Ergodicity Breaking in Thermal Biological Electron Transfer? Cytochrome C Revisited II

Abstract

It was recently suggested that cytochrome c operates in an ergodicity-breaking regime characterized by unusually large energy gap thermal fluctuations and associated reorganization free energies for heme oxidation of up to 3.0 eV. The large fluctuations were reported to lower activation free energy for oxidation of the heme cofactor by almost a factor of 2 compared to the case where ergodicity is maintained. Our group has recently investigated this claim computationally at several levels of theory and found no evidence for such large energy gap fluctuations. Here we address the points of our earlier work that have raised critizism and we also extend our previous investigation by considering a simple linear polarizability model for cytochrome c oxidation. We find very consistent results among all our computational approaches, ranging from classical molecular dynamics, to the linear polarizability model to QM(PMM)/MM to full QM(DFT)/MM electrostatic emdedding. None of them support the notion of unusually large energy gap fluctuations or ergodicity breaking. The deviation between our simulations and the ones reported in [J. Phys. Chem. B 2017, 121, 4958] is traced back to an unusually large electric field at the Fe site of the heme c cofactor in that study, not seen in our simulations, neither with the AMBER nor with the CHARMM force field. While ergodicity breaking effects may well occur in other biological ET, our numerical evidence suggests that this is not the case for cytochrome c.

Structural Determinants of Redox Conduction Favor Robustness over Tunability in Microbial Cytochrome Nanowires

“…Consequently, λ rxn in Omc- E, S, and Z, respectively, is nearly the same as λ st : 0.481 to 0.871, 0.429 to 0.983, and 0.556 to 0.892 eV. The observation that λ st ≈ λ i var ≈ λ f var implies that ergodicity-breaking is not observed as a mechanism for lowering the activation barrier to electron transfer in all three “nanowires” on the timescale of the current dynamical simulations. − Standard Marcus theory applies in this case. All three “nanowires” have very similar outer-sphere reorganization energies, even though the protein matrices and heme solvent accessibilities are very different.…”

Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin

“…The field vector from each MD snapshot (sample) was rotated to the coordinate frame used in the ZINDO calculations, following the procedure described in ref. 91, and then used to construct the PMM Hamiltonian, eqn (7). The field strength and orientation found in azurin are consistent with a recent study of Bim and Alexandrova, 92 who studied local field in a group of more than 30 cupredoxins and observed that the field vectors are typically pointing to the opposite direction than and vectors.…”

“…The polarizability evaluated by ZINDO on QC-5 has magnitude ∼4 Å 3 , which is by one order lower value than polarizabilities of redox sites in cytochromes. 91 This indicates that the transition dipole moments μ ij are small and so are their scalar products with the intrinsic field E . As these products determine the off-diagonal Hamiltonian elements (eqn (7)), the resulting Hamiltonian is practically quasi-diagonal.…”

“…Therefore, the perturbative description is justified for this system as, for example, in solvated cytochromes and other proteins. 40,41,43,45,91 Quality of the calculation is, of course, affected by the chosen computational setup. Before we apply the PMM to the heterogeneous interfaces of azurin on gold surfaces, we explore these effects on the relaxed vacuum azurin structure discussed in the next section.…”

Are Electrical Characterizations Consistent with the Cytochrome Structures ofGeobacter‘Nanowires’

“…94,95 Polarizability of the heme active site may further lower the reorganization energy, as proposed for cytochrome c on the basis of semi-empirical quantum chemistry (ZINDO/S) calculations, 96 although this point has been debated. [97][98][99] However, density functional theory calculations for the hemes in the cytochrome filaments found only <0.04 eV shifts in the reorganization energy when relaxing vacuum-optimized electron densities in the presence of the perturbing protein/water environment (Tables S4-S6. 74 Polarizability corrections are not expected to vary widely between proteins, as evidenced by recommendations of system-independent scaling factors.…”