Kinetic models for chemotaxis: hydrodynamic limits and spatio-temporal mechanisms

Area of Science:

• Mathematical Biology
• Cellular Biophysics
• Theoretical Ecology

Background:

• Chemotaxis models traditionally focus on spatial chemoattractant gradients.
• Cells' ability to sense temporal chemoattractant changes is crucial for accurate movement.
• Existing models struggle to explain phenomena like the chemotactic wave paradox.

Purpose of the Study:

• To develop and rigorously analyze a kinetic model for chemotaxis that incorporates temporal chemoattractant sensing.
• To derive the macroscopic limit of this kinetic model, resulting in a novel drift equation.
• To apply the model to resolve the chemotactic wave paradox using numerical simulations.

Main Methods:

• Rigorous mathematical derivation of the macroscopic limit from kinetic equations.
• Development of a drift equation with time-dependent chemotactic sensitivity.
• Coupling the macroscopic equation with a slime mold (Dictyostelium discoideum) activation-inhibition model for chemoattractant production.

Main Results:

• A new drift equation for chemotaxis was derived, incorporating temporal chemoattractant sensing.
• The model successfully resolved the chemotactic wave paradox in numerical experiments.
• The model reproduced characteristic chemoattractant waves observed in Dictyostelium discoideum.

Conclusions:

• Kinetic models incorporating temporal chemoattractant sensing offer a more complete description of cell movement.
• The derived macroscopic equation provides a powerful tool for studying complex chemotactic behaviors.
• This approach enhances our understanding of collective cell migration and pattern formation in biological systems.