A mathematical model for dispersal of bacterial inoculants colonizing the wheat rhizosphere

Abstract

A mathematical model has been constructed to describe bacterial growth and movement in the rhizosphere. In the model, bacteria are introduced into the soil on inoculated seeds and growth occurs, after seed germination, on material produced as root exudates. Movement of substrates away from the rhizosphere into the bulk soil is by diffusion and microbial movement is mediated by carriage on the root surface. The relationship between specific growth rate and substrate concentration is described by Monod kinetics and death occurs at a constant specific rate. An important component of the model is treatment of the effects of matric potential on the distribution and activity of bacteria in different microhabitats. Simulation of the model quantifies the distribution of both bacteria and substrate with depth and time in the rhizosphere and demonstrates significant differences between substrate concentrations at high and low matric potentials. Sensitivity analysis of model predictions indicates the parameters which govern microbial growth to be more important determinants of microbial movement than plant-associated parameters. Predictions of the model compared well with experimental data on microbial movement in the rhizosphere of wheat plants grown in microcosms, and inoculated with luminescence-marked Pseudomonas fluorescens, and provide the basis for quantitative risk assessment following environmental release of genetically-engineered microorganisms.