MULTISCALE MODELS OF TAXIS-DRIVEN PATTERNING IN BACTERIAL POPULATIONS

Understanding bacterial spatial patterning remains a challenge despite advances in single-cell behavior. While individual responses to chemical gradients are well studied, predicting large-scale patterns is difficult. Traditional models like Patlak-Keller-Segel equations describe macroscopic movement but lack direct links to microscopic behavior. Run-and-tumble bacteria have seen progress in linking behavior to equations, but limitations persist. Time-dependent signals and hydrodynamics are underexplored in these models. Existing methods rely on simplifications that may not capture full biological complexity. Closure assumptions in moment equations introduce uncertainty. This gap motivates new approaches that integrate multiple factors influencing bacterial movement.

This research aims to improve multiscale modeling of bacterial taxis-driven patterning. The goal is to bridge microscopic behavior and macroscopic dynamics more accurately. The focus is on extending existing models to natural environments with time-varying signals. The study introduces a more biologically realistic turning rate function. It also incorporates hydrodynamic effects near surfaces. A novel method for solving moment equations without closure assumptions is developed. The approach is tested against Monte Carlo simulations for validation. The ultimate aim is to derive equations for chemotactic movement governed by multiple signals.

The researchers extended prior models by incorporating time-dependent signals. They used a generalized turning rate function to better reflect biological behavior. Hydrodynamic forces near surfaces were modeled as an additional factor. A new solution approach for moment equations was developed without closure assumptions. Numerical simulations compared macroscopic equations to Monte Carlo results. The method was applied to scenarios with multiple chemotactic signals. The transport equation was used as a basis for deriving moment equations. Validation was performed through comparison with established simulation techniques.

The lowest-order macroscopic equation matched Monte Carlo simulations across various signal protocols. The new method for solving moment equations showed good agreement with detailed simulations. Time-dependent signals were successfully modeled using the extended framework. Hydrodynamic effects near surfaces were incorporated without disrupting model accuracy. The generalized turning rate improved biological realism of movement predictions. Multiple chemotactic signals were modeled using the derived equations. The approach avoided closure assumptions while maintaining predictive power. Results suggest the method captures essential dynamics of bacterial taxis.

The authors demonstrated that macroscopic equations can accurately predict bacterial patterning when extended with time-dependent signals. The new method for solving moment equations proved effective without requiring closure assumptions. Hydrodynamic effects near surfaces were successfully incorporated into the model. The generalized turning rate function improved biological realism of movement predictions. The approach was validated against Monte Carlo simulations under various conditions. Multiple chemotactic signals were modeled using the derived equations. The results suggest this framework can better capture bacterial taxis dynamics. The study provides a foundation for future work on multiscale bacterial patterning.