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Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics

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  • Till D. Frank

Abstract

Mathematical modeling has become an indispensable part of systems biology which is a discipline that has become increasingly popular in recent years. In this context, our understanding of bistable signaling pathways in terms of mathematical modeling is of particular importance because such bistable components perform crucial functions in living cells. Bistable signaling pathways can act as switches or memory functions and can determine cell fate. In the present study, properties of mathematical models of bistable signaling pathways are examined from the perspective of synergetics, a theory of self-organization and pattern formation founded by Hermann Haken. At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. How to determine these order parameters for bistable signaling pathways at saddle-node bifurcation points is shown. The procedure is outlined in general and an explicit example is worked out in detail.

Suggested Citation

  • Till D. Frank, 2016. "Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-7, October.
    • Handle: RePEc:hin:jnlamp:8938970
    DOI: 10.1155/2016/8938970
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    Cited by:

    1. Frank, T.D., 2020. "COVID-19 interventions in some European countries induced bifurcations stabilizing low death states against high death states: An eigenvalue analysis based on the order parameter concept of synergetic," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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