Carbon−Deuterium Vibrational Probes of Amino Acid Protonation State

Furthermore, the predicted harmonic intensities of the C−D2 probe vibrations were extraordinarily sensitive to the protonation state of the nearby a...
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2009, 113, 8218–8221 Published on Web 05/22/2009

Carbon-Deuterium Vibrational Probes of Amino Acid Protonation State C. S. Miller and S. A. Corcelli* Department of Chemistry and Biochemistry, UniVersity of Notre Dame, Notre Dame, Indiana 46556 ReceiVed: April 16, 2009; ReVised Manuscript ReceiVed: May 16, 2009

The protonation state of titratable amino acid residues has profound effects on protein stability and function. Therefore, correctly determining the acid dissociation constant, pKa, of charged residues under physiological conditions is an important challenge. The general utility of site-specific carbon-deuterium (C-D) vibrational probes as reporters of the protonation state of arginine, aspartic acid, glutamic acid, and lysine amino acid side chains was examined using density functional theory (DFT) calculations. Substantial shifts were observed in the anharmonic vibrational frequencies of a C-D2 probe placed immediately adjacent to the titratable group. Lysine exhibited the largest C-D2 frequency shifts upon protonation, 44.9 cm-1 (symmetric stretch) and 69.5 cm-1 (asymmetric stretch). Furthermore, the predicted harmonic intensities of the C-D2 probe vibrations were extraordinarily sensitive to the protonation state of the nearby acidic or basic group. Accounting for this dramatic change in intensity is essential to the interpretation of an infrared (IR) absorption spectrum that contains the signature of both the neutral and charged states. The acidic (aspartic acid and glutamic acid) and basic (arginine, histidine, and lysine) amino acid residues often play a key role in many important biological processes, such as enzymatic reactions, photosynthesis, and molecular recognition. In addition, the formation of salt bridges, the direct interaction of negatively charged (acidic) amino acid residues with positively charged (basic) amino acid residues, dramatically affects the stability of folded proteins.1 Some proteins can be denatured by shifting the acid dissociation equilibrium constant, pKa, of a small number of protonatable residues.1-8 In solution, the protonation state of acidic and basic amino acid residues changes abruptly with a small variation in pH. In contrast, when these same residues are located in solvent-inaccessible protein environments, they exhibit a broad range of pKa values.8-10 The dependence of the pKa of acidic and basic amino acids on their environment makes the precise assignment of their physiologically most relevant protonation state(s) ambiguous. For example, titration experiments have identified aspartic acid residues in protein environments with pKa values ranging from less than 2 to 6.7,8 and a deprotonated lysine residue in the hydrophobic core of staphylococcal nuclease with a pKa of 5.6.9-12 Knowledge of the correct pKa of charged residues in proteins is also essential for modeling biological processes with molecular-based simulation, where the protonation state of these residues must be explicitly specified at the outset of the simulation and where incorrect assignments can lead to instability and inaccurate results. X-ray crystallography is of limited utility in determining the protonation state of charged amino acid residues, because hydrogen atoms are only observed in solved structures with resolutions considerably better than 1.5 Å.13,14 Even when the human aldose reductase was solved with a resolution of 0.66 Å, only 54% of the hydrogen atoms were resolved.14 However, * To whom correspondence should be addressed. E-mail: scorcell@ nd.edu.

10.1021/jp903520s CCC: $40.75

when hydrogen atoms are not explicitly present in crystal structures, C-O bond lengths can provide indirect evidence of the protonation state of aspartic acid (Asp) and glutamic acid (Glu) residues.14 NMR has been used successfully to measure the pKa of specific residues,15-22 although there are several limitations. Primarily, solution NMR is applicable for globular proteins up to approximately 100 kDa,23 which excludes membrane-bound proteins or larger proteins. Additionally, determining the pKa of protonatable residues with NMR requires experiments to be performed in solutions of varying, nonphysiological pH. Since many proteins have a maximum thermodynamic stability at or near neutral pH, they may become denatured over the large pH range required for this technique.1 There has also been intense activity to develop robust and accurate atomistic-based methodologies to predict the pKa of individual charged residues in proteins.24-32 Infrared (IR) absorption spectroscopy offers several advantages for investigating the protonation states of acidic and basic amino acid residues in proteins. In general, IR spectroscopy is not limited to small globular proteins, and it can also be applied to proteins that are difficult to crystallize (e.g., membrane-bound proteins and protein aggregations). Since vibrational frequencies are known to be exquisitely sensitive to the electrostatic and chemical properties of their local environment, the difference in charge between a protonated and deprotonated acidic or basic residue represents a substantial perturbation that is resolvable in the IR absorption spectrum of a suitably chosen vibrational probe. The IR time scale is also an inherent advantage; the spectral signatures of the protonated and deprotonated side chains would be resolved in an IR absorption spectrum as long as the states are not interconverting on a subpicosecond time scale. An ideal vibrational probe of the protonation state of acidic and basic amino acid residues would have the following properties: (1) it would absorb in a different region of the IR  2009 American Chemical Society

Letters spectrum than the other vibrations in the protein, (2) it would be decoupled from the other protein vibrations, (3) the label would not perturb the native protein structure or the pKa of the residue of interest, (4) the probe would be sufficiently versatile to be site-specifically incorporated to study individual residues, and (5) the vibrational frequency of the probe would be sensitive to the protonation state of acidic and basic amino acid residues. The carbon-deuterium (C-D) vibrational probe is an excellent candidate for investigating amino acid protonation state. C-D stretches absorb at approximately 2000-2300 cm-1, which falls in a transparent region of the protein IR absorption spectrum. By virtue of having a frequency that is different from the other vibrations in the protein, C-D stretches are adiabatically decoupled from these other modes and generally only report on their local environment. C-D vibrational probes are exceptionally nonperturbative to protein structure, and their presence in the vicinity of an acidic or basic residue would have a negligible effect on its pKa. Furthermore, C-D probes are extremely versatile and sensitive to their local environment;33-48 for example, they have been site-specifically incorporated in amino acid side chains to study protein unfolding induced by chemical denaturant,41 as well as redox-dependent protein flexibility in cytochrome c.39 In addition, alpha-carbon-deuterium (CR-D) vibrational probes have been utilized to study membrane proteins,45-47 and have been shown to be extraordinarily sensitive to peptide backbone conformation.40,42-44 Weinkam et al. have recently studied the alkaline-induced unfolding of cytochrome c using C-D vibrational probes.48 In particular, as part of their investigation, they incorporated a labeled lysine residue, in which all four CH2 groups on its side chain had been deuterated (Lys-d8), into cytochrome c at the specific locations of native Lys residues. Using this approach, they were able to ascertain the pH at which Lys72, Lys73, and Lys79 deprotonate by assigning an observed pH-dependent shift in their IR absorption spectra to the deprotonation event. A similar shift was observed in a control experiment of a protected Lys-d8 amino acid in solutions of varying pH. Their study demonstrated clearly that C-D IR absorption spectra are sensitive to pH, and therefore to the protonation state of the basic amino acid lysine. It is important to note that the pH at which a given Lys residue is observed to deprotonate, defined by the presence of an equal population of protonated and deprotonated residues, is not necessarily relevant to the pKa of the residue in the native protein at physiological pH; the protein has become partially denatured, causing the Lys residues to become solvent accessible. Using this principle, Weinkam et al. were able to determine the order in which the labeled Lys residues became solvent accessible, as a function of pH, thus providing detailed and important information regarding the mechanism of pH-induced unfolding of cytochrome c. Using density functional theory (DFT), we have systematically investigated the sensitivity of C-D stretch vibrational frequencies to the protonation state of aspartic acid, arginine, glutamic acid, and lysine in Vacuo. Each of the side chains, R, was incorporated into a model dipeptide molecule (CH3COHN-CH(R)-CONH-CH3), as shown in Figure 1, and calculations were performed with the B3LYP49-51 functional and the aug-cc-pVDZ52 basis set in Gaussian 03.53 These model dipeptide compounds are neutral unless R is charged, and they would be highly amenable to study in the gas phase. The augcc-pVDZ basis set was utilized because it provides a reasonable description of anionic molecular species in the gas phase. With the exception of the Rdp cation, the geometries of the neutral and charged dipeptides were fully optimized. However, when

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Figure 1. (A) Model dipeptide compound, where R represents various amino acid side chains. (B) Acidic and basic side chains considered in this study: aspartic acid dipeptide (Ddp), glutamic acid dipeptide (Edp), lysine dipeptide (Kdp), and arginine dipeptide (Rdp).

TABLE 1: Unscaled Harmonic and Anharmonic Vibrational Frequencies of C-D2 Probes Immediately Adjacent to the Protonatable or Deprotonatable Group in Acidic (Ddp and Edp) and Basic (Kdp and Rdp) Model Dipeptidesa amino acid harmonic (cm-1) anharmonic (cm-1) relative intensity Ddp (0) Ddp (-1) Edp (0) Edp (-1) Kdp (0) Kdp (+1) Rdp (0) Rdp (+1)b

2249.1 2228.2 2217.0 2192.5 2200.7 2249.6 2218.1 2214.3

2340.2 2313.9 2282.0 2278.2 2274.2 2346.7 2291.0 2308.8

2218.2 2198.5 2184.1 2158.2 2166.8 2211.7 2183.1 2177.4

2308.8 2285.2 2251.2 2237.9 2236.3 2305.8 2253.1 2265.1

1.3 3.8 1.4 5.5 6.9 1.6 6.8 4.4

1.0 4.4 1.0 6.8 5.7 1.0 3.9 1.0

a The lower (higher) frequency for each molecule is the symmetric (asymmetric) C-D2 stretch. Harmonic intensities are reported relative to the weakest absorption in each charged or neutral dipeptide. b The geometry of Rdp (+1) was optimized with the CR-Cβ-Cγ-Cδ dihedral angle constrained at -179.2°, the value obtained from the full optimization of Rdp (0).

the geometry of the Rdp cation was fully optimized, the side chain exhibited a large conformational change to allow the charged group to hydrogen-bond with an amide carbonyl. Such an interaction is unlikely in a protein or solution environment. Therefore, for the purposes of examining the effect of Rdp deprotonation on the C-D2 vibrational frequencies, we constrained the CR-Cβ-Cγ-Cδ dihedral angle to its value in the neutral Rdp molecule, -179.2°. Harmonic vibrational frequencies and intensities were calculated with the C-D2 probe located adjacent to the protonatable or deprotonatable group (Table 1). We also calculated anharmonic C-D2 stretch vibrational frequencies using methods described in detail previously.40 Briefly, these calculations entail mapping the two-dimensional Born-Oppenheimer potential energy surface for the C-D2 stretches (with the D-C-D angle held fixed) on a uniform 8 × 8 grid. The anharmonic vibrational energy levels are then

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TABLE 2: Unscaled Anharmonic Vibrational Frequency Shifts between Charged and Uncharged Kdp, ∆ω ≡ ωcation ωneutral, as a Function of the Location of the C-D2 Probe in the Lysine Side Chain probe

∆ωsym (cm-1)

∆ωasym (cm-1)

Cε-D2 Cδ-D2 Cγ-D2 Cβ-D2

44.9 11.0 14.6 6.1

69.5 18.8 22.7 6.1

obtained by explicitly constructing and diagonalizing the Hamiltonian in a product basis set of Morse oscillator functions. In all cases, the C-D2 probe vibrational frequencies were sensitive to the protonation state of the dipeptide. For the acidic dipeptides, Ddp and Edp, the C-D2 probe vibrational frequencies shifted to lower frequencies upon deprotonation of the neutral to form the anion. The same trend was observed for the basic dipeptides, Kdp and Rdp, whose C-D2 vibrational frequencies red-shifted when the cation was deprotonated to form the neutral. The magnitudes of the calculated shifts were generally similar for the harmonic and anharmonic calculations but varied considerably for the different dipeptides. The largest difference between the harmonic and anharmonic calculations was for the shift in the asymmetric C-D2 stretch vibrational frequency of Edp upon deprotonation, 3.8 cm-1 (harmonic) versus 13.3 cm-1 (anharmonic). Rdp exhibited the smallest anharmonic frequency shifts upon a change in protonation state: 5.7 and 12.0 cm-1 for the symmetric and asymmetric C-D2 stretches, respectively. Most likely, this is because the C-D2 probe is furthest from the charged group in Rdp, and the Rdp positive charge is the most diffuse. In contrast, the other basic dipeptide, Kdp, had the most dramatic anharmonic C-D2 frequency shifts: 44.9 cm-1 (symmetric) and 69.5 cm-1 (asymmetric). The acidic dipeptides, Ddp and Edp, also exhibited robust anharmonic C-D2 frequency shifts upon deprotonation, ranging from 13.3 to 25.9 cm-1. Two trends were observed for the relative harmonic intensities of the C-D2 stretches. First, the symmetric stretch was more intense than the asymmetric stretch for the neutral and positively charged dipeptides; however, this trend was reversed for the anions. In addition, the more negatively charged molecules had dramatically higher C-D2 stretch intensities than their neutral (for acidic residues) or positive charged (for basic residues) counterparts. For example, in Kdp, the symmetric and asymmetric C-D2 stretches are predicted to be 4.3 and 5.7 times more intense in the neutral molecule than in the cation. For the acidic dipeptides, the C-D2 stretch intensities were between 2.9 and 6.8 times more intense for the deprotonated side chain. Accounting for this change in intensity upon change in protonation state is essential to the interpretation of an IR absorption spectrum that contains the signature of both states. While it would be sensible to fit such a spectrum to a pair of absorbances and to assign them to a protonated and deprotonated state, it would be incorrect to equate directly the relative areas or peak heights to the populations of the two states without factoring in the inherent differences in intensities. We also analyzed the effect of varying the location of the C-D2 vibrational probe within the Kdp side chain (Table 2 and Table S-1 in the Supporting Information). As expected, the anharmonic C-D2 vibrational frequencies exhibit significantly larger shifts when the probe is closer to the deprotonation site; the symmetric and asymmetric Cε-D2 stretches shift by 44.9 and 69.5 cm-1 upon deprotonation of Rdp, whereas the Cβ-D2 stretches each shift by just 6.1 cm-1. However, the trend is not

Letters completely monotonic, because the Cδ-D2 frequencies exhibit smaller shifts (11.0 and 18.1) than Cγ-D2 (14.6 and 22.7). These calculations support the idea that the reduced sensitivity of the C-D2 vibrational probe in Rdp is due to its lack of direct proximity to the charged group. Interestingly, the calculated magnitudes of the C-D2 frequency shifts upon a change in the protonation state of Kdp are considerably larger than the spectral shifts reported by Weinkam et al. for Lys72-d8, Lys73-d8, and Lys72-d8 in cytochrome c, which ranged from 4 to 6.6 cm-1. There are two plausible explanations for the large discrepancy: the absence of protein and aqueous solvation in our calculations, and an intrinsic difference in the sensitivity of Lys-d2 versus Lys-d8. To explore the latter possibility, we performed a harmonic frequency calculation of neutral and cationic Kdp-d8 (Table S-2 in the Supporting Information). Kdp-d8 contains eight C-D stretch vibrational frequencies, which can be separated into four lower frequency symmetric stretch modes and four higher frequency asymmetric stretch modes. The intensity-weighted average of the four symmetric C-D stretch modes was 2200.1 cm-1 for neutral Kdp-d8 and 2203.9 cm-1 for cationic Kdp-d8, a shift of 3.8 cm-1. Similarly, the asymmetric C-D stretches of Kdp-d8 shift by 2.6 cm-1 upon protonation. The calculated shifts are commensurate with the measurements of Weinkam et al. who analyzed the IR absorption line shape corresponding to the symmetric C-D stretches of Lys-d8 residues in cytochrome c. Although solvent effects are likely to be an important factor in quantitatively predicting C-D vibrational frequencies in proteins or other condensed-phase environments, these calculations suggest that there is at least a partial cancelation of solvent effects for shifts in C-D vibrational frequencies when acidic and basic side chains change protonation state. Moreover, these calculations demonstrate that utilizing Cε-D2 labels in Lys would provide far more sensitivity to protonation state than fully deuterating the side chain, albeit with a loss of overall molar absorptivity. Finally, it is again important to note that there is a substantial difference in the intensities of the C-D absorptions in neutral Kdp-d8 compared to cationic Kdp-d8. The average intensities of both the symmetric and asymmetric C-D stretches of neutral Kdp-d8 are more than twice as large as those in protonated Kdp-d8. In conclusion, we have analyzed the properties of site-specific C-D2 probes as reporters of the protonation state of both acidic and basic amino acid side chains. As a result of our calculations, two specific principles for the design and interpretation of future experimental studies employing these probes emerge: (1) a single C-D2 probe placed in the immediate vicinity of the charged group will provide maximal sensitivity to its protonation state, and (2) the intensities of the C-D2 IR absorbances are highly sensitive to the protonation state of the nearby acidic or basic group. The latter effect must be properly accounted for when determining the relative populations of the neutral and charged states from analysis of the C-D2 IR absorption line shapes. The general technique of utilizing C-D2 labels as reporters of protonation state offers tremendous promise. In particular, it could be used to determine the pKa of acidic and basic amino acid residues under physiological conditions, and time-resolved experiments could determine the direct or indirect role such residues play in enzymatic reactions involving proton transfer or transport. Future studies are essential to understand the role of the protein environment on the vibrational frequencies of C-D2 probes of acidic and basic amino acid protonation states.

Letters Acknowledgment. S.A.C. gratefully acknowledges the support of the National Science Foundation (CHE-0845736) and the American Chemical Society Petroleum Research Fund (PRF# 48432-G6). Supporting Information Available: Tables showing harmonic and anharmonic vibrational frequencies for neutral and charged lysine dipeptide as a function of the location of the C-D2 probe and harmonic C-D stretch vibrational frequencies for neutral and charged Kdp-d8. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Anderson, D. E.; Becktel, W. J.; Dahlquist, F. W. Biochemistry 1990, 29, 2403. (2) Meeker, A. K.; GarciaMoreno, B.; Shortle, D. Biochemistry 1996, 35, 6443. (3) Whitten, S. T.; Garcia-Moreno, B. Biochemistry 2000, 39, 14292. (4) Hu, C. Q.; Sturtevant, J. M.; Thomson, J. A.; Erickson, R. E.; Pace, C. N. Biochemistry 1992, 31, 4876. (5) Pace, C. N.; Laurents, D. V.; Thomson, J. A. Biochemistry 1990, 29, 2564. (6) Yang, A. S.; Honig, B. J. Mol. Biol. 1993, 231, 459. (7) Schwehm, J. M.; Fitch, C. A.; Dang, B. N.; Garcia-Moreno, B.; Stites, W. E. Biochemistry 2003, 42, 1118. (8) Forsyth, W. R.; Antosiewiez, J. M.; Robertson, A. D. Proteins: Struct., Funct., Genet. 2002, 48, 388. (9) Fitch, C. A.; Karp, D. A.; Lee, K. K.; Stites, W. E.; Lattman, E. E.; Garcia-Moreno, B. Biophys. J. 2002, 82, 3289. (10) Takayama, Y.; Castaneda, C. A.; Chimenti, M.; Garcia-Moreno, B.; Iwahara, J. J. Am. Chem. Soc. 2008, 130, 6714. (11) Garcia-Moreno, B.; Dwyer, J. J.; Gittis, A. G.; Lattman, E. E.; Spencer, D. S.; Stites, W. E. Biophys. Chem. 1997, 64, 211. (12) Stites, W. E.; Gittis, A. G.; Lattman, E. E.; Shortle, D. J. Mol. Biol. 1991, 221, 7. (13) Dauter, Z.; Lamzin, V. S.; Wilson, K. S. Curr. Opin. Struct. Biol. 1995, 5, 784. (14) Ahmed, H. U.; Blakeley, M. P.; Cianci, M.; Cruickshank, D. W. J.; Hubbard, J. A.; Helliwell, J. R. Acta Crystallogr., Sect. D 2007, 63, 906. (15) Baker, W. R.; Kintanar, A. Arch. Biochem. Biophys. 1996, 327, 189. (16) Khare, D.; Alexander, P.; Antosiewicz, J.; Bryan, P.; Gilson, M.; Orban, J. Biochemistry 1997, 36, 3580. (17) McIntosh, L. P.; Hand, G.; Johnson, P. E.; Joshi, M. D.; Korner, M.; Plesniak, L. A.; Ziser, L.; Wakarchuk, W. W.; Withers, S. G. Biochemistry 1996, 35, 9958. (18) Perez-Canadillas, J. M.; Campos-Olivas, R.; Lacadena, J.; del Pozo, A. M.; Gavilanes, J. G.; Santoro, J.; Rico, M.; Bruix, M. Biochemistry 1998, 37, 15865. (19) Plesniak, L. A.; Connelly, G. P.; Wakarchuk, W. W.; McIntosh, L. P. Protein Sci. 1996, 5, 2319. (20) Shrager, R. I.; Sachs, D. H.; Schechte, An; Cohen, J. S.; Heller, S. R. Biochemistry 1972, 11, 541. (21) Sorensen, M. D.; Led, J. J. Biochemistry 1994, 33, 13727. (22) Andre, I.; Linse, S.; Mulder, F. A. A. J. Am. Chem. Soc. 2007, 129, 15805. (23) Griswold, I. J.; Dahlquist, F. W. Nat. Struct. Biol. 2002, 9, 567. (24) Ghosh, N.; Cui, Q. J. Phys. Chem. B 2008, 112, 8387.

J. Phys. Chem. B, Vol. 113, No. 24, 2009 8221 (25) Ghosh, N.; Prat-Resina, X.; Gunner, M. R.; Cui, Q. Biochemistry 2009, 48, 2468. (26) Kato, M.; Warshel, A. J. Phys. Chem. B 2006, 110, 11566. (27) Kim, J.; Mao, J.; Gunner, M. R. J. Mol. Biol. 2005, 348, 1283. (28) Li, G. H.; Cui, Q. J. Phys. Chem. B 2003, 107, 14521. (29) Riccardi, D.; Cui, Q. J. Phys. Chem. A 2007, 111, 5703. (30) Riccardi, D.; Schaefer, P.; Cui, Q. J. Phys. Chem. B 2005, 109, 17715. (31) Simonson, T.; Carlsson, J.; Case, D. A. J. Am. Chem. Soc. 2004, 126, 4167. (32) Warshel, A.; Russell, S. T. Q. ReV. Biophys. 1984, 17, 283. (33) Naraharisetty, S. R. G.; Kasyanenko, V. M.; Zimmermann, J.; Thielges, M. C.; Romesberg, F. E.; Rubtsov, I. V. J. Phys. Chem. B 2009, 113, 4940. (34) Chin, J. K.; Jimenez, R.; Romesberg, F. E. J. Am. Chem. Soc. 2001, 123, 2426. (35) Chin, J. K.; Jimenez, R.; Romesberg, F. E. J. Am. Chem. Soc. 2002, 124, 1846. (36) Cremeens, M. E.; Fujisaki, H.; Zhang, Y.; Zimmermann, J.; Sagle, L. B.; Matsuda, S.; Dawson, P. E.; Straub, J. E.; Romesberg, F. E. J. Am. Chem. Soc. 2006, 128, 6028. (37) Kinnaman, C. S.; Cremeens, M. E.; Romesberg, F. E.; Corcelli, S. A. J. Am. Chem. Soc. 2006, 128, 13334. (38) Romesberg, F. E. ChemBioChem 2003, 4, 563. (39) Sagle, L. B.; Zimmermann, J.; Matsuda, S.; Dawson, P. E.; Romesberg, F. E. J. Am. Chem. Soc. 2006, 128, 7909. (40) Miller, C. S.; Ploetz, E. A.; Cremeens, M. E.; Corcelli, S. A. J. Chem. Phys. 2009, 130, 125103. (41) Sagle, L. B.; Zimmermann, J.; Dawson, P. E.; Romesberg, F. E. J. Am. Chem. Soc. 2006, 128, 14232. (42) Mirkin, N. G.; Krimm, S. J. Phys. Chem. A 2004, 108, 10923. (43) Mirkin, N. G.; Krimm, S. J. Phys. Chem. A 2007, 111, 5300. (44) Mirkin, N. G.; Krimm, S. J. Phys. Chem. B 2008, 112, 15267. (45) Arbely, E.; Arkin, I. T. J. Am. Chem. Soc. 2004, 126, 5362. (46) Torres, J.; Arkin, I. T. Biophys. J. 2002, 82, 1068. (47) Torres, J.; Kukol, A.; Arkin, I. T. Biophys. J. 2000, 79, 3139. (48) Weinkam, P.; Zimmermann, J.; Sagle, L. B.; Matsuda, S.; Dawson, P. E.; Wolynes, P. G.; Romesberg, F. E. Biochemistry 2008, 47, 13470. (49) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (50) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (51) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200. (52) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007. (53) Frisch, M. J. ; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian Inc.: Wallingford, CT, 2004.

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