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The dimensionless numbers of the shaping of plant axes and crowns through tropism and elasticity : a physicist approach of the biological regulation of plant morphogenesis.
The shape of plant stems and/or of the whole crown of isolated trees are conspicuous traits of each species, while at the same time-varying a lot depending on the environment in which the plant grew. A major process involved in this shaping is stem tropism, i.e. oriented growth directed by external clues. In plant stems, tropic driving involves the sensing by the organ of ii) its inclination vs. gravity and vs. light and ii) its own curvature (proprioception [1]).
In this talk, I review how the shaping of each stem during its growth is driven by 4 dimensionless numbers : i) the Balance number, the ratio of the sensitivity to the inclination angle to the sensitivity to curvature, scaled to the length of the reacting zone, ii) the Motion-pointing number, the ratio between the sensitivities to the inclination angles vs. gravity and light, iii) the Weeping number, the ratio between the intrinsic bending rate and the proprioceptive sensitivity, scaled to the radius of the stem and iv) the elastic sagging number El, the ratio between the elastic length and specific gravity. The morpho-spaces that can be generated by varying these 4 dimensionless numbers are presented and discussed.
In a second time, I will briefly show how a model of stem tropic growth can be included in a model of crown shaping, in which the interaction between the crown and the light feeds back on the tropic orientation of the growth of branches ([2] ), while growth coupling through the signaling between branches plays the role of a surface tension smoothing the surface. Thereby the crown becomes an analog of a growing droplet of magnetic fluid.
I a third time, I will present how all this can help understand the effects of major genes and environmental cues on plant shape.
To conclude, I will emphasize the control loop of shoot shaping in plants. I will also discuss the approach of addressing biological growth problems as the driving of the growth kinematics through the biological sensing of physical signals, thereby providing feedback from the upscale structures (e.g. crown on the individual axis) [3].
[1] Moulia B., Douady S. and Hamant O., 2021 Fluctuations shape plants through proprioception. Science 372, eabc6868
[2] Duchemin L, Eloy C, Badel E, Moulia M. 2018 Tree crowns grow into self-similar shapes controlled by gravity and light sensing J. Roy Soc Interface. 15 (142), 20170976.
[3] Moulia, B., Badel, E., Bastien, R., Duchemin, L. and Eloy, C. 2022, The shaping of plant axes and crowns through tropisms and elasticity : an example of morphogenetic plasticity beyond the shoot apical meristem (Tansley Review). New Phytologist . 233 (6) : 2354-2379