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

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 ≈ r n . This implies interchanges p n ⇄ 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 E a 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.