A modified two‐compartment model of the root: response to a pressure clamp

Abstract

A, membrane area Cs, solute concentration LP, hydraulic conductivity P, pressure Π, osmotic pressure ω, solute permeability QV, volume flow rate Qs, solute flow rate Qs*, active solute flow rate, σ, reflection coefficient of apical root ‘membrane’ t, time τ, time constant Va, apical xylem volume superscript a, apical xylem superscript b, basal xylem superscript x, xylem (apical and basal) superscript o, external medium Magnani et al. (Planta 199, 296–306, 1996) have described a model of the root in which apoplastic transport of water occurs in the older (basal) regions, and intercellular transport occurs in the younger (apical) regions. They tested this model by performing pressure‐clamp experiments on excised root systems, and found that their model gave a good fit to the data. In the present study, their model is extended to include solute transport across an apical root ‘membrane’, with reflection coefficient, σ. When σ = 1 (i.e. no apoplastic transport across the root membrane) the model yields solutions for the volume flow rate that are identical in form to those of Magnani et al. (1996). Hence, given that their solutions provide a good description of the data, it seems possible to explain these data without invoking apoplastic water transport in the apical zone. For σ < 1, the predicted behaviour is more complex. It is concluded that the analysis of Magnani et al. (1996) overestimates the apoplastic hydraulic conductance of the basal zone (which could, in principle, be zero), and underestimates the intercellular hydraulic conductance of the apical zone. The magnitude of these errors depends on the solute permeability of the apical root membrane. The analysis suggests that solute transport parameters should be included in models of water transport across plant roots, even when σ≈ 1. For the exosmotic pressure clamp, this is emphasized by considering the case where σ = 1, and the basal region is replaced with a chamber filled with water. Under this regime, the volume‐relaxation time constant does not depend on the membrane hydraulic conductance, but is determined by the solute permeability.