AUTHOR=Bastien Renaud , Douady Stéphane , Moulia Bruno TITLE=A Unifying Modeling of Plant Shoot Gravitropism With an Explicit Account of the Effects of Growth JOURNAL=Frontiers in Plant Science VOLUME=Volume 5 - 2014 YEAR=2014 URL=https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2014.00136 DOI=10.3389/fpls.2014.00136 ISSN=1664-462X ABSTRACT=

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, was presented, in which the dynamics of the tropic movement is only determined by the conflicting controls of (1) graviception that tends to curve the plants toward the vertical, and (2) proprioception that tends to keep the stem straight. This model was found to be valid for many species and over two orders of magnitude of organ size. However, the motor of the movement, the elongation, was purposely neglected in the AC model. If growth effects are to be taken into account, it is necessary to consider the material derivative, i.e., the rate of change of curvature bound to 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 directly expresses the curvature variation as a function of the median elongation and of the distribution of the differential growth. By using this extended model, called the ACĖ model, growth is found to have two main destabilizing effects on the tropic movement: (1) passive orientation drift, which occurs when a curved element elongates without differential growth, and (2) fixed curvature, when an element leaves the elongation zone and is no longer able to actively change its curvature. By comparing the AC and ACĖ models to experiments, these two effects are found to be negligible. Our results show that the simplified AC mode can be used to analyze gravitropism and posture control in actively elongating plant organs without significant information loss.