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Stability of localized wave fronts in bistable systems
Steffen Rulands1, Ben Klünder, Erwin Frey
1Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, München, Germany.
Physical Review Letters
|February 5, 2013
Summary
This study explores how localized wave fronts in biological systems can be stabilized. Findings show that regulating positional signals and low binding cooperativity enhance wave-front stability against perturbations.
Area of Science:
- * Mathematical modeling of biological systems.
- * Theoretical biophysics and systems biology.
- * Wave propagation phenomena in biological contexts.
Background:
- * Localized wave fronts are crucial in diverse biological processes, from cellular dynamics to ecological patterns.
- * Bistable models with self-activation and degradation are common frameworks for studying pattern formation.
- * Understanding wave-front stability is key to predicting system behavior and resilience.
Purpose of the Study:
- * To determine conditions for wave-front localization in bistable models with spatial inhomogeneity.
- * To analyze wave-front stability against extrinsic perturbations and internal noise.
- * To investigate the influence of regulatory mechanisms and molecular interactions on stability.
Main Methods:
- * Analysis of a broad class of bistable mathematical models.
- * Incorporation of self-activation, degradation, and spatially inhomogeneous activating agents.
- * Stability analysis considering external perturbations and intrinsic stochasticity.
Main Results:
- * Identified conditions enabling wave-front localization.
- * Demonstrated enhanced stability through positional signal regulation.
- * Observed increased stability with low binding cooperativity, contrary to intuition.
- * Revealed contrasting effects of self-activation on stability concerning different destabilizing factors.
Conclusions:
- * Positional signal regulation and low binding cooperativity are key for stabilizing biological wave fronts.
- * The interplay between self-activation and destabilizing factors significantly impacts wave-front stability.
- * Findings offer insights into robust pattern formation in biological systems.
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