Medium reorganization energy and enzymatic reaction activation energy

Reorganization and activation energies for charge transfer reactions occurring inside a dielectric sphere have been calculated by solving the problem of polar medium reorganization within and outside a dielectric sphere placed in another infinite dielectric. The dielectric sphere is assumed to simulate a protein globule, i.e. an enzyme molecule. It has been shown that for some reaction types the activation energy tends to decrease as the globule radius increases and that for each of the reaction types considered there is an optimal globule radius an increase of which does not bring about any tangible activation energy reduction. The calculated optimal radii for different processes are in good agreement with the increasing molecular sizes in the series: ribonuclease less than or equal to lysozyme less than serine proteinases approximately equal to cysteine proteinases less than NAD-dependent dehydrogenases. The calculated radii are usually about 1.5 to 1.7 times (and molecular masses about 4-5 times) smaller than the experimental ones. The reasons for this discrepancy are discussed and it has been suggested that the approximate nature of the treatment of a protein globule as a structureless dielectric is the main reason. It is shown that charge transfer at an acute angle to the globule surface is the optimum process. For endoergonic reaction stages it is the net charge transfer towards the periphery and for exoergonic ones that in the reverse direction which are advantageous. These conclusions are consistent with the data about the structure of the above-mentioned enzymes.