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Potential Landscape and Probabilistic Flux of a Predator Prey Network

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  • Chunhe Li
  • Erkang Wang
  • Jin Wang

Abstract

Predator-prey system, as an essential element of ecological dynamics, has been recently studied experimentally with synthetic biology. We developed a global probabilistic landscape and flux framework to explore a synthetic predator-prey network constructed with two Escherichia coli populations. We developed a self consistent mean field method to solve multidimensional problem and uncovered the potential landscape with Mexican hat ring valley shape for predator-prey oscillations. The landscape attracts the system down to the closed oscillation ring. The probability flux drives the coherent oscillations on the ring. Both the landscape and flux are essential for the stable and coherent oscillations. The landscape topography characterized by the barrier height from the top of Mexican hat to the closed ring valley provides a quantitative measure of global stability of system. The entropy production rate for the energy dissipation is less for smaller environmental fluctuations or perturbations. The global sensitivity analysis based on the landscape topography gives specific predictions for the effects of parameters on the stability and function of the system. This may provide some clues for the global stability, robustness, function and synthetic network design.

Suggested Citation

  • Chunhe Li & Erkang Wang & Jin Wang, 2011. "Potential Landscape and Probabilistic Flux of a Predator Prey Network," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-9, March.
    • Handle: RePEc:plo:pone00:0017888
    DOI: 10.1371/journal.pone.0017888
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    Cited by:

    1. Chunhe Li & Jin Wang, 2013. "Quantifying Cell Fate Decisions for Differentiation and Reprogramming of a Human Stem Cell Network: Landscape and Biological Paths," PLOS Computational Biology, Public Library of Science, vol. 9(8), pages 1-14, August.
    2. Wio, H.S. & Deza, J.I. & Sánchez, A.D. & García-García, R. & Gallego, R. & Revelli, J.A. & Deza, R.R., 2022. "The nonequilibrium potential today: A short review," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Rowan D Brackston & Eszter Lakatos & Michael P H Stumpf, 2018. "Transition state characteristics during cell differentiation," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-24, September.

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