Forms and gravitropic movements of plants stems: Universal modelling and phenotyping
Most of the plants are mostly vertical and straight on all or a part of their aerial systems. To reach this postural shape, stems display complex movements related to environmental perceptions, gravity for instance, or internal perceptions, the own deformation of the organ. When a stem is tilted from the vertical, without light, it starts to curve locally in order to align each part of its axis vertically. During this movement, different transitory shapes can be observed, depending on the species. Some stems never overshoot the vertical whereas others display C-shape or even S-shape. A minimal dynamical modeling of the gravitropic movement has been developed. This modeling only depends on two parameters. A first parameter describes the way the plants curve in order to reach the vertical, the graviceptive term. The second term describes the proprioception, tending to reduce the curvature of the organ. A gravipropriotropic steady state, between straightening and curvature of the stem, is then reached. An adimensionless number, B, can then be defined as the ratio between the graviceptive and propioceptive sensitivities . This unique number describes at the same time, the steady state shape and the transient movements displayed. It allows to compare several species even if their characteristic time and length are quite different. An experimental estimation of B is proposed as the rate of the length of the curved zone on the final shape on the effective length of the stem. The comparison of the estimation of B with a simple description of the transitory shapes of the movement was in accordance with the gravirpopiceptive model. Moreover,this sets a phenotyping protocole for plant gravitropism. More advanced analysis of deviations between the model and the experiments demonstrates that elongation and apical influences are second order. We also found a non trivial relation between oscillating propagative behaviour of elongation rate and curvature rate. This suggests a better regulation than expected probably linked to auxin polarised transport and cell elongating motor cycle.