Canalisation

What this actually is

Every plant in this window is grown by simulating one molecule: auxin, the hormone that tells plant cells where to become things. Cells pump it at each other through PIN proteins sitting in their walls. That is the entire mechanism.

The trick is that a cell has two ways to decide which wall to put its pumps on, and it chooses between them based on how much auxin it is holding:

Up-the-gradient polarisation makes auxin pile into isolated maxima. On the growing tip, each maximum becomes a leaf — and because each one drains the tissue around it, the next can only appear in the gap left over. That competition, not any rule, is what produces the divergence angle in the top right. It is measured off the plant while you watch, never assigned.

With-the-flux polarisation does the opposite: flux begets more flux, so diffuse flow collapses into narrow canals. Run it in a leaf blade with sources near the margin and a sink at the stalk, and it carves a vein network. The bright filaments in every frond were canalised, edge by edge, from a blank sheet of cells.

Two shapes, one mechanism, separated by a threshold. That unification is the claim made by Bayer and colleagues (2009) and Cieslak and colleagues (2019); the up-the-gradient half follows Smith and colleagues (2006), the canalisation half goes back to Sachs (1969) and Mitchison (1980).

Things worth trying: push meristem growth up and watch the phyllotaxis reorganise; drop transport until the maxima stop forming and the plant runs out of leaves; cut the apex and watch a dormant bud take over, because the auxin that was suppressing it is gone.

Where it falls short, and what I tried

Real shoot meristems settle onto 137.5° far more tightly than this one does. Here the angle wanders — the readout shows the spread, and it is the number this tissue is actually producing, not one it has been nudged toward. Two experiments went looking for the reason.

Was the inhibition too short-ranged? An organ's inhibition reaches about √(D/μ) ≈ 4.5 cells, while the pattern's own spacing is ~5.8 — so only about two previous organs get a say, and a Fibonacci spiral needs four or five to carry the phase. I added a second, slower signal made by organ founder cells with its own diffusion and decay, so its reach could be tuned independently, and swept it from 4 to 17 cell diameters. It changed nothing: the spread stayed flat across every range and every strength. The reason is worth keeping — a field with a long enough reach to remember the last five organs is also nearly uniform across a meristem this size, so it has no idea which direction to point. Range and positional information trade against each other.

Could a new organ be slotting in at a different radius instead of waiting for a gap? The band that can found an organ is several cells deep, so yes, in principle. Narrowing it to a thin generative ring did tighten things — spread fell by about a third and the fraction of organs landing near the mean roughly tripled — but the shoot then made almost no leaves at all. That control is the generative ring slider: turn it down and watch the angle sharpen while the plant starves. The trade-off is the finding.

Both results are negative, and both point the same way: in a single reaction–transport field on an idealised disc, the rate at which sites become available and the sharpness with which one is chosen are governed by overlapping constants. You can have a crisp angle or a productive shoot, not both. Which is presumably why the published models spend their effort on the tissue — real meristem geometry, layered epidermis, mechanical feedback — rather than on the chemistry alone.