Reproduction-time statistics and segregation patterns in growing populations

Area of Science:

• Microbiology
• Statistical Physics
• Complex Systems

Background:

• Microbial colony pattern formation under space-limited growth is a key area of research.
• Existing models often simplify individual reproduction times, potentially missing crucial pattern dynamics.

Purpose of the Study:

• To investigate the impact of individual reproduction time statistics on microbial colony sectoring patterns.
• To generalize the Eden growth model by incorporating a tunable parameter for reproduction time distributions.
• To analyze the universality class and scaling relations of the generalized model.

Main Methods:

• Generalizing the Eden growth model with a one-parameter family of reproduction time distributions (variation coefficient δ).
• Employing numerical simulations and heuristic arguments to study pattern formation.
• Analyzing the Kardar-Parisi-Zhang (KPZ) universality class and scaling relations.
• Validating the model with experimental data from Saccharomyces cerevisiae.

Main Results:

• Reproduction time statistics significantly alter sectoring patterns in microbial colonies.
• The generalized model remains within the Kardar-Parisi-Zhang universality class.
• Changes in patterns are quantitatively predictable through modified prefactors in scaling relations.
• The variation coefficient effectively captures the impact of realistic reproduction time distributions.

Conclusions:

• Individual reproduction time variability is a critical factor in microbial colony pattern formation.
• The generalized Eden model provides a robust framework for studying these patterns.
• The findings have implications for understanding microbial growth dynamics and complex system behavior.