George Némethy

Structure of β-sheets: Origin of the right-handed twist and of the increased stability of antiparallel over parallel sheets☆

Abstract The energies of two and three-chain antiparallel and parallel β-sheets have been minimized. The chains were considered to be equivalent. In each case, chains consisting of four and of eight l -alanine residues, respectively, with CH3CO- and -NHCH3 end groups were examined. Computations were carried out both for chains constrained to have a regular structure (i.e. the same φ and ψ dihedral angles for each residue) and for chains in which the regularity constraint was relaxed. All computed minimum-energy β-sheets were found to have a right-handed twist, as observed in proteins. As in the case of right-handed α-helices, it is the intrastrand non-bonded interaction energy that plays the key role in forcing β-sheets of l -amino acid residues to adopt a right-handed twist. The non-bonded energy contribution favoring the right-handed twist is the result of many small pairwise interatomic interactions involving the CβH3 groups. Polyglycine β-sheets, lacking the CβH3 side-chains, are not twisted. The twist of the poly- l -alanine sheet diminishes as the number of residues per chain increases, in agreement with observations. The twist of the four-residue chain increases somewhat (because of interstrand non-bonded interactions, also involving the CβH3 groups) in going from a single chain to a two-chain antiparallel structure, but then decreases slightly in going from a two-chain to a three-chain structure. β-Sheets in observed protein structures sometimes have a larger twist than those in the structures computed here. This may be due to irregularities in amino acid sequence and in hydrogenbonding patterns in the observed sheets, or to long-range interactions in proteins. The minimized energies of parallel β-sheets are considerably higher than those of the corresponding antiparallel β-sheets, indicating that parallel β-sheets are intrinsically less stable. This finding about the two kinds of β-sheets agrees with suggestions based on analyses of β-sheets observed in proteins. The energy difference between antiparallel and parallel β-sheets is due to closer packing of the chains and a more favorable alignment of the peptide dipoles in the antiparallel structures. The hydrogen-bond geometry in the computed antiparallel structures is very close to that proposed by Arnott et al. (1967) for the β-form of poly- l -alanine.

Role of interchain interactions in the stabilization of the right-handed twist of β-sheets*

Conformational energy computations have been carried out for parallel and antiparallel beta-sheets composed of poly-L-Val and poly-L-Ile peptide chains, each consisting of four and of six residues, respectively, with CH3CO- and-NHCH3 end groups. The beta-sheets considered contained three and five equivalent chains, respectively. All computed minimum-energy beta-sheets were found to have a large right-handed twist of a magnitude that corresponds to the mean twist of beta-sheets observed in globular proteins. The twist has the same sign but is much larger than in beta-sheets of poly-L-Ala, because of intra- and interchain interactions between the bulky beta-branched side-chains. While the right-handed twist is a result of intrachain interactions between side-chains in the case of poly-L-Val, these interactions would favor a left-handed twist in poly-L-Ile, and the right-handed twist in the latter is a result of interchain interactions. Parallel beta-sheets are more stable than antiparallel sheets for both poly-L-Val and poly-L-Ile, in contrast to poly-L-Ala. This result agrees with observations on the preferred orientation of the chains in oligopeptides that form beta-structures. It also explains the observed high relative frequencies of occurrence of Val and Ile residues in parallel beta-sheets, as compared with antiparallel sheets, in globular proteins.

Stereochemical requirements for the existence of hydrogen bonds in β-bends

Abstract β-bends in proteins are characterized by a range of dihedral angles. They can be classified into eight groups, according to the orientation of the three peptide groups comprising the bend. The possibility of formation of intra-bend hydrogen bonds, involving NH and CO groups, depends on the relative orientation of the peptide groups, and hence differs for various types of bends. Therefore, nuclear magnetic resonance, infrared, or Raman spectroscopic data on hydrogen bonding or the shielding of NH groups can be used in some cases to distinguish between various types of bends.

Interactions between an α-helix and a β-sheet: Energetics of αβ packing in proteins☆

Conformational energy computations have been carried out to determine the favorable ways of packing a right-handed α-helix on a right-twisted antiparallel or parallel β-sheet. Co-ordinate transformations have been developed to relate the position and orientation of the α-helix to the β-sheet. The packing was investigated for a CH3CO-(L-Ala)16-NHCH3 α-helix interacting with five-stranded β-sheets composed of CH3CO-(L-Val)6-NHCH3 chains. All internal and external variables for both the α-helix and the β-sheet were allowed to change during energy minimization. Four distinct classes of low-energy packing arrangements were found for the α-helix interacting with both the parallel and the antiparallel β-sheet. The classes differ in the orientation of the axis of the α-helix relative to the direction of the strands of the right-twisted β-sheet. In the class with the most favorable arrangement, the α-helix is oriented along the strands of the β-sheet, as a result of attractive non-bonded side-chain-side-chain interactions along the entire length of the α-helix. A class with nearly perpendicular orientation of the helix axis to the strands is also of low energy, because it allows similarly extensive attractive interactions. In the other two classes, the helix is oriented diagonally relative to the strands of the β-sheet. In one of them, it interacts with the convex surface near the middle of the saddle-shaped twisted β-sheet. In the other, it is oriented along the concave diagonal of the β-sheet and, therefore, it interacts only with the corner regions of the sheet, so that this packing is energetically less favorable. The packing arrangements involving an antiparallel and a parallel β-sheet are generally similar, although the antiparallel β-sheet has been found to be more flexible. The major features of 163 observed αβ packing arrangements in 37 proteins are accounted for in terms of the computed structural preferences. The energetically most favored packing arrangement is similar to the right-handed βαβ crossover structure that is observed in proteins; thus, the preference for this connectivity arises in large measure from this energetically favorable interaction.

Prediction of the location of structural domains in globular proteins

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation |i-j| in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.

Energy of stabilization of the right-handed βαβ crossover in proteins☆

An explanation in terms of conformational energies is provided for the observed nearly exclusive preference of the βαβ structure for forming a right-handed, rather than a left-handed, crossover connection. Conformational energy computations have been carried out on a model βαβ structure, consisting of two six-residue Val β-strands and of a 12-residue Ala α-helix, connected by two flexible four-residue Ala links to the strands. The energy of the most favorable right-handed crossover is 15.51 kcal/mol lower than that of the corresponding left-handed cross-over. The right-handed crossover is a strain-free structure. Its energy of stabilization arises largely from the interactions of the two β-strands with one another and with the α-helix. On the other hand, the left-handed crossover is either disrupted after energy minimization or it remains conformationally strained, as indicated by an energetically unfavorable left twisting of the β-sheet and by the presence of high-energy local residue conformations. In the energetically most favorable right-handed crossover, the right twisting of the β-sheet and its manner of interacting with the α-helix are identical with those computed earlier for isolated β-sheets and for packed αβ structures. This result supports a proposed principle that it is possible to account for the main features of frequently occurring structural arrangements in globular proteins in terms of the properties of their component structural elements.

Use of proton nuclear Overhauser effects for the determination of the conformations of amino acid residues in oligopeptides.

Abstract The use of the Nuclear Overhauser Effect to determine backbone and side-chain conformations of oligopeptides is discussed. The distance between the H α proton of a given residue and the amide proton of the following residue depends only on the dihedral angle ψ. A calibration curve is given for the determination of ψ from the Nuclear Overhauser Effect involving these protons. In amino acids with branched side chains, e.g., threonine, isoleucine, and valine, the Nuclear Overhauser Effect involving the H β proton and the amide proton in either the same or the following residue gives limited information about both χ 1 and either or ψ. The Nuclear Overhauser Effect involving the H α and H γ protons in leucine gives information about χ 1 and χ 2 .

Interactions between two β-sheets energetics of β/β packing in proteins

The analysis of the interactions between regularly folded segments of the polypeptide chain contributes to an understanding of the energetics of protein folding. Conformational energy-minimization calculations have been carried out to determine the favorable ways of packing two right-twisted beta-sheets. The packing of two five-stranded beta-sheets was investigated, with the strands having the composition CH3CO-(L-Ile)6-NHCH3 in one beta-sheet and CH3CO-(L-Val)6-NHCH3 in the other. Two distinct classes of low-energy packing arrangements were found. In the class with lowest energies, the strands of the two beta-sheets are aligned nearly parallel (or antiparallel) with each other, with a preference for a negative orientation angle, because this arrangement corresponds to the best complementary packing of the two twisted saddle-shaped beta-sheets. In the second class, with higher interaction energies, the strands of the two beta-sheets are oriented nearly perpendicular to each other. While the surfaces of the two beta-sheets are not complementary in this arrangement, there is good packing between the corner of one beta-sheet and the interior part of the surface of the other, resulting in a favorable energy of packing. Both classes correspond to frequently observed orientations of beta-sheets in proteins. In proteins, the second class of packing is usually observed when the two beta-sheets are covalently linked, i.e. when a polypeptide strand passes from one beta-sheet to the other, but we have shown here that a large contribution to the stabilization of this packing arrangement arises from noncovalent interactions.

Strong interaction between disulfide derivatives and aromatic groups in peptides and proteins

Abstract The intermolecular interaction energy of complexes of dimethyldisulfide with benzene and cyclohexane, respectively, was computed as function of the relative distance and orientation within each pair of molecules. The energy of the most stable orientation of the dimethyldisulfide-cyclohexane complex is −2.57 kcal/mol, while that of the most stable orientation of the dimethyldisulfide-benzene complex is −3.33 kcal/mol. The energy difference of ∼0.8 kcal/mol is due to favorable specific nonbonded interactions between the sulfur atoms and the atoms of the aromatic ring. Proper parameterization of empirical interatomic energies, used in computations in this laboratory, accounts for these interactions without the need for a special sulfur-aromatic potential energy function.

Prediction of the packing arrangement of strands in β-sheets of globular proteins

A method is proposed for predicting the adjacency order in which strands pack in a β-sheet in a protein, on the basis of its amino acid sequence alone. The method is based on the construction of a predicted contact map for the protein, in which the probability that various residue pairs are close to each other is computed from statistically determined average distances of residue pairs in globular proteins of known structure. Compact regions, i.e., portions of the sequence with many interresidue contacts, are determined on the map by using an objective search procedure. The proximity of strands in a β-sheet is predicted from the density of contacts in compact regions associated with each pair of strands. The most probable β-sheet structures are those with the highest density of contacts. The method has been tested by computing the probable strand arrangements in a five-strand β-sheet in five proteins or protein domains, containing 62–138 residues. Of the theoretically possible 60 strand arrangements, the method selects two to eight arrangements as most probable; i.e., it leads to a large reduction in the number of possibilities. The native strand arrangement is among those predicted for three of the five proteins. For the other two, it would be included in the prediction by a slight relaxation of the cutoff criteria used to analyze the density of contacts.