Fluctuation relations, effective temperature, and ageing of enzymes: The case of protein electron transfer

Proteins catalyzing chemical reactions are glassy systems in which the reaction time is often below the time of conformational relaxation. The protein is not able to sample its configuration space on the reaction time, leading to nonergodic ensemble averages. This phenomenology makes the effective configurational temperature of the protein significantly higher than the kinetic temperature of the bath. The effective temperature is expressed in terms of the fluctuation-dissipation ratio quantifying the violation of the fluctuation dissipation theorem (FDT). For reactions of protein electron transfer, the ratio of configurational and kinetic temperatures is given by the ratio of two reorganization energies related to, correspondingly, thermal fluctuations of the thermal bath and linear response of the bath to electron arriving to the active site. The violation of the FDT leads to a significant depression of the activation barrier achieved trough nonergodic exploration of the protein configuration space. The time of conformational dynamics, leading to equilibration, establishes the ageing time during which the enzyme has to be reset to its original configuration. Experimental evidence and numerical simulations indicate a factor of 2-3 violation of the FDT for protein electron transfer at physiological temperatures. Lowering temperature freezes the protein into a state consistent with the FDT through a glass transition. Design principles of physiological energy chains are discussed by postulating the need to maintain FDT violated to support catalytic function.