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Competitive aggregation dynamics using phase wave signals.

Hidetsugu Sakaguchi¹, Satomi Maeyama¹

¹Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.

Journal of Theoretical Biology

|June 24, 2014

Summary

This study models slime mold aggregation dynamics, showing how competing patterns lead to a single dominant aggregation cluster. Spiral patterns also emerge and compete, resulting in one survivor.

Keywords:

Clustering Mathematical model Phase waves Slime mold

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Area of Science:

Computational biology
Mathematical modeling
Nonlinear dynamics

Background:

Slime mold exhibits complex aggregation behaviors.
Understanding competitive dynamics is crucial for biological pattern formation.
Phase waves and target patterns are observed in slime mold aggregation.

Purpose of the Study:

To model the competitive aggregation dynamics of slime mold in two dimensions.
To investigate the role of phase waves as aggregation signals.
To explore pattern formation using the complex Ginzburg-Landau equation.

Main Methods:

Coupled equations for phase and cell concentration (n) were developed.
Phase waves were utilized as tactic signals for aggregation.
The complex Ginzburg-Landau equation was employed as an alternative phase equation.

Main Results:

Initial aggregation clusters formed target patterns.
Competition between target patterns led to a single dominant pattern.
Spiral patterns emerged with the Ginzburg-Landau equation, also resulting in a single dominant spiral.

Conclusions:

The model successfully simulates competitive aggregation in slime mold.
Pattern competition drives the emergence of a single dominant structure.
The choice of phase equation influences the type of emergent patterns (target vs. spiral).