Free energy of charge transfer and intraprotein electric field: method of calculation depends on the charge state of protein at a given structure

Abstract

Free energy of charge transfer presents a basic characteristic of reactions such as protonation, oxido-reduction and similar. Evaluation of this quantity requires calculation of charging energy. Proteins are structured dielectrics, and a consistent incorporation of their structure into calculation of intraprotein electric field results in expression for charging energy of an active group in protein, which is essentially different from that for a simple dielectric. An algorithm for semi-continuum calculation of relevant free energies is described. First of the two components of charging energy in protein, energy of the medium response to charge redistribution in reactants, should be always calculated as the charging energy by the charge redistribution using the static dielectric constant of protein. The second term is interaction energy of the charge redistribution with the `frozen' electric field of the system before reaction. Charges of protein groups, at which the protein structure has been determined, are often different from those before reaction of charge transfer, so is the corresponding intraprotein field. The field is expressed through either both the optical and static dielectric constants of protein or only optical one depending on whether the charges of protein groups before reaction and upon structural analysis are the same or not. Proper allowance for difference in charges of reacting groups before reaction and upon structural analysis of protein is thermodynamically necessary and quantitatively important. The expression for activation free energy for charge transfer in proteins is derived in the form presenting explicitly an invariant contribution of protein structure.