Discovery of a significant,nontopological preference for antiparallel alignment of helices with parallel regions in sheets

To help elucidate the role of secondary structure packing preferences in protein folding, here we present an analysis of the packing geometry observed between alpha-helices and between alpha-helices and beta-sheets in 1316 diverse, nonredundant protein structures. Finite-length vectors were fit to the alpha-carbon atoms in each of the helices and strands, and the packing angle between the vectors, Omega, was determined at the closest point of approach within each helix-helix or helix-sheet pair. Helix-sheet interactions were found in 391 of the proteins, and the distributions of Omega values were calculated for all the helix-sheet and helix-helix interactions. The packing angle preferences for helix-helix interactions are similar to those previously observed. However, analysis of helix-strand packing preferences uncovered a remarkable tendency for helices to align antiparallel to parallel regions of beta-sheets, independent of the topological constraints or prevalence of beta-alpha-beta motifs in the proteins. This packing angle preference is significantly diminished in helix interactions involving mixed and antiparallel beta-sheets, suggesting a role for helix-sheet dipole alignment in guiding supersecondary structure formation in protein folding. This knowledge of preferred packing angles can be used to guide the engineering of stable protein modules.     

Interhelical angle and distance preferences in globular proteins

Orientational preferences between interacting helices within globular proteins have been studied extensively over the years. A number of classical structural models such as "knobs into holes" and "ridges into grooves" were developed decades ago to explain perceived preferences in interhelical angle distributions. In contrast, relatively recent works have examined statistical biases in angular distributions which result from spherical geometric effects. Those works have concluded that the predictions of classical models are due in large part to these biases. In this article we perform an analysis on the largest set of helix-helix interactions within high-resolution structures of nonhomologous proteins studied to date. We examine the interhelical angle distribution as a function of spatial distance between helix pairs. We show that previous efforts to normalize angle distribution data did not include two important effects: 1), helices can interact with each other in three distinct ways which we refer to as "line-on-line," "endpoint-to-line," and "endpoint-to-endpoint," and each of these interactions has its own geometric effects which must be included in the proper normalization of data; and 2), all normalizations that depend on geometric parameters such as interhelical angle must occur before the data is binned to avoid artifacts of bin size from biasing the conclusions. Taking these two points into account, we find that there are very pronounced preferences for helices to interact at angles of approximately +/-160 and +/-20 degrees in the line-on-line case. This pattern persists when the closest alpha-carbons in the helices vary from 4 to 12 A. The endpoint-to-line and endpoint-to-endpoint cases also exhibit distinct preferences when the data is normalized properly. Analysis of the local structural interactions which give rise to these preferences has not been studied here and is left for future work.     

Non-randomness in side-chain packing: the distribution of interplanar angles

We analyze the distributions of interplanar angles between interacting side chains with well-defined planar regions, to see whether these distributions correspond to random packing or alternatively show orientational preferences. We use a non-homologous set of 79 high-resolution protein chain structures to show that the observed distributions are significantly different from the sinusoidal one expected for random packing. Overall, we see a relative excess of small angles and a paucity of large interplanar angles; the difference between the expected and observed distributions can be described as a shift of 5% of the interplanar angles from large (≥60°) to small (<30°) values. By grouping the residue pairs into categories based on chemical similarity, we find that some categories have very non-sinusoidal interplanar angle distributions, whereas other categories have distributions that are close to sinusoidal. For a few categories, observed deviations from a sinusoidal distribution can be explained by the electrostatic anisotropy of the isolated pair potential energy. In other cases, the observed distributions reflect the longer range effects of different possible interaction geometries. In particular, geometries that disrupt external hydrogen bonding are disfavored. Proteins 29:370–380, 1997. © 1997 Wiley-Liss, Inc.     

Helix-helix packing angle preferences for finite helix axes

Recently, James Bowie addressed the question of how to normalize correctly the distribution of observed helix-helix packing angles in proteins (Bowie, Nature Struct. Biol. 4:915–917, 1997). A hitherto unrealized yet significant bias toward crossed packing angles was revealed. However, the derived random reference distribution of packing angles requires that helices have to be assumed as infinite in length. Here, we complement Bowie's analysis by consideration of the more realistic case where helices are of finite length. As a result, the statistical bias toward near perpendicular packings appears to be even stronger. Proteins 33:457–459, 1998. © 1998 Wiley-Liss, Inc.     

Robust Driving Forces for Transmembrane Helix Packing

The packing structures of transmembrane helices are traditionally attributed to patterns in residues along the contact surface. In this view, besides keeping the helices confined in the membrane, the bilayer has only a minor effect on the helices structure. Here, we use two different approaches to show that the lipid environment has a crucial effect in determining the cross-angle distribution of packed helices. We analyzed structural data of a membrane proteins database. We show that the distribution of cross angles of helix pairs in this database is statistically indistinguishable from the cross-angle distribution of two noninteracting helices imbedded in the membrane. These results suggest that the cross angle is, to a large extent, determined by the tilt angle of the individual helices. We test this hypothesis using molecular simulations of a coarse-grained model that contains no specific residue interactions. These simulations reproduce the same cross-angle distribution as found in the database. As the tilt angle of a helix is dominated by hydrophobic mismatch between the protein and surrounding lipids, our results indicate that hydrophobic mismatch is the dominant factor guiding the transmembrane helix packing. Other short-range forces might then fine-tune the structure to its final configuration.     

QHELIX: A Computational Tool for the Improved Measurement of Inter-Helical Angles in Proteins

Knowledge about the assembled structures of the secondary elements in proteins is essential to understanding protein folding and functionality. In particular, the analysis of helix geometry is required to study helix packing with the rest of the protein and formation of super secondary structures, such as, coiled coils and helix bundles, formed by packing of two or more helices. Here we present an improved computational method, QHELIX, for the calculation of the orientation angles between helices. Since a large number of helices are known to be in curved shapes, an appropriate definition of helical axes is a prerequisite for calculating the orientation angle between helices. The present method provides a quantitative measure on the irregularity of helical shape, resulting in discriminating irregular-shaped helices from helices with an ideal geometry in a large-scale analysis of helix geometry. It is also capable of straightforwardly assigning the direction of orientation angles in a consistent way. These improvements will find applications in finding a new insight on the assembly of protein secondary structure. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Comparison of helix interactions in membrane and soluble alpha-bundle proteins

Helix-helix interactions are important for the folding, stability, and function of membrane proteins. Here, two independent and complementary methods are used to investigate the nature and distribution of amino acids that mediate helix-helix interactions in membrane and soluble alpha-bundle proteins. The first method characterizes the packing density of individual amino acids in helical proteins based on the van der Waals surface area occluded by surrounding atoms. We have recently used this method to show that transmembrane helices pack more tightly, on average, than helices in soluble proteins. These studies are extended here to characterize the packing of interfacial and noninterfacial amino acids and the packing of amino acids in the interfaces of helices that have either right- or left-handed crossing angles, and either parallel or antiparallel orientations. We show that the most abundant tightly packed interfacial residues in membrane proteins are Gly, Ala, and Ser, and that helices with left-handed crossing angles are more tightly packed on average than helices with right-handed crossing angles. The second method used to characterize helix-helix interactions involves the use of helix contact plots. We find that helices in membrane proteins exhibit a broader distribution of interhelical contacts than helices in soluble proteins. Both helical membrane and soluble proteins make use of a general motif for helix interactions that relies mainly on four residues (Leu, Ala, Ile, Val) to mediate helix interactions in a fashion characteristic of left-handed helical coiled coils. However, a second motif for mediating helix interactions is revealed by the high occurrence and high average packing values of small and polar residues (Ala, Gly, Ser, Thr) in the helix interfaces of membrane proteins. Finally, we show that there is a strong linear correlation between the occurrence of residues in helix-helix interfaces and their packing values, and discuss these results with respect to membrane protein structure prediction and membrane protein stability.     

Helical packing patterns in membrane and soluble proteins

This article presents the results of a detailed analysis of helix-helix interactions in membrane and soluble proteins. A data set of interacting pairs of helices in membrane proteins of known structure was constructed and a structure alignment algorithm was used to identify pairs of helices in soluble proteins that superimpose well with pairs of helices in the membrane-protein data set. Most helix pairs in membrane proteins are found to have a significant number of structural homologs in soluble proteins, although in some cases, primarily involving irregular helices, no close homologs exist. An analysis of geometric relationships between interacting helices in the two sets of proteins identifies some differences in the distributions of helix length, interfacial area, packing angle, and distance between the polypeptide backbones. However, a subset of soluble-protein helix pairs that are close structural homologs to membrane-protein helix pairs exhibits distributions that mirror those observed in membrane proteins. The larger average interface size and smaller distance of closest approach seen for helices in membrane proteins appears due in part to a relative enrichment of alanines and glycines, particularly as components of the AxxxA and GxxxG motifs. It is argued that membrane helices are not on average more tightly packed than helices in soluble proteins; they are simply able to approach each other more closely. This enables them to interact over longer distances, which may in turn facilitate their remaining in contact over much of the width of the lipid bilayer. The close structural similarity seen between some pairs of helices in membrane and soluble proteins suggests that packing patterns observed in soluble proteins may be useful in the modeling of membrane proteins. Moreover, there do not appear to be fundamental differences between the magnitude of the forces that drive helix packing in membrane and soluble proteins, suggesting that strategies to make membrane proteins more soluble by mutating surface residues are likely to encounter success, at least in some cases.     

How to untwist an alpha-helix: structural principles of an alpha-helical barrel

Recent crystallographic studies have revealed that 12 alpha-helices can pack in an anti-parallel fashion to form a hollow cylinder of nearly uniform radius. In this architecture, which we refer to as an alpha-barrel, the helices are inclined with respect to the cylindrical axis, and thus they curve and twist. As with conventional coiled-coils, the helices of the barrel associate via "knobs-into-holes" interactions; however, their packing is distinct in several important ways. First, the alpha-barrel helices untwist in comparison with the helices found in two-stranded coiled-coils and, as a consequence of this distortion, their knobs approach closely one end of the complementary holes. This effect defines a requirement for particular size and shape of the protruding residues, and it is associated with a relative axial translation of the paired helices. Second, as each helix packs laterally with two neighbours, the helices have two sequence patterns that are phased to match the two interfaces. The two types of interface are not equivalent and, as one travels around the circumference of the cylinder's interior, they alternate between one type where the knobs approach the holes straight-on, and a second type in which they are inclined. The choice of amino acid depends on the interface type, with small hydrophobic side-chains preferred for the direct contacts and larger aliphatic side-chains for the inclined contacts. Third, small residues are found preferentially on the inside of the tube, in order to make the "wedge" angle between helices compatible with a 12-member tube. Finally, hydrogen-bonding interactions of side-chains within and between helices support the assembly. Using these salient structural features, we present a sequence template that is compatible with some underlying rules for the packing of helices in the barrel, and which may have application to the design of higher-order assemblies from peptides, such as nano-tubes. We discuss the general implications of relative axial translation in coiled-coils and, in particular, the potential role that this movement could play in allosteric mechanisms.     

Serine and threonine residues bend alpha-helices in the chi(1) = g(-) conformation

The relationship between the Ser, Thr, and Cys side-chain conformation (chi(1) = g(-), t, g(+)) and the main-chain conformation (phi and psi angles) has been studied in a selection of protein structures that contain alpha-helices. The statistical results show that the g(-) conformation of both Ser and Thr residues decreases their phi angles and increases their psi angles relative to Ala, used as a control. The additional hydrogen bond formed between the O(gamma) atom of Ser and Thr and the i-3 or i-4 peptide carbonyl oxygen induces or stabilizes a bending angle in the helix 3-4 degrees larger than for Ala. This is of particular significance for membrane proteins. Incorporation of this small bending angle in the transmembrane alpha-helix at one side of the cell membrane results in a significant displacement of the residues located at the other side of the membrane. We hypothesize that local alterations of the rotamer configurations of these Ser and Thr residues may result in significant conformational changes across transmembrane helices, and thus participate in the molecular mechanisms underlying transmembrane signaling. This finding has provided the structural basis to understand the experimentally observed influence of Ser residues on the conformational equilibrium between inactive and active states of the receptor, in the neurotransmitter subfamily of G protein-coupled receptors.     

Amino acid composition of parallel helix-helix interfaces

Amino acids at helix-helix parallel interfaces influence arrangement of helices and interhelical angles. Parallel interfaces in 79 proteins were considered. Location of amino acids at the positions analogous to a and d in GCN4 leucine zipper nomenclature shows that certain combinations of amino acids characteristic for parallel packing occur more often than could be expected by chance. Repeating sequence combinations occur at a and d positions of parallel helix-helix interfaces with similar values of interhelical angles not only in homologous proteins but also within the same protein and in nonhomologous proteins. Within each group of observed combinations correlation exists between the size of amino acid and magnitude of the interhelical angle.     

Alpha-alpha linking motifs and interhelical orientations

While the geometry and sequence preferences of turns that link two beta-strands have been exhaustively explored, the corresponding preferences for sequences that link helical structures have been less well studied. Here we examine the interhelical geometry of two connected helices as a function of their link's length. The interhelical geometry of a helical pair appears to be significantly influenced by the number of linking residues. Furthermore, for relatively short link lengths, a very limited number of predominant conformations are observed, which can be categorized by their phi/psi angles. No more than two predominant linking backbone conformations are observed for a given link length, and some linking backbone conformations correlate strongly with distinctive interhelical geometric parameters. In this study, sequence and hydrogen-bonding patterns were defined for predominant interhelical link motifs. These results should assist in both protein structure prediction and de novo protein design.     

Helix‐sheet packing in proteins

The three‐dimensional structure of a protein is organized around the packing of its secondary structure elements. Although much is known about the packing geometry observed between α‐helices and between β‐sheets, there has been little progress on characterizing helix–sheet interactions. We present an analysis of the conformation of αβ₂ motifs in proteins, corresponding to all occurrences of helices in contact with two strands that are hydrogen bonded. The geometry of the αβ₂ motif is characterized by the azimuthal angle θ between the helix axis and an average vector representing the two strands, the elevation angle ψ between the helix axis and the plane containing the two strands, and the distance D between the helix and the strands. We observe that the helix tends to align to the two strands, with a preference for an antiparallel orientation if the two strands are parallel; this preference is diminished for other topologies of the β‐sheet. Side‐chain packing at the interface between the helix and the strands is mostly hydrophobic, with a preference for aliphatic amino acids in the strand and aromatic amino acids in the helix. From the knowledge of the geometry and amino acid propensities of αβ₂ motifs in proteins, we have derived different statistical potentials that are shown to be efficient in picking native‐like conformations among a set of non‐native conformations in well‐known decoy datasets. The information on the geometry of αβ₂ motifs as well as the related statistical potentials have applications in the field of protein structure prediction. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Helix geometry in proteins

In this report we describe a general survey of all helices found in 57 of the known protein crystal structures, together with a detailed analysis of 48 alpha-helices found in 16 of the structures that are determined to high resolution. The survey of all helices reveals a total of 291 alpha-helices, 71 3(10)-helices and no examples of pi-helices. The conformations of the observed helices are significantly different from the "ideal" linear structures. The mean phi, psi angles for the alpha- and 3(10)-helices found in proteins are, respectively, (-62 degrees, -41 degrees) and (-71 degrees, -18 degrees). A computer program, HBEND, is used to characterize and to quantify the different types of helix distortion. alpha-Helices are classified as regular or irregular, linear, curved or kinked. Of the 48 alpha-helices analysed, only 15% are considered to be linear; 17% are kinked, and 58% are curved. The curvature of helices is caused by differences in the peptide hydrogen bonding on opposite faces of the helix, reflecting carbonyl-solvent/side-chain interactions for the exposed residues, and packing constraints for residues involved in the hydrophobic core. Kinked helices arise either as a result of included proline residues, or because of conflicting requirements for the optimal packing of the helix side-chains. In alpha-helices where there are kinks caused by proline residues, we show that the angle of kink is relatively constant (approximately 26 degrees), and that there is minimal disruption of the helix hydrogen bonding. The proline residues responsible for the kinks are highly conserved, suggesting that these distortions may be structurally/functionally important.     

The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide chains: a study of 1830 independently computed conformations

In this paper we study the statistical geometry of ensembles of poly (L-alanine) conformations computed by several different distance geometry algorithms. Since basic theory only permits us to predict the statistical properties of such ensembles a priori when the distance constraints have a very simple form, the only constraints used for these calculations are those necessary to obtain reasonable bond lengths and angles, together with a lack of short- and long-range atomic overlaps. The geometric properties studied include the squared end-to-end distance and radius of gyration of the computed conformations, in addition to the usual rms coordinate and phi/psi angle deviations among these conformations. The distance geometry algorithms evaluated include several variations of the well-known embed algorithm, together with optimizations of the torsion angles using the ellipsoid and variable target function algorithms. The conclusions may be summarized as follows: First, the distribution with which the trial distances are chosen in most implementations of the embed algorithm is not appropriate when no long-range upper bounds on the distances are present, because it leads to unjustifiably expanded conformations. Second, chosing the trial distances independently of one another leads to a lack of variation in the degree of expansion, which in turn produces a relatively low rms square coordinate difference among the members of the ensemble. Third, when short-range steric constraints are present, torsion angle optimizations that start from conformations obtained by choosing their phi/psi angles randomly with a uniform distribution between -180 degrees and +180 degrees do not converge to conformations whose angles are uniformly distributed over the sterically allowed regions of the phi/psi plane. Finally, in an appendix we show how the sampling obtained with the embed algorithm can be substantially improved upon by the proper application of existing methodology.     

Revisiting the Ramachandran plot from a new angle

The pioneering work of Ramachandran and colleagues emphasized the dominance of steric constraints in specifying the structure of polypeptides. The ubiquitous Ramachandran plot of backbone dihedral angles (φ and ψ) defined the allowed regions of conformational space. These predictions were subsequently confirmed in proteins of known structure. Ramachandran and colleagues also investigated the influence of the backbone angle τ on the distribution of allowed φ/ψ combinations. The “bridge region” (φ ≤ 0° and −20° ≤ ψ ≤ 40°) was predicted to be particularly sensitive to the value of τ. Here we present an analysis of the distribution of φ/ψ angles in 850 non-homologous proteins whose structures are known to a resolution of 1.7 Å or less and sidechain B-factor less than 30 Ų. We show that the distribution of φ/ψ angles for all 87,000 residues in these proteins shows the same dependence on τ as predicted by Ramachandran and colleagues. Our results are important because they make clear that steric constraints alone are sufficient to explain the backbone dihedral angle distributions observed in proteins. Contrary to recent suggestions, no additional energetic contributions, such as hydrogen bonding, need be invoked.     

Structure prediction of the dimeric neu/ErbB-2 transmembrane domain from multi-nanosecond molecular dynamics simulations

Dimerization of the neu/ErbB-2 receptor tyrosine kinase is a necessary but not a sufficient step for signaling. Despite the efforts expended to identify the molecular interactions responsible for receptor-receptor contacts and particularly those involving the transmembrane domain, structural details are still unknown. In this work, molecular dynamics simulations of the helical transmembrane domain (TM) of neu and ErbB-2 receptors are used to predict their dimer structure both in the wild and oncogenic forms. A global conformational search method, applied to define the best orientations of parallel helices, showed an energetically favorable configuration with the specific mutation site within the interface, common for both the nontransforming and the transforming neu/ErbB-2 TM dimers. Starting from this configuration, a total of 10 simulations, about 1.4 ns each, performed in vacuum, without any constraints, show that the two helices preferentially wrap in left-handed interactions with a packing angle at about 20°. The resulting structures are nonsymmetric and the hydrogen bond network analysis shows that helices experience π local distortions that facilitate inter-helix hydrogen bond interactions and may result in a change in the helix packing, leading to a symmetric interface. For the mutated sequences, we show that the Glu side chain interacts directly with its cognate or with carbonyl groups of the facing backbone. We show that the connectivity between interfacial residues conforms to the knobs-into-holes packing mode of transmembrane helices. The dimeric interface described in our models is discussed with respect to mutagenesis studies. Received: 12 March 1999 / Revised version: 23 August 1999 / Accepted: 23 August 1999     

Empirical evaluation of the influence of side chains on the conformational entropy of the polypeptide backbone

Changes in amino acid side chains have long been recognized to alterthe range and distribution of ?, ψ angles found in the main chain of polypeptides. Altering the range and distribution of ?, ψ angles also alters the conformational entropy of the flexible denatured state and may thus stabilize or destabilize it relative to the comparatively conformationally rigid native state. A database of 12,320 residues from 61 nonhomologous, high resolution crystal structures was examined to determine the ?, ψ conformational preferences of each of the 20 amino acids. These observed distributions in the native state of proteins are assumed to also reflect the distributions found in the denatured state. The distributionswere used to approximate the energy surface for each residue, allowing the calculation of relative conformational entropies for each residue relative to glycine. In the most extreme case, replacement of glycine by proline, conformational entropy changes will stabilize the native state relative to the denatured state by ?0.82 ± 0.08 kcal/mol at 20°C. Surprisingly, alanine is found to be the most ordered residue other than proline. This unexpected result is a result of the high percentage of alanines found in helical conformations. This either indicates that the observed distributions in the native state do not reflect the distributions in the denatured state, or that alanine is much more likely to adopt a helical conformation in the denatured state than residues with longer side chains. Among those residues with ?, ψ angles compatible with helix incorporation the percentage of alanines actually in helices is very similar to other residues. This and the consistent ordering of alanine relative to other residues regardless of secondary structure are evidence that ?, ψ distributions in native states reflect those in the denatured states. © 1995 Wiley-Liss, Inc.     

Predicting the side‐chain dihedral angle distributions of nonpolar,aromatic, and polar amino acids using hard sphere models

The side‐chain dihedral angle distributions of all amino acids have been measured from myriad high‐resolution protein crystal structures. However, we do not yet know the dominant interactions that determine these distributions. Here, we explore to what extent the defining features of the side‐chain dihedral angle distributions of different amino acids can be captured by a simple physical model. We find that a hard‐sphere model for a dipeptide mimetic that includes only steric interactions plus stereochemical constraints is able to recapitulate the key features of the back‐bone dependent observed amino acid side‐chain dihedral angle distributions of Ser, Cys, Thr, Val, Ile, Leu, Phe, Tyr, and Trp. We find that for certain amino acids, performing the calculations with the amino acid of interest in the central position of a short α‐helical segment improves the match between the predicted and observed distributions. We also identify the atomic interactions that give rise to the differences between the predicted distributions for the hard‐sphere model of the dipeptide and that of the α‐helical segment. Finally, we point out a case where the hard‐sphere plus stereochemical constraint model is insufficient to recapitulate the observed side‐chain dihedral angle distribution, namely the distribution P(χ₃) for Met. Proteins 2014; 82:2574–2584. © 2014 Wiley Periodicals, Inc.