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.     

Is counterion delocalization responsible for collapse in RNA folding?

Although energetic and phylogenetic methods have been very successful for prediction of nucleic acid secondary structures, arrangement of these secondary structure elements into tertiary structure has remained a difficult problem. Here we explore the packing arrangements of DNA, RNA, and DNA/RNA hybrid molecules in crystals. In the conventional view, the highly charged double helix will be pushed toward isolation by favorable solvation effects; interactions with other like-charged stacks would be strongly disfavored. Contrary to this expectation, we find that most of the cases analyzed ( approximately 80%) exhibit specific, preferential packing between elements of secondary structure, which falls into three categories: (i) interlocking of major grooves of two helices, (ii) side-by-side parallel packing of helices, and (iii) placement of the ribose-phosphate backbone ridge of one helix into the major groove of another. The preponderance of parallel packing motifs is especially surprising. This category is expected to be maximally disfavored by charge repulsion. Instead, it comprises in excess of 50% of all packing interactions in crystals of A-form RNA and has also been observed in crystal structures of large RNA molecules. To explain this puzzle, we introduce a novel model for RNA folding. A simple calculation suggests that the entropy gained by a cloud of condensed cations surrounding the helices more than offsets the Coulombic repulsion of parallel arrangements. We propose that these condensed counterions are responsible for entropy-driven RNA collapse, analogous to the role of the hydrophobic effect in protein folding.     

Analysis of Four-Way Junctions in RNA Structures

RNA secondary structures can be divided into helical regions composed of canonical Watson-Crick and related base pairs, as well as single-stranded regions such as hairpin loops, internal loops, and junctions. These elements function as building blocks in the design of diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze existing RNA four-way junctions in terms of base-pair interactions and 3D configurations. Specifically, we identify nine broad junction families according to coaxial stacking patterns and helical configurations. We find that helices within junctions tend to arrange in roughly parallel and perpendicular patterns and stabilize their conformations using common tertiary motifs such as coaxial stacking, loop-helix interaction, and helix packing interaction. Our analysis also reveals a number of highly conserved base-pair interaction patterns and novel tertiary motifs such as A-minor-coaxial stacking combinations and sarcin/ricin motif variants. Such analyses of RNA building blocks can ultimately help in the difficult task of RNA 3D structure prediction.     

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.     

Does 5S RNA from E. coli have a pseudoknotted structure?

Chemical modification and limited enzymatic hydrolysis on isolated E. coli 5S RNA have provided informations on the secondary- and tertiary structure compatible with pseudoknotted structures for the A- and B-conformers of the molecule. Changes in the accessibility and reactivity of nucleotides in loop C and at the stem of helix IV in two different 5S RNA conformers are highly suggestive for interactions between bases C35 to C37 with G105 to G107 for the A-form and C38 to U40 and A94 to G96 with additional interactions of C35, C37 with G98 and G100 for the B-form. In both cases the molecules are folded forming pseudoknots and two quasi--continuous double stranded helices with coaxial stacking. The two structures are in perfect agreement with the biochemical data concerning the stability of the molecule and the chemical reactivities of individual nucleotides of the 5S RNA A- and B-conformers.     

Packing of transmembrane helices in bacteriorhodopsin folding: structure and thermodynamics

We propose a coarse-grained (CG) model to study the native structure and physical properties of helical membrane proteins (HMPs) using off-lattice computer simulations. Instead of considering sequence heterogeneity explicitly, we model its effect on the packing of helices by employing a mean packing parameter r(0), which is calculated from an all-atom (AA) model. Specifically, this CG model is applied to investigate the packing of helices in bacteriorhodopsin (BR), and predicts the seven helix bundle structure of BR with a root mean square deviation (RMSD) in coordinates of helix backbone atoms (N, C, C(alpha)) of 3.99 A from its crystal structure. This predicted structure is further refined in an AA model by Amber and the refined structure has a RMSD (in coordinates of helix backbone atoms) of 2.64 A. The predicted packing position, tilting angle, and orientation angle of each helix in the refined structure are consistent with experimental data and their physical origins can be well understood in our model. Our results show that a reasonably good structure of BR can be predicted by using such a dual-scale approach, provided that its secondary structure is known. Starting from a random initial configuration, the folded structure can be obtained in days using a regular desktop computer. Various thermodynamic properties of helix packing of BR are also investigated in this CG model.     

An unusual structure formed by antisense-target RNA binding involves an extended kissing complex with a four-way junction and a side-by-side helical alignment

The antisense RNA CopA binds to the leader region of the repA mRNA (target: CopT). Previous studies on CopA-CopT pairing in vitro showed that the dominant product of antisense RNA-mRNA binding is not a full RNA duplex. We have studied here the structure of CopA-CopT complex, combining chemical and enzymatic probing and computer graphic modeling. CopI, a truncated derivative of CopA unable to bind CopT stably, was also analyzed. We show here that after initial loop-loop interaction (kissing), helix propagation resulted in an extended kissing complex that involves the formation of two intermolecular helices. By introducing mutations (base-pair inversions) into the upper stem regions of CopA and CopT, the boundaries of the two newly formed intermolecular helices were delimited. The resulting extended kissing complex represents a new type of four-way junction structure that adopts an asymmetrical X-shaped conformation formed by two helical domains, each one generated by coaxial stacking of two helices. This structure motif induces a side-by-side alignment of two long intramolecular helices that, in turn, facilitates the formation of an additional intermolecular helix that greatly stabilizes the inhibitory CopA-CopT RNA complex. This stabilizer helix cannot form in CopI-CopT complexes due to absence of the sequences involved. The functional significance of the three-dimensional models of the extended kissing complex (CopI-CopT) and the stable complex (CopA-CopT) are discussed.     

Consecutive terminal GU pairs stabilize RNA helices

Consecutive GU pairs at the ends of RNA helices provide significant thermodynamic stability between -1.0 and -3.8 kcal/mol at 37 °C, which is equivalent to approximately 2 orders of magnitude in the value of a binding constant. The thermodynamic stabilities of GU pairs depend on the sequence, stacking orientation, and position in the helix. In contrast to GU pairs in the middle of a helix that may be destabilizing, all consecutive terminal GU pairs contribute favorable thermodynamic stability. This work presents measured thermodynamic stabilities for 30 duplexes containing two, three, or four consecutive GU pairs at the ends of RNA helices and a model to predict the thermodynamic stabilities of terminal GU pairs. Imino proton NMR spectra show that the terminal GU nucleotides form hydrogen-bonded pairs. Different orientations of terminal GU pairs can have different conformations with equivalent thermodynamic stabilities. These new data and prediction model will help improve RNA secondary structure prediction, identification of miRNA target sequences with GU pairs, and efforts to understand the fundamental physical forces directing RNA structure and energetics.     

High-resolution prediction of protein helix positions and orientations

We have developed a new method for predicting helix positions in globular proteins that is intended primarily for comparative modeling and other applications where high precision is required. Unlike helix packing algorithms designed for ab initio folding, we assume that knowledge is available about the qualitative placement of all helices. However, even among homologous proteins, the corresponding helices can demonstrate substantial differences in positions and orientations, and for this reason, improperly positioned helices can contribute significantly to the overall backbone root-mean-square deviation (RMSD) of comparative models. A helix packing algorithm for use in comparative modeling must obtain high precision to be useful, and for this reason we utilize an all-atom protein force field (OPLS) and a Generalized Born continuum solvent model. To reduce the computational expense associated with using a detailed, physics-based energy function, we have developed new hierarchical and multiscale algorithms for sampling the helices and flanking loops. We validate the method using a test suite of 33 cases, which are drawn from a diverse set of high-resolution crystal structures. The helix positions are reproduced with an average backbone RMSD of 0.6 A, while the average backbone RMSD of the complete loop-helix-loop region (i.e., the helix with the surrounding loops, which are also repredicted) is 1.3 A.     

Helix Capping in RNA Structure

Helices are an essential element in defining the three-dimensional architecture of structured RNAs. While internal basepairs in a canonical helix stack on both sides, the ends of the helix stack on only one side and are exposed to the loop side, thus susceptible to fraying unless they are protected. While coaxial stacking has long been known to stabilize helix ends by directly stacking two canonical helices coaxially, based on analysis of helix-loop junctions in RNA crystal structures, herein we describe helix capping, topological stacking of a helix end with a basepair or an unpaired nucleotide from the loop side, which in turn protects helix ends. Beyond the topological protection of helix ends against fraying, helix capping should confer greater stability onto the resulting composite helices. Our analysis also reveals that this general motif is associated with the formation of tertiary structure interactions. Greater knowledge about the dynamics at the helix-junctions in the secondary structure should enhance the prediction of RNA secondary structure with a richer set of energetic rules and help better understand the folding of a secondary structure into its three-dimensional structure. These together suggest that helix capping likely play a fundamental role in driving RNA folding.     

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.     

Simulation studies on bacteriorhodopsin bundle of transmembrane α segments

Bacteriorhodopsin (BR) is a membrane protein which pumps protons through the plasma membrane. Seven transmembrane BR helical segments are subjected to simulation studies in order to investigate the packing process of transmembrane helices. A Monte Carlo simulated annealing protocol is employed to optimize the helix bundle system. Helix packing is optimized according to a semi-empirical potential mainly composed of six components: a bilayer potential, a crossing angle potential, a helix dipole potential, a helix-helix distance potential, a helix orientation potential and a helix-helix distance restraint potential (a loop potential). Necessary parameters are derived from theoretical studies and statistical analysis of experimentally determined protein structures. The structures from the simulations are compared with the experimentally determined structures in terms of geometry. The structures generated show similar shapes to the experimentally suggested structure even without the helix-helix distance restraint potential. However, the relative locations of individual helices were reproduced only when the helix-helix distance restraint potential was used with restraint conditions. Our results suggest that transmembrane helix bundles resembling those observed experimentally may be generated by simulations using simple potentials. Received: 19 April 1999 / Revised version: 6 September 1999 / Accepted: 17 September 1999     

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.     

Close packing of helices 3 and 12 of 16 S rRNA is required for the normal ribosome function

The along-groove packing motif is a quasi-reciprocal arrangement of two RNA double helices in which a backbone of each helix is closely packed within the minor groove of the other helix. At the center of the inter-helix contact, a GU base pair in one helix packs against a Watson-Crick base pair in the other helix. Here, based on in vivo selection from a combinatorial gene library of 16 S rRNA and on functional characterization of the selected clones, we demonstrate that the normal ribosome performance requires that helices 3 and 12 be closely packed. In some clones the Watson-Crick and GU base pairs exchange in their positions between the two helices, which affects neither the quality of the helix packing, nor the ribosome function. On the other hand, perturbations in the close packing usually lead to a substantial drop in the ribosome activity. The functionality of the clones containing such perturbations may depend on the presence of particular elements in the vicinity of the area of contact between helices 3 and 12. Such cases do not exist in natural 16 S rRNA, and their selection enriches our knowledge of the constraints imposed on the structure of ribosomal RNA in functional ribosomes.     

Helix packing moments reveal diversity and conservation in membrane protein structure

Helical membrane proteins are more tightly packed and the packing interactions are more diverse than those found in helical soluble proteins. Based on a linear correlation between amino acid packing values and interhelical propensity, we propose the concept of a helix packing moment to predict the orientation of helices in helical membrane proteins and membrane protein complexes. We show that the helix packing moment correlates with the helix interfaces of helix dimers of single pass membrane proteins of known structure. Helix packing moments are also shown to help identify the packing interfaces in membrane proteins with multiple transmembrane helices, where a single helix can have multiple contact surfaces. Analyses are described on class A G protein-coupled receptors (GPCRs) with seven transmembrane helices. We show that the helix packing moments are conserved across the class A family of GPCRs and correspond to key structural contacts in rhodopsin. These contacts are distinct from the highly conserved signature motifs of GPCRs and have not previously been recognized. The specific amino acid types involved in these contacts, however, are not necessarily conserved between subfamilies of GPCRs, indicating that the same protein architecture can be supported by a diverse set of interactions. In GPCRs, as well as membrane channels and transporters, amino acid residues with small side-chains (Gly, Ala, Ser, Cys) allow tight helix packing by mediating strong van der Waals interactions between helices. Closely packed helices, in turn, facilitate interhelical hydrogen bonding of both weakly polar (Ser, Thr, Cys) and strongly polar (Asn, Gln, Glu, Asp, His, Arg, Lys) amino acid residues. We propose the use of the helix packing moment as a complementary tool to the helical hydrophobic moment in the analysis of transmembrane sequences.     

General architecture of the alpha-helical globule

A model is presented for the arrangement of alpha-helices in globular proteins. In the model, helices are placed on certain ribs of "quasi-spherical" polyhedra. The polyhedra are chosen so as to allow the close packing of helices around a hydrophobic core and to stress the collective interactions of the individual helices. The model predicts a small set of stable architectures for alpha-helices in globular proteins and describes the geometries of the helix packings. Some of the predicted helix arrangements have already been observed in known protein structures; others are new. An analysis of the three-dimensional structures of all proteins for which co-ordinates are available shows that the model closely approximates the arrangements and packing of helices actually observed. The average deviations of the real helix axes from those in the model polyhedra is +/- 20 degrees in orientation and +/- 2 A in position (1 A = 0.1 nm). We also show that for proteins that are not homologous, but whose helix arrangements are described by the same polyhedron, the root-mean-square difference in the position of the C alpha atoms in the helices is 1.6 to 3.0 A.     

Proline-induced distortions of transmembrane helices

Proline residues in the transmembrane (TM) alpha-helices of integral membrane proteins have long been suspected to play a key role for helix packing and signal transduction by inducing regions of helix distortion and/or dynamic flexibility (hinges). In this study we try to characterise the effect of proline on the geometric properties of TM alpha-helices. We have examined 199 transmembrane alpha-helices from polytopic membrane proteins of known structure. After examining the location of proline residues within the amino acid sequences of TM helices, we estimated the helix axes either side of a hinge and hence identified a hinge residue. This enabled us to calculate helix kink and swivel angles. The results of this analysis show that proline residues occur with a significant concentration in the centre of sequences of TM alpha-helices. In this location, they may induce formation of molecular hinges, located on average about four residues N-terminal to the proline residue. A superposition of proline-containing TM helices structures shows that the distortion induced is anisotropic and favours certain relative orientations (defined by helix kink and swivel angles) of the two helix segments.     

Secondary structure of the central region of bacteriophage MS2 RNA. Conservation and biological significance

The RNA of the Escherichia coli RNA phages is highly structured with 75% of the nucleotides estimated to take part in base-pairing. We have used enzymatic and chemical sensitivity of nucleotides, phylogenetic sequence comparison and the phenotypes of constructed mutants to develop a secondary structure model for the central region (900 nucleotides) of the group I phage MS2. The RNA folds into a number of, mostly irregular, helices and is further condensed by several long-distance interactions. There is substantial conservation of helices between the related groups I and II, attesting to the relevance of discrete RNA folding. In general, the secondary structure is thought to be needed to prevent annealing of plus and minus strand and to confer protection against RNase. Superimposed, however, are features required to regulate translation and replication. The MS2 RNA section studied here contains three translational start sites, as well as the binding sites for the coat protein and the replicase enzyme. Considering the density of helices along the RNA, it is not unexpected to find that all these sites lie in helical regions. This fact, however, does not mean that these sites are recognized as secondary structure elements by their interaction partners. This holds true only for the coat protein binding site. The other four sites function in the unfolded state and the stability of the helix in which they are contained serves to negatively control their accessibility. Mutations that stabilize helices containing ribosomal binding sites reduce their efficiency and vice versa. Comparison of homologous helices in different phage RNAs indicates that base substitutions have occurred in such a way that the thermodynamic stability of the helix is maintained. The evolution of individual helices shows several distinct size-reduction patterns. We have observed codon deletions from loop areas and shortening of hairpins by base-pair deletions from either the bottom, the middle or the top of stem structures. Evidence for the coaxial stacking of some helical segments is discussed.     

Transmembrane helix orientation and dynamics: insights from ensemble dynamics with solid-state NMR observables

As the major component of membrane proteins, transmembrane helices embedded in anisotropic bilayer environments adopt preferential orientations that are characteristic or related to their functional states. Recent developments in solid-state nuclear magnetic resonance (SSNMR) spectroscopy have made it possible to measure NMR observables that can be used to determine such orientations in a native bilayer environment. A quasistatic single conformer model is frequently used to interpret the SSNMR observables, but important motional information can be missing or misinterpreted in the model. In this work, we have investigated the orientation of the single-pass transmembrane domain of viral protein ”u“ (VpuTM) from HIV-1 by determining an ensemble of structures using multiple conformer models based on the SSNMR ensemble dynamics technique. The resulting structure ensemble shows significantly larger orientational fluctuations while the ensemble-averaged orientation is compatible with the orientation based on the quasistatic model. This observation is further corroborated by comparison with the VpuTM orientation from comparative molecular dynamics simulations in explicit bilayer membranes. SSNMR ensemble dynamics not only reveals the importance of transmembrane helix dynamics in interpretation of SSNMR observables, but also provides a means to simultaneously extract both transmembrane helix orientation and dynamics information from the SSNMR measurements.     

FR3D: finding local and composite recurrent structural motifs in RNA 3D structures

New methods are described for finding recurrent three-dimensional (3D) motifs in RNA atomic-resolution structures. Recurrent RNA 3D motifs are sets of RNA nucleotides with similar spatial arrangements. They can be local or composite. Local motifs comprise nucleotides that occur in the same hairpin or internal loop. Composite motifs comprise nucleotides belonging to three or more different RNA strand segments or molecules. We use a base-centered approach to construct efficient, yet exhaustive search procedures using geometric, symbolic, or mixed representations of RNA structure that we implement in a suite of MATLAB programs, “Find RNA 3D” (FR3D). The first modules of FR3D preprocess structure files to classify base-pair and -stacking interactions. Each base is represented geometrically by the position of its glycosidic nitrogen in 3D space and by the rotation matrix that describes its orientation with respect to a common frame. Base-pairing and base-stacking interactions are calculated from the base geometries and are represented symbolically according to the Leontis/Westhof basepairing classification, extended to include base-stacking. These data are stored and used to organize motif searches. For geometric searches, the user supplies the 3D structure of a query motif which FR3D uses to find and score geometrically similar candidate motifs, without regard to the sequential position of their nucleotides in the RNA chain or the identity of their bases. To score and rank candidate motifs, FR3D calculates a geometric discrepancy by rigidly rotating candidates to align optimally with the query motif and then comparing the relative orientations of the corresponding bases in the query and candidate motifs. Given the growing size of the RNA structure database, it is impossible to explicitly compute the discrepancy for all conceivable candidate motifs, even for motifs with less than ten nucleotides. The screening algorithm that we describe finds all candidate motifs whose geometric discrepancy with respect to the query motif falls below a user-specified cutoff discrepancy. This technique can be applied to RMSD searches. Candidate motifs identified geometrically may be further screened symbolically to identify those that contain particular basepair types or base-stacking arrangements or that conform to sequence continuity or nucleotide identity constraints. Purely symbolic searches for motifs containing user-defined sequence, continuity and interaction constraints have also been implemented. We demonstrate that FR3D finds all occurrences, both local and composite and with nucleotide substitutions, of sarcin/ricin and kink-turn motifs in the 23S and 5S ribosomal RNA 3D structures of the H. marismortui 50S ribosomal subunit and assigns the lowest discrepancy scores to bona fide examples of these motifs. The search algorithms have been optimized for speed to allow users to search the non-redundant RNA 3D structure database on a personal computer in a matter of minutes.