The Allen–Cahn-Based Approach to Cross-Scale Modeling Bacterial Growth Controlled by Quorum Sensing
Year: 2025
Type: article
Abstract: This study, grounded in traveling wave theory, develops a cross-scale reaction-diffusion model to describe nutrient-dependent bacterial growth on agar surfaces and applies it to \textit {in silico} investigations of microbial population dynamics. The approach is based on the coupling of a modified Allen-Cahn equation with formulation of quorum sensing signal dynamics, incorporating a nutrient-dependent regulatory threshold and stochastic diffusion. A closed-loop model of bacterial growth regulated by quorum sensing is developed through theoretical analysis, numerical simulations, and computational experiments. The model is implemented using Yanenko's computational scheme, which incorporates iterative processing and corrective refinement via Heun's method to account for nonlinear components. Numerical simulations are carried out in Matlab, allowing for accurate computation of spatio-temporal patterns and facilitating the identification of key mechanisms governing the collective behavior of bacterial communities.
Source: Mathematics
DOI: 10.3390/math13183013
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4414334280