Tunneling-to-Hopping Transition in Multiheme Cytochrome Bioelectronic Junctions

Multiheme cytochromes (MHCs) have attracted much interest for use in nanobioelectronic junctions due to their high electronic conductances. Recent measurements on dry MHC junctions suggested that a coherent tunneling mechanism is operative over surprisingly long long distances (>3 nm), which challenges our understanding of coherent transport phenomena. Here we show that this is due to (i) a low exponential distance decay constant for coherent conduction in MHCs (β = 0.2 Å^-1) and (ii) a large density of protein electronic states which prolongs the coherent tunneling regime to distances that exceed those in molecular wires made of small molecules. Incoherent hopping conduction is uncompetitive due to the large energy level offset at the protein-electrode interface. Removing this offset, e.g., by gating, we predict that the transport mechanism crosses over from coherent tunneling to incoherent hopping at a protein size of ∼7 nm, thus enabling transport on the micrometer scale with a shallow polynomial (∼1/r) distance decay.