Pre-Publicación 2026-21
Idulfo Arrocha, Raimund Bürger, María Gómez, Yolanda Vásquez:
Modeling and numerical simulation of the colonization of plant growth-promoting bacteria in the rice rhizosphere
Abstract:
In Panama, rice (Oryza sativa L.) production entails high economic and environmental costs due to a heavy dependence on chemical fertilizers. As a sustainable alternative, the use of plant growth-promoting rhizobacteria (PGPR) is being evaluated, but its successful deployment requires a quantitative understanding of how inoculated bacteria spread and colonize the highly competitive rhizosphere. Since this process is complex and expensive to study experimentally, we formulate and solve numerically a mathematical model, based on a system of coupled partial differential equations, for the spatiotemporal dynamics of PGPR in response to root exudation. Them spatially two-dimensional domain arises from an axisymmetric cylindrical coordinate system and incorporates a moving boundary representing the growing rice root. The model couples a reaction-diffusion equation for the substrate (root exudates) with a reaction-diffusion-advection equation for the bacterial biomass, combining Monod growth kinetics with directed motility through chemotaxis of Keller–Segel type. Approximate solutions are computed by a finite volume spatial discretization and an implicit-explicit time-integration algorithm designed to be positivity preserving. The scheme is validated against the classical one-dimensional steady-state scenario of Newman and Watson (1977). Two-dimensional simulations based on literature parameters reveal that chemotaxis and the substrate diffusion coefficient are the dominant factors governing colonization efficiency, and exhibit a temporal lag in biomass growth as well as the inability of the population to instantly colonize newly formed root tissue at the growing tip. The model provides a predictive tool for evaluating inoculation strategies and optimizing PGPR use in sustainable agriculture.
