Investigating Information Dynamics in Living Systems through the Structure and Function of Enzymes

Abstract

Enzymes are proteins that accelerate intracellular chemical reactions often by factors of 10(5) - 10(12)s(-1). We propose the structure and function of enzymes represent the thermodynamic expression of heritable information encoded in DNA with post-translational modifications that reflect intra- and extra-cellular environmental inputs. The 3 dimensional shape of the protein, determined by the genetically-specified amino acid sequence and post translational modifications, permits geometric interactions with substrate molecules traditionally described by the key-lock best fit model. Here we apply Kullback-Leibler (K-L) divergence as metric of this geometric "fit" and the information content of the interactions. When the K-L 'distance' between interspersed substrate p(n) and enzyme r(n) positions is minimized, the information state, reaction probability, and reaction rate are maximized. The latter obeys the Arrhenius equation, which we show can be derived from the geometrical principle of minimum K-L distance. The derivation is first limited to optimum substrate positions for fixed sets of enzyme positions. However, maximally improving the key/lock fit, called 'induced fit,' requires both sets of positions to be varied optimally. We demonstrate this permits and is maximally efficient if the key and lock particles p(n), r(n) are quantum entangled because the level of entanglement obeys the same minimized value of the Kullback-Leibler distance that occurs when all p(n) approximate to r(n). This implies interchanges p(n) reversible arrow br(n) randomly taking place during a reaction successively improves key/lock fits, reducing the activation energy E-a and increasing the reaction rate k. Our results demonstrate the summation of heritable and environmental information that determines the enzyme spatial configuration, by decreasing the K-L divergence, is converted to thermodynamic work by reducing Ea and increasing k of intracellular reactions. Macroscopically, enzyme information increases the order in living systems, similar to the Maxwell demon gedanken, by selectively accelerating specific reaction thus generating both spatial and temporal concentration gradients.