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Multi-scale Analysis of Bacterial Growth Under Stress Treatments
Published on: November 28, 2019
A multiscale approximation in a heat shock response model of E. coli
1Mathematical Biosciences Institute, Ohio State University, Columbus, OH, USA. kang.235@mbi.osu.edu
BMC Systems Biology
|November 23, 2012
Summary
This study simplifies a complex Escherichia coli heat shock response model using multiscale approximation. The derived reduced models accurately capture the full model's dynamics across different time scales.
Area of Science:
- Systems Biology
- Computational Biology
- Biochemical Reaction Networks
Background:
- The Escherichia coli heat shock response model exhibits multiscale characteristics due to wide variations in species numbers and reaction rates.
- Previous work by Srivastava, Peterson, and Bentley (2001) established this complex model.
- Stochastic reaction network theory by Kang and Kurtz (2012) provides a foundation for multiscale analysis.
Purpose of the Study:
- To apply a multiscale approximation method to a complex biological model, specifically the E. coli heat shock response.
- To derive simplified, reduced models that accurately represent the dynamics of the full, complex model.
- To illustrate the application of advanced mathematical techniques to biological systems.
Main Methods:
- Employed the method of separation of time-scales and model reduction for stochastic reaction networks.
- Scaled species numbers and rate constants by powers of a scaling parameter, creating a one-parameter family of continuous-time Markov chain models.
- Determined appropriate scaling exponents satisfying balance conditions to derive limiting models in three distinct time scales.
Main Results:
- Developed three reduced models in different time scales that approximate the behavior of the full 9-species, 18-reaction E. coli heat shock model.
- These limiting models reside in lower-dimensional spaces and possess simpler structures compared to the full model.
- Species numbers were either approximated as constants or averaged, simplifying the network's complexity.
Conclusions:
- The multiscale approximation method successfully simplifies complex biological models while preserving essential dynamics.
- The derived simplified models effectively capture the dynamics of the full heat shock response model across relevant time scales.
- Convergence of scaled species numbers to their limits was achieved, with error estimation using the central limit theorem.
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