Travelling waves in hybrid chemotaxis models

Area of Science:

• Mathematical Biology
• Biophysics
• Computational Biology

Background:

• Chemotaxis models integrate agent-based cell dynamics with partial differential equations for chemical signals.
• Investigating traveling wave phenomena in hybrid bacterial chemotaxis models is crucial for understanding collective cell movement.
• Existing models often simplify cell behavior, necessitating more comprehensive approaches.

Purpose of the Study:

• To investigate the traveling wave properties of hybrid models for bacterial chemotaxis.
• To derive and analyze mesoscopic and macroscopic equations governing these hybrid models.
• To establish the conditions necessary for the existence of stationary traveling waves.

Main Methods:

• Utilizing an agent-based (individual-based) approach for bacteria, including internal signal transduction, proliferation, and death.
• Modeling the extracellular nutrient field (chemoattractant) using a partial differential equation.
• Deriving mesoscopic and macroscopic equations and establishing the existence of traveling wave solutions.

Main Results:

• Cell proliferation was identified as a necessary condition for the existence of non-transient (stationary) traveling waves.
• Numerical comparisons demonstrated good agreement in wave speeds between continuum and hybrid models for weak chemotaxis.
• Qualitative agreement was observed for strong chemotaxis, with oscillating wave behavior detected under slow cell adaptation, unexplained by mean-field approximations.

Conclusions:

• Hybrid models provide a robust framework for studying bacterial chemotaxis, capturing complex behaviors beyond simpler approximations.
• Cell proliferation is a critical factor in maintaining stable traveling waves in bacterial populations.
• The study highlights the limitations of mean-field approximations in explaining certain emergent wave dynamics.