192Long-range electronic interactions between electron donorsand acceptors in proteins depend on the structure of theintervening polypeptide. Several methods have beendeveloped for calculating these weak couplings. Newchallenges in protein electron-transfer research includeidentifying the role of protein dynamics, and characterizingmultistep tunneling over very long distances.AddressesBeckman Institute, MC 139-74, California Institute of Technology,Pasadena, California 91125, USA; e-mail: [email protected] Opinion in Chemical Biology 2000, 4:192–1981367-5931/00/$ — see front matter© 2000 Elsevier Science Ltd. All rights reserved.AbbreviationsA acceptorD donorET electron-transferHABelectronic coupling matrix elementR distance between the reactantsTP tunneling pathwayUB uniform barrierIntroductionElectron transfers, the simplest chemical reactions, per-vade chemistry and biology. Theoretical efforts beginningin the late 1950s and continuing to the present day haveprovided a remarkably detailed description of electron-transfer (ET) reactions [1]. The semiclassical model isgiven in Equation 1:(1)where kETis the first-order rate constant for electrontransfer from a donor (DD) to an acceptor (AA) held at fixeddistance and orientation as a function of temperature (T),reaction driving force (–∆G°), nuclear reorganization ener-gy (λ), and electronic coupling matrix element (HAB) [2];kBis the Boltzmann constant and h is the Planck constant.The reorganization parameter reflects the changes instructure and solvation associated with electron transferfrom DDto AA. A balance between nuclear reorganizationand reaction driving force determines the transition-stateconfiguration and, hence, the height of the energy barrierfor the ET process. The nonadiabatic expression inEquation 1 is appropriate when the DD–AAinteraction isweak and the transition state must be reached many timesbefore an electron transfers. Electron-transfer reactions can proceed at very high rateswhen DDand AAare separated by long distances. The electron tunnels through a potential barrier between DDand AA; for a square barrier, the tunneling probabilityreflected by HABwill exhibit an exponential dependenceon the distance between the reactants (RR) [3]. The3.4 Å–1distance-decay constant (β) estimated for ETacross a vacuum limits transfer distances to ≤10 Å in theabsence of a medium between DDand AA[4]. ET measure-ments in synthetic donor–bridge–acceptor complexes,however, have produced β values of 0.8–1.2 Å–1; electronscan be transferred across 15 Å in microseconds [5]. Thegradual decrease in rate with distance is attributed tosuperexchange coupling via hole and electron states ofthe intervening bridge. The question with regard to pro-teins is, how does the heterogeneous array of bonded andnonbonded contacts in a folded polypeptide mediatelong-range electronic coupling?Tunneling in proteinsIn 1961 McConnell [6] described the superexchangecoupling across a bridge constructed from identical sub-units as the product of the coupling decays for eachbridge element. Beratan, Onuchic, and Hopfield [7] gen-eralized this approach with the tunneling pathway (TP)description of electronic coupling in proteins. The TPmodel reduces the complex array of interatomic interac-tions in a folded polypeptide to just three types: covalentbonds, hydrogen bonds, and through-space contacts.Each contact is assigned a coupling decay value (εC, εH,and εS, respectively); the overall coupling for a pathwaybetween DDand AAis given by the product of the decayfactors for the components of the pathway [4]. This pre-scription for the calculation of relative HABvalues led tothe development of a search algorithm for finding opti-mal coupling pathways through proteins [8]. The keyprediction of the TP model is that DD–AAcoupling in aprotein is extremely sensitive to the structure of theintervening medium [9].Dutton and coworkers [10–12,13•] argue that pathwayoptimization is not an important factor in the design ofredox proteins. Instead, they suggest that the manifoldcontacts in a folded polypeptide, like those in a rigid sol-vent matrix, would create a uniform barrier (UB) toelectron tunneling [10]. The UB model predicts thatrates will exhibit an exponential dependence on RR, with-out regard for the structure of the intervening medium.Analysis of a variety of ET rates, especially those fromthe photosynthetic reaction center, produced a universaldistance-decay constant of 1.4 Å–1for protein ET [10].Uncertainty about the appropriate DD–AAdistance mea-sure (edge-to-edge, center-to-center) has fueled thedebate about whether protein ET rate data support theUB or the TP model [12,14–16]. +∆−=TkGHTkhkBABBET 4)(exp 42223λλλπoElectron tunneling pathways in proteinsJay R WinklerCh4212.qxd 03/15/2000 09:07 Page 192Electron tunneling pathways in proteins Winkler 193An extensive set of ET rate and distance measurementsfrom Ru-modified proteins offers strong evidence in sup-port of structure-dependent couplings (Figure 1) [17••].The high-driving-force ET rates measured in these pro-teins are quite close to electronic-coupling-limitedvalues (i.e. –∆G° =λ) [18,19]. Metal–metal DD–AAdis-tances in 30 modified proteins ranged over 15 Å and ET rate constants spanned six orders of magnitude. The scatter in the data illustrates conclusively that the UB model does not adequately describe long-range couplings in proteins. In cytochrome c, for example, two modified proteins have comparable ET rates (Ru(His72), 9.0 × 105s–1; Ru(His39),3.2 × 106s–1), yet the Ru–Fe distances differ by 6.5 Å(His72, 13.8 Å; His39, 20.3 Å). In addition, the shortestRu–Fe distances in Ru(His81) and Ru(His50) deriva-tives of high-potential iron–sulfur protein differ by only1.5 Å, but the rate of ET is 340 times slower in theRu(His50) derivative [20•]. The UB model has been refined to account for the pack-ing density of the protein in the region between redoxsites [12,13•]. Although this approach ignores chemicalbonding, it embodies many of the same elements as theTP model. A survey of structures indicates that the pack-ing densities between redox sites are not substantiallydifferent from those in other parts of ET proteins. On thebasis of this analysis, Dutton and co-workers [13•] con-clude that although long-range couplings depend onprotein structure, nature has not optimized