A Unifying Modeling of Plant Shoot Gravitropism With an Explicit Account of the Effects of Growth - Bastien, Renaud; Douady, Stéphane; Moulia, Bruno (Frontiers in Plant Science, 2014)
Gravitropism, the slow reorientation of plant growth in response to gravity, is a major determinant of the form and posture of land plants. Recently a universal model of shoot gravitropism, the AC model, has been presented, in which the dynamics of the tropic movement is only determined by the contradictory controls of i) graviception, that tends to curve the plants towards the vertical, and ii) proprioception, that tends to keep the stem straights. This model was found valid over a large range of species and over two order of magnitude in organ size. However the motor of the movement, the elongation, has been neglected in the AC model. Taking into account explicit growth effects, however, requires consideration of the material derivative, i.e. the rate of change of curvature bound to an expanding and convected organ elements. Here we show that it is possible to rewrite the material equation of curvature in a compact simplified form that express directly the curvature variation as a function of the median elongation and of the distribution of the differential growth. Through this extended model, called the ACE model, two main destabilizing effects of growth on the tropic movement are identified : i) the passive orientation drift, which occurs when a curved element elongates without differential growth and ii) the fixed curvature which occurs when a element leaves the elongation zone and is no longer able to change its curvature actively. By comparing the AC and ACE models to experiments, these two effects were however found negligible, revealing a probable selection for rapid convergence to the steady state shape during the tropic movement so as to escape the growth destabilizing effects, involving in particular a selection over proprioceptive sensitivity. Then the simplified AC mode can be used to analyze gravitropism and posture control in actively elongating plant organs without significant information loss.