Investigating electron conductivity regimes in the bacterial cytochrome wire OmcS

The anaerobic bacterium \textit{Geobacter sulfurreducens} produces extracellular, electronically conductive cytochrome polymer wires that are conductive over micron length scales. Structure models from cryo-electron microscopy data show OmcS wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. The geometric arrangement of heme along OmcS wires is conserved in many multiheme c-type cytochromes and other recently discovered microbial cytochrome wires. However, the mechanism by which this arrangement of heme molecules support electron transport through proteins and supramolecular heme wires is unclear. Here, we investigate the site energies, inter-heme coupling, and long-range electronic conductivity within OmcS. We introduce an approach to extract charge carrier site information directly from Kohn-Sham density functional theory, without employing projector schemes. We show that site and coupling energies are highly sensitive to changes in inter-heme geometry and the surrounding electrostatic environment, as intuitively expected. These parameters serve as inputs for a quantum charge carrier model that includes decoherence corrections with which we predict a diffusion coefficient comparable with other organic-based electronic materials. Based on these simulations, we propose that dynamic disorder, particularly due to perturbative inter-heme vibrations allow the carrier to overcome trapping due to the presence of static disorder \textit{via} small frequency-dependent fluctuations. These studies provide insights into molecular and electronic determinants of long-range electronic conductivity in microbial cytochrome wires and highlight design principles for bioinspired, heme-based conductive materials.