A Mathematical Model of Auxin-mediated Radial Growth in Trees

A mathematical model is presented to describe the coupling between the concentration of indole-3-acetic acid (IAA) in the cambial region of a tree branch and the radial expansion of the branch during active growth. The main features of the model are (1) the branch cambium is treated as an approximately cylindrical surface of negligible thickness, (2) the rate of radial growth is proportional to the mass of IAA per unit area on the cambial surface, and (3) IAA is transported basipetally through the cambium at a constant speed. We neglect the role of elastic strains in the determination of branch shape, and the effects of IAA synthesis and metabolization in the cambium, so the model is not quantitatively accurate. However, the model does reproduce several important qualitative features of tree growth including the approximate area-preserving property of tree branch junctions and the ability of a branch to maintain its shape despite perturbations due to injury.