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Discontinuous phase transition in chemotactic aggregation with density-dependent pressure.

Gyu Ho Bae1, Seung Ki Baek1

  • 1Department of Physics, Pukyong National University, Busan 48513, Korea.

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|October 3, 2019
PubMed
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Small organisms aggregate due to chemical attraction overcoming repulsive forces. This study models this biological aggregation using partial differential equations, revealing a discontinuous transition forming boundary aggregates.

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Area of Science:

  • Mathematical Biology
  • Chemical Ecology
  • Statistical Physics

Background:

  • Microorganisms utilize chemical signals for communication and collective behavior.
  • Density-dependent repulsive forces, modeled as effective pressure, influence organism distribution.
  • Phase transitions from homogeneous states to aggregated structures are observed in biological systems.

Purpose of the Study:

  • To model the aggregation dynamics of small organisms in a confined two-dimensional space.
  • To investigate the interplay between chemical attraction and effective pressure.
  • To analyze the nature of the phase transition from homogeneous distribution to aggregation.

Main Methods:

  • Utilized a two-dimensional Patlak-Keller-Segel model, a system of partial differential equations.
  • Analyzed the system's Lyapunov functional to understand stability and transitions.
  • Interpreted results within a thermodynamic framework, relating Lyapunov functional to free energy.

Main Results:

  • Demonstrated that the aggregation transition occurs discontinuously.
  • Showed that aggregates form preferentially near the boundary of the disk.
  • Identified the Lyapunov functional as analogous to free energy in a thermodynamic context.

Conclusions:

  • The interplay of attraction and repulsion drives discontinuous aggregation in confined microbial systems.
  • Boundary effects significantly influence the spatial organization of aggregated organisms.
  • The Patlak-Keller-Segel model provides a robust framework for understanding collective biological behavior through a thermodynamic lens.