The diffusive transport of gibberellins and abscisic acid through the aleurone layer of germinating barley grain: a mathematical model

摘要

A mathematical model of the diffusive transport of abscisic acid (ABA) and gibberellins (GAs) through the aleurone layer of barley (Hordeum vulgare L.) grain is presented. The model consists of two partial differential equations describing the accumulation of phytohormone in the apoplastic and symplasmic compartments of the aleurone layer, both spatially and temporally. The mathematical model contains the morphology of the barley grain and the physicochemical properties of the two phytohormones. A mathematical derivation of the accumulation ratios for the two phytohormones between the symplast and apoplast under equilibrium conditions resulted in different distribution mechanisms for GAs and ABA. A sensitivity analysis of the accumulation ratio for GAs indicated high sensitivity to the apoplastic pH and the membrane potential, whereas the accumulation ratio for ABA proved to be most sensitive to the pH difference between the apoplast and symplast. The diffusive transport time for GAs to the basal site of the aleurone layer as calculated with the mathematical model is within a physiologically plausible timescale according to experimental data from the literature. Abscisic acid cannot be transported by diffusion to the end of the aleurone layer as quickly as GAs, according to model simulations. Therefore, the functional role of ABA in germination is likely to be in the vicinity of the embryo.