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Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity

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  • Svetoslav G. Nikolov

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
    Department of Mechanics, University of Transport, Geo Milev Str., 158, 1574 Sofia, Bulgaria
    Department of Systems Biology and Bioinformatics, University of Rostock, 18051 Rostock, Germany
    Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen, 91052 Erlangen, Germany)

  • Vassil M. Vassilev

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

  • Momchil I. Nenov

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

Abstract

The objective of this paper is to find new dynamic perspectives in a well-known two dimensional nonlinear system which is a modification of the phosphofructo kinase model by incorporating recycling of the product, p , into the substrate, s . Specifically, we investigate the affect of the negative cooperativity on the number of equilibria and their stability. Moreover, in the parameter space, we analyze analytically and numerically the number of periodic oscillations (solutions) and their stability using Lyapunov coefficients (in other words, quantities and focus values). Thus, we obtain that three different dynamical conditions (regimes) take place: (1) structurally unstable, (2) the existence of an unstable limit cycle with an external stable limit cycle, and (3) the existence of a stable limit cycle with an external unstable limit cycle. Moreover, for a zero rate of product synthesis (due to e.g., defective enzyme), we obtain that the modified system has a first integral.

Suggested Citation

  • Svetoslav G. Nikolov & Vassil M. Vassilev & Momchil I. Nenov, 2025. "Investigation of a Biochemical Model with Recycling in Case of Negative Cooperativity," Mathematics, MDPI, vol. 13(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:260-:d:1566917
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    References listed on IDEAS

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