Analytical Solution of the Proprio-Graviceptive equation for shoot gravitropism of plants

TL;DR

This paper derives explicit analytical solutions to the generalized gravi-proprioceptive equations describing how plants sense gravity and curvature, advancing understanding of plant gravitropism mechanisms.

Contribution

It provides the first explicit analytical solutions to the complex gravi-proprioceptive equations using Bessel functions, building on prior theoretical work.

Findings

Explicit solutions in terms of Bessel functions

Enhanced understanding of plant sensing mechanisms

Mathematical framework for plant gravitropism

Abstract

We derive the analytical solutions to the second order generalised gravi-proprioceptive equation given in our recent paper [Bastien et al. 2012]. These equations show how plants adjust to the surrounding gravitation field and highlight the fact that the plant must be able to not only sense its local posture with respect to the gravitational field, but also to sense its own local curvature. In [Bastien et al. 2012] we obtained explicit analytical solutions of these equations in terms of (sums of) Bessel functions, and in the present paper we derive these solutions.