Mathematical analysis of the chemosmotic polar diffusion of auxin through plant tissues

Equations have been developed to describe the diffusional movement of a weak acid such as the auxin indoleacetic acid through a long file of vacuolated cells, where cellular accumulation is driven by the pH gradients across the cell membranes. If the permeability to the auxin anion is greater at one end of the cell than at the other, diffusional movement takes the form of polar transport, which exhibits: a nearly constant velocity either for the front or for a pulse of radioactive auxin, the capacity to move auxin against an external gradient of concentration, and a polar ratio that increases exponentially with the length of the section. The determinants of velocity include both diffusion through the vacuole and permeation steps at the cell membranes. Except for the permeabilities of the membranes to the anion, values are now available for all of the physical parameters in the equations. With reasonable estimates of permeability coefficients for the anion, the equations predict a velocity of transport of about 1 cm hr(-1), which agrees well with measured values. The analysis indicates, however, that the underlying cellular polarity may be greater than has been heretofore assumed. We thus demonstrate that the hypothesis of chemosmotic polar diffusion is capable of accounting quantitatively for the major features of auxin transport and provides a theoretical framework whose elements can be tested in future experiments.