the boundary of "one cell" a matter of definition. Fungal hyphae are often similarly continuous. Thiomargarita magnifica, described in 2022, is a bacterium up to 2 cm long, visible without a microscope, which manages the diffusion problem by confining almost all its volume to a fluid-filled vacuole so that the living layer stays thin.
Viruses fail the theory outright. A virus has a genome and a protein coat, no membrane of its own in many cases, no ribosomes, no metabolism, and reproduces only by commandeering a cell. Whether it is alive is a question about the word rather than about the virus, and the useful version of the question is what the minimum equipment for autonomous life turns out to be: a boundary, a genome, ribosomes, and a way of making ATP. That list is the syllabus of this course.
Example. A colleague says the cell theory is circular, since a cell is defined as the unit of life and life is defined as being made of cells. Is the objection fair?
Not really, and seeing why is worth the effort. The theory makes claims that could have come out false and did not. It could have turned out that tissue is a continuous substance in which nuclei are scattered, which is what the reticular theory of the nervous system asserted until Cajal's staining showed neurons to be separate cells. It could have turned out that cells form spontaneously from broth, which is what Schwann believed and Pasteur disproved with an experiment anyone can repeat. It could have turned out that different tissues are built on different principles. Each is a real alternative that was defeated by evidence, which is the mark of a claim with content. The definitional element is real but small: the boundary cases above show that "one cell" sometimes has to be stipulated. Stipulating a boundary at the edges is not the same as assuming the answer in the middle.
Now you. A giant amoeba and an ostrich egg are both single cells far larger than the diffusion limit suggests. Before reading on, say what you would look for in each to explain how they manage.
Answer
Look for either active stirring or an inert bulk. Large amoebae and plant cells take the first route: cytoplasmic streaming, driven by motor proteins along actin filaments, physically circulates the contents so that transport is bulk flow rather than diffusion, and a slow current across a millimetre beats diffusion easily. An ostrich egg takes the second: most of its volume is stored yolk, chemically inert, and the living cytoplasm and nucleus occupy a small disc a few millimetres across on its surface. The same trick appears in Thiomargarita, where a vacuole fills the middle. The general rule is that no cell escapes the diffusion law, so a large one either pumps its contents around or arranges for most of its volume not to be alive.
Everything in this lesson depended on there being an inside and an outside, and nothing in it said what the boundary is made of. That turns out to be answerable with an experiment from 1925 involving red blood cells, acetone and a trough of water, and the answer sets up the central difficulty of the next several lessons: the boundary that makes a cell possible is almost perfectly impermeable to the things a cell needs.