Mapping electron tunneling pathways: an algorithm that finds the "minimum length"/maximum coupling pathway between electron donors and acceptors in proteins

The covalent, hydrogen bonded, and van der Waals connectivity of proteins can be represented with geometrical objects called graphs. In these graphs, vertices represent bonds and the connections between them, edges, represent bond-bond interactions. We describe a model in which edge lengths are associated with the wave function decay between interacting pairs of bonds, and a minimum distance graph-search algorithm is used to find the pathways that dominate electron donor-acceptor interactions in these molecules. Predictions of relative electron transfer rates can be made from these pathway lengths. The results are consistent with many experimentally measured electron-transfer rates, although some anomalies exist. Presentation of the pathway coupling between the donor (or acceptor) and every other atom in a given protein as a color-coded map provides a design tool for tailored electron-transfer proteins