EVOLUTION OF ENZYME-ACTIVITY - IS DIFFUSION CONTROL IMPORTANT - ACTIVATION PARAMETERS IN THE REACTIONS OF FERRIC HEME SPECIES WITH HYDROGEN-PEROXIDE

There is a finite energy of activation for a diffusion-controlled reaction. It can be calculated by comparing a combination of the Stokes-Einstein relation between the diffusion coefficient of a solute molecule and the viscosity of a solvent and the Smoluchowski equation for a diffusion-controlled rate constant to the rate equation of simple transition state theory. The entropy of activation for a diffusion-controlled reaction can also be obtained. Comparison is made of the enthalpy and entropy of activation for a diffusion-controlled reaction to the enthalpies and entropies of reaction of a series of heme-containing proteins and a simple heme with hydrogen peroxide. For nonenzymatic species the enthalpy of activation is greater than that for the ionization of hydrogen peroxide, indicating that they react with the conjugate base of hydrogen peroxide. For the peroxidases and catalases, both the enthalpy and entropy of activation are less than that for both hydrogen peroxide ionization and a diffusion-controlled reaction. The latter result indicates reaction with unionized hydrogen peroxide, which gives the enzymes a huge advantage over the nonenzymatic species at physiological pH. It also indicates that the peroxidases and catalases do not operate by a diffusion-controlled mechanism. Our conclusion is that the hypothesis of the diffusion-controlled limit being the ultimate criterion of a perfectly evolved enzyme is too restrictive. Rather, enzymes evolve in such a manner that they ultilize the binding energy of the substrate to lower the enthalpy of activation below that for a diffusion-controlled reaction, in compensation for the necessary low entropy of activation required to form a transition state which is much more highly ordered than that of the separated reactants.