Protein Electron Transfer Reorganization Energy Spectrum from Normal Mode Analysis. 2. Application to Ru-Modified Cytochrome c

In an accompanying paper (part 1) we presented a model (NMRES) that describes the coupling of protein fluctuations to electron transfer. The NMRES model, employing normal mode analysis that incorporates Tanford−Kirkwood reaction field energies, relates each normal mode to a mode-specific reorganization energy (<EQUATION><EQNDATA>%@mt;sys@%λ%@sx@%%@ital@%k%@rsf@%%@be@%prot%@sxx@%%@mx@%</EQNDATA> </EQUATION>), ultimately yielding a protein λ spectrum. In this paper we have successfully applied the NMRES model and analyzed intramolecular electron transfer in Ru-modified cytochrome c (at His33). The NMRES estimate for the total protein λ was found to be 15.6 kcal/mol, while the bulk solvent contribution was found to be 7.2 kcal/mol. Of this 15.6 kcal/mol, the high-frequency inner sphere protein modes contributed 3.2 kcal/mol (<EQUATION><EQNDATA>%@mt;sys@%λ%@sx@%in%@be@%prot%@sxx@%%@mx@%</EQNDATA> </EQUATION>), while the remaining 12.4 kcal/mol (<EQUATION><EQNDATA>%@mt;sys@%λ%@sx@%out%@be@%prot%@sxx@%%@mx@%</EQNDATA> </EQUATION>) arose from the low-frequency outer sphere protein modes, the focus of this paper. Out of about 600 “soft” low-frequency modes, 60% contributed very little, while the remaining 40% contributed more or less equally. There were no special soft modes in terms of contribution to <EQUATION><EQNDATA>%@mt;sys@%λ%@sx@%out%@be@%prot%@sxx@%%@mx@%</EQNDATA> </EQUATION>, structurally or energetically. In other words, although not all the soft modes contributed, those that did shared the coupling more or less equally, implying that minor changes in the dynamic structure will not alter the total λ significantly. This could be the reason that the experimental λ on Ru-modified (at various His sites) cytochrome c is found to be almost invariant.