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Entropy production in enzymatic reactions

Theoretical studies from past years show that the principle of maximum entropy production (MEP) is widely accepted optimization principle used for quantitative explanation of many non-equilibrium phenomena [1]. From this point of view, the MEP principle is also of basic importance for understanding of biological systems, which operate in non-linear regime, far away from equilibrium state. For example, it was shown [2] that a rotary enzyme ATP-synthase produces entropy at a maximal value. The MEP principle was applied to analysis of one of the most important transition in the entire reaction scheme of this enzyme and it was able to predict the values of kinetic parameters associated with this transition, that are close to experimental values. We prove analytically in this work that maximal entropy production and optimal forward reaction rate constant can be associated with any chosen transition connecting two given basic free energy levels [3] in the case of an arbitrarily complex steady-state reaction scheme of an enzyme that can exist in a finite number of discrete states. The MEP principle is then applied to the analysis of the three-state kinetic scheme of enzymatic reaction considered in terms of generalized Michaelis-Menten steady-state kinetics. These three states are governed by three backward and three forward kinetic constants. By applying as constraints the maximal value of the product of forward reaction rate constants, constant free energy differences between enzymatic states, and constant thermodynamic force, we calculated Shannon entropy and entropy production as a function of any chosen couple of two forward rate constants. We show numerically and analytically that under these conditions there is a maximum in the net substrate to product steady-state flux, total entropy production and Shannon entropy of the system for the same optimal value of all three forward reaction rate constants. In conclusion, this is the first theoretical study were maximum entropy production is found for any given transition between two functionally important enzyme states and for the entire reaction scheme of an enzymatic reaction plus surrounding bath with substrates and products. We point out that the MEP principle and maximum Shannon entropy principle [4] can be treated as powerful physical selection principles for the evolutionary optimization of enzymes. [1] Martyushev, L.M., Seleznev V.D. Maximum entropy production principle in physics, chemistry and biology. (2006) Physics Reports 426: 1-45. [2] Dewar, R.C., Juretić, D., Županović, P. The functional design of the rotary enzyme ATP synthase is consistent with maximum entropy production.(2006) Chem. Phys. Lett. 430: 177-182. [3] Hill, T.L. Free Energy Transduction in Biology, Academic Press, London, 1977 [4] Jaynes, E.T. Probability Theory, Cambridge Univ. Press, 2003.

maximum entropy production; Michaelis-Menten kinetics; Shannon's entropy

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