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Dynamic hysteresis in the velocity and dissipation of stochastic Michaelis–Menten kinetics

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Abstract

In this work, we have studied a single molecule enzyme catalysis reaction in presence of oscillatory substrate concentration. The stochastic kinetics is modelled in terms of a chemical master equation. Depending on the oscillation frequency, hysteresis can occur in the system which is dynamic in nature. The time-dependent driving keeps the system out-of-equilibrium associated with dissipation. The interplay between the timescales of the system kinetics and the external driving necessitates the splitting of the total entropy production rate into adiabatic and nonadiabatic contributions. Analyses of these quantities give insights into the various balance conditions of the reaction fluxes and their roles in governing the nonequilibrium thermodynamics of the system. Interestingly, the net velocity of catalysis and the dissipation along with its various parts are found to exhibit hysteresis that vanish in the low and high-frequency ranges of substrate oscillation. However, the average (over a period) velocity as well as the average dissipation show hyperbolic increase with frequency to saturation. We have proposed an experimental protocol to realize such features using periodic stepwise injection of substrate at specified rates.

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Acknowledgments

K.B. acknowledges the University Grants Commission (UGC), India for Dr. D. S. Kothari Fellowship and Prof. K. Bhattacharyya for useful discussions.

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  1. Department of Chemistry, University of Calcutta, Kolkata, 700009, India

    Kinshuk Banerjee

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  1. Kinshuk Banerjee
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Banerjee, K. Dynamic hysteresis in the velocity and dissipation of stochastic Michaelis–Menten kinetics. J Math Chem 53, 1412–1425 (2015). https://doi.org/10.1007/s10910-015-0496-4

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  • DOI: https://doi.org/10.1007/s10910-015-0496-4

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