Distribution of Hemerythrin’s Conformational Substates from Kinetic Investigations at Low Temperature
In addition to their biologically essential macroscopic motions, proteins also present equilibrium fluctuations; in other words, they exist in a large number of slightly different structures that react at different rates. As a consequence, the protein ensemble is kinetically inhomogeneous and must be described by a continuous distribution function of rate constants, f(k). At physiological temperature and low viscosity, the fluctuations are so rapid in comparison to most protein reactions that the differences in reaction rates are averaged out. Exponential kinetics are observed, but the corresponding rate constant is actually an average value, <k>. In contrast, at low temperature and high viscosity, each conformational substate (CS) remains frozen and reacts at its own rate; the kinetics turn into a superposition of an infinite number of exponentials. Such non-exponential kinetics are related to the probability distribution of the rate constants by N(t) = ∫f(k) exp(-kt).dk. These concepts have emerged from extensive flash photolysis investigations of liganded hemoproteins (1,2) and, more recently, of Hr (3). Although there is no a priori reason why the average rate, <k>, measured under physiological conditions should obey a simple Arrhenius’s law as does any elementary reaction rate (k = A exp[-H/RT]), it can be shown that this might be the case under sufficiendy general conditions (3,4), provided that A and H are replaced by effective parameters A eff and H eff . Our ultimate understanding of the significance of these effective values and of their correlation with the substates* parameters must be based on the knowledge of the distribution,f(k).
KeywordsEntropy Enthalpy Recombination Tate Photolysis
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