23796
J. Phys. Chem. B 2006, 110, 23796-23800
Water Effects on Electron Transfer in Azurin Dimers Agostino Migliore,*,†,‡ Stefano Corni,† Rosa Di Felice,† and Elisa Molinari†,‡ National Center on nanoStructures and bioSystems at Surfaces (S3) of INFM-CNR, Modena, Italy, and Dipartimento di Fisica, UniVersita` di Modena e Reggio Emilia, Via Campi 213/A, Modena, Italy ReceiVed: July 24, 2006; In Final Form: September 20, 2006
Recent experimental and theoretical analyses indicate that water molecules between or near redox partners can significantly affect their electron-transfer (ET) properties. Here, we study the effects of intervening water molecules on the electron self-exchange reaction of azurin (Az) by using a newly developed ab-initio method to calculate transfer integrals between molecular sites. We show that the insertion of water molecules in the gap between the copper active sites of Az dimers slows down the exponential decay of the ET rates with the copper-to-copper distance. Depending on the distance between the redox sites, water can enhance or suppress the electron-transfer kinetics. We show that this behavior can be ascribed to the simultaneous action of two competing effects: the electrostatic interaction of water with the protein subsystem and its ability to mediate ET coupling pathways.
1. Introduction Protein electron-transfer (ET) reactions represent a major concern in the current nanoscale research for two main reasons: (1) they play a crucial role in vital processes of living cells1 and (2) modern electronics aims at exploiting the intrinsic functions of biomolecules to implement nanoelectronic devices.2-4 Long-distance tunneling is the major electron-transfer mechanism in proteins,5,6 and the accurate prediction of the inherent ET rates is a long-standing challenge. Indeed, several factors, subject of experimental7 and theoretical8-10 investigations, can concur to determine the rates of biological ET processes, such as the structure and the energies of the donor and acceptor groups, the distance between them, the structure of interposed protein portions, and the thermal atomic motion. Further factors relevant to the intermolecular electron transfer are the docking of the redox partners and the properties of the often intervening solvent.11 Water is the most important molecular environment for electron transfer. It can affect intermolecular ET rates by means of its electrostatic and quantum interactions with the protein system, which can play a central role in determining the best ET pathway and the activation free energy.8,12 Many experimental7,13,14 and theoretical15 studies have been focused on the efficiency of water in mediating electron-transfer reactions, with special attention to its influence on the distance dependence of ET rates. Several questions remain yet debated.6 Both singleexponential14 and multiple-exponential12 decay modes of the ET rates were found. In some circumstances, water appeared to be a poor electron-transfer mediator14 or appeared not to influence the ET processes significantly,16 while it has been recently suggested that water molecules in the interface of covalently cross-linked azurin dimers could increase the inherent electron-transfer rate.13 Even the existence of specific electrontunneling pathways (not observed directly) is still debated,17,18 * Author to whom correspondence should be addressed. Phone: +39059-2055315; fax: +39-059-2055651; e-mail:
[email protected]. † National Center on nanoStructures and bioSystems at Surfaces (S3) of INFM-CNR. ‡ Universita ` di Modena e Reggio Emilia.
although recent theoretical calculations support the idea of specific ET paths.19 The present paper is devoted to the ab-initio computation of the electron-transfer matrix elements, or transfer integrals,20 for the electron self-exchange between Az active sites at different distances, in the presence of two interposed water molecules. The ET system is modeled after the X-ray structure of Az dimers, where such water molecules were observed.13 The transfer integrals are important factors in controlling the rates of many electron-transfer reactions. Within the context of Marcus’ ET theory,21 they can be easily combined with estimates of the reorganization energy to evaluate the ET rates, measured in kinetic experiments. Much progress has been recently made in computing transfer integrals22-27 through several quantum chemical methods,19,20,22,28,29 and the increasing availability of both electron-transfer kinetic data and powerful computational tools enabled several comparisons between theory and experiment.30 However, electronic couplings between molecules are difficult to calculate accurately, because they are often extremely small, and some inherent problems are still unresolved.6 In particular, proteins are generally too large systems for exhaustive ab-initio calculations, thus requiring the usage of approximate computational methods, such as semiempirical31 and proteinfragment27 approaches. The method exploited in this paper29 overcomes some usual limitations of such approaches. In particular, it can use a complete multielectron scheme (i.e., does not rely on a single-particle scheme), thus comprising electronic relaxation effects; it does not use empirical parameters; it does not require the knowledge of the transition-state coordinate and of excited-state quantities. We have implemented the method in a density-functional theory (DFT) scheme.29 DFT is the best compromise between accuracy and computational feasibility for studying large metal-ion complexes, such as the Az sites investigated in our work. DFT is also the best approach for calculating electronic properties of solid crystal systems. Thus, it addresses the desirable purpose of treating biological and inorganic components with the same method, in view of possible applications involving both components together.
10.1021/jp064690q CCC: $33.50 © 2006 American Chemical Society Published on Web 10/31/2006
Water-Mediated Electron Transfer in Azurin
J. Phys. Chem. B, Vol. 110, No. 47, 2006 23797 energy, kB is the Boltzmann’s constant, T is the temperature, and UIF is the transfer integral. The latter measures the coupling between the initial (I) and final (F) ET diabatic states. Starting from the secular equation for the ground state of the system, we obtained the following expression for the modulus of the transfer integral:29
|UIF| ) Figure 1. Models of the azurin dimer active sites investigated in the present paper in a ball-and-stick representation. C, N, O, S, and H atoms are shown as green, blue, red, yellow, and white spheres. Cu ions are shown as pink spheres. D and A indicate the donor group and the acceptor group, respectively. (a) Minimal atomic set. All the five Cu ligands are included with relevant functional groups neglecting the full atomic structure of the residues. (b) “Complete” atomic model. All the atoms of the five ligand amino acids are included, except for a pruning along the backbone, tested elsewhere.29
2. System Definition and Methods The electron self-exchange reaction under study is
[Az(I)-Az(II)]dimer f [Az(II)-Az(I)]dimer
kET )
x
[
]
∆EIFab
a2 - b2
|
(3)
where ∆EIF is the energy difference between the ET states I and F, and a, b are their respective overlaps with the ground state of the system. The approximations done to derive eq 3 are discussed in detail in ref 29. Here, we only remark that eq 3 implies a relatively weak assumption on the overlap 〈ψI|ψF〉, that is, |〈ψI|ψF〉|2 , 1. Within the theoretical framework of ref 29, eq 3 provides the best estimate of the transfer integral also when the two-state approximation is not fulfilled. All quantities in eq 3 were derived from ab-initio DFT computations. The energy difference ∆EIF is given by the relation
∆EIF ) (ED + EA) - (ED+ + EA-) + UD-A - UD+-A- (4) (1)
were [Az(I)-Az(II)]dimer refers to the dimer with one reduced and one oxidized Az. We analyze the influence of two intervening water molecules on the ET rate, focusing our attention on the evaluation of the transfer integral at several distances between the ET centers. Modeling the Protein Structure. Generally, because of the tunneling nature of the electron transfer between redox sites, the involved protein regions are relatively small.6 Moreover, the geometries of the active sites in blue copper proteins appear reasonably well reproduced by in vacuo DFT calculations.32 Thus, we made electronic structure calculations on the model systems of Figure 1, whose nuclear coordinates (derived from X-ray-diffraction data) were drawn from the PDB file 1JVL. This PDB structure appears to be a reasonable choice to mimic the geometry of the short-living Az dimer in solution.13 Moreover, we did not consider the thermal atomic motion to distinguish more clearly the water effects and to be able to quantify them. The small atomic model of Figure 1a clearly shows that in each Az active site the copper ion is surrounded by five ligands in a distorted trigonal bipyramidal geometry, with three strong equatorial ligands (Cys112, His46, and His117) and two weakly bound axial ligands (Met121 and Gly45). Such a model was exploited to study, at a convenient computational cost, the dependence of the transfer integral on the distance between the redox sites, as measured by the copper-to-copper distance. The larger atomic model of Figure 1b was used to derive a more accurate estimate of the absolute transfer integral (and related ET rate) at the crystal copper-to-copper distance of 14.6 Å. Computing Transfer Integrals. Transfer integrals are crucial quantities in determining the rates of electron-transfer processes. Indeed, many ET reactions in protein systems involve weakly coupled donor and acceptor electronic states and, following Marcus’ theory, the inherent rate constants are provided by the high-temperature, nonadiabatic expression21 2 (∆G0 + λ)2 π |UIF | exp λkBT p 4λkBT
|
(2)
where λ is the reorganization energy, ∆G° is the reaction free
where ED (ED+) is the ground-state energy of the isolated molecule D (see Figure 1) in the reduced (oxidized) state of charge, EA (EA-) is the same for the molecule A in the oxidized (reduced) state, UD-A and UD+-A- are the energies of (essentially electrostatic) interaction between the donor and acceptor groups in the initial and final diabatic states, respectively. The implementation of eq 3 requires a suitable definition of the initial and final diabatic states. As customary28 for longrange through-space ET reactions between charge-localized states, we distinguished a donor group D (that is, the initially reduced Az active site), on which the transferring electron is initially localized, and an acceptor group A that receives the transferred electron (Figure 1). Hence, in the absence of water, we defined the initial vector state of the overall system as |ψI〉 ) |D〉|A〉 and the final vector state as |ψF〉 ) |D+〉|A-〉, where |D〉(|D+〉) indicates the reduced (oxidized) ground state of the isolated donor redox site, and |A-〉(|A〉) indicates the reduced (oxidized) ground state of the isolated acceptor redox site. In the presence of water, we included in the donor and acceptor groups the respective adjacent water molecules. The total ground state can be written as |ψ-〉 ) a|ψI〉 + b|ψF〉 + c|ψT〉, where the vector state c|ψT〉 effectively takes into account what goes beyond the two-state approximation. All the relevant wave functions were obtained as single Slater determinants of the lowest-lying-occupied KS spin-orbitals for both the involved closed-shell and open-shell systems. As a matter of fact, for open-shell systems, the single-determinant wave function is not a total spin eigenfunction, so that the average value of the total spin operator deviates from the exact value (spin contamination).33 It was already discussed elsewhere29 that spin contamination was negligible for the systems under study.34 Computational Details. The pruning scheme (Figure 1) was the same as in our recent study of the Azurin dimer without intervening water.29 The relaxation of the H atoms added to saturate the dangling bonds, as well as the computation of the electronic quantities needed to derive transfer integrals, was performed through the PWSCF code35 (on an IBM SP5 parallel computer). The system was simulated in the repeated supercell approach, using the DFT-generalized gradient approximation (GGA), a PW91 exchange-correlation functional, a plane-wave basis set with an energy cutoff of 25 Ry, and ultrasoft pseudopotentials36 for reproducing the atomic core potentials.
23798 J. Phys. Chem. B, Vol. 110, No. 47, 2006
Migliore et al.
TABLE 1: Transfer Integrals for the Minimal Model without Water (|UIF|2) and with Water (|UIF|w2) at Each Cu-to-Cu Distance R R (Å)
|UIF|2 (eV2)
|UIF|w2 (eV2)
10.0 11.0 12.0 13.0 14.0 14.6 15.0 16.0
1.02 × 10-2 7.97 × 10-4 5.50 × 10-5 7.87 × 10-6 1.31 × 10-7 8.17 × 10-8 5.63 × 10-8 2.46 × 10-10
1.69 × 10-3 2.53 × 10-4 3.56 × 10-5 8.27 × 10-6 7.33 × 10-7 3.36 × 10-7 1.97 × 10-7 4.53 × 10-9
The size of the simulation cell was 24 × 26.4 × 28.8 Å3 for the minimal model of Figure 1a and 26 × 27 × 33 Å3 for the larger model of Figure 1b. The first choice ensured that the minimum interdimer copper-to-copper distance was 19 Å, which is significantly larger than any of the copper-to-copper intradimer distances considered in the present work. Moreover, the minimum vacuum thickness between two replicas was above 15 Å for both models. The electrical neutrality of the simulation cell was recovered by balancing the positive charge of the oxidized site with a jellium background. Once the wave functions of the ground state and the diabatic states (as well as the energies ED, ED+, EA, and EA- in eq 4) were obtained through the PWSCF code, the overlap integrals a and b were derived from the wave functions with the DTI program.37 The interactions UD-A and UD+-A- were calculated by using the NWChem package.38 Quadrupole-quadrupole and higher order electrostatic interactions were safely neglected. 3. Results and Discussion Distance-Dependent Water Effects. We evaluated the dependence of the squared transfer integral |UIF|2 on the distance between the azurin redox sites, as measured by the copper-tocopper distance R, for the minimal model of Figure 1a, both in the absence and in the presence of two interfacial water molecules. The chosen values of R are reported in the first column of Table 1. The water molecules (where present) were held fixed in the X-ray configuration, while the protein groups were translated symmetrically, along the original Cu-to-Cu direction in the dimer X-ray structure. The coefficient |c|2, which measures the quality of the two-state approximation, resulted almost independent of the distance R (ranging in the interval 0.06 ÷ 0.07), thus suggesting that the small coupling with a third interfering state |ψT〉 has, essentially, an intrasite character. The values of |UIF|2 in the presence and absence of the interfacial water molecules are reported in Table 1 and are plotted in Figure 2 on a logarithmic scale. By performing a linear regression on each set of computed points, we obtained the bestfit straight lines displayed in Figure 2. In both cases, the squared transfer integrals decay exponentially with the donor-acceptor distance R, as expected for most biological systems and particularly for those involved in long-range ET reactions. However, the introduction of the water dimer in the gap between the redox sites slows down appreciably the exponential decay of |UIF|2 in such a way that the decay constant passes from the value β ) 1.19 Å-1 (2.75 Å-1 on a neperian logarithm scale) typical of the electron tunneling through vacuum7,19 to the value βw ) 0.87 Å-1. We evaluated the average packing density between the Cu active sites in the presence and absence of interfacial water, trying to explain the different behavior in terms of the packing density method.17 However, we found that this method does not resolve between the two situations, because there is little change in the average packing density between
Figure 2. Squared transfer integrals vs the Cu-to-Cu distance R for the minimal protein model in the absence (dark squares and solid bestfit line) and in the presence (circles and dashed best-fit line) of the interfacial water molecules, reported on a log scale. The respective decay constants are β ) 1.19 Å-1 and βw ) 0.87 Å-1.
the copper sites after the insertion of the water molecules over the entire distance range. In both cases, the average packing density is about 0.37, with a spread of 0.10, leading to a decay constant of 0.91 Å-1, which is between β and βw. Depending on the donor-acceptor distance, the interfacial water can enhance or thwart the electron-transfer reaction. More precisely, the transfer integral is reduced for copper-to-copper distances less than R ≈ 13 Å, while it is increased for longer distances; in particular, it is appreciably enhanced at the crystal copper-to-copper distance R ) 14.6 Å. This behavior can be ascribed to the simultaneous action and interplay of two main factors. Indeed, on one hand water is instinctively thought to act as a “bridge” by mediating the ET coupling pathways; on the other hand, its electrostatic interaction with the protein subsystem can promote or prevent some accumulation of protein electronic charge toward the interface between the two redox sites, thus correspondingly favoring or opposing the electrontransfer process. To shed light on the second aspect, we analyzed the change in the Mulliken population of the donor protein group induced by the electrostatic field of the adjacent water molecule.39 The variation of the Mulliken charge on each atom, with respect to the case without water, is reported in Figure 3a for a Cu-Cu distance of 14.6 Å. The main feature is a transfer of electronic charge from the H atoms that saturate the nitrogen of His117 to Gly45, which is out of the copper-to-copper direction. Therefore, at this distance the charge redistribution clearly opposes the interprotein electron transfer, giving a negative compensation of the natural bridging role. This unfavorable electrostatic effect of water is slowly quenched for increasing R, as a consequence of the larger distance between each Az and the adjacent water molecule. In fact, we find that the overall loss of electronic charge on the aforementioned H atoms passes from the value 0.0185e at R ) 13 Å to the value 0.0037e at R ) 16 Å. We argue that, for sufficiently small donor-acceptor distances, the bridging role of water molecules is not fully expressed because the tunneling can be facilitated directly by the protein atoms with no mediation, and in addition it is compensated by the generation of a counter electric field opposing the ET reaction in the region between azurins. Thus, the transfer integral (and, correspondingly, the ET rate) turns out to be smaller than in absence of water up to R ≈ 13 Å. On the other hand, for larger donor-acceptor distances, the water molecules, although preserving an unfavorable electrostatic effect, become overwhelmingly the principal mediator of the
Water-Mediated Electron Transfer in Azurin
J. Phys. Chem. B, Vol. 110, No. 47, 2006 23799
Figure 3. Change in the Mulliken charge of the donor Az induced by the electrostatic field of the adjacent water molecule. The charge variation is computed relative to the “dry” condition. The coordination bonds of the Cu ion with the equatorial ligands are shown as dashed lines. (a) Minimal atomic set. (b) Complete atomic model.
electron tunneling across the Az-Az vacuum interface, leading to transfer integrals significantly larger than in the absence of water. Effects of the Atomic Model at a Fixed Distance. Given the relevance of the configuration with the copper-to-copper distance of 14.6 Å (the X-ray value), we calculated its transfer integral by employing the more complete atomic model of Figure 1b. In this way, we probed the geometrical approximations in our study. The main difference between the “complete” model and the minimal one consists of the addition of the two His117. These residues protrude from the respective protein matrixes into the gap between the redox sites, thus increasing the interprotein through bond region and reducing considerably the overall tunneling barrier for the electron transfer from one protein to the other.29 In addition, the conjugated imidazole rings of the two His117 are expected to be efficient in supporting charge propagation because of their delocalized electron character. Indeed, at R ) 14.6 Å, the squared transfer integral for the present model, with the interfacial water dimer included, is 1.04 × 10-5 eV2, to be compared with the value 8.91 × 10-5 eV2 (see ref 29) for the larger model without water and with the value 3.36 × 10-7 eV2 obtained for the minimal model. The crucial role of the residues His117 in mediating electron transfer is confirmed. On the other hand, at the crystal Cu-to-Cu distance R ) 14.6 Å, the introduction of the water molecules into the gap between the proteins reduces significantly the ET rate. An explanation of this effect can be given coherently with the analysis on the behavior of the minimal model illustrated in Figure 2. In fact, as shown in Figure 3b, the electrostatic field of the adjacent water molecule induces a drastic reduction of the electron charge on the most exposed H atom, which amounts to nearly the 40% of its original Mulliken charge. This electronic
charge draws back toward the nitrogen of His117 and other atoms behind it, in a direction opposite to the interprotein ET reaction. Moreover, the residues His117 aid the electron tunneling across the protein-protein interface, so that the water molecules do not preserve their role of principal mediator in electron shuttling. On the whole, water comes out to have an unfavorable effect on the interprotein ET reaction. Stated otherwise, the two His117 reduce the effective gap between the donor and acceptor groups, so that, for the more comprehensive model, R ) 14.6 Å falls within the range of copper-to-copper distances for which the interfacial water molecules partially suppress ET processes. By inserting the transfer integrals for the minimal and larger models at R ) 14.6 Å in eq 2 (with a temperature T of 298 K, a reorganization energy λ of 0.8 eV,40 and ∆G° ) 0, as it is the case for a self-exchange reaction), we obtain the ET rates kET ) 2.6 × 106 s-1 and kET ) 8.1 × 107 s-1, respectively. Both values are well above the experimental lower limit of 5 × 104 s-1 and thus are in general agreement with it, although a stricter comparison between theory and experiment will require a suitable conformational sampling. 4. Conclusions We have distinguished, quantified, and rationalized different effects of two water molecules on the ET reaction between the redox sites in azurin dimers by using a newly developed abinitio method to calculate the kinetically relevant transfer integrals and a suitable analysis of the water-protein electrostatic interaction. The restriction to fixed reciprocal orientations of the water and protein subsystems allowed us to separate different aspects, possibly tangled by atomic thermal motion. On the other hand, a future study including the conformational
23800 J. Phys. Chem. B, Vol. 110, No. 47, 2006 sampling can be on purpose directed toward the analysis of the corresponding averaged factors and of their possible interplay. Here, we have shown that water molecules introduced between protein active sites can promote or oppose electron transfer as a consequence of the simultaneous action of two factors, namely, the water-protein electrostatic interaction and the quantum mediation by water of the electron tunneling between the redox sites. Thus, water can be an efficient or poor electron-transfer mediator according to its relative conformation between the ET partners. A general result, not traceable back to the sole bridging aspect, is that interfacial water slows down the exponential decay of the ET rates with the distance between the redox sites. From a methodological point of view, all the approaches that have been developed for the evaluation of transfer integrals are inevitably subjected to various approximations. Despite such limitations,29 we trust the main results of the present work to be particularly robust because they come out from a comparison of two situations for the same basic system (Az dimer with and without intersite water) within the same computational scheme. Since the transfer integrals play a key role in determining the rate constants (measured in kinetic experiments) of the biochemical redox reactions and their accurate prediction is a particularly pressing issue, we believe that our theoretical and computational approach may be a promising framework for the investigation of charge-transfer mechanisms in biological environments. Along this way, the application to protein crystals may be a particular rewarding test because in the crystal phase structural ambiguity is drastically reduced and more experimental results were achieved, in particular about ET reactions in Fe/Zn cytochrome c crystals,41 that can be analyzed as interesting benchmark systems. Acknowledgment. We thank Andrea Ferretti, Carlo Cavazzoni, and Arrigo Calzolari for computational support and fruitful scientific discussions. Funding was provided by INFM-CNR in terms of allocation of computer time at the CINECA supercomputing facilities (Bologna, Italy) and by MIUR-IT through project FIRB-NOMADE. References and Notes (1) Berg, J. M.; Stryer, L.; Tymoczko J. L. Biochemistry, 5th ed.; Freeman: New York, 2002. (2) Nitzan, A. Annu. ReV. Phys. Chem. 2001, 52, 681-750. (3) Aviram, A.; Ratner, M.; Mujica, V. Molecular Electronics II. Annals of the New York Academy of Sciences; The New York Academy of Sciences: New York, 2003; Vol. 960. (4) Maruccio, G.; Biasco, A.; Visconti, P.; Bramanti, A.; Pompa, P. P.; Calabi, F.; Cingolani, R.; Rinaldi, R.; Corni, S.; Di Felice, R.; Molinari, E.; Verbeet, M. P.; Canters, G. W. AdV. Mater. 2005, 17, 816-822. (5) Page, C. C.; Moser, C. C.; Chen, X.; Dutton, P. L. Nature (London) 1999, 402, 47-52. (6) Stuchebrukhov, A. A. Theor. Chem. Acc. 2003, 110, 291-306. (7) Osyczka, A.; Moser, C. C.; Daldal, F.; Dutton, P. L. Nature (London) 2004, 427, 607-612. (8) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265322. (9) Skourtis, S. S.; Balabin, I. A.; Kawatsu, T.; Beratan, D. N. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3552-3557. (10) Nishioka, H.; Kimura, A.; Yamato, T.; Kawatsu, T.; Kakitani, T. J. Phys. Chem. B 2005, 109, 1978-1987. (11) Liang, Z. X.; Kurnikov, I. V.; Nocek, J. M.; Mauk, A. G.; Beratan, D. N.; Hoffman, B. M. J. Am. Chem. Soc. 2004, 126, 2785-2798. (12) Lin, J.; Balabin, I. A.; Beratan, D. N. Science 2005, 310, 13111313.
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