Exact analytic solutions for a global equation of plant cell growth

Mariusz Pietruszka (1)

1 Faculty of Biology and Environmental Protection, University of Silesia

A generalization of the Lockhart equation for plant cell expansion in case is presented. The goal is to account for the temporal variation in the wall mechanical properties - in this case by making the wall extensibility a time dependent parameter. We introduce a time differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short- time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional () ∝ exp(exp()), properly describing the volumetric growth and, consequently, growth rate as its time derivative.

Mots clés: Growth functional; Plant cells; Wall extensibility

Mariusz Pietruszka. Exact analytic solutions for a global equation of plant cell growth. Journal of Theoretical Biology, 2010, 264 (2), pp.457. ⟨10.1016/j.jtbi.2010.02.012⟩. ⟨hal-00585799⟩