In recent years it has become possible to design simple and stable polypeptides that accommodate functional elements of natural proteins. Redox active nanoscale materials such as porphyrin binding proteins are of immense interest because of their potential use as bioelectronic devices or as catalysts in light-energy harvesting processes coupled to hydrogen and oxygen production. Because of their simple structure, stability, and relative ease with which they can be mutated, designed redox proteins offer the possibility of systematic study of the various factors that govern the rate of biological electron transfer (ET) reactions.
In the Marcus picture of non-adiabatic electron transfer the rate is determined by three key quantities: reorganization free energy λ, redox potential difference of the two cofactors or free energy difference ΔA and electronic coupling between donor and acceptor (see bottom left picture). While redox potentials of cofactors bound to proteins can be measured to high precision, the reorganization free energy is not an experimental observable and has to be determined indirectly and often with rather large uncertainties by fitting experimental data to the rate expression of Marcus. In this regard, computer simulations are a valuable alternative for quantitative estimation of reorganization free energies. Moreover, the validity of the linear response assumption leading to parabolic free energy curves in Marcus theory does not have to be asserted but can be assessed using force field based, or better, ab initio MD with enhanced sampling methods.
In recent work we have calculated the reorganization free energy of four Ru-modified heme containing proteins (see top left picture), cytochrome c with a Ru-pentammine complex docked to His33 (cca), cytochrome c and b5 with a Ru-bipyridine complex docked to His33 (ccb, cb5b), and a four-helix bundle protein (4-helix) [JACS10, JACS06]), using recently developed QM/MM and QM+MM simulation protocols [PCCP08]. We found that in each protein the contribution of the redox active cofactors to the activation barrier is minor, less than 10 %, whereas the majority is due to the protein and solvent. Our results indicate that in three out of the four proteins studied (ccb, cb5b and the four-helix bundle protein) protein reorganization can be considered as a collective effect, that involves many residues, each contributing a small fraction. This suggests that reorganization free energy may not be significantly lowered by single point mutations of these proteins. Judging from the simulations of the 4-helix bundle, a very effective way to decrease reorganization free energy is to reduce the exposure of the redox active cofactors to solvent. We regard this finding as important for the future design of artificial redox proteins. If a fast ET rate is to be maintained at small driving forces then it is essential to protect the engineered cofactor from the solvent and from the interaction with neighbouring ionizable protein residues. Future investigations will focus on multi-heme proteins that are used by bacteria shuttle electron within the cell and across the cell membrane.