A Generalized Entropy-Production Consistent with Perturbation Response in Biological Regulatory Systems

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  • Sakata Katsumi
    Department of Life Science and Informatics, Maebashi Institute of Technology Department of Radiation Effects Research, National Institute of Radiological Sciences
  • Yu Isseki
    Department of Life Science and Informatics, Maebashi Institute of Technology
  • Katam Ramesh
    Department of Biological Sciences, Florida A&M University
  • Saito Toshiyuki
    Department of Radiation Effects Research, National Institute of Radiological Sciences

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Generalized entropy-production (GEP) is a measure of increased disorderliness in natural systems. In this article, a novel GEP is proposed, which is formulated as a quadratic form based on Jacobian matrix derived from the ordinary differential equations for the target systems. The proposed GEP has an advantage associated with eigenvalues of the Jacobian matrix, which characterizes the perturbation response of the target system. The results showed that, in numerical experiments for four biological regulatory systems the proposed GEP was consistent with perturbation response such that with the decrease in an average of the proposed GEP, the deviation from the steady state by impulsive perturbation has converged fast. The proposed GEP makes the property, a system often transitions to a new state with lower entropy, found by Kondepudi and Prigogine in chemical systems is applicable to the four biological regulatory systems.

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