PROTEIN ELECTRON-TRANSFER REORGANIZATION ENERGY-SPECTRUM FROM NORMAL-MODE ANALYSIS - 1 - THEORY

We present an analytical model that describes the coupling of protein fluctuations to electron transfer, The model treats both the protein a nd the bulk solvent to couple to electron transfer, The protein is rep resented by a low-dielectric cavity containing explicit protein atoms, and the bulk solvent is represented by a high-dielectric continuum su rrounding the cavity. Protein fluctuations are modeled by collective n ormal modes with solvation energies incorporated through explicit reac tion field energies. The shifts of the equilibrium normal mode variabl es upon electron transfer, related to the mode-specific couplings and reorganization energies, are calculated assuming the difference of the potential energy surfaces before and after electron transfer by a hyp er plane in the normal mode vector space. This linear coupling assumpt ion allows only one set of normal mode vectors to span both the reacta nt and product equilibrium conformations. The model is equivalent to a reduced spin-boson formalism (protein only); however, unlike previous work within this formalism, the bath modes are not spatially anonymou s in our treatment. They are associated with unambiguous frequency and spatial signatures allowing a spectral analysis of protein reorganiza tion energy with one-to-one connection with actual protein fluctuation . This aspect of our model is very crucial since it allows, for the fi rst time, to make a direct connection between actual protein motion an d electron transfer, as demonstrated by a simulation presented in an a ccompanying paper (J. Phys. Chem. 1998, 102, XXX).