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Fixed-Point Computation of Equilibria in Biochemical Regulatory Networks

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Book cover Hybrid Systems Biology (HSB 2019)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 11705))

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Abstract

The analysis of equilibria of ordinary differential equations (ODEs) that represent biochemical reaction networks is crucial in order to understand various functional properties of regulation in systems biology. In this paper, we develop a numerical algorithm to compute equilibria under the assumption that the regulatory network satisfies certain graph-theoretic conditions which lead to fixed-point iterations over an anti-monotonic function. Unlike generic approaches based on Netwon’s method, our algorithm does not require the availability of the Jacobian of the ODE vector field, which may be expensive when the dimensionality of the system is large. More important, it produces an estimation (through over-approximation) of the entire set of equilibria, with the guarantee of yielding the unique equilibrium of the ODE in the case that the returned set is a singleton. We demonstrate the applicability of our algorithm to two signaling pathways of MAPK and EGFR.

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Acknowledgments

The authors thank the anonymous reviewers for helpful comments. Max Tschaikowski is supported by a Lise Meitner Fellowship funded by the Austrian Science Fund (FWF) under grant number M-2393-N32 (COCO).

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Authors and Affiliations

  1. IMT School for Advanced Studies Lucca, Lucca, Italy

    Isabel Cristina Pérez-Verona & Mirco Tribastone

  2. Technische Universität Wien, Vienna, Austria

    Max Tschaikowski

Authors
  1. Isabel Cristina Pérez-Verona
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  2. Mirco Tribastone
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  3. Max Tschaikowski
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Correspondence to Max Tschaikowski .

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Editors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    Milan Češka

  2. University of London, Royal Holloway, Egham, UK

    Nicola Paoletti

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Pérez-Verona, I.C., Tribastone, M., Tschaikowski, M. (2019). Fixed-Point Computation of Equilibria in Biochemical Regulatory Networks. In: Češka, M., Paoletti, N. (eds) Hybrid Systems Biology. HSB 2019. Lecture Notes in Computer Science(), vol 11705. Springer, Cham. https://doi.org/10.1007/978-3-030-28042-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-28042-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28041-3

  • Online ISBN: 978-3-030-28042-0

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