Simplified procedure for steady-state root nutrient uptake with linearized Michaelis-Menten kinetics
A 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 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, the steady-state approach is attractive for the representation of the tremendous heterogeneity of root-soil systems because of its adaptability and simplicity.
Gräfe, J. & R.O. Kuchenbuch, 2002. Simplified procedure for steady-state root nutrient uptake with linearized Michaelis-Menten kinetics. Journal of Plant Nutrition and Soil Science 165(6), 719-724.