Distance metrics for heme protein electron tunneling

There is no doubt that distance is the principal parameter that sets the order of magnitude for electron-tunneling rates in proteins. However, there continue to be varying ways to measure electron-tunneling distances in proteins. This distance uncertainty blurs the issue of whether the intervening protein medium has been naturally selected to speed or slow any particular electron-tunneling reaction. For redox cofactors lacking metals, an edge of the cofactor can be defined that approximates the extent in space that includes most of the wavefunction associated with its tunneling electron. Beyond this edge, the wavefunction tails off much more dramatically in space. The conjugated porphyrin ring seems a reasonable edge for the metal-free pheophytins and bacteriopheophytins of photosynthesis. For a metal containing redox cofactor such as heme, an appropriate cofactor edge is more ambiguous. Electron-tunneling distance may be measured from the conjugated heme macrocycle edge or from the metal, which can be up to 4.8 A longer. In a typical protein medium, such a distance difference normally corresponds to a approximately 1000 fold decrease in tunneling rate. To address this ambiguity, we consider both natural heme protein electron transfer and light-activated electron transfer in ruthenated heme proteins. We find that the edge of the conjugated heme macrocycle provides a reliable and useful tunneling distance definition consistent with other biological electron-tunneling reactions. Furthermore, with this distance metric, heme axially- and edge-oriented electron transfers appear similar and equally well described by a simple square barrier tunneling model. This is in contrast to recent reports for metal-to-metal metrics that require exceptionally poor donor/acceptor couplings to explain heme axially-oriented electron transfers.