Converting genetic information to non-equilibrium cellular thermodynamics in enzyme-catalyzed reactions

Abstract

Living systems use genomic information to maintain a stable highly ordered state far from thermodynamic equilibrium but the specific mechanisms and general principles governing the interface of genetics and thermodynamics has not been extensively investigated. Genetic information is quantified in unitless bits termed "Shannon entropy", which does not directly relate to thermodynamic entropy or energy. Thus, it is unclear how the Shannon entropy of genetic information is converted into thermodynamic work necessary to maintain the non-equilibrium state of living systems. Here we investigate the interface of genetic information and cellular thermodynamics in enzymatic acceleration of a chemical reaction $S+E\to ES\to E+P$, where $S$ and $E$ are substrate and enzyme, $ES$ is the enzyme substrate complex and $P$ product. The rate of any intracellular chemical reaction is determined by probability functions at macroscopic (Boltzmann distribution of the reactant kinetic energies governed by temperature) or microscopic (overlap of reactant quantum wave functions) scales - described, respectively, by the Arrhenius and Knudsen equations. That is, the reaction rate, in the absence of a catalyst, is governed by temperature which determines the kinetic energy of the interacting molecules. Genetic information can act upon a when the encoded string of amino acids folds into a 3-deminsional structure that permits a lock/key spatial matching with the reactants. By optimally superposing the reactants' wave functions, the information in the enzyme increases the reaction rate by up to15 orders of magnitude under isothermal conditions. In turn, the accelerated reaction rate alters the intracellular thermodynamics environment as the products are at lower Gibbs free energy which permits thermodynamic work $\left(W_{max}=-\Delta G\right)$. Mathematically and biologically, the critical event that allows genetic information to produce thermodynamic work is the folding of the amino acid string specified by the gene into a 3-dimensional shape determined by its lowest energy state. Biologically, this allows the amino acid string to bind substrate and place them in an optimal spatial orientation. These key-lock are mathematically characterized by Kullback-Leibler Divergence and the interactions with the reaction channel now represent Fisher Information (the second derivative Kullback-Leibler divergence), which can take on the units of the process to which it is applied. Interestingly, Shannon is typically derived by "coarse graining" Shannon information. Thus, living system, by acting at a quantum level, "fine grain" Shannon information.

Keywords: Arrhenius equation; Enzymes; Fisher Information; Information in living systems; Knudsen distribution; thermodynamics.