HELANAL: a program to characterize helix geometry in proteins

A detailed analysis of structural and position dependent characteristic features of helices will give a better understanding of the secondary structure formation in globular proteins. Here we describe an algorithm that quantifies the geometry of helices in proteins on the basis of their C alpha atoms alone. The Fortran program HELANAL can extract the helices from the PDB files and then characterises the overall geometry of each helix as being linear, curved or kinked, in terms of its local structural features, viz. local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes. Even helices with large radius of curvature are unambiguously identified as being linear or curved. The program can also be used to differentiate a kinked helix and other motifs, such as helix-loop-helix or a helix-turn-helix (with a single residue linker) with the help of local bending angles. In addition to these, the program can also be used to characterise the helix start and end as well as other types of secondary structures.     

Structural and sequence characteristics of long alpha helices in globular proteins.

Elucidation of the detailed structural features and sequence requirements for alpha helices of various lengths could be very important in understanding secondary structure formation in proteins and, hence, in the protein folding mechanism. An algorithm to characterize the geometry of an alpha helix from its C(alpha) coordinates has been developed and used to analyze the structures of long alpha helices (number of residues > or = 25) found in globular proteins, the crystal structure coordinates of which are available from the Brookhaven Protein Data Bank. All long alpha helices can be unambiguously characterized as belonging to one of three classes: linear, curved, or kinked, with a majority being curved. Analysis of the sequences of these helices reveals that the long alpha helices have unique sequence characteristics that distinguish them from the short alpha helices in globular proteins. The distribution and statistical propensities of individual amino acids to occur in long alpha helices are different from those found in short alpha helices, with amino acids having longer side chains and/or having a greater number of functional groups occurring more frequently in these helices. The sequences of the long alpha helices can be correlated with their gross structural features, i.e., whether they are curved, linear, or kinked, and in case of the curved helices, with their curvature.     

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.     

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.     

Probing a label-free local bend in DNA by single molecule tethered particle motion

Being capable of characterizing DNA local bending is essential to understand thoroughly many biological processes because they involve a local bending of the double helix axis, either intrinsic to the sequence or induced by the binding of proteins. Developing a method to measure DNA bend angles that does not perturb the conformation of the DNA itself or the DNA-protein complex is a challenging task. Here, we propose a joint theory-experiment high-throughput approach to rigorously measure such bend angles using the Tethered Particle Motion (TPM) technique. By carefully modeling the TPM geometry, we propose a simple formula based on a kinked Worm-Like Chain model to extract the bend angle from TPM measurements. Using constructs made of 575 base-pair DNAs with in-phase assemblies of one to seven 6A-tracts, we find that the sequence CA₆CGG induces a bend angle of 19° ± 4°. Our method is successfully compared to more theoretically complex or experimentally invasive ones such as cyclization, NMR, FRET or AFM. We further apply our procedure to TPM measurements from the literature and demonstrate that the angles of bends induced by proteins, such as Integration Host Factor (IHF) can be reliably evaluated as well.     

Spatial translational motions of base pairs in DNA molecules: Application of the extended matrix generator method

We have used the elementary generator matrices outlined in the preceding paper to examine the conformational plasticity of the nucleic acid double helix. Here we investigate kinked DNA structures made up of alternating B- and A-type helices and intrinsically curved duplexes perturbed by the intercalation of ligands. We model the B-to-A transition by the lateral translation of adjacent base pairs, and the intercalation of ligands by the vertical displacement of neighboring residues. We report a complete set of average configuration-dependent parameters, ranging from scalars (i.e., persistence lengths) to first- and second-order tensor parameters (i.e., average second moments of inertia), as well as approximations of the associated spatial distributions of the DNA and their angular correlations. The average structures of short chains (of lengths less than 100 base pairs) with local kinks or intrinsically curved sequences are essentially rigid rods. At the smallest chain lengths (10 base pairs), the kinked and curved chains exhibit similar average properties, although they are structurally perturbed compared to the standard B-DNA duplex. In contrast, at lengths of 200 base pairs, the curved and kinked chains are more compact on average and are located in a different space from the standard B- or A-DNA helix. While A-DNA is shorter and thicker than B-DNA in x-ray models, the long flexible A-DNA helix is thinner and more extended on average than its B-DNA counterpart because of more limited fluctuations in local structure. Curved polymers of 50 base pairs or longer also show significantly greater asymmetry than other DNAs (in terms of the distribution of base pairs with respect to the center of gravity of the chain). The intercalation of drugs in the curved DNA straightens and extends the smoothly deformed template. The dimensions of the average ellipsoidal boundaries defining the configurations of the intercalated polymers are roughly double those of the intrinsically curved chain. The altered proportions and orientations of these density functions reflect the changing shape and flexibility of the double helix. The calculations shed new light on the possible structural role of short A-DNA fragments in long B-type duplexes and also offer a model for understanding how GC-specific intercalative ligands can straighten naturally curved DNA. The mechanism is not immediately obvious from current models of DNA curvature, which attribute the bending of the chain to a perturbed structure in repeating tracts of A · T base pairs. © 1994 John Wiley & Sons, Inc.     

Description of local and global shape properties of protein helices

A new method, dubbed “HAXIS” is introduced to describe local and global shape properties of a protein helix via its axis. HAXIS is based on coarse-graining and spline-fitting of the helix backbone. At each Cα anchor point of the backbone, a Frenet frame is calculated, which directly provides the local vector presentation of the helix. After cubic spline-fitting of the axis line, its curvature and torsion are calculated. This makes a rapid comparison of different helix forms and the determination of helix similarity possible. Distortions of the helix caused by individual residues are projected onto the helix axis and presented either by the rise parameter per residue or by the local curvature of the axis. From a non-redundant set of 2,017 proteins, 15,068 helices were investigated in this way. Helix start and helix end as well as bending and kinking of the helix are accurately described. The global properties of the helix are assessed by a polynomial fit of the helix axis and the determination of its overall curving and twisting. Long helices are more regular shaped and linear whereas short helices are often strongly bent and twisted. The distribution of different helix forms as a function of helix length is analyzed.     

Sequence and structure patterns in proteins from an analysis of the shortest helices: implications for helix nucleation

The shortest helices (three-length 3(10) and four-length alpha), most abundant among helices of different lengths, have been analyzed from a database of protein structures. A characteristic feature of three-length 3(10)-helices is the shifted backbone conformation for the C-terminal residue (phi,psi angles: -95 degrees,0 degrees ), compared to the rest of the helix (-62 degrees,-24 degrees ). The deviation can be attributed to the release of electrostatic repulsion between the carbonyl oxygen atoms at the two C-terminal residues and further stabilization (due to a more linear geometry) of an intrahelical hydrogen bond. A consequence of this non-canonical C-terminal backbone conformation can be a potential origin of helix kinks when a 3(10)-helix is sequence-contiguous at the alpha-helix N-terminal. An analysis of hydrogen bonding, as well as hydrophobic interactions in the shortest helices shows that capping interactions, some of them not observed for longer helices, dominate at the N termini. Further, consideration of the distribution of amino acid residues indicates that the shortest helices resemble the N-terminal end of alpha-helices rather than the C terminus, implying that the folding of helices may be initiated at the N-terminal end, which does not get propagated in the case of the shortest helices. Finally, pairwise comparison of beta-turns and the shortest helices, based on correlation matrices of site-specific amino acid composition, and the relative abundance of these short secondary structural elements, leads to a helix nucleation scheme that considers the formation of an isolated beta-turn (and not an alpha-turn) as the helix nucleation step, with shortest 3(10)-helices as intermediates between the shortest alpha-helix and the beta-turn. Our results ascribe an important role played by shortest 3(10)-helices in proteins with important structural and folding implications.     

High-Resolution Crystal Structures of Protein Helices Reconciled with Three-Centered Hydrogen Bonds and Multipole Electrostatics

Theoretical and experimental evidence for non-linear hydrogen bonds in protein helices is ubiquitous. In particular, amide three-centered hydrogen bonds are common features of helices in high-resolution crystal structures of proteins. These high-resolution structures (1.0 to 1.5 Å nominal crystallographic resolution) position backbone atoms without significant bias from modeling constraints and identify Φ = -62°, ψ = -43 as the consensus backbone torsional angles of protein helices. These torsional angles preserve the atomic positions of α-β carbons of the classic Pauling α-helix while allowing the amide carbonyls to form bifurcated hydrogen bonds as first suggested by Némethy et al. in 1967. Molecular dynamics simulations of a capped 12-residue oligoalanine in water with AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications), a second-generation force field that includes multipole electrostatics and polarizability, reproduces the experimentally observed high-resolution helical conformation and correctly reorients the amide-bond carbonyls into bifurcated hydrogen bonds. This simple modification of backbone torsional angles reconciles experimental and theoretical views to provide a unified view of amide three-centered hydrogen bonds as crucial components of protein helices. The reason why they have been overlooked by structural biologists depends on the small crankshaft-like changes in orientation of the amide bond that allows maintenance of the overall helical parameters (helix pitch (p) and residues per turn (n)). The Pauling 3.6₁₃ α-helix fits the high-resolution experimental data with the minor exception of the amide-carbonyl electron density, but the previously associated backbone torsional angles (Φ, Ψ) needed slight modification to be reconciled with three-atom centered H-bonds and multipole electrostatics. Thus, a new standard helix, the 3.6_13/10-, Némethy- or N-helix, is proposed. Due to the use of constraints from monopole force fields and assumed secondary structures used in low-resolution refinement of electron density of proteins, such structures in the PDB often show linear hydrogen bonding.     

Molecular Modelling Study of the Netropsin Complexation With a Nucleic Acid Triple Helix

Abstract

A detailed molecular mechanical study has been made on the complexes of netropsin with the double stranded oligonucleotide (dA)₁₂.(dT)₁₂ and with the triple helix (dA)₁₂.(dT)₁₂.(dT)₁₂. The complexes were built using computer graphics and energy refined using JUMNA program. In agreement with circular dichroïsm experiments we have shown that 3 netropsins can bind the minor grooves of the triple helix and of the double helix. The groove geometry in the duplex and in the triplex is very similar. However a detailed analysis of the energetic terms shows, in agreement with thermal denaturation studies, that the affinity of netropsin toward the double helices is larger than towards triple helices.     

Sequence and conformational preferences at termini of α‐helices in membrane proteins: Role of the helix environment

α‐helices are amongst the most common secondary structural elements seen in membrane proteins and are packed in the form of helix bundles. These α‐helices encounter varying external environments (hydrophobic, hydrophilic) that may influence the sequence preferences at their N and C‐termini. The role of the external environment in stabilization of the helix termini in membrane proteins is still unknown. Here we analyze α‐helices in a high‐resolution dataset of integral α‐helical membrane proteins and establish that their sequence and conformational preferences differ from those in globular proteins. We specifically examine these preferences at the N and C‐termini in helices initiating/terminating inside the membrane core as well as in linkers connecting these transmembrane helices. We find that the sequence preferences and structural motifs at capping (Ncap and Ccap) and near‐helical (N' and C') positions are influenced by a combination of features including the membrane environment and the innate helix initiation and termination property of residues forming structural motifs. We also find that a large number of helix termini which do not form any particular capping motif are stabilized by formation of hydrogen bonds and hydrophobic interactions contributed from the neighboring helices in the membrane protein. We further validate the sequence preferences obtained from our analysis with data from an ultradeep sequencing study that identifies evolutionarily conserved amino acids in the rat neurotensin receptor. The results from our analysis provide insights for the secondary structure prediction, modeling and design of membrane proteins. Proteins 2014; 82:3420–3436. © 2014 Wiley Periodicals, Inc.     

DNA bending: the prevalence of kinkiness and the virtues of normality.

DNA bending in 86 complexes with sequence-specific proteins has been examined using normal vector plots, matrices of normal vector angles between all base pairs in the helix, and one-digit roll/slide/twist tables. FREEHELIX, a new program especially designed to analyze severely bent and kinked duplexes, generates the foregoing quantities plus local roll, tilt, twist, slide, shift and rise parameters that are completely free of any assumptions about an overall helix axis. In nearly every case, bending results from positive roll at pyrimidine-purine base pair steps: C-A (= T-G), T-A, or less frequently C-G, in a direction that compresses the major groove. Normal vector plots reveal three well-defined types of bending among the 86 examples: (i) localized kinks produced by positive roll at one or two discrete base pairs steps, (ii) three-dimensional writhe resulting from positive roll at a series of adjacent base pairs steps, or (iii) continuous curvature produced by alternations of positive and negative roll every 5 bp, with side-to-side zig-zag roll at intermediate position. In no case is tilt a significant component of the bending process. In sequences with two localized kinks, such as CAP and IHF, the dihedral angle formed by the three helix segments is a linear function of the number of base pair steps between kinks: dihedral angle = 36 degrees x kink separation. Twenty-eight of the 86 examples can be described as major bends, and significant elements in the recognition of a given base sequence by protein. But even the minor bends play a role in fine-tuning protein/DNA interactions. Sequence-dependent helix deformability is an important component of protein/DNA recognition, alongside the more generally recognized patterns of hydrogen bonding. The combination of FREEHELIX, normal vector plots, full vector angle matrices, and one-digit roll/slide/twist tables affords a rapid and convenient method for assessing bending in DNA.     

Uniformity,ideality, and hydrogen bonds in transmembrane alpha-helices

Protein environments substantially influence the balance of molecular interactions that generate structural stability. Transmembrane helices exist in the relatively uniform low dielectric interstices of the lipid bilayer, largely devoid of water and with a very hydrophobic distribution of amino acid residues. Here, through an analysis of bacteriorhodopsin crystal structures and the transmembrane helix structure from M2 protein of influenza A, some helices are shown to be exceptionally uniform in hydrogen bond geometry, peptide plane tilt angle, and backbone torsion angles. Evidence from both the x-ray crystal structures and solid-state NMR structure suggests that the intramolecular backbone hydrogen bonds are shorter than their counterparts in water-soluble proteins. Moreover, the geometry is consistent with a dominance of electrostatic versus covalent contributions to these bonds. A comparison of structure as a function of resolution shows that as the structures become better characterized the helices become much more uniform, suggesting that there is a possibility that many more uniform helices will be observed, even among the moderate resolution membrane protein structures that are currently in the Protein Data Bank that do not show such features.     

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.     

Insight into Signal Transduction: Structural Alterations in Transmembrane Helices Probed by Multi-1 ns Molecular Dynamics Simulations

Abstract

The hypothesis of structural alteration in transmembrane helices for signal transduction process is viewed by molecular dynamics simulation techniques. For the c-erbB-2 transmembrane domain involved in oncogenicity, the occurrence of conformational changes has been previously described as transition from the α to π helix. This dynamical feature is thoroughly analyzed for the wild phenotype and oncogenic sequences from a series of 18 simulations carried out on one nanosecond time scale. We show that these structural events do not depend upon the conditions of simulations like force field or starting helix coordinates. We demonstrate that the oncogenic mutations Val659 Glu, Gin and Asp do not prevent the transition. Furthermore, we show that β branched residues, in conjunction with Gly residues in the c-erbB-2 sequence, act as destabilizers for the α helix structure, π deformations are tightly related to other local structural motifs found in soluble and membrane proteins. These structural alterations are discussed in term of structure-activity relationships for the c-erbB-2 activating mechanism mediated by transmembrane domain dimerization.     

Global secondary structure packing angle bias in proteins

While studies of secondary structure interactions have focused on local interacting features, there is a need for a more global characterization of packing-induced aligned packing of secondary structures. This study presents an analysis of the distribution of globally sampled secondary structures within selected subunits of a selected set of multimeric proteins. Comparisons are made between the distribution of the cosines of angles between triplets of linear segments associated to secondary structures and a theoretically obtained distribution for triplets of random uniformly distributed unit vectors. We show that, among all pairs of helix or strand segments, planar configurations appear more frequently than expected for uniformly distributed vectors, and alignment is strongly preferred compared to that expected for uniformly distributed vector triplets. Among all secondary structure triplets, pairs of angle cosines between helix strand segments deviate from uniformity corresponding to alignment and anti-alignment. Furthermore, among all helix or strand segments, including non-interacting secondary structures, the distribution of a single angle cosine indicates a strong preference for alignment and anti-alignment. Selection for interactive triplets shows results consistent with prior studies. Lastly, angle pairs are not statistically independent, indicating that alignment between two helix or strand segments is more likely if another helix or strand is aligned with either of the first two helices or strands. Selection for interactive segment triplets shows results consistent with prior studies.     

Helix-helix interactions and their impact on protein motifs and assemblies

Protein secondary structure elements are arranged in distinct structural motifs such as four-α-helix bundle, 8α/8β TIM-barrel, Rossmann dinucleotide binding fold, assembly of a helical rod. Each structural motif is characterized by a particular type of helix-helix interactions. A unique pattern of contacts is formed by interacting helices of the structural motif. In each type of fold, edges of the helix surface, which participate in the formation of helix-helix contacts with preceding and following helices, differ. This work shows that circular arrangements of the four, eight, and sixteen α-helices, which are found in the four-α-helical motif, TIM-barrel 8α/8β fold, and helical rod of 16.3¯ helices per turn correspondingly, can be associated with the mutual positioning of the edges of the helix surfaces. Edges (i, i+1)−(i+1, i+2) of the helix surface are central for the interhelical contacts in a four-α-helix bundle. Edges (i, i+1)−(i+2, i+3) are involved in the assembly of four-α-helix subunits into helical rod of a tobacco mosaic virus and a three-helix fragment of a Rossmann fold. In 8α/8β TIM-barrel fold, edges (i, i+1)−(i+5, i+6) are involved in the octagon arrangement. Approximation of a cross section of each motif with a polygon (n-gon, n=4, 8, 16) shows that a good correlation exists between polygon interior angles and angles formed by the edges of helix surfaces.     

Influence of the g− conformation of Ser and Thr on the structure of transmembrane helices

In order to study the influence of Ser and Thr on the structure of transmembrane helices we have analyzed a database of helix stretches extracted from crystal structures of membrane proteins and an ensemble of model helices generated by molecular dynamics simulations. Both complementary analyses show that Ser and Thr in the g? conformation induce and/or stabilize a structural distortion in the helix backbone. Using quantum mechanical calculations, we have attributed this effect to the electrostatic repulsion between the side chain Oγ atom of Ser and Thr and the backbone carbonyl oxygen at position i ? 3. In order to minimize the repulsive force between these negatively charged oxygens, there is a modest increase of the helix bend angle as well as a local opening of the helix turn preceding Ser/Thr. This small distortion can be amplified through the helix, resulting in a significant displacement of the residues located at the other side of the helix. The crystal structures of aquaporin Z and the β₂-adrenergic receptor are used to illustrate these effects. Ser/Thr-induced structural distortions can be implicated in processes as diverse as ligand recognition, protein function and protein folding.     

Kinked structures of isolated nicotinic receptor M2 helices: A molecular dynamics study

The pore-lining M2 helix of the nicotinic acetylcholine receptor exhibits a pronounced kink when the corresponding ion channel is in a closed conformation [N. Unwin (1993) Journal of Molecular Biology, Vol. 229, pp. 1101–1124]. We have performed molecular dynamics simulations of isolated 22-residue M2 helices in order to identify a possible molecular origin of this kink. In order to sample a wide range of conformational space, a simulated annealing protocol was used to generate five initial M2 helix structures, each of which was subsequently used as the basis of 300 ps MD simulations. Two helix sequences (M2α and M2δ) were studied in this manner, resulting in a total often 300 ps trajectories. Kinked helices present in the trajectories were identified and energy minimized to yield a total of five different stable kinked structures. For comparison, a similar molecular dynamics simulation of a Leu₂₃ helix yielded no stable kinked structures. In four of the five kinked helices, the kink was stabilized by H bonds between the helix backbone and polar side-chain atoms. Comparison with data from the literature on site-directed mutagenesis of M2 residues suggests that such polar side-chain to main-chain H bonds may also contribute to kinking of M2 helices in the intact channel protein. © 1994 John Wiley & Sons, Inc.