J. Phys. Chem. B 2004, 108, 18065-18072
18065
Stabilization and Destabilization of the Cδ-H‚‚‚OdC Hydrogen Bonds Involving Proline Residues in Helices Haobo Guo, Robert F. Beahm, and Hong Guo* Department of Biochemistry and Cellular and Molecular Biology and Center of Excellence for Structural Biology, UniVersity of Tennessee, KnoxVille, Tennessee 37996 ReceiVed: May 8, 2004; In Final Form: August 27, 2004
There are a large number of helices in proteins that contain the Cδ-H‚‚‚OdC hydrogen bonds involving Pro. Ab initio and density functional methods at HF/6-31G*, B3LYP/6-31+G**, B3LYP/6-311+G**, and MP2/ 6-31+G** levels are used to determine the factors that may lead to the stabilization (destabilization) of these Cδ-H‚‚‚OdC hydrogen bonds. The calculations are performed for 16 helical models with their structures generated from the X-ray structures of proteins. The direct Cδ-H and OdC interaction is not stabilizing for the cases where the Cδ-H‚‚‚OdC hydrogen bond immediately precedes a peptide hydrogen bond between (i+1)NH and (i-3)CdO groups (here i is the Pro residue number). The direct Cδ-H and OdC interaction is generally stabilizing for the cases where this peptide hydrogen bond is absent. Therefore, the formation of the (i+1)NH‚‚‚(i-3)CdO peptide hydrogen bond is likely to force the C-H and OdC moieties into less favorable positions for the interaction. The strength of the Cδ-H‚‚‚OdC hydrogen bonds is significantly enhanced by cooperative hydrogen bonding involving the peptide hydrogen bonds in the helices and the capping interactions at the N-termini. The enhancement can be as large as 3-5 kcal/mol. The results suggest that the stability of the C-H‚‚‚OdC hydrogen bond depends on its environment, and this factor should be taken into consideration in the discussion of the energetic contribution of the C-H‚‚‚OdC hydrogen bonds to the stability.
Introduction Weak interactions are widely observed in the structures of biological systems.1-3 One type of weak interactions that has attracted considerable attention recently in the structural biology community is the interaction involving the C-H group.2-32 Short C-H‚‚‚O contacts have been found in proteins, peptides, and DNA.7-32 These C-H‚‚‚O contacts show the stereochemical features and directionality of conventional hydrogen bonds (Hbonds) and are called C-H‚‚‚O H-bonds. It is believed that the C-H‚‚‚O H-bonds can make energetically favorable contributions to the stability as well as to the strength of protein-ligand (protein-protein) interactions. This led to calls for a revision of crystallographic constrained refinement programs and force fields which treat nonbonded C‚‚‚O interactions as exclusively repulsive.7a,30 Quantum mechanical calculations have been performed to determine the energetics of the C-H‚‚‚O H-bonds in the complexes of small molecules.34a-34d The C-H‚‚‚O H-bond energies can be as much as 2-4 kcal/mol in the gas-phase. However, a recent experimental study35a showed that the CR-H (Ala51)‚‚‚O (Thr24) H-bond in bacteriorhodopsin (bR) is not stabilizing. This is rather surprising, as the stability of this CRH‚‚‚O H-bond in the membrane protein might be expected to be particularly important because of a low dielectric and minimal competition from water.35a This led to the suggestion that “the C-H‚‚‚O H-bonds may simply facilitate packing rather than provide a strongly favorable energetic stabilization of the folded structure”.35a Moreover, the strength of a CR-H‚‚‚O hydrogen bond (0.88 kcal/mol) in a lipid bilayer was also weaker than those from the theoretical calculations.35b Therefore, it is of * Corresponding author.
considerable interest to determine the factors that might affect the strength of the C-H‚‚‚O interactions in proteins. Such studies may provide additional insights into the interplay of the C-H‚‚‚O H-bonds and other interactions in biological systems as well as possible treatments of such interactions in molecular mechanics force fields.36 Previous surveys of X-ray structures indicate that the environment (i.e., the groups and residues that are not involved in the C-H‚‚‚O interactions) may play an important role for the formation of the C-H‚‚‚O H-bonds. Indeed, the C-H‚‚‚O H-bonds mainly occur in certain areas of proteins. For instance, the CR-H‚‚‚O H-bonds were widely observed in β-sheets (see Figure 1),7,8 and it was suggested that the contribution of the CR-H‚‚‚O interactions to the structural stability is more substantial in β-sheets than in any other region. By contrast, few CR-H‚‚‚O H-bonds were observed in R-helices, and no statistical analysis was possible.7a There are different ways that the formation of the C-H‚‚‚O H-bonds may be helped by the environment. For instance, in many examples of the C-H‚‚‚OdC interactions, the C-H group is near at least another conventional H-bond (see Figure 1 for the β-sheets). Thus, there is a possibility that it is the formation of the stronger conventional H-bond that brings the C-H and OdC moieties together. If this is the case, the question remains as to whether the direct interaction between the C-H and Od C groups could still be stabilizing. This is because the C-H and OdC groups may not be able to maintain their optimal positions for the interaction because of the influence of the stronger neighboring H-bond. Another way that the environment may promote the formation of the C-H‚‚‚OdC H-bond is through cooperative hydrogen bonding. There are different types of cooperative effects of
10.1021/jp0480192 CCC: $27.50 © 2004 American Chemical Society Published on Web 10/22/2004
18066 J. Phys. Chem. B, Vol. 108, No. 46, 2004
Figure 1. Some typical C-H‚‚‚O interactions observed in β-sheets (Subtilisin Carlsberg).49 The CdO groups are involved in both conventional hydrogen bonds with the N-H groups (white dotted lines) as well as the CR-H‚‚‚OdC H-bonds (red dotted lines). Also, the CRH‚‚‚OdC interaction (e.g., that involving Val149 or Leu90) is generally a part of H-bond networks.
hydrogen bonding (see refs 37a and 38 for reviews). The cooperative effect that may enhance the C-H‚‚‚OdC interaction is the so-called π-bond cooperativity. In this case, the cooperative effect occurs for interactions involving certain molecular fragments where the H-bond donor and acceptor are different and linked to each other by chemical bonds with π electron character. One such molecular fragments is the peptide linkage where the N-H and CdO groups connected by a C-N partial double bond can act as a hydrogen bond donor and acceptor, respectively. The previous studies suggested that the interactions involving these two groups of the peptide linkage can be highly cooperative;37-43 for example, the CdO group for which the corresponding N-H group is involved in hydrogen bonding (e.g., as in R-helices) is often a better H-bond acceptor than the one for which the N-H is not.37g The implication for the C-H‚‚‚OdC H-bonds is that the OdC group may be able to make more favorable interactions with the C-H groups if the corresponding N-H group is involved in a conventional H-bond in proteins. Here, we apply quantum mechanical methods to study the Cδ-H‚‚‚OdC interactions in R-helices containing Pro and to understand the energetic origin for their stability. We try to answer the two questions raised above and determine how the Cδ-H‚‚‚OdC interactions are stabilized or destabilized by their neighboring interactions (i.e., the stabilization and destabilization of the Cδ-H‚‚‚OdC H-bonds). That is, whether the conventional H-bonds next to the Cδ-H‚‚‚OdC H-bonds can affect the strength of the Cδ-H‚‚‚OdC interactions and what is the role of cooperative hydrogen bonding? To our knowledge, these questions have not been addressed in previous studies on the Cδ-H‚‚‚OdC H-bonds. Although Pro has no free N-H group and cannot form the conventional N-H‚‚‚OdC hydrogen bond, there are a large number of R-helices containing Pro. It has been observed that the Cδ protons of Pro in R-helices frequently form close contacts with the carbonyl groups in the preceding turns and are therefore involved in the Cδ-H‚‚‚OdC interactions.9 One important feature of these Cδ-H‚‚‚OdC H-bonds is that, unlike the C-H H-bonds in some other areas of proteins, they are able to stand on their own in many of the cases. Indeed, a statistical survey9a showed that about two-thirds of helices containing Pro do not have the peptide H-bonds following the Cδ-H‚‚‚OdC H-bonds (i.e., between the (i+1)NH and
Guo et al. (i-3)CdO groups. Here, i is the Pro residue number). Thus, the helices containing Pro offer a unique opportunity for understanding the effects of the neighboring conventional H-bonds on the Cδ-H‚‚‚OdC interactions. This may be achieved by comparing the interactions for the helices without and with the (i+1)NH‚‚‚(i-3)CdO H-bonds and determining the general trends of the interaction energies in the two types of the systems. Moreover, the helices can also be used to understand the role of cooperative hydrogen bonding in the stabilization of the Cδ-H‚‚‚OdC H-bonds because of the wide existence of conventional H-bond networks in the systems. One of the main purposes of the present study as well as many of the previous theoretical investigations of the CH‚‚‚O H-bonds is to understand the possible energetic contributions of such interactions to the stability for proteins. There are different ways that quantum mechanical calculations may be used for such purpose. The previous studies34a-34e of the CH‚‚‚O H-bonds have been mainly based on the C-H hydrogenbonded systems containing small molecules (e.g., N,N-dimethylformamide dimmer, small amino acid-water complexes, and N-methylmaleimide-dimethyl sulfoxide complex) without the use of the structural information from proteins. An advantage of such an approach is that high-level ab initio methods with large basis sets can be applied to these systems because of their small size; robust geometry optimization can also be performed. The results of such calculations can answer some important questions. They include the following: Is there a possibility for the existence of favorable C-H‚‚‚O interactions? How strong might the interactions be? This approach can also be used to reveal certain properties of the C-H‚‚‚O H-bonds (e.g., IR and NMR spectroscopic properties).34c-34e However, there are limitations in trying to understand the energetic properties of the C-H‚‚‚O H-bonds in proteins without use of the structural information from the proteins. For instance, the relative positions for the groups involved in a C-H‚‚‚O interaction in a complex of small molecules can be different from that in a protein. This can lead to different interaction energies for the two different systems. Moreover, the steric repulsions and polarization (e.g., from the neighboring groups and residues) that the C-H‚‚‚O H-bonds may experience in proteins cannot be simply included in the calculations on the basis of the complexes of small molecules. Therefore, it is difficult to determine the factors that might affect the strength of the C-H‚‚‚O interactions in various regions of proteins or under different conditions which we would like to study. This problem can be demonstrated by the discrepancies in the recent theoretical and experimental studies. For example, high-level ab intio calculations suggested that the CR-H (Ala amino acid)‚‚‚O (water) interaction could provide a stabilization energy of 2.1 kcal/mol.34c This is in contrast to the experimental study35a which showed that the CR-H (Ala51)‚‚‚O (Thr24) hydrogen bond in bR is not stabilizing (see above). To avoid the problems associated with the use of the structures of small molecule complexes, we adopt a different approach in this study.33b The coordinates of the non-hydrogen atoms in the helical models used in this study were obtained directly from the X-ray structures of proteins. A major advantage for this approach is that the interacting groups have the relative positions and environment that closely resemble those in the protein structures (e.g., some of the steric interactions from the neighboring groups as well as the cooperative effect of hydrogen bonding can be included in the calculations). However, there are certain complications in this approach as well. One major problem is that there are some uncertainties for the atomic positions in the X-ray structures (the protein structures that we
Hydrogen Bonds Involving Proline Residues use in this study have a resolution of 2 Å or better). These uncertainties could have significant effects on the results of the calculations and make the theoretical predictions less reliable. To reduce the possible errors associated with the use of the X-ray structures, we study 16 helical models and focus on the general trends of the energetic results rather than on the individual energy values. The fundamental assumption here is that while individual interaction energies may be significantly affected by the structural uncertainties from experiment, the general trends that emerge from the calculations on the two questions mentioned above may be less sensitive.33a-33b In the previous surveys of biological structures, the CH‚‚‚O H-bonds are defined on the basis of only the geometrical information (see, for instance, refs 6-9 for more detailed discussions of the definitions and structural features of the CH‚‚‚O H-bonds). This is true even when the C-H‚‚‚O interaction is energetically unfavorable.35a The Cδ-H‚‚‚OdC H-bonds studied in this paper have already been defined in the early survey (ref 9a). To be consistent with the previous study, we will use the same definition for the Cδ-H‚‚‚OdC H-bond used in ref 9a, even though other definitions may be used (e.g., on the basis of electron distribution between the donor and acceptor). This allows us to focus on the study of the interplay between the C-H‚‚‚O H-bonds and other interactions in the helices containing Pro as well as the corresponding energetic effects on the formation of the C-H‚‚‚O H-bonds. We defer a detailed analysis of different contributions to the C-H‚‚‚O interaction energies as well as comparison of electronic properties of the C-H‚‚‚O H-bonds with those of conventional H-bonds to a later study. The results of the calculations on the model systems show that the direct Cδ-H and OdC interaction is not stabilizing for the cases where the Cδ-H‚‚‚OdC hydrogen bond immediately precedes a peptide hydrogen bond between (i+1)NH and (i-3)CdO groups (here, i is the Pro residue number). The direct Cδ-H and OdC interaction is generally stabilizing for the cases where this peptide hydrogen bond is absent. Therefore, the C-H and OdC moieties are likely to be forced into less favorable positions for the interaction by its neighboring (i+1)NH ‚‚‚(i3)CdO peptide H-bond. Moreover, the strength of the Cδ-H‚ ‚‚OdC hydrogen bonds is significantly enhanced by cooperative hydrogen bonding involving the peptide H-bonds in the helices and the capping interactions at the N-termini. The enhancement can be as large as 3-5 kcal/mol. A significant portion of the enhancement consists of nonadditive, many-body effects that cannot be simply reflected by the pairwise interactions. The results suggest that the stability of the C-H‚‚‚OdC hydrogen bond depends on its environment (i.e., the peptide groups and capping residues not directly involved in the C-H‚‚‚OdC interactions), and this factor should be taken into consideration in the discussion of the energetic contribution of the C-H‚‚‚ OdC hydrogen bonds to the stability. Methods Sixteen R-helices were obtained from the X-ray structures in the Brookhaven Protein Data Bank which contain close CδH‚‚‚OdC contacts involving Pro; these helices have been surveyed previously.9 The protein structures of this study have a resolution of 2 Å or better. The PDB ID’s (Pro residue position) for the corresponding proteins are 1CNS (i ) 127), 1DBS (i ) 91), 1HPM (i ) 316), 1PII (i ) 101), 1PY6 (i ) 50), 1TYS (i ) 175), 1UDG (i ) 34), 1YTB (i ) 232), 2GDM (i ) 108), 2GST (i ) 124), 2HBG (i ) 105), 2SCP (i ) 131), 3SDH (i ) 117), 4ENL (i ) 74), 8TLN (i ) 69), and 131L
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Figure 2. The portions of the helices (up to Pro residue) selected to build the model systems for the calculations (the helix in 1PY6 is not plotted). Except for Pro and capping residues, only the backbone atoms are shown for clarity. The atoms involved in the Cδ-H‚‚‚OdC interactions or belonging to cooperative H-bond networks are plotted in ball-and-stick. The arrows indicate the positions where the N-terminal regions of systems A are truncated to generate systems B (see Figure 3b, left, for 2SCP). The truncated parts are used as C2 (see Figure 3c for 2SCP) for determining the energies of the through-space electrostatic interactions between the truncated parts and A1 (i.e., the system containing the Pro ring, see text).
(i ) 86). Portions of the helices (up to the Pro residues), which were used to build our model systems for the calculations, are given in Figure 2. Except for the Pro and capping residues, only the backbone atoms are shown. For each helix in Figure 2, a model system A was generated on the basis of the following procedures: (1) all the side chains (except for Gly and Ala) were replaced by Ala; (2) the following groups (atoms) were deleted: the carbonyl group of the Pro residue (e.g., Pro-131 in 2SCP), the CR atom and side chain of the residue at position i-1 (e.g., i-1 ) 130 for 2SCP), the peptide linkage between the residues at positions i-2 and i-1, and the side chain of the residue at position i-2; (3) hydrogen atoms were built using the MOE package.45 The model building procedures given above lead to A with its two subunits, A1 (the subunit containing the Pro ring) and A2 (the subunit containing conventional H-bond networks), interacting with each other through the Cδ-H‚‚‚OdC H-bonds. Thus, A contains not only the Cδ-H‚‚‚OdC H-bonds, but also additional groups from the original helix that may stabilize the Cδ-H‚‚‚OdC interactions through cooperative hydrogen bonding (see Introduction). A model system B was then generated from A by removing these additional groups in A2 capable of inducing the cooperative effects (i.e., the N-terminal region of the helix starting from the arrow in Figure 2 were removed). B contains two subunits, B1 ()A1) and B2. Finally, a model system C was generated from A by removing B2. This leads to two subunits, C1 (dB1)A1) and C2, interacting with each other through long-range, electrostatic interactions. The interaction
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Figure 3. Examples of model systems A, B, and C (2SCP). (a) A and the definition of the corresponding interaction energy (∆E). A consists of two subunits, A1 (the C-H bond donor group) and A2 (the C-H bond acceptor group). The Cδ-H‚‚‚OdC H-bond is a part of hydrogenbonding networks. (b) B and the definition of the corresponding interaction energy (∆). B consists of two subunits, B1 (the C-H bond donor which is the same as A1) and B2 (the C-H bond acceptor). B2 was generated from A2 by removing the N-terminus part starting from the arrow in Figure 2. The removed part was replaced by a hydrogen atom. (c) C and the definition of the corresponding interaction energy (∆′). C consists of two subunits, C1 (which is the same as A1 and B1) and C2. C2 was generated from A2 by replacing the B2 part (without the added hydrogen atom, see b above) by a hydrogen atom. C1 and C2 interact with each other through through-space electrostatic interactions. The cooperative effect (∆∆E) is defined as the difference between ∆E and ∆. The many-body effect (∆∆) is defined as the difference between ∆∆E and ∆′.
energies between the two subunits in A, B, and C are defined as ∆E, ∆, and ∆′, respectively. The cooperative effect (∆∆E) on the Cδ-H‚‚‚OdC H-bonds is defined as the difference between the interaction energies for A and B (i.e., ∆∆E ) ∆E - ∆). The many-body effect (∆∆) is defined as the nonadditive contribution to the Cδ-H‚‚‚OdC interaction energy in A (i.e., ∆∆ ) ∆E - ∆ - ∆′). Figure 3a, b, and c shows examples of A, B, and C, respectively, in 2SCP; the definitions for the different energy terms mentioned above are also given. As can be seen from Figure 3a (left), both the Cδ-H‚‚‚OdC H-bond between A1 and A2 and the conventional H-bond networks (i.e., near the N-terminal region and including the capping interaction) exist in A. For B (Figure 3b), the groups that may stabilize the CδH‚‚‚OdC H-bond through cooperative hydrogen bonding have been removed. For C (Figure 3c), C1 and C2 interact with each other through long-range, electrostatic interactions, because of the removal of B2 in the middle of A. The interaction energies (∆E, ∆, and ∆′) were obtained from ab initio calculations. The calculations were performed using GAUSSIAN9847 at HF/6-31G*, B3LYP/6-31+G**, B3LYP/6-311+G**, and MP2/6-31+G** levels with correction for basis set superposition error (BSSE).48 The correction for BSSE has also been included in the previous studies of the C-H‚‚‚O H-bonds,34a-34d and the BSSE-corrected interaction energies have been used for the estimate of the strength of the C-H‚‚‚O interactions in the complexes of small molecules. The
Guo et al. inclusion of the correction for BSSE generally makes the CδH‚‚‚OdC interactions less favorable by about 0.4 kcal/mol at the B3LYP level and about 0.8-2.1 kcal/mol at the HF and MP2 levels. However, it has little effect on ∆∆E and ∆∆. The MP2 calculations were only performed on eight selected systems containing 85 atoms or less. Four of the helices selected for the MP2 calculations have the (i+1)NH‚‚‚ (i-3)CdO peptide H-bonds, whereas the rest of them do not. Moreover, the selection was made such that four models have the charged capping residues (and four models do not). The positions of the hydrogen atoms built using the MOE program45 were optimized in some of the cases, and the geometry optimization for the hydrogen atoms had little effect on the results (e.g.,
