The Strength with Which a Peptide Group Can Form a Hydrogen Bond

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J. Phys. Chem. B 2007, 111, 11312-11317

The Strength with Which a Peptide Group Can Form a Hydrogen Bond Varies with the Internal Conformation of the Polypeptide Chain Steve Scheiner† Department of Chemistry & Biochemistry, Utah State UniVersity, Logan, Utah 84322-0300 ReceiVed: June 7, 2007; In Final Form: July 5, 2007

The strength of the H-bond formed between a dipeptide and a proton acceptor molecule is assessed by correlated ab initio quantum calculations for a broad range of different conformations of the dipeptide. The H-bond energy is very sensitive to the internal (φ,ψ) angles, even when the geometry of the H-bond does not vary significantly from one conformation to another. This result indicates that the peptide NH is a much less potent proton donor in certain conformations than in others. In particular, extended conformations of a polypeptide are capable of only weak H-bonds. Thus, the interstrand NH‚‚‚O H-bonds in parallel and antiparallel β-sheets are expected to be significantly weaker than those found in other conformations, such as helices, ribbons, and β-bends, even if the H-bond geometries are similar.

Introduction There are a number of different factors that are commonly understood to influence the structure adopted by a protein molecule. First of course are the short-range interactions between each pair of neighboring peptides along the polypeptide chain, as influenced by the (φ,ψ) dihedral angles of each dipeptide connection. Longer range effects arise when peptide units that are nonadjacent along the primary sequence come into proximity to one another as the chain folds. The hydrogen bonds between various amino acid residues represent some of the most important of the latter forces. Indeed, such H-bonds were integral to the formulation of the concept of the R-helix, a secondary structure that is ubiquitous in scores of proteins.1,2 The H-bonds are formed between peptide units that are separated from one another by three intervening residues along the chain. Parallel and antiparallel β-sheets, too, are thought to heavily depend upon H-bonds for their stability, in this case connecting peptide units on different strands.3-5 In fact, it is the rare peptide in a protein, even if not part of an R-helix or β-sheet, that is not involved in at least one H-bond.6 The actual amount of stabilization energy that an interpeptide H-bond lends to a protein has been a topic of active debate over the years.7-14 Issues that have complicated a resolution of this question include the nature of the interior of the protein, competition between interpeptide H-bonds and peptide-water interactions, effects of neighboring residues and ions, and conformational entropic considerations. More fundamental, however, is the actual interaction energy that arises when the two residues are brought together to form a H-bond, absent the aforementioned complications. It is well understood that the strength of a H-bond is affected by the chemical nature of the molecules involved. There has also been an appreciation for many years that this interaction energy is subject to “external” considerations. That is, the interaction energy weakens if the two residues are stretched apart, or if the H-bond is bent so as to deform from the preferred NH‚‚‚O linearity. An issue that has received scant attention to date deals with the effects of “internal” constraints upon the strength of the †

E-mail: [email protected].

H-bond. More specifically, the chief elements of flexibility within the skeleton of a polypeptide chain are the φ and ψ dihedral angles around the CR atom. Since protein residues occupy wide swaths of Ramachandran (φ,ψ) space, it is natural to wonder if the H-bond strength might be affected by the internal conformation, as defined by these dihedrals. For example, these angles lie in the vicinity of (-60°,-40°) in the R-helix, while the antiparallel β-sheet is characterized by angles around (-140°,140°), defining a very different conformation of the polypeptide chain. Given the substantial variance in the internal structure, then, one might inquire whether the peptide NH will be as potent a proton donor group in one geometry as in the other. Indeed, prior calculations have led to the belief that this sensitivity of H-bond energy to internal structure is more than mere idle speculation. For example, 17O and 14N nuclear quadrupole coupling parameters have been shown previously to vary along with these dihedral angles.15 With specific regard to energetics, one work, for example, demonstrated16 that the intermolecular NH‚‚‚O H-bond formed by a dipeptide in its extended structure (related to the β-sheet) is very much weaker than the same interaction when associated with the C7 geometry favored by the dipeptide.17-22 This finding was supported by later calculations23 which focused more precisely on the β-sheet in both its parallel and antiparallel forms. The primary issue to which this work is addressed, then, deals with the manner in which intermolecular H-bond energetics are affected not by the external, interpeptide geometric parameters, nor by chemical modification, but rather by the internal properties of each subsystem, as characterized by the (φ,ψ) dihedral angles. Rather than restrict attention to a small number of prescribed internal structures, a full range of Ramachandran space is sampled, to provide more complete information that will be relevant to the many configurations adopted by amino acid residues in real proteins. The matter of the basic interaction energy is the natural province of quantum calculations, which are well suited to evaluation of this quantity, free of complicating solvent effects or other environmental factors. After establishing an appropriate model system, one can freeze the (φ,ψ) angles in any pair of

10.1021/jp074414r CCC: $37.00 © 2007 American Chemical Society Published on Web 08/30/2007

Strength of Peptide Group Formed H-Bond

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11313

Figure 1. Diagram of model dipeptide studied, illustrating definition of (φ,ψ) angles. (a) Antiparallel β-sheet where these angles are equal to (-140°,140°). (b) R-Helix conformation: (-60°,-40°).

desired values and then optimize the remainder of the geometry, and thereby arrive at the interaction energy of the pair of subsystems. Models and Methods An appropriate model must include two peptide units, connected through a CR carbon atom.5,13,24-29 Consistent with prior studies by this group16,23 and others,12,19,29-31 the model dipeptide examined is a glycyl derivative, CH3CONHCH2CONH2. Earlier work has shown13,18,22,32,33 that the data presented below would be affected very little by enlarging the model via replacement of one of the HR atoms by an R group more representative of larger amino acids such as alanine. Figure 1 illustrates this model dipeptide and the formal definition of the dihedral angles φ(CNCRC) and ψ(NCRCN). A conformation similar to the antiparallel β-sheet, in which the (φ,ψ) angles are equal to (-140°,140°), is depicted in Figure 1a, while Figure 1b illustrates the dipeptide in an R-helix arrangement, with (φ,ψ) ) (-60°,-40°).34,35 A water molecule is employed as proton acceptor for the dipeptide’s NH group. The small size of this molecule minimizes steric constraints, thereby permitting an analysis of the H-bonding ability of the dipeptide. As this work focuses upon the strength of the H-bond, it is crucial to use a quantum chemical technique that dependably reproduces this property, in an accurate and cost-effective manner. MP2 theory has proven a reliable workhorse in this regard, including the most important correlation effects such as dispersion, when coupled with a suitable basis set,36-45 and is especially useful for larger polypeptide systems.46 The 6-31+G** basis was used here, as its polarization and diffuse functions are well designed to cover intermolecular interactions of the H-bonding sort. All calculations, therefore, were carried out at the MP2/6-31+G** level. Basis set superposition error was removed from all intermolecular interaction energies via the Boys-Bernardi counterpoise procedure.47-50 All ab initio quantum calculations were performed using the Gaussian 03 suite51 of codes. Results Conformational Energy. Before addressing the issue of intermolecular H-bonding, it is first important to consider how the energetics of the dipeptide vary over the relevant range of Ramachandran space. This information describes how easily the system can access certain regions of this space, and which areas are simply too high in energy to occur with any regularity. Figure 2 illustrates the behavior of the conformational energy of the dipeptide in the regions of the Ramachandran map that are most commonly observed in proteins. In each case, after

Figure 2. Contour map of calculated energies (kcal/mol) of dipeptide in the β-region (upper) and R-region (lower) of the Ramachandran plot. Energies are relative to fully extended conformation (φ,ψ) ) (-180°,180°) in upper left corner.

selecting the (φ,ψ) angles, the remainder of the geometry was fully optimized. The upper region encompasses residues that are typically located in sections of the protein that contain β-sheets (parallel and antiparallel), β-bends, 2.27 ribbons, PPII, and the collagen triple helix,34,35 and will be referred to here collectively as the β-region. The area covered extends from -180° to -40° for the φ angle, with 40° < ψ < 180°. The helices commonly contain residues with (φ,ψ) angles in the lower (R) region, with ψ covering the range between -80° and -20°; this range includes also the 310- and π-helices. In addition to the R-helices and β-sheets, both parallel and antiparallel, these two regions cover the great majority2 of the conformations that are adopted by protein residues; only a very slim minority would be found outside of these areas. Conformational energies are referenced to the fully extended (φ,ψ) ) (-180°,180°), in the upper left corner, taken as an arbitrary zero. The surface is rather flat in the β-region, with a broad (blue) swath within 2 kcal/mol of the reference point, and essentially the entire region within 4 kcal/mol. There are some structures that are more stable than the fully extended conformation, in the purple region with φ ∼ -80°, albeit only 1 or 2 kcal/mol lower in energy. One might conclude that there are no internal energetic factors that would prohibit occupancy of any part of the upper β-region of Ramachandran space. The conformational energy in the R-region varies to a greater degree, with some conformations in the lower right section 6-8 kcal/mol above (-180°,180°). Some of the higher energy conformations in the lower right portion are likely due to a close encounter between the two O atoms. For example, this R(O‚‚‚O) distance is 3.03 Å for (-40°,-80°) and 3.10 Å for (-60°,-80°). Indeed, a correlation can be drawn between the interoxygen distance and the conformational energy, with a general trend for higher energies to be associated with shorter values of R(O‚‚‚O), most strikingly when this distance is less than about 3.2 Å.

11314 J. Phys. Chem. B, Vol. 111, No. 38, 2007 However, in general, the reasonably low energies throughout most of the R- and β-regions allow residues to adopt these conformations within the context of entire protein molecules. It is worth stressing that the energies illustrated in Figure 2 refer to the dipeptide as such, and are hence only very loosely indicative of the energy associated with a full protein wherein each residue participates in long-range and short-range interactions with its neighbors. Nonetheless, the conformational energies of Figure 2 are useful in elucidating the region of the (φ,ψ) map that is accessible to a residue within the context of a protein. It is relevant to note that the data in Figure 2 are consistent with calculated conformational energies of the Ala analogue,26,28 or other residues such as glutamine25 or glutamate,52 confirming the relevance of the glycyl data to the general situation. Further enlargement to leucine, valine, and isoleucine has little effect upon energetics.46 H-Bond Energies. For each pair of (φ,ψ) angles, the H-bonding capacity of the N-H group was computed by placing a water molecule near the NH to act as proton acceptor. A full geometry optimization complicates the analysis, as the water molecule moves away from the dipeptide NH and toward the carbonyl O. The result is a cyclic complex that includes not only the desired NH‚‚‚Ow H-bond, but also an OwH‚‚‚O of comparable strength. Not only does the presence of two concurrent H-bonds make it difficult to extract the strength of the NH‚‚‚Ow H-bond of interest,30 but also the second H-bond causes a very significant deformation of the NH‚‚‚Ow geometry, with the θ(NH‚‚‚O) angle distorted by 40-50° from linearity. In order to avoid the complicating presence of this second H-bond, the O atom of water was restricted to lie along the N-H axis, maintaining a linear H-bond. To further ensure the absence of a second OwH‚‚‚O H-bond, the φ(HOw‚‚‚HNO) dihedral angles between the water H atoms and the carbonyl O were held to (90°. Other than these two restrictions, and the obvious maintenance of a selected pair of (φ,ψ) angles, the geometry of the complex was fully optimized at the MP2/631+G** level. The H-bond energy was taken as usual as the difference in energy between the complex and the pair of separately optimized monomers (the dipeptide and the HOH molecule), corrected for basis set superposition error. The H-bond energy was thus computed for each configuration of the dipeptide, and the results are presented as a contour plot in Figure 3. It is immediately apparent that there is a great deal of sensitivity of the H-bond energy to the conformation of the dipeptide. The orange and red sections, which collectively cover a wide section of the Ramachandran map, represent H-bond energies in the 4-6 kcal/mol range, typical of NH‚‚‚O bonds of this sort. However, this quantity drops dramatically as one moves toward the upper left corner, i.e., as the conformation of the dipeptide approaches the fully extended conformation. Indeed, the H-bond energy is less than 1 kcal/mol in the very upper left corner of the map. The importance of this reduction is underscored by the large number of protein residues that have dihedral angles in the area encompassed by the contours representing H-bond energies of less than 4 kcal/mol (yellow, green, blue, and violet regions of Figure 3). This rather large area is roughly encompassed by φ angles between -180° and -100°, with ψ varying between 100° and 180°. Given the greatly reduced H-bond strength for this set of conformations, it is important to ascertain the reason for this effect. A number of recent calculations from this laboratory16,23 have focused in particular on the fully extended (φ,ψ) ) (180°,180°) conformation of the dipeptide, and had provided preliminary indications of the weakness of the associated

Scheiner

Figure 3. NH‚‚‚O hydrogen bond energies (kcal/mol) of dipeptide plus water molecule within the R- and β-regions of the Ramachandran map. Letters indicate standard locations of (a) R-helix, (b) 310-helix, (c) π-helix, (d) parallel β-sheet, (e) antiparallel β-sheet, (f) 2.27 ribbon, (g) collagen triple helix, (h) PPII, and (i) type II β-bend.

Figure 4. Geometries optimized for dipeptide-water system, with dipeptide in (a) (φ,ψ) ) (180°,180°) and (b) (-80°,80°) conformations.

NH‚‚‚O bond, when compared to another particular arrangement, the C7 structure.16 The latter conformation is commonly observed in dipeptides in particular, and is located in the purple region of the β-section of Figure 2, at roughly (φ,ψ) ) (-85°,75°), about 1 kcal/mol lower in energy than the fully extended structure. The particular structures optimized here for these sorts of configurations are illustrated in Figure 4. The H-bond energy computed for the fully extended (φ,ψ) ) (180°,180°) conformation in Figure 4a was 0.65 kcal/mol. This value is very much smaller than the 5.34 kcal/mol calculated for (-80°,80°) in Figure 4b, typical of the red region of Figure 3, even though the H-bond lengths for the two systems are comparable. With regard to the latter point, it is typical to find a strong correlation between the strength of a H-bond and the distance separating the donor from the acceptor. However, Figure 5 which compares these two quantities for the β-region of configurational space, illustrates that this correlation is a weak

Strength of Peptide Group Formed H-Bond

Figure 5. Comparison of hydrogen bond energy with the intermolecular H-bond distance, between the HN proton and the water O acceptor, within the β-region of the configuration space.

one. In the first place, the various H-bond lengths fall within a fairly narrow regime, between 1.98 and 2.06 Å. While there is a trend for a good number of the data points to exhibit a weakening of the H-bond strength as this bond is stretched, there are also a large number of exceptions. Most notably, some of the points near the upper right portion of Figure 5 indicate that the strength of the H-bond is maintained at about 5 kcal/mol, even as the intermolecular separation is increased. It is thus apparent that the H-bond length does not hold the key to understanding the pattern of H-bond energies in this system. Rationale for Low H-Bond Energies. This finding had warranted a careful assessment of a number of possible causes of the weak NH‚‚‚O bond of the fully extended conformation,53 which had concluded that the prime factor is electrostatic in origin. More specifically, the fully extended conformer places the carbonyl O of the adjacent peptide unit in close proximity to the NH that is to be donated to another peptide or other proton acceptor. While this association is not properly disposed to form an internal H-bond of any consequence, the partial negative charge of this carbonyl O acts as a sort of barrier that impedes the approach of the proton acceptor. Of course this finding had been limited to only one particular conformer, the fully extended (-180°,180°) C5 structure. If this principle is in operation over a more extensive range of Ramachandran space, one might expect a relation between the strength of the H-bond formed by the NH group and its separation from the carbonyl O atom in the adjacent peptide. In particular, as the carbonyl O is moved further from the proton that is to be donated to an oncoming acceptor, its effect on the electrostatic potential should diminish accordingly. Hence, this internuclear (HN-O) distance was evaluated for each of the configurations in the entire β-region of Figure 3, i.e., for -180° < φ < -40° and 40° < ψ < 180°. The relationship pictured in Figure 6 depicts the dramatic reduction in H-bond energy that arises when the carbonyl O atom lies too close to this proton, particularly when this distance is less than about 3 Å. Another indication of this effect resides in the change in the HN-O distance as the acceptor approaches. Due to the putative repulsion between the carbonyl O atom of the dipeptide and the incoming proton acceptor (water O atom in this case), the former moves out of the way of the acceptor as much as other

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Figure 6. Comparison of hydrogen bond energy with the intramolecular distance between the HN proton and the carbonyl O of the other peptide unit, optimized within the dipeptide-water complex.

Figure 7. Contour plot of the optimized intermolecular O-O separation (in Å) between the water and the carbonyl O of the dipeptide, within the β-section of Ramachandran space.

considerations will permit, and consequently farther from the proton as well. Consequently, the HN-O distance elongates by as much as 0.3-0.4 Å, particularly in the neighborhood of the fully extended dipeptide, where this distance is shorter to begin with. Yet another confirmation of the electrostatic repulsion between the carbonyl O atom and the proton acceptor O of the water arises from an inspection of the internuclear (O-O) distance optimized for the complexes in the β-region of the Ramachandran map. This distance is illustrated as a contour plot in Figure 7, and its similarity in character to the H-bond energies in the β-section of Figure 3 is obvious, reinforcing the direct effect of this interoxygen repulsion upon the H-bond energy. Conclusions and Discussion The results presented here illustrate that there is a surprising sensitivity of the energy to be realized when a H-bond is formed, to the particular internal conformation of the polypeptide. More specifically, the H-bond energy nearly vanishes in the fully extended structure, wherein (φ,ψ) ) (-180°,180°). This region of low H-bond energy extends well beyond this particular point,

11316 J. Phys. Chem. B, Vol. 111, No. 38, 2007 requiring deviations of some 80° away from the aforementioned angles in order to achieve the interaction energy characteristic of the R-helical region. The parallel and antiparallel β-sheets fall in this region of diminished H-bond energy, so one might expect the interstrand NH‚‚‚O interactions to be somewhat weaker than in other common secondary structures, such as helices or the 2.27 ribbon or type II β-bend. Within the context of the helices, the R-, 310-, and π-helices would all appear to be capable of “full-strength” H-bonds, very similar in magnitude from one helix to the next. The prime source of this variability of H-bond strength appears to reside in the proximity of the carbonyl O of one peptide unit to the NH donor group of the adjacent peptide along the polypeptide chain. The partial negative charge of this O atom diminishes the electrostatic potential in the vicinity of the NH, making it a less inviting target to an incoming proton acceptor group. The carbonyl oxygen lies closest to the NH proton in extended conformations, characteristic of β-sheet structure. The results presented here were derived from the interaction of a glycyl dipeptide with water as proton acceptor. One may question first whether the small Gly residue offers a suitable model for a more general amino acid. Of course, the small HR atoms of glycine make accessible a more extensive region of Ramachandran space than is available to larger residues.25 However, with regard to H-bonding capabilities, previous work indicates that replacement of one H atom of Gly with a larger group has very little effect upon the results.13,24,33 When Gly was replaced by Ala, for example,23 there was virtually no change in computed H-bond energies of interacting dipeptides; similarities were noted as well for even larger side chains as in Ser and Val.54 Earlier computations55 had compared Gly with a number of other amino acids, and found the strength of its H-bond to water to be similar to those of Ala, Val, Ser, and Cys. It is hence anticipated that the results reported here are not limited to Gly alone, but are applicable to the full range of amino acids, albeit with slight modifications. In particular, the largest perturbations might be anticipated in those conformations wherein the atoms of the residue’s R group approach closely the NH of the peptide which is forming the H-bond. In such a case, one could then apply the principles formulated here, taking into account the ability of a nearby group to affect the electrostatic potential around the NH. Nor would one anticipate any sizable perturbations from the use of a peptide larger than a dipeptide. For example, the H-bond geometries computed10 for a pair of tetrapeptides is virtually indistinguishable from smaller chains. Energetics of longer chains, up to octapeptide dimers, reveal essentially no change from the data for shorter chains.10 A similar insensitivity of trends to elongation of the β-sheet strands was also observed.5 A water molecule was used here as a generic proton acceptor in part due to its prevalence within proteins. It is also useful in that its small size enables it to fit into small spaces, with a minimum of steric repulsion, to enable an accurate assessment of the H-bonding energy without other complicating factors.30 HOH is of course not an ideal model for the carbonyl O proton acceptor of a neighboring peptide, so one might anticipate that interpeptide H-bond binding energies might be a little different in magnitude from peptide‚‚‚OH2 bonds. However, the focus of this work lies not in the establishment of a highly accurate quantitative assessment of the H-bond energy itself, but is more oriented toward the effects upon this quantity of internal rotations within the polypeptide chain. In the evaluation of the

Scheiner inherent proton-donating ability of a peptide NH, the hydroxyl O of water should serve as a suitable model of a general proton acceptor. Along that same line, even though the MP2/6-31+G** method is capable of providing excellent estimates of H-bond energies involving peptides,8,13,19,30 higher levels of theory would be required for absolute accuracy. In any case, this level of theory, with its diffuse and polarization functions, is certainly able to provide very reliable measures of the changes in the H-bond energy that arise from perturbations30,37,56 such as internal rotations within the dipeptide, and which are the focus of this work. The data presented here refer to the in vacuo situation wherein the proton donor and acceptor molecules are present in isolation of any surroundings. The interior of a protein molecule is of course different, and the H-bonded pair would be enveloped by other portions of the protein including solvent in some circumstances. It is accepted that the binding energy of a H-bond is affected by its surroundings; however, the effects of the environment tend to be uniform,30,57 not favoring one particular conformation over another.16 One would thus not expect the dislocation of the dipeptide-water complex under examination here into a different environment, whether aqueous or protein, to materially alter the finding that the H-bond energy is sensitive to the internal conformation of the polypeptide chain. Finally, there has been some thought58 that the energetics of H-bond formation of a polypeptide might be directly correlated with the dipole moment of a segment of the latter. However, an analysis of the computed data showed no evidence of any such correlation. Again it is stressed that the results presented here pertain to the intrinsic capability of the peptide NH to form a H-bond. Each individual interaction will of course be sensitive to the intermolecular geometry it adopts within the context of the full protein. Thus, any H-bond can be weakened if the proton donor and acceptor are forced to stretch apart, or to fit into a nonlinear alignment, by constraints of the protein conformation. The present paper documents that even in the absence of any such external geometric constraints the potential strength of a peptidecontaining H-bond is rather sensitive to the internal conformation of the dipeptide. References and Notes (1) Cantor, C. R.; Schimmel, P. R. Biophysical Chemistry; Freeman: San Francisco, 1980; Vol. 1. (2) Lehninger, A. L.; Nelson, D. L.; Cox, M. M. Principles of Biochemistry, 2nd ed.; Worth: New York, 1993. (3) Pauling, L.; Corey, R. B. Proc. Natl. Acad. Sci. U.S.A. 1951, 37, 729-740. (4) Richardson, J. S. Nature 1977, 268, 495-500. (5) Perczel, A.; Ga´spa´ri, Z.; Csizmadia, I. G. J. Comput. Chem. 2005, 26, 1155-1168. (6) Baker, E. N.; Hubbard, R. E. Prog. Biophys. Mol. Biol. 1984, 44, 97-179. (7) Mo¨hle, K.; Gussmann, M.; Rost, A.; Cimiraglia, R.; Hofmann, H. J. J. Phys. Chem. A 1997, 101, 8571-8574. (8) Beachy, M. D.; Chasman, D.; Murphy, R. B.; Halgren, T. A.; Friesner, R. A. J. Am. Chem. Soc. 1997, 119, 5908-5920. (9) Gresh, N.; Guo, H.; Salahub, D. R.; Roques, B. P.; Kafafi, S. A. J. Am. Chem. Soc. 1999, 121, 7885-7894. (10) Zhao, Y. L.; Wu, Y. D. J. Am. Chem. Soc. 2002, 124, 1570-1571. (11) Rossmeisl, J.; Kristensen, I.; Gregersen, M.; Jacobsen, K. W.; Nørskov, J. K. J. Am. Chem. Soc. 2003, 125, 16383-16386. (12) Viswanathan, R.; Asensio, A.; Dannenberg, J. J. J. Phys. Chem. A 2004, 108, 9205-9212. (13) Wang, C.-S.; Zhang, Y.; Gao, K.; Yang, Z.-Z. J. Chem. Phys. 2005, 123, 024307. (14) Fu, Y.; Gao, J.; Bieschke, J.; Dendle, M. A.; Kelly, J. W. J. Am. Chem. Soc. 2006, 128, 15948-15949.

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