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

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 equati ons describing the accumulation of phytohormone in the apoplastic and sympl asmic compartments of the aleurone layer, both spatially and temporally. Th e mathematical model contains the morphology of the barley grain and the ph ysicochemical properties of the two phytohormones. A mathematical derivatio n of the accumulation ratios for the two phytohormones between the symplast and apoplast under equilibrium conditions resulted in different distributi on mechanisms for GAs and ABA. A sensitivity analysis of the accumulation r atio for GAs indicated high sensitivity to the apoplastic pH and the membra ne potential, whereas the accumulation ratio for ABA proved to be most sens itive to the pH difference between the apoplast and symplast. The diffusive transport time for GAs to the basal site of the aleurone layer as calculat ed with the mathematical model is within a physiologically plausible timesc ale according to experimental data from the literature. Abscisic acid canno t be transported by diffusion to the end of the aleurone layer as quickly a s GAs, according to model simulations. Therefore, the functional role of AB A in germination is likely to be in the vicinity of the embryo.