Coherence-assisted electron diffusion across the multi-heme protein based bacterial nanowire.

Biological electron transfer (ET) is one of the most studied biochemical processes due to its immense importance in biology. For many years, biological ET was explained using the classical incoherent transport mechanism, i.e. sequential hopping. One of the relatively recent major observations in this field is long-range extracellular ET (EET), where some bacteria were shown to mediate electrons for extremely long distances on the micrometer length scales across individual nanowires. This fascinating finding has resulted in several suggested mechanisms that might explain this intriguing EET. More recently, the structure of a conductive G. sulfurreducens nanowire has been solved, which showed a highly ordered quasi-1D wire of a hexaheme cytochrome protein, named OmcS. Based on this new structure, we suggest here several electron diffusion models for EET, involving either purely hopping or several degrees of mixed hopping and coherent transport, in which the coherent part is due to a local rigidification of the protein structure, associated with a decrease in the local reorganization energy. The effect is demonstrated for two closely packed heme sites as well as for longer chains containing up to several dozens porphyrins. We show that the pure hopping model probably cannot explain the reported conductivity values of the G. sulfurreducens nanowire using conventional values of reorganization energy and electronic coupling. On the other hand, we show that for a wide range of the latter energy values, the mixed hopping-coherent model results in superior electron diffusion compared to the pure hopping model, and especially for long-range coherent transport, involving multiple porphyrin sites.