Tunneling-to-Hopping Transition in Multiheme Cytochrome Bioelectronic Junctions

Abstract

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.

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

“…60 After the MD relaxation of this chemisorbed structure, the top Au(111) surface representing the second gold contact was added to the model. Following the simulation protocol recently demonstrated on cytochrome junctions, 13,18 the inter-slab distance was then optimized by sequential lowering of the top surface while evaluating the local stress tensor 61,62 on a grid spanning the simulation cell until the pressure in the protein region was close to zero. The resulting junction structure has the separation distance between two gold surfaces equal to 28.75 Å.…”

“…[5][6][7][8][9][10] There is an ongoing debate about the nature and mechanism of electronic-charge transport at such heterogeneous interfaces as the experimental measurements suggest that an electron can either incoherently hop or coherently tunnel through biomolecular junctions. [11][12][13][14][15][16][17][18] A detailed understanding of these phenomena and their control is key for optimizing and designing the aforementioned applications.…”

Near-Temperature-Independent Electron Transport Well beyond Expected Quantum Tunneling Range via Bacteriorhodopsin Multilayers

“…The approximated β values (from eq ) are 0.5, 0.3, 0.25, 0.1, and 0.05 nm –1 for a single, double, triple bilayer, T-44, and T-60 multilayer junctions, respectively (inset to Figure C). These β values, especially of the thicker multilayers, are low compared to those obtained for other, well-studied proteins that are efficient ETp media, particularly PS-I (0.8–1.6 nm –1 ), models of STC protein stacks (2 nm –1 ), azurin (1.8 nm –1 ), and ferritin (0.3–1.3 nm –1 ) . To make a more consistent comparison, β values were extracted from results obtained with the same protein junction configuration (Si/SiO x /linker/protein/Au-pad), all at 0.1 V applied bias, and plotted against the experimentally derived different protein films’ thickness values (Figure S9).…”

“…Recently, Gupta et al 45 reported a low β (0.28 nm −1 ) and activationless ETp in a ferritin system, interpreted as electron tunneling over the 7.5 nm polypeptide matrix-incorporated FeO(OH) junction. Interestingly, 7.5 nm is beyond the 7 nm limit of quantum mechanical tunneling through multiheme proteins, derived by Futera et al 44 The latter, theoretical analyses of experimentally observed currents via a multiheme cytochrome protein led to the conclusion that the transport mechanism will change from coherent tunneling to incoherent hopping for ETp over >∼7 nm protein distances. That conclusion holds in these highly electron-rich proteins if ETp is not limited by interfacial ET between the electrode and the protein.…”

Long-Range Conductivity in Proteins Mediated by Aromatic Residues

“…Delocalized valence-band orbitals have been offered as an alternative explanation for long-range conductance in dry multi-heme proteins, where it is proposed that the transmission is via direct tunneling across the whole protein with a very small effective decay constant. , In the case of the multiheme wires, OmcS and OmcZ, a small shift in heme–heme separation causes a thousand-fold change in conductance, suggestive of significant delocalization effects or changes in contact resistance. The timescales of localized medium vibrations and charge tunneling, ℏ / V , overlap in the protein studied here (see below) likely trapping the charge at the hopping sites and limiting quantum coherence and delocalization.…”