Effects of medium polarization and pre-existing field on activation energy of enzymatic charge-transfer reactions

The highly organized spatial structure of proteins' polar groups results in the existence of a permanent intraprotein electric field and in protein's weak dielectric response, i.e. its low dielectric constant. The first factor affects equilibrium free energy gap of a charge-transfer reaction, the second (medium polarization effect) influences both equilibrium and non-equilibrium (reorganization) energies, decreasing the latter substantially. In the framework of the rigorous 'fixed-charge-density' formalism, the medium polarization component of the reaction activation energy has been calculated, both for the activation energy of the elementary act proper, and the effective activation energy accounting for the charges' transfer from water into a low-dielectric structureless medium. In all typical cases of reactions, the energy spent for charge transfer from water into structureless 'protein' is larger than the gain in activation energy due to the protein's low reorganization energy. Therefore, the low dielectric constant of proteins is not sufficient to ensure their high catalytic activity, and an additional effect of the pre-existing intraprotein electric field, compensating for an excessive charging energy, is necessary. Only a combined action of low reorganization energy and pre-existing electric field provides proteins with their high catalytic activity. The dependence of activation energy on the globule geometry has been analyzed. It is shown that, for each reaction, an optimum set of geometric parameters exists. For five hydrolytic enzymes, the optimum globule radii have been calculated using the experimental geometry of their active sites. The calculated radii agree satisfactorily with the real sizes of these macromolecules, both by absolute and by relative values.