J. Phys. Chem. B 2005, 109, 3681-3689
3681
Effect of Solvent upon CH‚‚‚O Hydrogen Bonds with Implications for Protein Folding Steve Scheiner* and Tapas Kar Department of Chemistry and Biochemistry, Utah State UniVersity, Logan, Utah 84322-0300 ReceiVed: NoVember 22, 2004; In Final Form: December 15, 2004
The series of CH‚‚‚O bonds formed between CFnH4-n (n ) 0-3) and water are studied by quantum calculations under vacuum and in various solvents, including aqueous environment. The results are compared with the OH‚‚‚O bond of the water dimer in the same solvents. Increasing polarity of the solvent leads in all cases to a lessening of the H-bond interaction energy, in a uniform fashion such that the CH‚‚‚O bonds all remain weaker than OH‚‚‚O in any solvent. These H-bond weakenings are coupled to a shortening of the intersubunit separation. The contraction of the covalent CH bond to the bridging proton is reduced as the solvent becomes more polar, and the blue shift of its stretching vibration is likewise diminished. A process is considered that simulates protein folding by starting from a pair of noninteracting subunits in aqueous solvent and then goes to a H-bonded pair within the confines of a protein environment. This process is found to be energetically more favorable for some of the CH‚‚‚O H-bonds than for the nominally stronger conventional OH‚‚‚O H-bond. This finding suggests that CH‚‚‚O bonds can make important energetic contributions to protein folding, on par with those made by traditional H-bonds.
Introduction The hydrogen bond is one of the most widely studied sorts of molecular interactions, motivating for example a number of monographs over the years.1,2 Although the phenomenon has been known since the early part of the 20th century,3,4 old ideas evolve, and new aspects continue to be discovered. For instance, the realm of the hydrogen bond has been extended of late to more weakly interacting systems, which encompass π electrons as proton acceptors5,6 instead of the more normally expected O or N lone electron pairs. Another type of H-bond that has undergone a resurgence of attention is that characterized by a CH donor, in place of the more common OH or NH groups. When first proposed many years ago,7,8 there was some resistance due to the low electronegativity of C which was presumed to make it a weak proton donor. However, a wealth of recent work9-11 has transformed the notion of a CH‚‚‚X H-bond (X ) O, N) from a sketchy hypothesis into a well-documented common observation. And, indeed, the supposed weakness of the CH donor group has not prevented this interaction from affecting the geometries adopted by a wide range of molecules and intermolecular orientations.12-14 The variety of systems wherein CH‚‚‚X bonds seem to play an important structural role extends to a plethora of biological macromolecules,15-18 adding to their importance. These CH‚‚‚X systems share numerous features with the more traditional H-bonds, such as geometric preference, NMR chemical shifts, and electron density patterns.19-21 On the other hand, there are a number of interesting facets which make them unique, mostly centering around the CH stretching frequency. This band, for a certain subset of CH‚‚‚X bonds, shifts to the blue and loses intensity,22,23 rather than the red shift and intensity magnification that have come to characterize the vast majority of H-bonds. While it is now apparent that CH‚‚‚X bonds may be present in a geometric sense in a score of different systems (i.e. the * To whom correspondence should be addressed. E-mail: scheiner@ cc.usu.edu.
atoms are arranged in a configuration consistent with H-bonding patterns), the energetic contribution of each such bond has been extremely difficult to assess. There have been only a handful of experimental estimates of this quantity that are usually rather indirect and clouded by a number of other complicating factors which are difficult to disentangle from the H-bond energy of interest. Karger et al.,24 for example, arrived at an estimate of 2 kcal/mol, while a later study25 proposed considerably smaller values. In the face of such experimental difficulties and conflicting data, researchers have turned to quantum calculations as a means of going directly to the heart of the problem and computing the interaction energy of a given H-bond. And, indeed, a large number of such calculations over the past several years have provided accurate estimates of H-bond energies for a variety of CH‚‚‚X contacts.22,26-28 Calculations of this type have also been used to probe the fundamental origins of the blue shift of the CH frequency in those systems where it occurs,29-33 yielding some interesting insights into this phenomenon, and reconfirming the character of the CH‚‚‚X interaction as a true H-bond. A prime difficuly in applying the quantum chemical results directly to an experimental situation deals with the surroundings. Most quantum calculations, particularly the most sophisticated and reliable, are carried out in vacuo, where the system of interest is isolated from any other molecules. This situation is quite distinct from that which is typically encountered in a real system, where the H-bond occurs in solution or within the confines of a molecule much larger than that explicitly considered in the calculations. It is hence crucial to consider environmental effects upon the CH‚‚‚X bond, not only its energetics but also its geometric and spectroscopic properties. Some very recent computations which have placed a CH‚‚‚X bond within a model solution environment34,35 have encouraged the hope that a systematic treatment of this problem might indeed be successful. It is thus to this issue that we turn our attention in this work. Rather than address one specific system that contains a particular
10.1021/jp0446736 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/03/2005
3682 J. Phys. Chem. B, Vol. 109, No. 8, 2005 CH‚‚‚X bond, the study examines, in a systematic manner, a full range of H-bond strengths, from extremely weak to those comparable to a conventional OH‚‚‚O bond. After computing the properties of each system in vacuo, it is then immersed in solvent and the properties of the H-bond monitored as the polarity of the solvent increases. In addition to the strength of each H-bond, the intermonomer separation is examined, as are the structural and spectroscopic properties of the bridging CH covalent bond. In particular, we inquire into whether the blue shift of this CH stretching frequency persists in solution. In the context of proteins, knowledge about the energetics of CH‚‚‚X H-bond formation is even more murky. Although it is widely believed that these bonds are too numerous to ignore, and that they may make some energetic contribution,15,17,36-38 quantitative information has been much harder to come by. It was stated, for example, that “nothing is known experimentally about the strength of these interactions”39 and “despite the occurrence of short CH‚‚X contacts, their free energy contribution remains to be assessed”,40 a knowledge gap that persists in that “there are few experimental studies of the energetic contribution from any type of C-H‚‚O H-bonds in protein or polypeptide systems”.41 Recent attempts to address this issue provide only rough and conflicting estimates. Empirical potentials42 estimate that the collection of CH‚‚‚O H-bonds, as a group, may contribute anywhere between 17 and 50% to the total interaction energy of protein-protein interfaces. A combined CD and NMR study of a model polypeptide found the binding energy may be 0.5 kcal/mol or zero, depending upon the direction of the bond.41 A more recent examination of a particular CH‚‚‚O H-bond within a protein43 estimated its energy as 0.9 kcal/mol, while another work in that same year44 found no evidence of an energetic contribution at all. These authors surmised that “many of the observed carbon H-bonds may simply be a consequence of close packing” and that their “mere presence does not imply energetic significance”. This work hence attempts to address an important open question of protein structure: what is the energetic contribution that a CH‚‚‚X bond may make to the protein folding process, if any? Method of Calculations We consider as proton donor each of the entire set of fluorosubstituted methanes, CFnH4-n, with n ) 0-3. CH4 is the weakest such donor; successive replacement of one, two, and three H atoms by F leads to a progressively stronger donor. This set of donors has served this purpose in the past,13,33,45 so there is a comprehensive set of data with which the present computations may be compared. Moreover, the CF2H2 molecule is of special importance here in that the strength of its CH‚‚‚O bond to water has been shown earlier to be essentially identical to that of a full glycine residue in a polypeptide.46 As in our own earlier gas-phase work,47 each fluoromethane is paired with a water molecule as proton acceptor. The H3CH‚‚‚OH2, FH2CH‚‚‚OH2, F2HCH‚‚‚OH2, and F3CH‚‚‚OH2 systems are illustrated in Figure 1a, where the X designations refer to either H or F. As a point of comparison, these CH‚‚‚O systems are compared to the water dimer pictured in Figure 1b. Consistent with earlier work, the CH‚‚‚O (and OH‚‚‚O) atoms were held in a fully linear alignment; the remainders of each geometry were fully optimized. Ab initio calculations were carried out using the GAUSSIAN03 code, with a double-ζ quality basis set augmented with polarization and diffuse functions, 6-31+G**.48 The B3LYP variant of density functional theory (DFT)49,50 was one means used to include correlation effects. Further calculations were performed that made use of the more
Scheiner and Kar
Figure 1. Structures studied for (a) complexes of fluoro-substituted methanes with water and (b) water dimer. Xn refer to either F or H.
extended augmented correlation-consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set,51 with correlation evaluated by the MP2 approach. Solvation effects were considered using a variety of methods, all based on the placement of the system of interest within a continuous medium, with a dielectric constant . The charge distribution of the solute causes a so-called reaction field to appear within the medium, which then acts back upon the solute. These changes are computed in a self-consistent manner, leading to their designation as the self-consistent reaction field (SCRF) approach. The most primitive such method is the original Onsager formalism,52,53 wherein the only component of the charge distribution considered is the dipole moment, hence referred to as the “dipole” variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM)54 embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF).55,56 A variant of this method is the conductor polarized continuum model (CPCM),57 wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The selfconsistent isodensity (SCI) PCM procedure58 determines the cavity self-consistently from an isodensity surface. The UAHF (united atom model for Hartree-Fock/6-31G*) definition59 was used for the construction of the solute cavity. Results The calculated properties of the various systems in the gas phase have already been reported at some length.19,47 In sum, the data indicated a growing strength of the H-bond as each successive H atom of CH4 is replaced by F. Each increment of H-bond energy is accompanied by a contraction of the intermolecular distance, as well as a slight shortening of the covalent C-H bond. Attention here is focused upon the effect of placing these H-bonding systems within the confines of a solvent. (1) Effects of Several Solvents. The solvation energies computed for each of three solvents are reported for F3CH‚‚‚OH2 in the first four rows of Table 1. The next rows refer to the isolated subunits, first F3CH, followed by HOH. Moving from left to right in Table 1 corresponds to progressively more polar solvent, beginning with CCl4 with a dielectric
Effect of Solvent upon CH‚‚‚O Hydrogen Bonds
J. Phys. Chem. B, Vol. 109, No. 8, 2005 3683
TABLE 1: Solvation Energies (kcal/mol) of F3CH‚‚‚OH2 and Its Individual Subunits, Computed at the B3LYP/6-31+G** Level species
method
) 2.2
) 4.3
) 78.4
F3CH‚‚‚OH2
dipole PCM CPCM SCI-PCM dipole PCM CPCM SCI-PCM dipole PCM CPCM SCI-PCM
-1.47 -2.05 -2.42 -2.71 -0.34 -0.61 -0.75 -1.09 -0.95 -1.73 -2.17 -2.35
-4.05 -4.05 -4.47 -4.47 -0.53 -1.25 -1.41 -1.73 -1.48 -3.67 -4.17 -3.70
-3.40 -8.06 -8.12 -6.02 -0.78 -2.52 -2.54 -2.61 -2.14 -7.70 -7.77 -5.45
F3CH
HOH
TABLE 2: Contributions of Solvation Energy to the Binding Energy (∆Esolv, kcal/mol) at the B3LYP/6-31+G** Level species CH4‚‚‚OH2
FCH3‚‚‚OH2
F2CH2‚‚‚OH2
F3CH‚‚‚OH2
HOH‚‚‚OH2
method
) 2.2
) 4.3
) 78.4
dipole PCM CPCM SCI-PCM dipole PCM CPCM SCI-PCM dipole PCM CPCM SCI-PCM dipole PCM CPCM SCI-PCM dipole PCM CPCM SCI-PCM
0.34 0.31 0.39 0.44 0.43 0.35 0.49 0.57 -0.12 0.19 0.37 0.54 -0.18 0.29 0.50 0.73 -0.51 0.28 0.49 0.52
0.56 0.61 0.68 0.67 0.48 0.75 0.89 0.94 -0.29 0.69 0.87 1.01 -2.04 0.87 1.11 0.97 -0.89 0.89 1.15 0.91
0.74 0.94 0.93 0.98 0.46 1.47 1.47 1.51 -0.57 1.68 1.69 1.69 -0.48 2.16 2.19 2.05 -1.45 2.41 2.45 1.49
constant of 2.2, to water with ) 78.4. Intermediate between these two extremes lies ether, with a dielectric constant of 4.3. There are several trends in the data that are immediately obvious. In nearly all cases, the solvation energy rises (becomes more negative) as the dielectric constant of the solvent increases. The values obtained with the most primitive dipole method tend
to be smaller in magnitude than those corresponding to the other procedures, in some cases much smaller (by a factor of 2 or 3). The PCM, CPCM, and SCIPCM methods yield generally similar solvation energies, albeit with some residual variation from one method to the next. Perhaps more important than the solvation energies of any of the individual species, are the differences between the complex on one hand and the sum of its constituents on the other. These differences correspond to the effect of each solvent upon the interaction energy, that is the correction that must be added to the gas-phase H-bond energy. As reported in the F3CH‚‚‚OH2 section of Table 2, these quantities are positive for the three PCM methods, indicating that the interaction energy is smaller (less negative) in solvent as compared to vacuum. Indeed, the deviations between these three methods with regard to the all-important ∆Esolv are considerably smaller than the variations in the solvation energies of the individual species. These ∆Esolv values are roughly 0.5, 1.0, and 2.1 kcal/mol, in CCl4, ether, and water, respectively. In striking contrast, the more primitive dipole approach predicts the opposite result, that interaction energies in solvent are more negative than in vacuo, as denoted by the negative values in the dipole row of ∆Esolv. The uppermost three sections of Table 2 illustrate that many of the same trends are observed for the other complexes as well. In all cases, the values of ∆Esolv computed by the PCM, CPCM, and SCIPCM approaches yield very similar values. This quantity becomes progressively more positive as the polarity of the solvent increases, consistent with a weakening of each H-bond. The solvation contribution to the interaction energy is rather similar for all four systems when ) 2, roughly on the order of 0.5 kcal/mol. In aqueous solvent, however, ∆Esolv is rather sensitive to the degree of fluoro substitution. This term is equal to just under 1 kcal/mol for CH4‚‚‚OH2 but climbs to more than double that magnitude for F3CH‚‚‚OH2 when ) 78. Of some importance is the comparable behavior of the water dimer, with its conventional OH‚‚‚O H-bond. The data, reported in the last four rows of Table 2, are remarkably similar to the values obtained for F3CH‚‚‚OH2 (with the exception of the primitive dipole results). Gas-phase interaction energies are reported in the second column of Table 3 for the full range of systems considered here. As listed, the interaction energies for proton donors CH4, FCH3,
TABLE 3: Interaction Energies (kcal/mol) Computed for the Complexes Combining the Fluorinated Methanes with Water ) 2.2 gas phasea
method
DFT
CH4‚‚‚OH2
-0.47 (-0.27) [-0.74]
FCH3‚‚‚OH2
-1.79 (-1.53) [-1.76]
F2CH2‚‚‚OH2
-2.86 (-2.67) [-2.60]
F3CH‚‚‚OH2
-4.16 (-3.88) [-3.70]
HOH‚‚‚OH2
-5.54 (-4.78) [-4.78]
dipole PCM CPCM SCIPCM dipole PCM CPCM SCIPCM dipole PCM CPCM SCIPCM dipole PCM CPCM SCIPCM dipole PCM CPCM SCIPCM
-0.13 -0.16 -0.08 -0.03 -1.36 -1.44 -1.30 -1.22 -2.98 -2.67 -2.49 -2.32 -4.35 -3.88 -3.66 -3.44 -6.05 -5.27 -5.05 -5.02
system
a
) 4.3 HF 0.22 0.04 0.10 -1.44 -1.07 -0.93 -0.82 -2.74 -2.25 -2.06 -1.83 -4.56 -3.46 -3.22 -2.92 -4.94 -4.37 -4.13 -3.96
DFT 0.09 0.14 0.21 0.20 -1.31 -1.04 -0.90 -0.85 -3.15 -2.18 -1.99 -1.85 -6.20 -3.30 -3.05 -3.19 -6.43 -4.65 -4.40 -4.63
B3LYP/6-31+G**; HF/6-31+G**value in parentheses; MP2/aug-cc-pVTZ in square brackets.
) 78.4 HF 0.49 0.33 0.39 -1.71 -0.63 -0.48 -0.43 -2.96 -1.68 -1.48 -1.27 -4.98 -2.76 -2.49 -2.25 -5.10 -3.64 -3.37 -3.39
DFT
HF
0.26 0.47 0.46 0.51 -1.33 -0.32 -0.32 -0.28 -3.43 -1.19 -1.17 -1.17 -4.64 -2.00 -1.98 -2.11 -6.99 -3.13 -3.10 -4.05
0.83 -0.03 -0.03 0.02 -2.15 0.12 0.14 -3.31 -0.63 -0.61 -0.47 -5.57 -1.28 -1.25 -1.28 -5.34 -1.97 -1.94 -2.58
3684 J. Phys. Chem. B, Vol. 109, No. 8, 2005
Figure 2. Interaction energies computed for each labeled proton donor with water as acceptor. Onsager function FO ) ( - 1)/( + 2), where refers to the dielectric constant of the medium. Solid lines represent B3LYP/6-31+G** data and broken lines MP2/aug-cc-pVTZ.
F2CH2, F3CH, and HOH with acceptor OH2 are -0.47, -1.79, -2.86, -4.16, and -5.54 kcal/mol, respectively, all computed at the B3LYP level with the 6-31+G** basis set. Values in parentheses refer to the same quantity, computed at the HartreeFock (HF) level, and are typically somewhat less attractive. Higher level MP2/aug-cc-pVTZ values in square brackets tend to be close to the B3LYP quantities, albeit not quite as negative. The data reported in the ensuing columns represent the interaction energies within the indicated models of solvent. (These quantities include the values of ∆Esolv from Table 2.) The interaction energies computed for each system with the PCM, CPCM, and SCIPCM methods all tend to be quite similar to one another, regardless of which solvent is considered. There is a tendency for the PCM method to yield the most negative interaction energy and SCIPCM the least negative, but, again, the differences between these three methods are fairly small. The primitive dipole approximation, on the other hand, is frequently quite at odds with the results of the other methods. Taking the F3CH‚‚‚OH2 system in aqueous solvent as an example, the DFT interaction energies of the former three methods lie in the range between -2.0 and -2.1 kcal/mol, while the dipole value is more than double the magnitude, at -4.6 kcal/mol. Due to the agreement between the PCM, CPCM, and SCIPCM methods, and the fact that CPCM data tend to fall approximately midway between the extremes of the other two, most of the following narrative and analysis make use of the CPCM results. The trends in the computed interaction energies may be visualized in Figure 2, which plots the correlated values of ∆E vs the Onsager function FO ) ( - 1)/( + 2) that relates to the permanent electric moment and polarizability of each solvent molecule.52,60 Note that FO ) 0 for the gas phase, wherein ) 1, and climbs to an asymptote of unity as the solvent becomes progressively more polar and approaches ∞. The high value of for water leads to FO ) 0.96, rather close to the theoretical limit of 1.0. The B3LYP/6-31+G** data are indicated by the solid lines, whereas the broken lines represent the binding energies computed with the more sophisticated MP2/aug-ccpVTZ treatment. In all cases, the rise in polarity of the solvent leads to a less negative value of ∆E, i.e., a weakening of the H-bond. Whether B3LYP/6-31+G** or MP2/aug-cc-pVTZ, this rise is very nearly a linear function of FO, and also reasonably regular in the sense that the energetic ordering of the various H-bonds remains the
Scheiner and Kar
Figure 3. B3LYP/6-31+G** optimized inter-subunit separation R(C‚‚‚O)/R(O‚‚‚O) for each labeled proton donor with water as acceptor.
same, regardless of the solvent. As the solvent becomes more polar, the spacing between the energies of the systems is reduced by a certain amount. For example, F3CH‚‚‚OH2 is more strongly bound than F2CH2‚‚‚H2O by 1.30 kcal/mol in the gas phase at the B3LYP/6-31+G** level, but this advantage is diminished to 0.81 kcal/mol in water. It is perhaps important to note that the conventional OH‚‚‚O H-bond of the water dimer behaves in very much a parallel fashion to the four CH‚‚‚O bonds illustrated in Figure 2, weakening at a similar rate as increases. Note, finally, that while there are some small quantitative differences between the B3LYP/6-31+G** and MP2/aug-ccpVTZ binding energies, the trends are essentially identical for each. The only significant difference is that the MP2/aug-ccpVTZ H-bond energies are slightly less sensitive to solvent polarity than are B3LYP/6-31+G** data. The optimized length of each H-bond is depicted in Figure 3, again as a function of ( - 1)/( + 2). The trend here is perhaps somewhat counterintuitive, in the sense that while the energetics of H-bond formation were shown in Figure 2 to weaken in more polar solvents, the two subunits are nonetheless drawn toward one another. For example, the R(C‚‚‚O) equilibrium distance in F3CH‚‚‚OH2 is 3.258 Å in the gas phase; it is reduced by 0.1 Å to 3.161 Å in aqueous solvent. This trend of reduced intermolecular separation with increasing solvent polarity is most obvious in the cases of the stronger H-bonds. The trend is nearly absent in FH2CH‚‚‚OH2 and is even reversed in H3CH‚‚‚OH2. As has been pointed out on a number of occasions, the CH covalent bond in CH‚‚‚O systems, particularly those with sp3hybridized C, is prone to contract upon H-bond formation. As evident by the data points on the far left of Figure 4, this contraction is noted in all of the substituted methane systems in the gas phase, just as the OH‚‚‚O bond of the water dimer undergoes the expected OH bond elongation. As the solvent becomes progressively more polar, there is a general trend for the C-H bond contractions to lessen; i.e., ∆r becomes less negative. In some cases, e.g. H3CH‚‚‚OH2, a small contraction in the gas phase can transform to a small stretch in more polar solvent. It might be noted that the strongest CH‚‚‚O interaction, between F3CH and OH2, does not necessarily correspond to the largest bond contraction, neither in the gas phase (as noted earlier) nor in polar solvent. Just as the CH contractions tend to lessen as rises, so does the OH elongation in the water dimer, as evident by the uppermost curve in Figure 4. One might expect there to be a correlation between the degree of CH (OH) bond contraction (elongation) and the amount of
Effect of Solvent upon CH‚‚‚O Hydrogen Bonds
Figure 4. Change in B3LYP/6-31+G** length of CH/OH bridging covalent bond of each labeled proton donor caused by complexation with water molecule as proton acceptor.
Figure 5. Change in B3LYP/6-31+G** vibrational frequency of CH/ OH bridging covalent bond of each labeled proton donor caused by complexation with water molecule as proton acceptor.
the blue (red) shift of the relevant stretching frequency. This supposition is largely confirmed by Figure 5, which illustrates the change in this frequency arising from formation of each H-bond. Consistent with the ∆r trends in Figure 4, the data indicate a progressively diminished blue shift of the CH stretching frequency as the solvent becomes more polar. The bathochromic shift of the OH stretch in the water dimer is likewise lowered in magnitude as the solvent polarity rises. (2) Contribution to Protein Folding. One of the central questions in biophysical chemistry has to do with the energetic import of a CH‚‚‚O bond within the context of a protein interior. To this end, reference is made to Figure 6, which characterizes the various relevant states in a cartoon format. State A in the upper left corner refers to a pair of isolated, noninteracting species, a proton donor AH, and acceptor B. The energy released upon combination to form a AH‚‚‚B complex in vacuo, state D, corresponds to the gas-phase H-bond energy typically arising from a quantum calculation, EHBvac. The same process of AH + B f AH‚‚‚B can also occur within the context of a protein (BfE) or in aqueous (or other) solvent (CfF). One can take the H-bond energies reported in Table 3 as reasonable approximations to each of these processes. The in vacuo values of EHBvac correspond to the gas-phase values listed in the second column of Table 3. The CfF process in aqueous solvent, EHBaq, is represented by the last two columns. EHBprot may be approximated by the data reported in the columns
J. Phys. Chem. B, Vol. 109, No. 8, 2005 3685
Figure 6. Schematic diagram illustrating H-bond formation between AH and B under vacuum, in protein, and in aqueous media.
corresponding to ) 4.3, the value normally taken to represent the overall dielectric constant in the interior of a protein.61,62 As described earlier, the H-bond strength of each sort of H-bond, whether CH‚‚‚O or OH‚‚‚O, weakens as one takes the system from vacuum, to protein, and finally to water. Under vacuum, the water dimer’s H-bond strength exceeds that of F3CH‚‚‚OH2 by 1.4 kcal/mol (at the B3LYP/6-31+G** level). This advantage remains at about this same level in protein/ether and recedes only slightly to 1.1 kcal/mol in water (using CPCM solvent approximation). Results at the HF level are similar to the DFT trends, as are the MP2/aug-cc-pVTZ data. In this context, then, it would be fair to say that the energetic advantage of the OH‚‚‚O bond remains nearly intact as the polarity of the solvent increases. In sum, the difference in energy between a CH‚‚‚O and OH‚‚‚O bond computed in vacuo is unlikely to change much upon immersion in a solvent environment. The BfE process (see Figure 6) begins with a pair of subunits, both within the context of a protein but not associated with one another. EHBprot corresponds to the energy released when these two subunits form a H-bond, again within the protein interior. Another question of considerable interest is related to the contribution made by an individual H-bond to the protein folding process. The protein molecule is envisioned first to be unfolded within aqueous solvent, and the potential H-bond has not yet formed, corresponding to state C in Figure 6. As the protein folds, the two groups come together to form their H-bond, now within the interior of the protein, state E. It is thus of some importance to estimate the energetics of this CfE process. Note that this transformation contains not only the energetics of the H-bond itself but also solvation effects. That is, a component of the CfE energetics represents the difference in solvation energy, between protein and water, of the isolated subunits on one hand and the H-bonded complex on the other. The computed energies of all states A-F are plotted for F3CH‚‚‚OH2 and HOH‚‚‚OH2 in Figure 7a,b, respectively. The left side of each refers to the isolated subunits, and the complexes are on the right. The uppermost energy levels represent the in vacuo situation, wherein the complexes lie lower in energy than the isolated subunits by 4.2 and 5.5 kcal/mol, respectively, for the two systems, as indicated. (These values are equal to 3.7 and 4.8, respectively, at the MP2/aug-cc-pVTZ level, as reported by the values in parentheses.) After solvation energies are considered, the energy levels within the protein ( ) 4.3) are lowered to those indicated (B and E). As mentioned
3686 J. Phys. Chem. B, Vol. 109, No. 8, 2005
Scheiner and Kar TABLE 4: Energetics (kcal/mol) Computed for the CfE Process, Which Takes a Pair of Noninteracting Subunits in an Aqueous Environment into Protein While Allowing Them To Form a H-bonda solvation method
CH4
PCM CPCM SCI-PCM
4.43 4.04 -
FCH3
F2CH2
F3CH
HOH
HF/6-31+G** 4.52 3.90 4.09 3.48 2.40 1.93
2.65 2.32 0.86
4.31 3.69 0.60
PCM CPCM SCI-PCM
B3LYP/6-31+G** 4.31 4.09 3.30 3.93 3.65 2.88 1.98 1.63 0.90
2.01 1.67 -0.56
3.42 2.79 -1.13
CPCM
MP2/aug-cc-pVTZ 3.03 2.96 2.32
1.28
2.33
a
Each proton donor listed was complexed with water as proton acceptor.
Figure 7. Energetics (kcal/mol) of desolvation and H-bond formation processes of (a) F3CH + OH2 and (b) HOH + OH2. States under vacuum (A and D), in protein (B and E), and in water (C and F) are indicated by appropriate labels. B3LYP/6-31+G** values are reported, with MP2/aug-cc-pVTZ values in parentheses.
above, the H-bond energies have both been reduced by the protein environment, to 3.1 and 4.4 for F3CH‚‚‚OH2 and HOH‚‚‚OH2, respectively. Solvation by water ( ) 78) stabilizes the states even more, as indicated by the lowest C and F levels. And, once more, the complexation energy is reduced even further, to 2.0 and 3.1 kcal/mol for the two systems. We now turn our attention to the CfE process, corresponding to the energy required to take a pair of uncomplexed subunits in an aqueous environment, and bring them into the protein while forming a H-bond between them. This process is represented by the bold arrows in Figure 7 and is endothermic for both the CH‚‚‚O and OH‚‚‚O bonded systems. This endothermicity is understandable from the standpoint that the exothermicity of forming the H-bond is more than offset by the endothermicity of bringing the system out of aqueous solution, into a protein environment with its lower dielectric. What is most interesting is a comparison of the energetics of CfE conversion in the two systems. While both CH‚‚‚O and OH‚‚‚O are endothermic, it is important to note that the former is less endothermic. In other words, the calculations suggest that the CH‚‚‚O bond is every bit as important in an energetic sense for protein folding as is the OH‚‚‚O bond, perhaps even more so. The energetics of the CfE process for all systems are reported in Table 4 at the HF, DFT, and MP2 levels, with two different basis sets and with various approximations to model the solvent. This table makes evident that the lesser endothermicity of the process for F3CH‚‚‚OH2, as compared to HOH‚‚‚OH2, is not restricted to B3LYP/6-31+G** but is common to the HF and MP2 levels as well, and with either basis set. PCM yields a similar relation between the values for
the two systems, again at either DFT or HF. The SCI-PCM values are less positive, even negative; values obtained for the two systems are within 0.5 kcal of one another, again indicating similarity between CH‚‚‚O and OH‚‚‚O. The more sophisticated MP2/aug-cc-pVTZ CfE energies for F3CH‚‚‚OH2 and HOH‚‚‚OH2 are 1.28 and 2.33 kcal/mol, respectively. The former CH‚‚‚O system is thus less endothermic by 1.05 kcal/ mol, very close indeed to the B3LYP/6-31+G** difference of 1.12 kcal/mol. The CRH group is the most prominent proton donor in CH‚‚‚O H-bonds within proteins.15 In this context, it is important to point out that the CF2H2 molecule resembles the CR of polypeptide residues in the sense that, in either case, the C atom is surrounded by two electronegative groups, F in the former case and peptide groups in the latter. It is hence not surprising that the CH‚‚‚O H-bond formed by CF2H2 is quite similar in strength to that formed by an amino acid like glycine,46 imbuing the CF2H2 molecule with particular relevance. In this context then, it is important to note that the F2HCH‚‚‚OH2 system yields CfE energetics that are comparable to those for the OH‚‚‚O bond of the water dimer. In Table 4, it may be seen that this similarity extends over all three levels of theory and with both PCM and CPCM. In fact, at the highest level of theory applied here, MP2/aug-cc-pVTZ, the CfE energies for F2HCH‚‚‚OH2 and HOH‚‚‚OH2 are virtually identical. It is worth reiterating an important distinction: The trends illustrated in Figure 2 refer to the process wherein a pair of noninteracting subunits within a given solvent are permitted to form a H-bonded complex within that same environment. Each of these H-bond formation processes is exothermic, with the OH‚‚‚O bond stronger than any of the CH‚‚‚O complexes, giVen the same solVent. Moreover, the exothermicity diminishes with rising solvent polarity, and uniformly so that the trends of relative strength are common to any particular dielectric. It may be noted, however, that these trends can be altered if different solvents are considered for each. For example, the H-bond energy of F3CH‚‚‚OH2 in solvent with ) 2.2 is stronger than the OH‚‚‚O bond of the water dimer in aqueous solution. It would hence be fair to claim that a conventional OH‚‚‚O bond would contribute more to protein stability than would CH‚‚‚O if one is discussing the formation of the bond after the two subunits have been placed within the interior of the protein. The CfE process mentioned above, associated with protein folding in aqueous solution, refers to moving the two noninteracting subunits from a state where they are both fully solvated in water, into the protein interior while letting them form a H-bond. As such, this process contains the so-called “desolvation
Effect of Solvent upon CH‚‚‚O Hydrogen Bonds penalty” associated with this transfer out of aqueous environment. This penalty, an endothermic term, works in opposition to the exothermicity of the H-bond formation. It is this penalty which thus accounts for the endothermicity of the entire process, and the positive values in Figure 7. It is in the CfE process where the CH‚‚‚O bond can equal, or even exceed, the OH‚‚‚O interaction in terms of energetic contribution to protein folding, as evidenced by the less positive values for some of the CH‚‚‚O bonds in Table 4, as compared to HOH‚‚‚OH2. Probing the source of this point in greater detail, it is clear from Figure 7 that, in all cases, complexed or uncomplexed, CH‚‚‚O or OH‚‚‚O, the energy is raised when any of the species are brought from aqueous solution into a protein environment. Where the two sorts of H-bonds differ is in the quantitative aspects of this effect. The destabilization of the two CH‚‚‚O states on the left, by transition from aqueous to protein environment, is considerably smaller than that of the OH‚‚‚O states on the right. This places the protein manifold in closer proximity to the aqueous manifold, leaving a smaller energy gap to jump from C to E. Adopting more quantitative language, the H-bond energy of the OH‚‚‚O bond is 3.1 kcal/ mol in water, 1.1 kcal/mol greater than that of the CH‚‚‚O bond. However, the OH‚‚‚O complex is destabilized by 5.9 kcal/mol upon displacement to protein, larger by 2.2 kcal/mol than the CH‚‚‚O destabilization of 3.7. The latter 2.2 kcal/mol difference in desolvation penalty exceeds the original OH‚‚‚O H-bond advantage by 1.1 kcal/mol, the ultimate disadvantage of the OH‚‚‚O bond (2.8 vs 1.7 kcal/mol for CH‚‚‚O). Discussion There are a number of factors that differentiate the calculations reported herein from the real situations they are intended to model. First, it is readily apparent that a homogeneous continuum serves as an inexact model for a solvent or protein, with its discrete solvent molecules or neighboring groups, and the lack of explicit dynamic time dependence in these methods. Nonetheless, continuum models have achieved what is now a long history of successful applications to a range of chemical problems.63-65 It is encouraging also that, despite the approximate nature of our treatment of solvation, our finding of a 3 kcal/mol endothermicity for the OH‚‚‚O H-bond is in striking coincidence with the result obtained for another conventional H-bond,66 applying a more sophisticated treatment of solvation. In any case, it was thought judicious to assess the magnitude of errors that might be incurred by use of a continuum model. Any deficit of this approach ought to be particularly noticeable in the case of aqueous solvation and the strong H-bonding interactions of neighboring water molecules. The F3CH‚‚‚OH2 complex was hence surrounded by a first sphere of explicit water molecules. There are five peripheral atoms in F3CH‚‚‚OH2, three F and two H, and one solvating water was permitted to interact with each. Of course, the F atoms of F3CH served as proton acceptors to these solvating molecules, and the H atoms of OH2 as donors, as illustrated in Figure 8. As in the case of the complexes themselves, all H-bonds were held to be linear (θOH‚‚‚X ) 180°). Following geometry optimization, the solvated complex was then placed in the larger cavity of the SCRF water dielectric continuum that contains not only the F3CH‚‚‚OH2 complex but also the five explicit solvent molecules. Each of the two constituent subunits of F3CH‚‚‚OH2 was permitted to interact with the appropriate number of explicit water molecules, as pictured in the upper part of Figure 8, and was likewise placed within the dielectric medium. The H-bond energy of this complex was then calculated as the difference in
J. Phys. Chem. B, Vol. 109, No. 8, 2005 3687
Figure 8. Geometries of partially solvated F3CH and OH2, and their complex F3CH‚‚‚OH2, all embedded in a dielectric continuum.
energy between the solvated complex and the sum of the two hydrated subunits. To ensure a fair comparison with the OH‚‚‚O bond in the water dimer, the HOH‚‚‚OH2 complex was also surrounded by five waters, three around the proton donor and two around the acceptor. (One of the molecules solvating the donor molecule was situated around its peripheral H; the other two donated protons to this molecule’s lone pairs.) The H-bond energies of the F3CH‚‚‚OH2 and HOH‚‚‚OH2 complexes, computed in this manner at the B3LYP/6-31+G** level, were -3.2 and -4.8 kcal/mol, respectively. These values are surprisingly similar to the H-bond energies, -2.0 and -3.1 kcal/mol, obtained above in aqueous solvent modeled as a dielectric continuum, with no explicit solvent molecules at all. Also of some importance, the pure continuum result that HOH‚‚‚OH2 is more tightly bound than F3CH‚‚‚OH2 in aqueous solvent by 1.1 kcal/mol, is changed only slightly, to 1.6 kcal/ mol, upon explicit introduction of the first hydration sphere. There is hence every reason to believe that the solvation models being applied here, while certainly not absolutely accurate in a quantitative sense, provide very reasonable approximations to the environments they are meant to reproduce. Another source of concern is the use of a single dielectric constant to model the interior of a protein. Separate domains within a protein might be better modeled by different values of . Moreover, there is some lingering debate62,67 concerning what value of dielectric constant would be most appropriate to use within a protein interior. Nonetheless, the application of a dielectric constant in the neighborhood of 4 has been used to good effect in a number of protein studies.61,62,68 Of course, a fluorinated hydrocarbon such as F3CH does not immediately and closely resemble the sorts of CH proton donors one might find within a protein, most common of which would be the CRH of each peptide residue. However, numerous studies have found evidence that the properties of the CH donor group are not very sensitive to the particular identity of the electro-
3688 J. Phys. Chem. B, Vol. 109, No. 8, 2005 negative groups by which it is surrounded33,69 and that in fact the two F atoms endow the F2HCH molecule with almost precisely the same proton-donating strength as the two electronegative groups surrounding the CRH group of a peptide.46 And, in that vein, it might be noted from Table 4 that the energy required to form the CH‚‚‚O bond involving F2HCH, while moving this bond from water to a protein interior, is very similar indeed to the same quantity reported for a OH‚‚‚O bond. In summary, the data support the notion that the CH‚‚‚O H-bond can make a contribution to protein folding that is close to, if not equal to, that of a conventional OH‚‚‚O bond. Indeed, this finding is not entirely without experimental support. Pierce et al.70 found that the replacement of a NH group of a thiazole species of a protein ligand by a CH had a surprisingly small (nearly no) effect upon the ligand’s binding constant. By a combined use of CD and NMR techniques, Kallenbach et al.41 noted that the energetic contribution of a CH‚‚‚O H-bond to polypeptide stability was very nearly equal to that of a NH‚‚‚O bond. They guessed that this near coincidence might be due to a lesser desolvation penalty for the former, nominally weaker CH‚‚‚O interaction, a conjecture which is now supported by our calculations. Summary The calculations reported in this work indicate that the H-bond energies of the various systems considered here all weaken as the polarity of the solvent rises. The relative ordering is unchanged, regardless of solvent. That is, the OH‚‚‚O H-bond in the water dimer is the strongest, followed by the CH‚‚‚O bonds in F3CH‚‚‚OH2, and then by F2HCH‚‚‚OH2, FH2CH‚‚‚OH2, and H3CH‚‚‚OH2 in that order. There is some compression of data as the solvent becomes more polar, in that the differences in binding energy become smaller, but this compression still retains the original order, even in the limit of infinite dielectric constant. All interaction energies remain negative, for both CH‚‚‚O and OH‚‚‚O, with the single exception of H3CH‚‚‚OH2, where the interaction energy takes a positive value as climbs above about 4. Analysis of the data for the source of this behavior reveals that the solvation energy of the complex on one hand and the isolated subunits on the other both increase as the solvent becomes more polar. However, the former is smaller in magnitude than the latter. The lesser stabilization of the complex than of the subunits results in the reduced complexation energy. As the solvent becomes more polar, the optimized H-bond length, expressed as the distance between subunits in the complex, becomes progressively shorter for both CH‚‚‚O and OH‚‚‚O systems. This trend is surprising and contradicts the normal supposition that H-bond lengths tend to lengthen as they weaken. This pattern is most evident in those systems that have an innately stronger H-bond, such as F3CH‚‚‚OH2 and HOH‚‚‚OH2. Along with the contracting inter-subunit separation, there are also changes in the covalent CH/OH bonds that involve the bridging proton. The CH bonds contract upon formation of the H-bond, while the OH bonds elongate. The degree of these changes diminishes as the solvent polarity rises. That is, the CH bond contraction is reduced, as is the OH elongation in the water dimer. The CH/OH stretching frequency behaves in a parallel fashion, with the blue shifts of the CH‚‚‚O systems becoming smaller in polar solvents, and the magnitude of the OH red shift likewise diminishing. The question of the quantitative contribution made by a CH‚‚‚O bond, or any H-bond for that matter, to protein structure
Scheiner and Kar is a complex one. If one is considering the transition from an uncomplexed pair of subunits in one medium to a complex within the same medium, the results mentioned above indicate that the conventional OH‚‚‚O bond is indeed consistently stronger than CH‚‚‚O, whether the medium is protein or any other. And the magnitude of the greater strength of the OH‚‚‚O bond is only slightly diminished upon going from vacuum to highly polar solvent. On the other hand, the energetics of CH‚‚‚O bond formation is not negligible, amounting to as much as several kilocalories per mole. Another, and related, question has to do with the process that begins with a pair of complexed subunits in aqueous solvent and ends with these two groups forming a H-bond within the confines of a protein molecule. This process, which parallels the folding of a protein in water, includes a desolvation penalty that must be considered along with the intrinsic H-bond energy. The balance of the various solvation energies is such that the CH‚‚‚O bond is not only comparable in strength to a traditional OH‚‚‚O bond but can actually make a quantitatively greater energetic contribution to protein folding. Of course, this result is predicated on certain models of the aqueous and protein environment, as well as abbreviated models of the groups forming the H-bond. Future work will consider other model systems. Acknowledgment. This work was supported by NIH Grant GM57936. References and Notes (1) The Hydrogen Bond. Recent DeVelopments in Theory and Experiments; Schuster, P., Zundel, G., Sandorfy, C., Eds.; North-Holland: Amsterdam, 1976. (2) Scheiner, S. Hydrogen Bonding: A Theoretical PerspectiVe; Oxford University Press: New York, 1997. (3) Moore, T. S.; Winmill, T. F. J. Chem. Soc. 1912, 101, 1635. (4) Latimer, W. M.; Rodebush, W. H. J. Am. Chem. Soc. 1920, 42, 1419. (5) Zwier, T. C. J. Phys. Chem. A 2001, 105, 8827. (6) Sarkhel, S.; Rich, A.; Egli, M. J. Am. Chem. Soc. 2003, 125, 8998. (7) Glasstone, S. Trans. Faraday Soc. 1937, 33, 200. (8) Dippy, J. F. J. Chem. ReV. 1939, 25, 151. (9) Blatchford, M. A.; Raveendran, P.; Wallen, S. L. J. Am. Chem. Soc. 2002, 124, 14818. (10) Mele, A.; Trand, C. D.; Lacerda, S. H. D. P. Angew. Chem., Int. Ed. 2003, 42, 4364. (11) Matsuura, H.; Yoshida, H.; Hieda, M.; Yamanake, S.; Harada, T.; Shin-ya, K.; Ohno, K. J. Am. Chem. Soc. 2003, 125, 13910. (12) Desiraju, G. R. Acc. Chem. Res. 2002, 35, 565. (13) Delanoye, S. N.; Herrebout, W. A.; van der Veken, B. J. J. Am. Chem. Soc. 2002, 124, 11854. (14) Garcı´a-Zarracino, R.; Ho¨pfl, H. Angew. Chem., Int. Ed. 2004, 126, 1507. (15) Derewenda, Z. S.; Lee, L.; Derewenda, U. J. Mol. Biol. 1995, 252, 248. (16) Lee, K. M.; Chang, H.-C.; Jiang, J.-C.; Chen, J. C. C.; Kao, H.-E.; Lin, S. H.; Lin, I. J. B. J. Am. Chem. Soc. 2003, 125, 12358. (17) Aravinda, S.; Shamala, N.; Bandyopadhyay, A.; Balaram, P. J. Am. Chem. Soc. 2003, 125, 15065. (18) Cordier, F.; Barfield, M.; Grzesiek, S. J. Am. Chem. Soc. 2003, 125, 15750. (19) Gu, Y.; Kar, T.; Scheiner, S. J. Mol. Struct. (THEOCHEM) 2000, 500, 441. (20) Bene, J. E. D.; Perera, S. A.; Bartlett, R. J.; Yan˜ez, M.; Mo´, O.; Elguero, J.; Alkorta, I. J. Phys. Chem. A 2003, 107, 3222. (21) Alkorta, I.; Elguero, J. J. Phys. Chem. B 2003, 107, 5306. (22) Alonso, J. L.; Antolı´nez, S.; Blanco, S.; Lesarri, A.; Lo´pez, J. C.; Caminati, W. J. Am. Chem. Soc. 2004, 126, 3244. (23) Diana, E.; Stanghellini, P. L. J. Am. Chem. Soc. 2004, 126, 7418. (24) Karger, N.; Amorim da Costa, A. M.; Ribeiro-Claro, J. A. J. Phys. Chem. A 1999, 103, 8672. (25) Tatamitani, Y.; Liu, B.; Shimada, J.; Ogata, T.; Ottaviani, P.; Maris, A.; Caminati, W.; Alonso, J. L. J. Am. Chem. Soc. 2002, 124, 2739. (26) Henn, M.; Jurkschat, K.; Mansfeld, D.; Mehring, M.; Schu¨rmann, M. J. Mol. Struct. (THEOCHEM) 2004, 697, 213.
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