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Entropy production and Shannon's entropy 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. In the present contribution the MEP principle is applied to general analyses of the three-state kinetic scheme of enzymatic reaction considered in terms of Michaelis-Menten kinetics. These three states are governed by three backward and three forward kinetic constants. The system was elaborated in terms of the Hills graph theory [3]. By applying additional constraints for maximal values of forward reaction rate constants as well as constant free energy differences between the enzyme states, we calculated Shannon informational entropy and entropy production as a function of two forward rate constants of the second and third state. We can show numerically that under these conditions there is a maximum in the total entropy production of the system and Shannon informational entropy of the system. In conclusion, this is the first theoretical study were the maximum of total entropy production is found for the entire reaction scheme of enzymatic reaction. We point out that the MEP principle can be treated as a powerful physical selection principle for the evolutionary optimization of enzymes. References [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. CPL 430: 177-182. [3] T.L. Hill. Free energy transduction in biology, Academic Press, London, 1

entropy production; information entropy

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