HELANAL: A Program to Characterize Helix Geometry in Proteins

Abstract

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^α 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

UDP-glucose dehydrogenase: substrate binding stoichiometry and affinity

Precise structural parameters of polyribonucleotides single stranded helices are determined as well as those of double stranded helices of poly 2′-O-methyl A and of poly A at neutral and acid pH. Infrared linear dichroism investigations indicate the similarity of the conformation of the sugar-phosphate backbone of these single and double stranded helices. The angles of the phosphate group for single stranded helix at neutral pH is found to be oriented at 48° for the 02P02 bisector and at about 65° for the 02–03 line to the helix axis. Similar values were found for double stranded poly A helix at acid pH. These structural parameters obtained for the first time on single stranded polynucleotide helices are proposed to be valid for other similar helical chains such as poly A segments of nuclear or messenger RNA and single stranded CCA acceptor end of transfer RNA.     

3D maps of RNA interhelical junctions

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5' and 3' helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2'. A rotation matrix R is computed, which rotates iH2' into iH2 and expresses the rotation parameters in terms of three Euler angles α(h), β(h) and γ(h). The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5' (-γ(h)) and 3' (α(h)) helices and an interhelical bend angle (β(h)). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.     

Use of techniques derived from graph theory to compare secondary structure motifs in proteins

A substructure matching algorithm is described that can be used for the automatic identification of secondary structural motifs in three-dimensional protein structures from the Protein Data Bank. The proteins and motifs are stored for searching as labelled graphs, with the nodes of a graph corresponding to linear representations of helices and strands and the edges to the inter-line angles and distances. A modification of Ullman's subgraph isomorphism algorithm is described that can be used to search these graph representations. Tests with patterns from the protein structure literature demonstrate both the efficiency and the effectiveness of the search procedure, which has been implemented in FORTRAN 77 on a MicroVAX-II system, coupled to the molecular fitting program FRODO on an Evans and Sutherland PS300 graphics system.     

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.     

Proline in alpha-helix: stability and conformation studied by dynamics simulation

Free-energy simulations have been used to estimate the change in the conformational stability of short polyalanine alpha-helices when one of the alanines is replaced by a proline residue. For substituting proline in the middle of the helix the change in free energy of folding (delta delta G degrees) was calculated as 14 kJ/mol (3.4 kcal/mol), in excellent agreement with the one available experimental value. The helix containing proline was found to be strongly kinked; the free energy for reducing the angle of the kink from 40 degrees to 15 degrees was calculated, and found to be small. A tendency to alternate hydrogen bonding schemes was observed in the proline-containing helix. These observations for the oligopeptide agree well with the observation of a range of kink angles (18-35 degrees) and variety of hydrogen bonding schemes, in the rare instances where proline occurs in helices in globular proteins. For substituting proline at the N-terminus of the helix the change in free energy of folding (delta delta G degrees) was calculated as -4 kJ/mol in the first helical position (N1) and +6 kJ/mol in the second helical position (N2). The observed frequent occurrence of proline in position N1 in alpha-helices in proteins therefore has its origin in stability differences of secondary structure. The conclusion reached here that proline may be a better helix former in position N1 than (even) alanine, and thus be a helix initiator may be testable experimentally by measurements of fraction helical conformation of individual residues in oligopeptides of appropriate sequence. The relevance of these results in regards to the frequent occurrence of proline-containing helices in certain membrane proteins is discussed.     

Helix kinks are equally prevalent in soluble and membrane proteins

Helix kinks are a common feature of α‐helical membrane proteins, but are thought to be rare in soluble proteins. In this study we find that kinks are a feature of long α‐helices in both soluble and membrane proteins, rather than just transmembrane α‐helices. The apparent rarity of kinks in soluble proteins is due to the relative infrequency of long helices (≥20 residues) in these proteins. We compare length‐matched sets of soluble and membrane helices, and find that the frequency of kinks, the role of Proline, the patterns of other amino acid around kinks (allowing for the expected differences in amino acid distributions between the two types of protein), and the effects of hydrogen bonds are the same for the two types of helices. In both types of protein, helices that contain Proline in the second and subsequent turns are very frequently kinked. However, there are a sizeable proportion of kinked helices that do not contain a Proline in either their sequence or sequence homolog. Moreover, we observe that in soluble proteins, kinked helices have a structural preference in that they typically point into the solvent. Proteins 2014; 82:1960–1970. © 2014 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

A model for the coupling of alpha-helix and tertiary contact formation

Peptides corresponding to excised alpha-helical segments of natural proteins can spontaneously form helices in solution. However, peptide helices are usually substantially less stable in solution than in the structural context of a folded protein, because of the additional interactions possible between helices in a protein. Such interactions can be thought of as coupling helix formation and tertiary contact formation. The relative energetic contributions of the two processes to the total energy of the folded state of a protein is a matter of current debate. To investigate this balance, an extended helix-coil model (XHC) that incorporates both effects has been constructed. The model treats helix formation with the Lifson-Roig formalism, which describes helix initiation and propagation through cooperative local interactions. The model postulates an additional parameter representing participation of a site in a tertiary contact. In the model, greater helix stability can be achieved through combinations of these short-range and long-range interactions. For instance, stronger tertiary contacts can compensate for helices with little intrinsic stability. By varying the strength of the nonlocal interactions, the model can exhibit behavior consistent with a variety of qualitative models describing the relative importance of secondary and tertiary structure. Moreover, the model is explicit in that it can be used to fit experimental data to individual peptide sequences, providing a means to quantify the two contributions on a common energetic basis.     

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.