Some Compartmental Models of the Root: Steady-state Behavior

Plots of the pressure difference (ΔP) applied to plant roots vs. the resulting volume flow rate (Qv) often exhibit an anomalous offset that has been difficult to explain. The present analysis suggests that solute build-up in two- and three-compartment models of the root cannot account for this offset. The Ginsburg–Newman three-compartment model explains the offset in terms of differing reflection coefficients for the membranes bounding the intermediate compartment. This model appears more promising, but it predicts a minimum in the plot of xylem-sap osmotic pressure vs. Qvwhich is not observed in practice. Fiscus hypothesized that an internal asymmetric distribution of non-mobile solutes is responsible for the offset. In the present study, this hypothesis is incorporated into a four-compartment model of the root that is conceptually related to the three-compartment model of Miller. But according to the four-compartment model, the asymmetric solute distribution does not arise because of solvent drag. Rather the anomalous offset is associated with a concentration gradient of photoassimilates (the non-mobile solutes) that exists in the absence of volume flow, and which drives the diffusive transport of these solutes from the stele to the cortex via endodermal plasmodesmata. This model is consistent with the existence of radial symplastic osmotic-pressure gradients, and it appears to have greater explanatory power than the Ginsburg–Newman model. In particular, it suggests explanations for diurnal variations inΔP –Qvcurves, as well as the effects of changing external solute concentrations. It also shows how the overall root reflection coefficient can be less than unity, even when the cell membranes are effectively ideally semipermeable, and there is negligible extracellular transport of water and solutes. The model makes a number of experimentally testable predictions.