K⁺ uptake by root systems grown in soil under salinity: I. A mathematical model

A novel theoretical model is proposed for K⁺ uptake by intact root systems from saline soil considering interactions with Na⁺, Ca²⁺ and Mg²⁺. The model assumes radial movement of ions towards the root governed by advection and diffusion flux mechanisms, and chemical exchange of the four cations according to Gapon isotherms, with Cl^- as the accompanying anion. Influx of K⁺ to the root surface is assumed as a function of its concentration in the soil solution at the root. This influx is governed by a saturable-cooperative term and a linear term for low and high K⁺ concentrations, respectively. Influx of Na⁺, above a critical value of its concentration, increases linearly with its concentration in the soil solution at the root surface. Uptake of Ca⁺²⁺ is controlled by the balance between influxes of anions and cations, which induces efflux of H⁺ or HCO₃^-, and interacts with calcite in a calcareous soil. The model may provide information about the behavior of ions at the root-soil interface which cannot be measured in situ.