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Processes 2019, 7(3), 163; https://doi.org/10.3390/pr7030163

Application of Parameter Optimization to Search for Oscillatory Mass-Action Networks Using Python

Department of Bioengineering, University of Washington, Seattle, WA 98105, USA
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Author to whom correspondence should be addressed.
Received: 21 February 2019 / Revised: 11 March 2019 / Accepted: 13 March 2019 / Published: 18 March 2019
(This article belongs to the Special Issue Methods in Computational Biology)
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Abstract

Biological systems can be described mathematically to model the dynamics of metabolic, protein, or gene-regulatory networks, but locating parameter regimes that induce a particular dynamic behavior can be challenging due to the vast parameter landscape, particularly in large models. In the current work, a Pythonic implementation of existing bifurcation objective functions, which reward systems that achieve a desired bifurcation behavior, is implemented to search for parameter regimes that permit oscillations or bistability. A differential evolution algorithm progressively approximates the specified bifurcation type while performing a global search of parameter space for a candidate with the best fitness. The user-friendly format facilitates integration with systems biology tools, as Python is a ubiquitous programming language. The bifurcation–evolution software is validated on published models from the BioModels Database and used to search populations of randomly-generated mass-action networks for oscillatory dynamics. Results of this search demonstrate the importance of reaction enrichment to provide flexibility and enable complex dynamic behaviors, and illustrate the role of negative feedback and time delays in generating oscillatory dynamics. View Full-Text
Keywords: parameter optimization; differential evolution; evolutionary algorithm; bistable switch; oscillator; turning point bifurcation; Hopf bifurcation; biological networks; mass-action networks; BioModels Database parameter optimization; differential evolution; evolutionary algorithm; bistable switch; oscillator; turning point bifurcation; Hopf bifurcation; biological networks; mass-action networks; BioModels Database
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Supplementary material

  • Externally hosted supplementary file 1
    Link: https://github.com/vporubsky/evolve-bifurcation
    Description: All supplementary materials required to generate the data and figures in the main text are available in the published-test-cases directory of the evolve-bifurcation Github repository. evolveBifurcation.py contains the sourcecode for the bifurcation-evolution algorithm described in the text. Optimized bifurcated BioModels represented in Antimony string format and time-course simulation .jpg output is included for all test cases. All randomly-generated networks are provided in Antimony string format and time-course simulation .jpg output for each network is included.
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Porubsky, V.L.; Sauro, H.M. Application of Parameter Optimization to Search for Oscillatory Mass-Action Networks Using Python. Processes 2019, 7, 163.

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