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

Anna Maslovskaya1, Christina Kuttler2, Yixuan Shuai3,4

  • 1Institute of Data Science and Artificial Intelligence, Innopolis University, Universitetskaya st. 1, 420500, Innopolis, Russia. a.maslovskaya@innopolis.ru.

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Summary
This summary is machine-generated.

This study models bacterial community evolution, combining colony growth, nutrient dynamics, and quorum sensing. The approach simulates dendritic bacterial growth and identifies critical population sizes for survival, even with the Allee effect.

Keywords:
a priori estimatesAllee effectAllen-Cahn modelBacterial communication modelBacterial growth modelFinite element simulationsReaction-diffusion systemUnique solvability

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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.