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Linear conjugacy in biochemical reaction networks with rational reaction rates

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Abstract

In this paper we show that the model form of a wide class of kinetic systems with rational terms in the reaction rates is invariant under a positive linear diagonal transformation. Thus, the concept of linear conjugacy defined originally for mass action systems is extended to rational biochemical models. The generalized Kirchhoff matrix and the kinetic weighting matrix of the linearly conjugate models are given as functions of the computed transformation parameters. It is shown through the illustrative examples that the dense realization of a linearly conjugate rational model may contain more reactions than that of a dynamically equivalent one due to the additional degrees of freedom introduced by the linear transformation. The proposed matrix-based representation is suitable for the computational search of preferred graph structures corresponding to linearly conjugate realizations of rational kinetic models.

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Acknowledgments

AG is supported by the funding from EU FP7 ITN “NICHE”, Project No. 289384. KMH acknowledges the funding from the National Research, Development and Innovation Office—NKFIH through Grant No. 115694. GSz acknowledges the support of the National Research, Development and Innovation Office—NKFIH through Grant No. NF104706. The authors thank Bernadett Ács for carefully reading the manuscript.

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Authors and Affiliations

  1. BioProcess Engineering Group, IIM-CSIC, Spanish Council for Scientific Research, Eduardo Cabello 6, 36208, Vigo, Spain

    Attila Gábor

  2. Process Control Research Group, Institute for Computer Science and Control of the Hungarian Academy of Sciences (MTA SZTAKI), Kende u. 13-17, 1111, Budapest, Hungary

    Katalin M. Hangos & Gábor Szederkényi

  3. Department of Electrical Engineering and Information Systems, University of Pannonia, Egyetem u. 10, 8200, Veszprém, Hungary

    Katalin M. Hangos

  4. Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, 1083, Budapest, Hungary

    Gábor Szederkényi

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  1. Attila Gábor
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  2. Katalin M. Hangos
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  3. Gábor Szederkényi
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Correspondence to Gábor Szederkényi.

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Gábor, A., Hangos, K.M. & Szederkényi, G. Linear conjugacy in biochemical reaction networks with rational reaction rates. J Math Chem 54, 1658–1676 (2016). https://doi.org/10.1007/s10910-016-0642-7

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  • DOI: https://doi.org/10.1007/s10910-016-0642-7

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