Active mixtures in a narrow channel: motility diversity changes cluster sizes

Area of Science:

• Active Matter Physics
• Statistical Mechanics
• Microbiology

Background:

• Persistent motion of bacteria leads to the formation of clusters with a stationary cluster size distribution (CSD).
• Understanding factors influencing CSD, such as motility diversity and confinement, is key to modeling bacterial behavior.

Purpose of the Study:

• To develop a minimal model assessing the importance of motility diversity and confinement on bacterial clusters in a narrow channel.
• To quantify the impact of polydispersity in tumbling rates on cluster size and CSD.

Main Methods:

• A 1D lattice model simulating run-and-tumble particles with a distribution of tumbling rates (α).
• Analysis of particle interactions, including crossing at a finite rate, to mimic quasi-1D confinement.
• Development of an effective theory to derive expressions for CSD and other key parameters.

Main Results:

• Motility diversity increases average cluster size (Lc) when particle crossing is absent, as slower particles trap faster ones.
• Finite crossing rates reduce Lc and the importance of diversity, though they can enhance phase separation.
• Model predictions, using Escherichia coli parameters, show a ~60% error in Lc estimation if polydispersity is ignored.

Conclusions:

• Motility diversity is a critical factor influencing bacterial cluster formation and CSD.
• Accurate modeling of bacterial systems requires accounting for polydispersity in motility parameters.
• The developed effective theory provides accurate predictions for CSD and other relevant metrics.