The Allen–Cahn-Based Approach to Cross-Scale Modeling Bacterial Growth Controlled by Quorum Sensing

Anna Maslovskaya (), Yixuan Shuai and Christina Kuttler
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Anna Maslovskaya: Laboratory of High Performance Computing, Innopolis University, 420500 Innopolis, Russia
Yixuan Shuai: Laboratory of High Performance Computing, Innopolis University, 420500 Innopolis, Russia
Christina Kuttler: Department of Mathematics, Technical University of Munich, 85748 Munich, Germany

Mathematics, 2025, vol. 13, issue 18, 1-27

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 in silico investigations of microbial population dynamics. The approach is based on the coupling of a modified Allen–Cahn equation with the 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 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.

Keywords: bacterial growth; Allen–Cahn approach; reaction-diffusion model; cross-scale model; stochastic mechanism; quorum sensing; traveling wave; numerical simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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