Run-and-tumble dynamics in a crowded environment: persistent exclusion process for swimmers.

Area of Science:

• Physics of complex systems
• Microbiology and biophysics
• Statistical mechanics

Background:

• Bacterial motility, or run-and-tumble dynamics, is crucial for their survival and colonization.
• Crowding effects in biological systems can alter individual particle behavior and lead to emergent collective phenomena.
• Understanding these dynamics is key to fields like microbial ecology and disease progression.

Purpose of the Study:

• To investigate the influence of crowding on the run-and-tumble dynamics of model swimmers.
• To quantify the relationship between particle density, randomization rate, and emergent collective behaviors like clustering.
• To provide insights into the initial mechanisms driving biofilm formation.

Main Methods:

• Utilized a discrete lattice model simulating mutually excluding particles with constant velocity.
• Incorporated a randomization rate (α) for particle direction changes to mimic run-and-tumble motion.
• Analyzed system behavior in stationary states across one and two dimensions to observe cluster formation and dynamics.

Main Results:

• Observed the spontaneous formation of dense particle clusters in stationary states due to crowding.
• Determined that characteristic cluster size scales with the randomization rate as α(-0.5) in both 1D and 2D.
• Found that stopping time within clusters exhibits power-law scaling with diffusive time, T(1d) ~ T(0.85) and T(2d) ~ T(0.8), influenced by cooperative effects.

Conclusions:

• Crowding fundamentally alters bacterial-like swimmer dynamics, leading to significant cluster formation.
• The identified scaling laws provide quantitative predictions for cluster size and particle trapping times.
• These findings offer a foundational understanding of early-stage biofilm development and collective bacterial behavior in confined environments.