One genome, hundreds of cell types — and a geometry problem that decides how big any of them is allowed to get.
Every cell in your body carries the same instructions. A neuron and a red blood cell differ only in which pages are open.
After fertilisation, cells divide without specialising. Then signal gradients across the early embryo switch different genes on in different places — position becomes identity.
Divide endlessly, and differentiate along different pathways. Adult niches like bone marrow and hair follicles keep them, or push them to proliferate and develop.
Totipotent (any cell, incl. placenta) → pluripotent (any body cell) → multipotent (a related family). Adult marrow is multipotent.
Green narrows to pink. Early embryonic cells can make anything, including the placenta; by the blastocyst stage the inner cell mass can make any body cell but not the placenta. Adult marrow stem cells are boxed into one lineage — blood — but still divide for a lifetime.
Two fates in one ball. By day five the zygote's descendants have already sorted into two populations: an outer trophoblast that will build the placenta, and an inner cell mass that will build everything else. Embryonic stem cells are inner-cell-mass cells — which is exactly why harvesting them is contested.
An inherited macular degeneration: a mutation impairs energy transport in retinal cells and they die. Trials inject retinal cells derived from embryonic stem cells to replace them.
Dopamine-secreting cells in the midbrain die, so movement becomes slow, rigid and tremulous. Trials replace them with dopamine-producing neurons grown from stem cells.
Embryonic cells are pluripotent but harvesting them destroys a blastocyst. Adult cells avoid that but are only multipotent. Is an unimplanted embryo a person, a potential person, or neither? Decide before the debate, then argue the other side.
Supply crosses a surface. Demand fills a volume. Those two scale differently, and the mismatch sets a ceiling on cell size — unless you cheat with shape.
Sperm ~5 µm, red cells 7–8 µm, an ovum ~120 µm, a muscle fibre up to 12 cm, a neuron over 1 m long but only ~10 µm wide. Size is itself a specialisation.
Double the side and surface area goes ×4 while volume goes ×8. For a cube, SA : V = 6 / L. The ratio halves every time you double the size.
Exchange depends on area; need (metabolism, heat, waste) depends on volume. When the ratio falls too far, the centre starves — so cells divide.
Long is allowed, fat is not. The giants on this line are long and thin: a neuron a metre long is still only ~10 µm wide, so no point inside it is far from a membrane. The muscle fibre gets away with 20–100 µm across only by having many nuclei spread along it.
Drag the slider. The shaded shell is the depth diffusion can serve in a given time — it stays the same thickness however big the cube gets. Watch what fraction of the inside it reaches.
Same rules as the agar cubes. In the phenolphthalein practical, the 0.3 cm block turns fully in seconds and the 1 cm block takes minutes — not because the acid moves slower, but because the centre is further away and there is less surface per unit of volume to bring it in.
Phenolphthalein agar goes clear as acid diffuses in. Enter the time each cube took to change completely; the bench does the geometry and plots ratio against time.
Temperature (kinetic energy), steepness of the gradient, and size of the particle. Small non-polar molecules (O₂, CO₂) cross membranes freely; ions and large polar molecules need help.
Acid moves at the same speed into every cube. The big cube takes longer because its centre is further away and there is less surface per unit volume to bring acid in.
| Side / cm | SA / cm² | V / cm³ | SA : V | Time to clear / s |
|---|
For the conclusion. As SA:V increases, time to clear falls — exchange is faster per unit of volume. Evaluate it too: cubes aren't spheres, "completely clear" is a judgement call (± several seconds), and the acid gradient falls as it is used up.
Flatten, fold, or grow microvilli — every trick is a way of buying membrane area without buying volume. Then two pairs of cells whose shapes are their jobs.
Tap a node to light up its links. The pink dashed link joins the two halves of this lesson.
Drag a term into a gap, or tap a term and then tap a gap. Two terms belong nowhere.
Single best answer. You get the reasoning as soon as you commit. HL items are marked.