Coarsening dynamics of chemotactic aggregates

Area of Science:

• Mathematical Biology
• Cellular Dynamics
• Pattern Formation

Background:

• Autochemotaxis, directed cell movement along secreted chemical gradients, is crucial for biological pattern formation.
• The Keller-Segel model and its variants describe phenomena like aggregate coarsening and chaotic dynamics.

Purpose of the Study:

• Analyze the long-time dynamics of mass-conserving Keller-Segel models.
• Investigate the mechanisms driving coarsening in chemotactic aggregates.
• Provide a framework for understanding autochemotactic cell population dynamics.

Main Methods:

• Singular perturbation theory to derive mass competition rates between aggregates.
• Analysis of diffusion- and reaction-limited coarsening regimes.
• Linear stability analysis of lateral instability using a nullcline-slope criterion.

Main Results:

• Derived rates of mass competition driving coarsening through self-amplifying mass transport and aggregate coalescence.
• Diffusion-limited coarsening rate aligns with previous quasi-steady-state analyses.
• Predicted lateral instability via a criterion paralleling spinodal decomposition.

Conclusions:

• Chemotactic aggregates exhibit dynamics analogous to phase-separating droplets.
• Coarsening is a fundamental process driven by mass competition and coalescence.
• Findings offer a quantitative basis for comparing chemotactic coarsening to nonequilibrium phase separation.