Modeling bacterial growth and Allee effect via Allen-Cahn theoretical framework

Area of Science:

• Microbiology
• Mathematical Biology
• Computational Biology

Background:

• Mathematical models are crucial for understanding microbial systems.
• Bacterial community dynamics are complex, influenced by growth, nutrient availability, and communication.
• The Allee effect describes a reduced per capita growth rate at low population densities.

Purpose of the Study:

• To develop and theoretically justify a mathematical model for bacterial community evolution in nutrient media.
• To formalize the formation of dendritic bacterial patterns and bacterial communication.
• To investigate the Allee effect in bacterial growth dynamics.

Main Methods:

• A coupled modeling approach combining Allen-Cahn, biomass-dependent nutrient concentration, and reaction-diffusion models.
• Theoretical analysis including proof of unique solvability and derivation of a priori estimates.
• Numerical implementation using the finite element method on the COMSOL Multiphysics platform.

Main Results:

• The mathematical model's unique solvability was proven for nutrient-dependent bacterial growth.
• Simulations using Pseudomonas strains revealed spatiotemporal dynamics of key substances.
• The model successfully simulates dendritic bacterial colony growth and identifies survival thresholds.

Conclusions:

• The developed coupled model provides a robust framework for simulating bacterial community evolution.
• The approach is applicable for controlling bacterial populations and understanding survival dynamics under the Allee effect.
• This work advances in silico studies for microbial systems and applied microbiology.