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Dimensionality reduction of bistable biological systems
A Zakharova1, Z Nikoloski, A Koseska
1Center for Dynamics of Complex Systems, University of Potsdam, Campus Golm, Karl-Liebknecht-Str. 24, 14476, Potsdam, Germany. zakharova-as@mail.ru
Bulletin of Mathematical Biology
|February 9, 2013
Summary
This study introduces a new method to analyze time hierarchies in biological systems with multiple stable states. This approach simplifies models while preserving key dynamics, aiding in understanding complex biological processes.
Area of Science:
- Dynamical systems biology
- Nonlinear dynamics
- Systems theory
Background:
- Biological systems exhibit time hierarchies and switch-like properties.
- Existing analysis methods for time hierarchies are limited to systems with a single stable steady state.
- Bistable nonlinear systems present challenges due to non-unique reference states.
Purpose of the Study:
- To extend reference-state analysis for investigating time hierarchies in bistable biological systems.
- To develop a novel method for analyzing systems with multiple stable states.
- To identify key components influencing dynamical properties beyond reactions.
Main Methods:
- Development and analysis of a novel reference-state analysis method.
- Application of the method to biological systems exhibiting bistability.
- Integration of nonlinear dynamics and multivariate statistics techniques.
Main Results:
- The proposed method effectively analyzes time hierarchies in bistable systems.
- Identified components beyond reactions that determine systemic dynamical properties.
- Demonstrated successful model simplification while preserving bistability in diverse biological systems.
Conclusions:
- The novel method extends time hierarchy analysis to bistable systems.
- This approach aids in understanding and simplifying complex biological models.
- Provides a foundation for extending reference-based analysis to systems with multiple stable states.
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