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An equation-free approach to analyzing heterogeneous cell population dynamics
Katherine A Bold1, Yu Zou, Ioannis G Kevrekidis
1Department of Chemical Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA.
Journal of Mathematical Biology
|April 13, 2007
Summary
We developed a computational method to model coupled biological oscillators, like yeast cells, by simplifying their complex dynamics. This approach efficiently analyzes population synchronization and identifies outlier behaviors.
Area of Science:
- Computational Biology
- Systems Biology
- Biophysics
Background:
- Biological systems often involve populations of coupled, heterogeneous oscillators.
- Modeling these systems requires capturing complex collective dynamics and individual variations.
- Yeast glycolytic oscillations serve as a model for coupled cellular behavior.
Purpose of the Study:
- To propose a novel computational approach for modeling populations of coupled, heterogeneous biological oscillators.
- To efficiently simulate and analyze the synchronization dynamics of yeast glycolytic oscillators.
- To develop methods for identifying and characterizing outlier behaviors within synchronized populations.
Main Methods:
- Utilizing generalized Polynomial Chaos (gPC) coefficients to represent species distributions.
- Employing equation-free (EF) methods for coarse-grained temporal evolution.
- Applying coarse projective integration and fixed-point algorithms for stability analysis.
Main Results:
- Reduced the complex dynamics of oscillator ensembles to the dynamics of fewer gPC coefficients.
- Successfully computed collective oscillatory solutions and their stability for yeast cell populations.
- Identified and characterized the behavior of a "rogue" oscillator deviating from synchronized dynamics.
Conclusions:
- The proposed computational approach effectively models collective dynamics in heterogeneous oscillator populations.
- Equation-free methods combined with gPC provide an efficient alternative to traditional simulations.
- This framework accelerates the analysis of complex biological systems and agent populations.
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