Homogenization of long-range auxin transport in plant tissues

A model for the cell-to-cell transport of the plant hormone auxin is presented. Auxin is a weak acid which dissociates into ions in the aqueous cell compartments. A microscopic model is defined by diffusion-reaction equations and a Poisson equation for a given charge distribution. The microscopic properties of the plant cell were taken into account through oscillating coefficients in the model. Via formal asymptotic expansion a macroscopic model was obtained. The effective diffusion coefficients and transport velocities are expressed by the solution of unit cell problems. Published experimental values of diffusivity and permeability were used to determine numerically the effective transport coefficients and the calculated transport velocity was shown to be of the same order as measured values.