The nature of tunneling pathway and average packing density models for protein-mediated electron transfer

The last 30 years have witnessed the development of increasingly successful theoretical approaches to predicting how a protein's chemical composition and three-dimensional structure influence its propensity to mediate electron-transfer reactions. Analysis has progressed from uniform-barrier models that neglect atomic detail, to pathway models that incorporate the specific nature of the bonding and the protein fold, to multipathway models that add coherently the contributions of pathways, to methods that average over accessible geometries. Large-scale electronic structure methods remain of somewhat limited use because: the demands of geometry sampling and electronic structure calculation are considerable, especially for slower ET events; qualitative new insights arising from the more intensive analysis have been moderate; and structure-function relations become increasingly difficult to derive from more complex models. For these reasons, simple models remain both useful and popular. The simplest structured-protein models employ tunneling pathway and average packing density analysis. These methods are derived from the same protein physics: electronic interactions decay much more rapidly through-space than through-bond. We show that for the majority of 38 donor-acceptor pairs in 28 proteins with determined X-ray structures, the two models are in qualitative agreement. However, for five of these donor-acceptor pairs, the pathway and the average packing density predictions are qualitatively different. The structural reasons for these differences are clear: (I) strong coupling pathways may exist in regions of unremarkable packing density, (2) explicit water molecules added to the X-ray structures can eliminate otherwise costly through-space jumps, (3) strong pathways situated beyond the zone sampled in average packing density analysis can dominate. We suggest that the instances of substantial differences between the two models can be used to probe ET tunneling mechanism. Differences, where they exist, point to specific structural motifs where pathway effects associated with a protein's three-dimensional structure might play a central role in ET kinetics.