A mathematical model of auxin-mediated radial growth in trees

A mathematical model is presented to describe the coupling between the conc entration of indole-3-acetic acid (IAA) in the cambial region of a tree bra nch and the radial expansion of the branch during active growth. The main f eatures of the model are (1) the branch cambium is treated as an approximat ely cylindrical surface of negligible thickness, (2) the rate of radial gro wth 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 branc h shape, and the effects of IAA synthesis and metabolization in the cambium , so the model is not quantitatively accurate. However, the model does repr oduce several important qualitative features of tree growth including the a pproximate area-preserving property of tree branch junctions and the abilit y of a branch to maintain its shape despite perturbations due to injury. (C ) 2001 Academic Press.