Acceptor Coupling Shortcuts in Electron Transfer within

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Donor/Acceptor Coupling Shortcuts in Electron Transfer within Ruthenium-Modified Derivatives of Cytochrome b562 Tatiana R. Prytkova,*,§ Vladislav V. Shunaev,‡ Olga E. Glukhova,‡ and Igor V. Kurnikov† §

Schmid College of Science & Technology, Chapman University, Orange, California 92866, United States Department of Chemistry, Carnegy Mellon University, Pittsburgh, Pennsylvania 15213, United States ‡ Department of Physics, Saratov State University, Saratov, 410012, Russia †

ABSTRACT: Quantitative theoretical studies of long-range electron transfer are still rare, and reliable computational methods to analyze these reactions are still being developed. We re-examined electron transfer reactions in ruthenium-modified cytochrome b562 derivatives focusing on accurate calculation of statistical average of electron transfer rates that are dominated by a small fraction of accessible protein conformations. We performed a series of ab initio calculations of donor/acceptor interactions over protein fragments sampled from long molecular dynamic trajectories and compared computed electron transfer rates to available experimental data. Our approach takes into account cofactor electronic structure and effects of solvation on the donor−acceptor interactions. It allows predicting absolute values of electron transfer rates in contrast to other computational methodologies that give only qualitative results. Our calculations reproduced with a good accuracy experimental electron transfer rates. We also found that electron transfer in some of the cytochrome b562 derivatives is dominated by “shortcut” conformations, where donor/acceptor interactions are mediated by nonbonded interactions of Ru ligands with protein surface groups. Several derivatives adopt long-lived conformations with the Ru complex interacting with negatively charged protein residues that are characterized by shorter Ru−Fe distances and higher ET rates. We argue that quantitative theoretical analysis is essential for detailed understanding of protein electron transfer and mechanisms of biological redox reactions. ΔG0 is the free energy change of the ET reaction, and λ is reorganization energy that characterizes the nuclear response of the system to the transfer of an electron from donor to acceptor. Protein chains separating donor and acceptor cofactors strongly influence electron transfer via electron and hole superexchange interactions.1 Simple models such as the exponential distance decay model2 or PATHWAYS model3 have been used frequently to describe electron tunneling through the protein; however, an accurate description of donor/acceptor superexchange interactions is provided only by quantum chemical calculations. The challenge of computing electronic coupling is essentially a quantum chemical problem for large molecular systems involving hundreds or thousands of atoms. It is complicated further by the dynamical flexibility of the protein and solvent. Our goal is to develop reliable theoretical methods able to quantitatively predict rates of longrange electron transfer reactions. Availability of such methods would allow to decipher catalytic mechanisms of many complex biological systems and can help to design artificial enzymes. Several research groups suggested methods to study electron transfer reactions,4−9 although a number of challenges remain regarding application of computational techniques to the quantitative prediction of ET rates of biological systems.

1. INTRODUCTION We report a quantitative theoretical study of long-range electron transfer (ET) reactions in a series of covalently modified proteins. Such reactions involve quantum mechanical tunneling of an electron between donor and acceptor chemical groups separated by 5−15 Å. Electron transfer events are essential steps of ubiquitous biological redox reactions and play an important role in many vital biochemical processes such as photosynthesis, cellular respiration, DNA repair, biodegradation, and biosynthesis. Redox cofactors such as metal coordination complexes and aromatic molecules are placed strategically in biocatalytic systems to achieve rates of electron transfer optimal for biological function. For example, electron transfer rates in photosynthesis are tuned to achieve maximum efficiency of charge separation. In long-range electron transfer reactions, donor and acceptor electronic states interact weakly. In this nonadiabatic electron transfer regime, the system can reach the activated state (characterized by equal instantaneous electron binding energies of donor and acceptor) many times before electron transfer occurs. In this case, electron transfer rate is given by the expression kET =

2π ℏ

⎛ (ΔG 0 + λ)2 ⎞ 1 |HDA|2 exp⎜ − ⎟ 4λkBT ⎠ ⎝ 4πλkBT

(1) Received: August 28, 2014 Revised: December 20, 2014

where HDA is the effective donor/acceptor interaction or the electronic coupling. © XXXX American Chemical Society

A

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2. METHODS Modeling Structure and Dynamics of Cytochrome b562 Derivatives. Structures of cytochrome b562 modified with Ru(bpy)2(Im)(HisX) at surface sites 12, 15, 19, 63, 70, 73, 86, 89, or 92 were generated using the program package Harlem19 from X-ray structure of the native protein.20 Figure 1 shows positions of His residues of derivatives of cytochrome b562 that were used as points of attachment of the

Recent QM/MM studies greatly advanced techniques for quantitative prediction of reorganization energy and redox potentials of biological electron transfer systems.10−13 Our computational approach consists of quantum chemical calculations of donor/acceptor electronic couplings over multiple molecular fragments sampled from molecular dynamics trajectories of biological ET systems. The calculations of donor−acceptor interactions also involve averaging of multiple donor−acceptor ligand-field states and take into account shifts of donor and acceptor states energies due to solvation. These features of the calculations are essential for quantitative predictions of electron transfer rates. Metalated proteins served as very useful model systems to study mechanisms of electron transfer reactions.14 A series of experimental and theoretical studies of these systems helped to characterize important factors governing electron tunneling through the protein such as donor−acceptor separation, cofactor redox potentials, protein secondary structure, and mobility. Previously, we reported calculations of electron transfer rates in Ru-modified derivatives of azurin15 and cytochrome b562.16 Calculations of azurin derivatives with smaller donor− acceptor distances (His83, His109, His122 derivatives) reproduce experimental data15 very accurately (less than 20% difference between computed and experimentally observed ET rates), whereas the computed ET rates in derivatives with larger donor/acceptor distances (His107, His124, His126) have been found to be smaller by a factor of 4−7 than the experimental rates.15 The computed ET rates in cytochrome b562 were of similar accuracy for most of the derivatives; however, for two derivatives, the computed ET rates were 1−2 orders of magnitude lower than experimental values.16 The computed ET rates were lower than corresponding experimental values in 7 out of 9 cytochrome b562 derivatives, indicating a possible systematic error in the computation procedure. In this work, we recomputed electron transfer rates in cytochrome b562 using much longer molecular dynamics simulations and updated techniques for calculation of donor/acceptor electronic couplings. We focused on representation of electronic states of heme cofactor that is very challenging for the size of the molecular systems considered and modeling of conformational mobility of the ruthenium coordination group that was largely overlooked in previous simulations. Modern quantum-chemical analysis now provides access to quantitative rate predictions. Here, we use quantum chemical calculation of donor−acceptor interactions, to develop an understanding of ET in ruthenium-modified cytochrome b562. While many Ru-modified proteins have been studied over the last 20 years, the largest single data set available is for the protein cytochrome b562.17 In this protein, there is more scatter in the logarithm of the ET rates as a function of distance compared to other Ru proteins. For example, the ET rates in Ru-modified azurin are nearly exponential in the donor− acceptor distance.18 ET kinetics in the photosynthetic reaction center too can be described with a simple exponential model.2 Results presented in this study demonstrate that electron transfer rate can be quantitatively predicted. We also show that, in order to get quantitative prediction, we have to take into account interaction of ruthenium complexes with the protein surface. Such an interaction can create particular constrained geometries that may enhance electronic coupling and increase electron transfer rates.

Figure 1. Cytochrome b562 derivatives.

Ru(2,2′-bipyridine)2(imidazole)2 redox group (RBP). Coordinates of Ru complex were taken from protein data bank entry 1BEX for ruthenium-modified azurin.21 Force constants of bonds involving the Ru atom were set to 100 kcal/(mol Å2), and force constants of valence angles involving Ru were set to 63 kcal/mol rad2. Partial atomic charges for the Ru complex were obtained using the RESP procedure22 from results of Hartree−Fock calculations with the 6-31G(d) basis set. AMBER 99SB force field23 parameters were set on protein residues. Modified protein structures were solvated in a box of about 9000 TIP3P water molecules. Na+ counterions were added to neutralize the systems. We performed 5000 steps of steepest decent energy minimization, followed by 1 ns equilibration molecular dynamics. Next, 100 ns production molecular dynamics runs were executed. The MD simulations were performed with the Amber 10 program.24 We used periodical boundary conditions with constant pressure constraints, Langevin thermostat at 300 K. The particle mesh Ewald (PME) approach was used to model electrostatic interactions.25 Protein Pruning for Quantum Chemical Calculations. Our quantum chemical calculations include only portions of the protein that significantly facilitate electronic coupling between the donor and acceptor. We used PATHWAYS analysis3 to map residues important for tunneling mediation. For each atom X of the ruthenated cytochrome b562 derivative, we computed PATHWAYS coupling to Fe (Hx,Fe) and to Ru (Hx,Ru). Atoms with products of coupling values Hx,Fe × Hx,Ru larger than a certain fraction (1% in these calculations) of Ru−Fe PATHWAYS coupling were included in a protein fragment for quantum chemical analysis. In addition, atoms of redox cofactors (Fe-porphyrin, bipyridine, and imidazole ligands of B

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Figure 2. (a) HOMO and HOMO-1 molecular orbitals in Hartree−Fock calculations. (b) HOMO and HOMO-1 molecular orbitals DFT (B3LYP) calculations. (c) HOMO and HOMO-1 molecular orbitals in Hartree−Fock calculations with correcting point charges (negative charge on Fe and positive charges on first coordination shell atoms of Fe).

elements on localized donor and acceptor orbitals obtained this way are slow changing functions of tunneling energy E. Offdiagonal elements of this reduced Hamiltonian between donor and acceptor orbitals give values of effective donor/acceptor electronic couplings that agree well with results obtained with a more involved energy splitting method used in our other works15 Donor/Acceptor Localized Orbitals. There is some uncertainty in the choice of donor/acceptor states for electronic coupling calculations between iron-porphyrin and ruthenium redox centers. We modeled the donor state of cytochrome b562 similarly as we did this in Ru-modified azurin coupling calculations.15 The top three occupied molecular orbitals of the Ru complex localized primarily on the Ru atom. The energies and expansion coefficients of these orbitals are sensitive to the geometry of the complex and differ for each MD snapshot of the system. We assume that all three upper occupied orbitals of the Ru complex have equal contributions to electron transfer. In ET rate calculations, we used root mean square (rms) average of donor/acceptor couplings computed for three Ru localized orbitals. The two highest occupied orbitals of reduced iron-porphyrin computed with the Hartree−Fock method are distributed on the π system of the porphyrin (Figure 2a). Fe localized occupied orbitals are much lower in energy at this level of calculations. In contrast, experimental results and higher level electronic structure calculations28,29 show that the donating state of ferroporphyrin mostly localized on the iron atom. Density functional theory calculations (B3LYP functional) result in HOMO and HOMO-1 localized on the iron (Figure 2b). To correct energies of occupied orbitals in H DA calculations, we set background point charges localized on the heme iron atom (negative) and atoms of the first coordination sphere of Fe (positive). Point charges shift energies of Fe localized molecular orbitals up relative to porphyrin localized MO. HOMO and HOMO-1 orbitals of heme in Hartree−Fock calculations with background charges were mostly localized on d-orbitals of Fe (Figure 2c). We use this set of point charges in our calculations of Hartree−Fock orbitals. To define localized redox orbitals for Green function calculations of donor/acceptor electronic coupling, we truncated top occupied molecular orbitals zeroing coefficients

Ru) and atoms belonging to the same chemical groups (amide groups, aromatic rings) as PATHWAYS selected atoms were also included in the quantum calculations. Dangling bonds were terminated with hydrogen atoms. We found that use of a reduced value of nonbonded decay parameter 1.1 Å −1 compared to 1.7 Ang−1 in original PATHWAYS parametrization permit a better agreement to ab initio quantum chemical calculations and allow better identification of protein residues important for superexchange calculations. Electronic Coupling Calculation, “Green Function Method”. Calculations of donor/acceptor electronic coupling were performed with the Green Function method26 based on Hartree−Fock solution of electronic structure of protein fragments. Protein fragments containing donor/acceptor groups and bridging protein groups mediating electronic superexchange interactions were identified using PATHWAYS pruning method with 1% cutoff criterion as described above. First, we performed ab initio Hartree−Fock calculations of fragments using the Gaussian program.27 The split-valence 321G basis set has been used as it was found adequate to describe superexchange interactions in our previous studies.15 We defined localized donor/acceptor orbitals (|Di> and |Ai>) by truncating computed molecular orbitals of the system zeroing LCAO/MO coefficients on all atoms except the donor group (for donor localized orbitals) or the acceptor group (for acceptor localized orbitals). Next, we computed a reduced Hamiltonian in the space of such defined donor/acceptor localized electronic states by computing the Green function GPP(E) projected to the space of localized redox orbitals: G PP kl =

k I⟩

1 ⟨I l E − EI

(2)

Here, k,l - localized donor and acceptor orbitals; |I⟩ - molecular orbitals (MO); and EI - MO energies of the system. Effective Hamiltonian on localized donor/acceptor states was computed by inversion of the Green function matrix GPP(E): −1 Heff pp (E) = ESPP − SPPG PP(E) SPP

(3)

Energy E for the Green function and effective Hamiltonian calculations was −0.2 au close to the energies of donor/ acceptor one-electron states. Effective Hamiltonian matrix C

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The Journal of Physical Chemistry B Table 1. RMS |HDA| Values Calculated for Nine Derivatives of Cytochrome b562 modified protein Ru(bpy)2(Im)(His12)b562 Ru(bpy)2(Im)(His15)b562 Ru(bpy)2(Im)(His19)b562 Ru(bpy)2(Im)(His63)b562 Ru(bpy)2(Im)(His70)b562 Ru(bpy)2(Im)(His73)b562 Ru(bpy)2(Im)(His86)b562 Ru(bpy)2(Im)(His89)b562 Ru(bpy)2(Im)(His92)b562

theor kET rate (s−1)

rms HDA (eV) 1.27 1.42 5.57 8.12 9.62 1.22 4.02 7.69 1.30

× × × × × × × × ×

−6

10 10−5 10−6 10−6 10−6 10−7 10−7 10−7 10−5

1.99 3.37 5.21 1.1 1.55 2.5 2.72 9.92 2.85

× × × × × × × × ×

7

10 106 105 106 106 102 103 103 106

expt kET rate (s−1) 2.60 1.90 6.70 7.90 2.30 4.90 2.90 4.40 1.00

× × × × × × × × ×

107 106 104 106 105 102 102 104 107

on atoms not belonging to Fe-porphyrin (for Fe-localized MOs) or Ru complex (for Ru-localized MOs). The subset of donor and acceptor atoms used for truncation did not affect strongly computed HDA values. Computed HDA values for a given geometry of the system did not differ substantially if all non-hydrogen atoms of Fe-porphyrin and Ru(bpy)2(Im)2 complex were used for redox oribtal truncation or if only Fe and Ru atoms with nearest N atoms were used for truncation. Solvent polarization strongly shifts energy levels of positively charged Ru complex. We model solvation effects in quantum chemical calculations with set negative point charges (−0.333 e) on six nitrogen atoms coordinating Ru. We have shown previously15 that this approximate method to account for solvation is adequate for donor/acceptor coupling calculations and gives results similar to more involved methods describing dielectric response such as Poisson−Boltzmann calculations. Figure 3. Theory vs experiment for 1% cutoff fragments for nine derivatives of cytochrome b562.

3. RESULTS AND DISCUSSION HDA Calculations for Cytochrome b562. We computed donor/acceptor coupling values for 100 molecular dynamics snapshots for each b562 derivative. .For the calculation of coupling, we extracted protein fragments using the PATHWAY pruning procedure with 1% cutoff criterion. Fragments contained 250−400 atoms. For each protein fragment, we performed Hartree−Fock calculations and calculated donor− acceptor couplings using the Green function method described above. To compare to experimental data,17 we calculated nonadiabatic electron transfer rates using the Marcus formula 1 and squared HDA coupling values averaged over MD snapshots. Electron transfer experiments in ruthenated cytochrome b562 derivatives proceed in the regime close to activationless with −ΔG0 ≈λ ≈ 0.8 eV, which has been etablished in experiments on driving force ET rate dependence.30 Thus, these values of ΔG0 and λ were used in calculations of ET rates. The computed donor/acceptor couplings and ET rates are presented in Table 1 and Figure 3. We can see from Figure 3 that excellent agreement received for derivatives His12, His15, His73, His92, and His86 within a factor of 5. For derivatives His19, His63, His70, and His89, agreement is good within a factor of 8. In order to compare our results with experiment, we have to calculate average square HDA. Figure 4 presents HDA values for individual snapshots of derivative His15 and cumulative moving rms average of HDA over MD snapshots. HDA values for individual snapshot differ by order of magnitude and strongly depend on geometry of individual snapshots. ET rate is dominated by a small number of geometries with strong couplings. Although convergence is slow, it can be seen from Figure 4 that 100 snapshots is sufficient to get reasonable convergence.

Figure 4. HDA calculated for individual snapshots of derivative b562 His15; each point for individual snapshot corresponds to rms six HDA, between two orbitals on heme group and three orbitals localized on RBP. After adding more snapshots, running average converges to rms HDA.

Our calculations show that interaction of positively charged RBP with negatively charged amino acids on the surface of ruthenated protein plays an important role in defining preferable conformation of Ru complex. The ruthenium complex is flexible and can acquire different positions on the surface of the protein complex with different Ru−Fe distances and ET rates. Ru−Fe distance distributions calculated from MD trajectories of cytochrome b562 derivatives are shown in Figure 5. Ru−Fe distance distributions for His86, His19, and His92 derivatives demonstrate a distinct bimodal character. ExaminaD

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Figure 5. Probability distribution of Ru−Fe distances calculated from 100 ns molecular dynamics trajectories: (a) derivatives 19, 86, and 92; (b) derivatives 12, 15, 63, 70, 73, and 89.

the case of His86 derivative, the “shortcut” conformation dominates the average electron transfer rate. PATHWAYS calculation shows that, in “shortcut” conformations of His86 and His19 derivatives, Best Path passes through negatively charged surface residues (Asp74 and Glu18) interacting electrostatically with RBP (Figure 6a,b). We performed quantum chemical calculations of electronic coupling on fragments of His86 and His19 derivatives with Asp74 and Glu18 excluded from calculations. The removal of Asp74 or Glu18 resulted in a dramatic (factor of 5−10) reduction of the computed donor/acceptor coupling. This shows that indeed surface residues Asp74 and Glu18 strongly participate in mediating donor/acceptor interactions between RBP and heme. The “shortcut” conformation of His92 derivative corresponding to the Fe−Ru distance maximum at 17 Å (Figure 5a) is characterized by interactions of RBP with Glu8 residue (Figure 6c). It should be noted that Glu8 is located on helix I while His92 is part of helix IV of cytochrome

tion of MD trajectories revealed that short distance maxima correspond to conformations where the positively charged RBP complex interacts strongly with negatively charged residues on the surface of the protein. His86 derivative acquires a long-lived “shortcut” conformation (Ru−Fe distance ∼ 24.5 Å) apparently as a result of interaction of the imidazole ligand of RBP with the Asp74 surface residue (Figure 6a). The long distance maximum (∼27.5 Å) of the Ru−Fe distance distribution corresponds to “loose” conformations where the RBP group is immersed in solution. ET rate calculations show that the average ET rate is dominated by “shortcut” conformations with RBP in contact with the protein surface. His19 derivative “shortcut” conformation is characterized by interaction of RBP with Glu18 (Figure 6b). The Ru−Fe distance in the “shortcut” conformation is around 19 Å much smaller than the average Ru−Fe distance for “loose” conformations corresponding to the second peak in Ru−Fe distance distribution ∼ 24 Å. As in E

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cut” conformations with RBP attached to the protein surface and donor/acceptor couplings mediated by nonbonded interactions of Ru ligands with surface residues of the protein. “Shortcut” conformations complicate an interpretation of electron transfer experiments in ruthenated proteins as a common assumption of such experiments that donor/acceptor interactions involving ruthenium are mediated by through-bond superexchange interactions involving a protein residue covalently attached to RBP. Detailed theoretical analysis may be necessary for quantitative interpretation of electron transfer experiments in other biological systems involving covalent attachment of metalated complexes. Convergence of the computed electron transfer rates in cytochrome b562 derivatives required ab initio calculations of donor/acceptor couplings over a large number (>100) of system fragment geometries. The average electron transfer rate has been found to be dominated by a small number of conformations with strong donor/acceptor couplings. The Green function method described here may make it easier to compute HDA values over multiple geometries compared to the energy splitting method used in our previous works. Computed ET rates averaged over MD sampled geometries reproduce experimental rates within a factor of 8. Calculations of donor/acceptor coupling over multiple molecular fragments have been done using the program HARLEM19 and become automated, so the methodology readily can be applied to computing absolute rates of electron transfer in complex biological redox systems.

Figure 6. Interaction of RBP with negatively charged amino acids on surface of: (a) Derivative His86: imidazole ring of RBP interacts with carboxyl of Asp74 creating pathway shortcut geometry. (b) Derivative His19: imidazole ring of RBP interacts with carboxyl of Glu18 creating pathway shortcut geometry. (c) Derivative His92: RBP interacts with Glu8 creating geometrical constraint with pick around 19.5 Å that enhances ET rate.

b562 (Figure 6c). Our calculations show that “shortcut” conformation of His92 derivative contributes much more to the average ET rate than “loose” conformations (Fe−Ru distance distribution maxima at 20 Å). However, Glu8 is not part of Best Path in PATHWAYS calculations and does not contribute significantly to superexchange calculations between RBP and heme. His12, His15, His63, His70, His73, and His89 cytochrome b562 derivatives have unimodal Fe−Ru distance distributions (Figure 5b). His12, His63, and His70 have more narrow Fe−Ru distance distributions than His15, His73, and His89 derivatives. The analysis of MD conformations shows that RBP in His12, His63, and His70 derivatives got constrained for most of the time at the surface of the protein by interaction with negatively charged residues (by Glu8 for His12, by Asp66 for His63, and by Asp74 for His70). At the same time, average ET rates in these derivatives are dominated by superexchange interactions through the His residue covalently attached to the RBP group. Derivatives His15, His73, and His89 have wider Fe−Ru distance distributions. The mobility of the RBP group is not constrained by interactions with surface protein residue groups for these derivatives. Donor/acceptor interactions in these derivatives are dominated by through-bond superexchange through covalent attachment of RBP to surface His residues.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (714) 628-7346 (T.R.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Research Corporation Award 20890.

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REFERENCES

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