Simplified procedure for steady‐state root nutrient uptake with linearized Michaelis‐Menten kinetics

Abstract

AbstractA mechanistic description of nutrient depletion of the soil volume around a root involves the solution of a cylindrical diffusion‐convection type differential equation with a non‐linear influx condition at the root surface and a no‐transfer or competition condition centred between two roots. As conventional numerical and analytical solution methods are complex and inflexible, approximations such as the steady‐state method are invaluable in this area. Because of its simplicity, the steady‐state approach to nutrient uptake by root systems is well suited to large plant simulation models. Here, we present an approximation of the Michaelis‐Menten function specifically for this approach, which is frequently used to quantify influx kinetics. When this linearization is used in uptake calculations along with the steady‐state method, no iterations per time step are required and analytical solutions for total nutrient uptake of non‐growing root systems can be found. A simulation study with an exact transient solution showed that the uncertainties with the steady‐state approach were greater than those caused by the described approximation scheme. Despite this, because of its adaptability and simplicity, the steady‐state approach is attractive for the representation of the tremendous heterogeneity of root‐soil systems.