Phyllotaxis
the spirals are counted, not admired
Concept

Auxin — where it appears

The plant hormone whose transport is the usual proposed mechanism for phyllotaxis. Its depletion around an existing primordium is what the inhibition in a placement rule is supposed to stand for, and pinning that correspondence down is a separate question from whether the rule works.

Named by 6 essays across 2 fields — each of them below, with the objects they name alongside it.

Which patterns grow on a ring of circumference 1.40. Modes 4 to 15 have positive growth rates and mode 8 is fastest. Integrating the full equations from a disordered start gives 8 peaks.

Turing's last problem

Turing's final work was on phyllotaxis and it was unpublished when he died. Its core is a ring of cells and two diffusing substances, and the thing it does is select a number of peaks — which can be predicted from the equations before anything is integrated, and then counted from what the integration produces.

mechanism · Reaction–diffusion 48 cells with a carrier that pumps auxin up the gradient. Each short line is one cell's polarisation — the neighbour it pumps towards, which is always the richer one. 10 peaks come out, at a contrast of 93%, from a start that was uniform to within 6%.

A pump that works uphill

The mechanism that actually has molecular support behind it does not use a diffusing inhibitor at all. Cells move auxin towards whichever neighbour already has more of it, which is the opposite of what transport is supposed to do — and it produces a spacing from a field that started uniform to within six per cent.

mechanism · Auxin Two runs of the same rule from unrelated starting angles. Both settle at 137.0°, within 0.5° of the golden angle, from seeds 166° apart.

Droplets with no biology in them

Douady and Couder dripped magnetised ferrofluid into a dish of silicone oil, and got spiral phyllotaxis with Fibonacci parastichy numbers out of a system containing no cells, no genes and no plant. That is the strongest evidence the pattern is physics — and the clearest warning about what a model can claim.

emergence · Analogue Which patterns grow on a ring of circumference 0.80. Modes 2 to 8 have positive growth rates and mode 4 is fastest. Integrating the full equations from a disordered start gives 4 peaks.

What a mechanism would have to show

Every model of phyllotaxis comes with the caveat that reproducing a pattern is not explaining it. That is easy to repeat and hard to make precise. Here it is made precise — a list of what an account of phyllotaxis would have to establish, with each item marked according to whether the models drawn in these essays establish it.

mechanism · Mechanism claims Three disturbances, three places to get in. The rule reads its neighbours, builds a profile of the energy at every azimuth, takes the least of it, and records a position. jostle noise enters at the neighbours; placement noise enters at the record. Two of the three are upstream of the choice and can change which minimum is taken; the third is downstream and never can.

A growing organ is part of the rule

Every model in the earlier essays places primordia on a surface and then treats the surface as furniture. But the surface grows between one placement and the next, and that growth reaches the rule through the only channel it has — where the neighbours are. What looks like a boundary condition turns out to be a term in the model.

mechanism · Mechanism claims Only noise that arrives before the choice can change what is chosen. Intact runs only, from the whole amplitude sweep. Placement noise displaces the node after the rule has picked an azimuth: 44 runs, none of which changed branch at any amplitude that left a lattice. Field noise perturbs the energy profile the rule picks over, so it can move the minimum into a neighbouring gap: 1 of 66 did.

Where the noise gets in

Ninety runs of noise applied after the rule has chosen, and not one changes branch. Fifty-six of noise applied to the choice itself, and one does. Only a disturbance upstream of the decision can restructure which nodes are neighbours of which — which is what a branch is.

emergence · Noise entry

Named alongside it

The objects these essays reach for when they reach for this one.

MechanismRateRiseWhorlBranchMeristemModel scopeNoiseThe placement rulePolar transportPrimordiumRepulsion

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