Simulation Model for Nutrient Uptake from Soil by a Growing Plant Root System

Mathematical models of nutrient uptake by plants are useful for investigating the effect of various soil and plant factors on nutrient flux to plant roots. The objective of this research was to develop a model based on theoretical considerations of the processes of nutrient uptake by plant roots growing in soil and then to test the model experimentally. The soil and plant factors used in the model were to be measured independent of final nutrient uptake. The model for flux by mass flow and diffusion to the root was patterned after that of Nye and Marriott. The absorption kinetics of the root were assumed to follow Michaelis-Menten kinetics. The Nye-Marriott model gives the nutrient Concentration at the root with time. From this accumulated uptake per cm² of root surface with time was calculated. Rate of root growth was assumed exponential for the growth of the young plant. Uptake per cm² of root with time was combined mathematically with rate of root growth to get total uptake with time by the plant. The present program assumes root hairs do not affect uptake and that roots do not compete for nutrients. A computer program was written for solution of the mathematical model. The factors required in the model from the soil are: effective average diffusion coefficient, initial nutrient concentration in solution, and buffering capacity. For the plant they are: the relation between nutrient concentration in solution and net influx into the root, water influx, root radius, initial root length, and rate of root growth. The model was tested for measuring K uptake by corn (Zea mays L.) from eight different soil-K combinations. The corn was grown in a growth chamber and K uptake was measured for the period of plant growth from 4 to 10 and 13 days. The calculated uptake, y, was correlated with observed uptake, x, by the equation y = 0.155 + 1.566 × (R² = 0.87) where y and are μmoles of K/plant. Calculated uptake was overestimated by about 50%, possibly because competition occurred between roots for soil K and K was not absorbed by the root as fast at night as in the day. The model should be useful for investigating the principles of nutrient absorption by plant roots from soil which can be used for developing more efficient systems of fertilizer application.