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.