Morphogen gradients

How does a sheet of identical cells decide which of them becomes a finger and which becomes the gap beside it?

A limb bud is a paddle of cells that are, as far as anyone can tell, equivalent. Days later some are cartilage in the middle of a finger and their immediate neighbours are the gap beside it, with nothing outside the bud having told them which was which. The standard answer is that a chemical gradient supplies each cell with its coordinates — and that answer is right about half of this problem and quietly wrong about the other half, which is the interesting part.

Take the coordinate idea seriously first. Suppose a small group of cells at one edge makes a diffusible molecule steadily, and that the molecule is broken down everywhere at a constant rate. At steady state, production, spreading and destruction balance, and the concentration falls off exponentially with distance from the source, with a characteristic length equal to the square root of the diffusion coefficient divided by the decay rate.

That expression is worth putting numbers into, because it tells you what a gradient can and cannot do. A signalling protein picking its way through tissue, repeatedly binding and releasing, moves at something like one square micrometre per second — an order of magnitude, not a measurement. Give it a half-life of an hour, so the decay rate is 0.693 divided by 3600 seconds, about 1.9 x 10^-4 per second. The square root of 1 divided by that is close to 72 micrometres: call it seven cell diameters. So a gradient of this kind is a short-range instrument. It can partition a field a few dozen cells wide. Ask it to specify position across a millimetre and the concentration difference between neighbouring cells sinks beneath the noise in making and reading it.

Given a gradient, how would a cell use it? By thresholds: respond one way above a high level, another way between two levels, another way below. That is the classic picture, and it is genuinely how some things work. In the fly embryo a maternal gradient partitions the future body axis, and adjacent nuclei distinguish concentration differences of roughly ten percent — close to the limit that counting molecules allows, a figure I am recalling rather than deriving. In the vertebrate neural tube, a gradient from the floor plate assigns distinct neuron types at different heights.

The evidence that a source really is instructive is a sufficiency experiment, not a correlation. Graft the small posterior region of a limb bud to the anterior edge and the limb develops a mirror-image set of digits. Replace the graft with a bead soaked in the signalling protein it makes and you get the same duplication. Something released from a point is being read at a distance as position.

So why is the coordinate story only half the answer? Because of what the question actually asked: finger, gap, finger, gap. A monotonic gradient falling smoothly from one edge does not have stripes in it. To get periodicity from thresholds alone you would need a separate threshold for every digit and every gap, each calibrated against a concentration that varies with the animal's size, its temperature and the hour — and the number of digits would then track the concentration. It does not. Digit number can be raised by reducing the dose of certain patterning genes, which is not what a concentration-reading device does.

What does produce repeating stripes is a different kind of mechanism entirely: a locally self-activating, laterally spreading inhibitory pair of signals — reaction and diffusion — whose intrinsic wavelength sets the spacing, with a cartilage-promoting factor and its antagonists behaving like such a system in the digit field. On this account the gradient is not drawing the fingers. It is setting the frame — which end is thumb, how wide the field is, how long it keeps growing — while the periodicity comes from the tissue organising itself. The hybrid is the current position and it is still argued over, so I would state it as the best-supported reading rather than a settled one.

A neighbouring mechanism is worth naming to keep the two apart. Lateral inhibition — cells that take a fate suppressing it in whoever they touch — also produces reliable patterns, and produces spacing without ever specifying position. A gradient does the opposite: it specifies position without producing spacing. The digit field appears to need both, which is precisely why neither account alone has ever closed the case.

Two refinements, then. Cells often integrate the signal over time rather than reading an instantaneous level, so exposure duration carries information alongside concentration — which loosens the demand for exquisite precision. And a gradient whose own signalling accelerates its degradation adjusts its length constant as a tissue grows, which is one way patterns scale with body size, though not the only proposal.

The claims are separable and each can be broken. If the source is instructive, an ectopic source must repattern the field — and a graft that produced no duplication at all would end the positional account for the limb. If periodicity is self-organised, then perturbing the presumed wavelength should change the number of digits while leaving the field's polarity intact, which is what reducing the relevant gene dose does. The refuting observation for the hybrid is a clean one: digit number tracking the concentration of the posterior signal monotonically, with spacing unaffected by anything that alters the reaction-diffusion pair, would send the whole pattern back to threshold-reading and make the self-organising component unnecessary.

• How a reaction-diffusion wavelength is measured in real tissue, and what evidence separates it from a prepattern.
• Why some patterns scale with body size and others do not, and what self-enhanced degradation contributes.

Every term the collection defines is gathered in the glossary.