Persistent exclusion processes: Inertia, drift, mixing, and correlation

Area of Science:

• Statistical Physics
• Mathematical Biology
• Agent-Based Modeling

Background:

• Biological systems often feature motile agents exhibiting persistent random motion and spatial exclusion (crowding).
• Understanding the collective behavior of such agents is crucial for modeling biological processes.

Purpose of the Study:

• To formulate and analyze lattice-based models for multiple persistent walkers with spatial exclusion.
• To derive and investigate continuum limit partial differential equations governing these systems.
• To explore the emergence of nonlinearity from persistence and exclusion effects.

Main Methods:

• Formulation of lattice-based models for persistent exclusion processes in 1D and 2D.
• Application of mean-field approximation to derive population-level partial differential equations.
• Analysis of nonlinear diffusion and advection-diffusion equations.
• Comparison of mean-field predictions with stochastic simulation results.

Main Results:

• The persistent exclusion process is generally described by a nonlinear diffusion equation.
• Nonlinearity arises from the interplay of motion persistence and volume exclusion.
• Linear diffusion is recovered in the absence of either persistence or exclusion.
• Generalization to multi-species systems and systems with global drift yields nonlinear advection-diffusion equations.

Conclusions:

• The developed models provide a framework for understanding collective motion in crowded biological systems.
• The interplay of persistence and exclusion fundamentally leads to nonlinear dynamics.
• The study offers methods for inferring persistence from simulation and potential applications to cell-imaging data.