The bioenergetics of axial plant growth I. Concept and model formulation

Abstract

The axial growth of plant tissue obeys the physical laws of energetics during deformation of a continuous medium. In this manuscript the concept of biological energy conservation is employed to formulate a mathematical model of axial plant growth. The model is derived from a statement of the exchange of the thermodynamic potential energy with the kinetic energy of deformation. This derivation does not invoke a force balance analogy with simple mechanical systems and has no turgor dependence. The mathematical expression for growth which results from energy conservation considerations is given by a system of coupled, nonlinear, first-order, partial diffrential equations in the material coordinate system for the local tissue displacement velocity, V(X, t) , and the longitudinal tissue strain, E(X, t) . The coefficient of the equations, γ 2 , is equal to the change of the tissue thermodynamic potential energy with respect to the longitudinal strain, dΘ/d E , divided by a tissue density term. This term is referred to as the “specific energy capacity” of tissue growth. The chemical components of the thermodynamic potential energy as applied to plant growth are the total water potential and the mole number of the carbon based components participating in biomass synthesis. The derivatives with respect to tissue strain of the turgor, osmotic potential and extent of the biosynthetic reactions, therefore, all participate in the performance of the work of growth. The result of this analysis indicates that an increased rate of biosynthetic reactions in the production of biomass and the biochemical loosening of the cell wall contribute to increased axial growth rates. An increased tissue osmotic potential and strain hardening of the cell wall, on the other hand, serve to decrease axial growth rates. The model formulation is unique to plant growth studies since it combines principles of mechanical energy conservation during deformation with a chemical thermodynamic description of the potential energy. The concept that the change of the thermodynamic potential energy performs the work of deformation is more general and applicable to biological systems than the currently employed force balance approach.