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Modeling in Systems Biology pp 225–251Cite as

Analysis of Dynamical Models of Signaling Networks with Petri Nets and Dynamic Graphs

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Part of the book series: Computational Biology ((COBO,volume 16))

Abstract

The static representation of biological interaction networks can be misleading. All interactions do not occur simultaneously. On the other hand, differential equations can represent a dynamical system, but the topology of the interactions is not explicitly accessible from the calculations of system dynamics. To have a graph representation of a dynamical system, we have developed the dynamic graph. We used the Petri net representation of an ODE system and invariant analysis to identify the main components of a signaling network and thus bridge the two formalisms. The result is a method that can be used to analyze the dynamics of the network topology. Its main feature is the highlighting of the function and interactions of regulatory motifs in the emergence of a complex biological behavior. The example used here is the Bhalla–Iyengar model of the MAPK/PKC signaling pathway in fibroblasts. A property of this pathway is the ability to operate both in a monostable or bistable regime. We show with dynamic graphs that both the topology and the kinetics of this model are responsible for this behavior.

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Notes

  1. 1.

    Conservative invariant analysis was performed with the software Charlie, a companion tool of Snoopy.

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Acknowledgements

The work is supported by NIH grants GM072853 and P50GM071558 to R.I.S.H. holds NSERC Postdoctoral Fellowship BP-342902. The Virtual Cell is supported by NIH Grant Number P41RR013186 from the National Center for Research Resources.

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Authors and Affiliations

    Authors
    1. Simon Hardy
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    2. Ravi Iyengar
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    Correspondence to Simon Hardy .

    Editor information

    Editors and Affiliations

    1. Institute for Computer Science, J.W. Goethe University Frankfurt, Robert-Mayer-Straße 11-15, Frankfurt am Main, 60325, Germany

      Ina Koch

    2. Department of Computer Science, Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

      Wolfgang Reisig

    3. Institute of Computer Science, Martin Luther Univ. Halle-Wittenberg, Von Seckendorff Platz 1, Halle, 06120, Germany

      Falk Schreiber

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    Hardy, S., Iyengar, R. (2011). Analysis of Dynamical Models of Signaling Networks with Petri Nets and Dynamic Graphs. In: Koch, I., Reisig, W., Schreiber, F. (eds) Modeling in Systems Biology. Computational Biology, vol 16. Springer, London. https://doi.org/10.1007/978-1-84996-474-6_11

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    • DOI: https://doi.org/10.1007/978-1-84996-474-6_11

    • Publisher Name: Springer, London

    • Print ISBN: 978-1-84996-473-9

    • Online ISBN: 978-1-84996-474-6

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