Cattaneo models for chemosensitive movement. Numerical solution and pattern formation

Area of Science:

• Biophysics
• Mathematical Biology
• Microbiology

Background:

• Chemosensitive movement is crucial for microorganisms.
• Classical models often assume infinite speed of response.
• Cattaneo's law offers a finite-speed alternative for propagation phenomena.

Purpose of the Study:

• To derive and apply models for chemosensitive movement based on Cattaneo's law.
• To investigate pattern formation in microbial systems using these models.
• To compare Cattaneo-based models with classical approaches.

Main Methods:

• Derivation of mathematical models incorporating Cattaneo's law.
• Application of models to experimental data of Dictyostelium discoideum, Salmonella typhimurium, and Escherichia coli.
• Development of a numerical scheme for model simulation.

Main Results:

• Successful modeling of pattern formation in studied microorganisms.
• Generation of testable predictions for Salmonella typhimurium pattern formation.
• Comparison of Cattaneo models with classical models, highlighting differences.

Conclusions:

• Cattaneo's law provides a viable framework for modeling chemosensitive movement.
• The derived models accurately capture observed microbial pattern formation.
• The study advances understanding of chemotaxis and microbial collective behaviors.