Electron tunneling in structurally engineered proteins Photosynthesis, respiration, nitrogen fixation, drug metabolism, DNA synthesis, and immune response are among the scores of biological processes that rely heavily on long-range (10 to 25 Ǻ) protein electron-transfer (ET) reactions. Semiclassical theory predicts that the rates of these reactions depend on the reaction driving force –ΔG o, a nuclear reorganization parameter λ, and electronic-coupling strength H AB between reactants and products at the transition state. The ET rates (k ET o ) reach their maximum values when the nuclear factor is optimized (–ΔG o = λ). These k ET o values are limited only by the strength of the electronic interaction (H AB 2 ) between the donor (D) and acceptor (A). Coupling-limited Cu 2+ to Ru 3+ and Fe 2+ to Ru 3+ ET rates have been extracted from kinetic studies on several Ru-modified proteins. In azurin, a blue copper protein, the distant D/A pairs are relatively well coupled (k ET o decreases exponentially with R(Cu-Ru); the decay constant is 1.1 Ǻ -1 ). In contrast to the extended peptides found in azurin and other β-sheet proteins, helical structures have tortuous covalent pathways owing to the curvature of the peptide backbone. The decay constants estimated from ET rates for D/A pairs separated by long sections of the a helix in myoglobin and the photosynthetic reaction center are between 1.25 and 1.6 Ǻ -1. Journal of Electroanalytical Chemistry 438 (1997) Hairy B. Gray and Jay R. Winkler: Abstract

Electron tunneling in proteins occurs in reactions where the electronic interaction between redox sites is relatively weak. The process is electronically non-adiabatic. The transition state for the reaction must be formed many times before there is a successful conversion from reactants to products. Semiclassical theory predicts that the reaction rate for electron transfer (ET) from a donor (D) to an acceptor (A) at fixed separation and orientation depends on the reaction driving force -ΔG o, a nuclear reorganization parameter λ, and the electronic-coupling strength H AB between reactants and products at the transition state. The D-A distance decay of protein ET rate constants depends on the capacity of the polypeptide matrix to mediate electronic couplings. In 1992, Dutton showed that the exponential distance-decay constant (1.4 Ǻ -1 ) could be used to estimate long-range ET rates in the bacterial photosynthetic reaction center (RC). It became late evident that the rate/distance correlation can be used to get indication of the coupling strengths in the intervening polypeptide structure in other proteins, as well. Marcus formalism of the ET

Plots of σ 1 vs. R β for an idealized β strand and α helix. The slope of the β-strand line is 1.37 (circles). For the α helix (squares), three different treatments of the hydrogen-bond interaction were used: 1) no mediation of coupling, α slope = 2.7: 2) Beratan-Onuchic parameterization of hydrogen-bond couplings, α H slope=1.72; 3) hydrogen bonds treated as covalent bonds, α Hc slope = 1.22.

Structure of Pseadomonas oeruginosa azurin including the histidine residues that have been coordinated to Ru(bpy) 2 (im) 2+ ; the Cys3-Cys26 disulfide group is also shown.

Plot of log k ET o vs. R: Ru-modified azurins (●); Cys3-Cys26(S 2 - ) → Cu 2+ ET in azurin (♦); Ru-modified Mb (■), and the RC (□). Dashed lines are distance decays predicted using the tunneling-pathway model for β strands and α helices. Solid lines are the best linear fits with an intercept at s -1 and correspond to distance decays of 1.1 Ǻ -l for azurin and 1.4 Ǻ -l for Mb and the RC.

Plot of log k ET o vs. R illustrating the different ET coupling zones. Zones are bounded by the following distance-decay lines: α zone, 1.25 and 1.6 Ǻ -1 ; β zone, 1.15 and 0.9 Ǻ -1. The lighter-gray shaded region is the interface between the α and β zones. For Ru- bpy-modified proteins, metal-metal separation distances are used. Distances between redox sites in the RC are reported as edge-edge separations.