Jamming and Attraction of Interacting Run-and-Tumble Random Walkers

Area of Science:

• Statistical Mechanics
• Active Matter Physics
• Theoretical Biology

Background:

• Bacterial dynamics and collective behaviors are crucial in biological systems.
• Understanding emergent phenomena like motility-induced phase separation (MIPS) requires microscopic models.
• Run-and-tumble motion is a fundamental model for bacterial motility.

Purpose of the Study:

• To develop an exact analytical model for the steady-state probability distribution of two interacting random walkers.
• To investigate the role of mutual exclusion and inter-particle attraction in bacterial dynamics.
• To explore the microscopic origins of motility-induced phase separation.

Main Methods:

• Modeling two interacting random walkers on a one-dimensional lattice.
• Incorporating run-and-tumble motion and mutual exclusion.
• Deriving an exact expression for the steady-state probability distribution.

Main Results:

• The stationary distribution exhibits a complex structure with jammed, attractive, and extended components.
• A significant jamming component persists even in the continuous space limit due to strong attraction.
• The model reveals a finite fraction of time spent in jammed configurations.

Conclusions:

• The study provides an exact solution for a minimal model of interacting active particles.
• The findings offer a microscopic perspective on motility-induced phase separation.
• The model highlights the importance of particle interactions in emergent collective behaviors.