Conformational fluctuations and protein reactivity. Determination of the rate-constant spectrum and consequences in elementary biochemical processes.

When a protein's active site happens to be strongly coupled with the protein structure, the rate constant of the reaction may eventually be modulated by the conformational fluctuations. Evidence for this effect has long been provided by extensive flash photolysis investigations of liganded hemoproteins and more recently of the non-heme respiratory protein hemerythrin in hydro-organic solvents. Within a given protein conformational substate, an elementary reaction step is characterized by one single free energy barrier and by a first-order rate constant, k, which changes with temperature according to an Arrhenius law. At physiological temperature and low viscosity, ultrafast conformational relaxation causes efficient averaging of the reaction rates and the protein displays exponential kinetics with an average rate constant (k). Under sufficiently general conditions, it can be shown that (k) also follows a simple Arrhenius law with 'effective' values of the pre-exponential factor Aeff and activation enthalpy Heff. It is found that Aeff strongly depends on the overall shape of the rate constant distribution and that Heff actually corresponds to the lower limit of the enthalpy of activation, i.e. the value associated with the highest possible reaction rate. The underlying distribution of rate constants can be reconstructed from a set of experiments in which the kinetics depart from an exponential, i.e. at low temperature and high viscosity. The most probable distribution of exponentials consistent with the observed kinetics of the geminate recombinations of oxygen with photodissociated hemerythrin has been determined by using a new approach, known as the maximum entropy method. The results are consistent with a single pre-exponential value and a distributed enthalpy spectrum. As expected, Heff does not coincide either with the most probable nor with the average value of the enthalpy. The most salient findings are that the probability for any protein molecule to have an enthalpy of activation equal to the effective value Heff vanishes and that Aeff differs by nearly three orders of magnitude from the true value A0. Biochemical reaction rates are actually average values, since protein reactions are measured under physiological conditions, where conformational relaxation is always fast. Our understanding of the significance of Aeff and Heff is therefore entirely dependent on the knowledge of the distribution function of the rate constants. In particular, enthalpy and entropy terms of similar reactions performed by different proteins cannot be compared as long as the distribution of the rate constants remains unknown.