Dielectric continuum model for calculating reorganization free energies of electron transfer in proteins

A dielectric continuum model is developed for calculating polarization reorganization energies of electron transfer reactions that occur in proteins. The model is based on an earlier microscopic formulation of the Marcus electron transfer theory. The classical Marcus result, lambda=Delta G(1-0)(op)-Delta G(1-0), for the free energy of polarization reorganization is derived from the microscopic theory. Both Delta G(1-0)(op) and Delta G(1-0) denote the electrostatic free energy due to a positive unit charge (+e) distributed in the region representing the electron donor and a negative unit charge (-e) distributed in the region representing the electron acceptor. In calculating Delta G(1-0)(op), the donor and acceptor as well as the environment surrounding them take the optical dielectric constant epsilon(op). In calculating Delta G(1-0), the donor and acceptor keep the optical dielectric constant but the environment takes the static dielectric constant epsilon. The environment consists of the protein matrix (where epsilon(op)=epsilon(op) and epsilon=epsilon(p)) and the solvent (where epsilon(op)=epsilon(s)(op) and epsilon=epsilon(s)). The polarization reorganization free energy can be approximated as the sum of two components lambda(1) and lambda(2). In calculating lambda(1), the protein region is extended outward to infinity. For the case where the donor and acceptor are modeled as spheres (with both radii equal to a and center-center distance at r) and the electron charge is put at either center, a Marcus result, lambda(1)=[(1/epsilon(p)(op))-(1/epsilon(p))][(1/a)-(1/r)]e(2), is found to be highly accurate (maximum error 4\%). In calculating lambda(2), the protein region is extended inward to fill the donor and acceptor. The magnitude of lambda(2) is usually much smaller than lambda(1). A toy electron-transfer protein is studied both by the dielectric continuum model and by implementing the microscopic formulation through computer simulations. Agreement of the results from the two approaches demonstrates the accuracy of the dielectric continuum model. (C) 1996 American Institute of Physics