A structured-population model of Proteus mirabilis swarm-colony development

Area of Science:

• Mathematical Biology
• Microbial Ecology
• Computational Science

Background:

• Proteus mirabilis swarm-colony development is a complex biological process.
• Existing models, like Esipov and Shapiro's, capture cell-cycle dynamics but lack spatial detail.
• Understanding spatial dynamics is crucial for modeling microbial colony growth.

Purpose of the Study:

• To develop and numerically compute continuous age- and space-structured models for Proteus mirabilis swarm-colony development.
• To improve upon existing models by incorporating explicit age-structure.
• To accurately represent both temporal and spatial regularity observed in experimental observations.

Main Methods:

• Utilizing composite hyperbolic-parabolic partial differential equations.
• Basing cell-cycle dynamics on established Esipov and Shapiro models.
• Employing computational methods with known convergence properties for numerical solutions.

Main Results:

• The new models, with explicit age-structure, successfully display both temporal and spatial regularity in numerical computations.
• This contrasts with the Esipov and Shapiro model, which only shows temporal regularity when solved accurately.
• The models provide a more comprehensive representation of swarm-colony development.

Conclusions:

• The developed age- and space-structured models offer a more accurate depiction of Proteus mirabilis swarm-colony development.
• These models are applicable to other biological systems with spatially dependent dynamics.
• The study highlights the importance of age-structure in modeling microbial spatial dynamics.