Moran Model of Spatial Alignment in Microbial Colonies

Area of Science:

• Mathematical Biology
• Population Dynamics
• Biophysics

Background:

• Understanding collective behavior in populations requires models that account for spatial interactions and growth dynamics.
• Cellular alignment and pattern formation are crucial phenomena in microbiology and developmental biology.

Purpose of the Study:

• To introduce a solvable spatial Moran model incorporating mechanical interactions and directional growth.
• To investigate the mechanisms driving population-level pattern formation, using E. coli as an example.

Main Methods:

• Developed an analytically tractable spatial Moran model.
• Applied a mean-field approximation for complete solvability.
• Simulated E. coli growth in a microfluidic trap to observe pattern emergence.

Main Results:

• The model elucidates pattern formation driven by a balance between boundary effects and cell-cell interactions.
• E. coli cells exhibit parallel alignment to trap boundaries when boundary effects dominate.
• Orthogonal alignment occurs when cell-cell interactions surpass a critical threshold.

Conclusions:

• The spatial Moran model provides insights into collective behavior driven by local and global interactions.
• This approach can be extended to various directionally growing cells and systems.
• The study highlights how mechanical forces and growth dynamics shape population-level spatial organization.