A Study about Nutrient Uptake by Roots. A Moving Boundary Model. Determination of Kinetic Parameters

J.C. REGINATO – D.A. TARZIA

Beijing

Congreso; XV IPNC-International Plant Nutrition Colloquium; 2005

C.J. Li et al. (Eds.)

The Barber-Cushman model is widely used to estimate the single nutrient uptake by a growing root system. The model solves the coupled equations of transport in the soil and absorption of nutrient by roots in fixed domains. The objective of this study is to determine whether a dynamical model, accounting for increasing root competition, could improve predictions of nutrient uptake. Our model includes assumptions of the Barber-Cushman model and the moving boundary approximation. The model predicts nutrient uptake by coupling nutrient flux to roots and nutrient absorption on a variable domain in time. The integral balance method and the immobilization domain method with two finite differences schemes were applied. The three model outputs were compared with measured and predicted (Barber-Cushman model) uptake of Mg, K, and P by pine seedling.  Predicted nutrient were close to that observed for K and P although for Mg the predicted uptake shows deviations similar to those of the Barber-Cushman model. The moving boundary model appears to provide a better description of coupling between transports, absorption of nutrient and root growth for plants growing in fixed soil volumes. Also, the relative importance of numerical method applied is shown. Furthermore, the model is applied to long term root uptake of a surface-applied, strongly absorbed, pollutant metal cation, such as radiocaesium, from soil. Simulations of the fraction removed from soil versus time as a function of buffer power, maximum influx and rate constant of the fixation reaction are shown. Moreover, due to the importance of exactitude of the kinetic parameters values for the computation of nutrient uptake, an alternative and simple method to calculate them is presented. The method uses the explicit integration in time of the differential equation obtained from the relationship between the decreasing of nutrient concentration in a given volume of solution culture and nutrient uptake by roots. Thus, the depletion curve C = C(t) is obtained. Then, by using the initial first (rate of nutrient uptake) and second derivative of the concentration C and the value of concentration at large times, explicit formulas for the maximum influx at infinity concentrations, the Michaelis-Menten constant and the efflux are obtained.