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

Structural determinants of a 10³-fold variation in electrical conductivity for helical homopolymers of tetra-, hexa-, and octa-heme cytochromes (named Omc- E, S, and Z, respectively) from Geobacter sulfurreducens are investigated with the Pathways model for electron tunneling, classical molecular dynamics, and hybrid quantum/classical molecular mechanics. Thermally averaged electronic couplings for through-space heme-to-heme electron transfer in the "nanowires" computed with density functional theory are ≤0.015 eV. Pathways analyses also indicate that couplings match within a factor of 5 for all "nanowires", but some alternative tunneling routes are found involving covalent protein backbone bonds (Omc- S and Z) or propionic acid-ligating His H-bonds on adjacent hemes (OmcZ). Reorganization energies computed from electrostatic vertical energy gaps or a version of the Marcus continuum expression parameterized on the total (donor + acceptor) solvent-accessible surface area typically agree within 20% and fall within the range 0.48-0.98 eV. Reaction free energies in all three "nanowires" are ≤|0.28| eV, even though Coulombic interactions primarily tune the site redox energies by 0.7-1.2 eV. Given the conserved energetic parameters, redox conductivity differs by < 10³-fold among the cytochrome "nanowires". Redox currents do not exceed 3.0 × 10^-3 pA at a physiologically relevant 0.1 V bias, with the slowest electron transfers being on a (μs) timescale much faster than typical (ms) enzymatic turnovers. Thus, the "nanowires" are proposed to be functionally robust to variations in structure that provide a habitat-customized protein interface. The 30 pA to 30 nA variation in conductivity previously reported from atomic force microscopy experiments is not intrinsic to the structures and/or does not result from the physiologically relevant redox conduction mechanism.