Generalized Crick equations for modeling noncanonical coiled coils

Crick envisaged the alpha-helical coiled coil to result from systematic bending of an alpha-helix such that every seventh residue was structurally equivalent, and he derived equations for the coordinates of the backbone atoms. Crick's predictions were vindicated experimentally and coiled-coil sequences were shown to have hydrophobic residues alternately spaced 3 and 4 residues apart. Nonetheless, in some coiled coils such canonical heptad repeats are interrupted by inserts of 3 or 4 residues generating decad and hendecad motifs. The supercoiling of the coiled coils varies with the sequence pattern, being left- or right-handed in purely heptad-based or hendecad-based motifs, respectively. To model coiled coils with a mixture of motifs, we describe how Crick's equations can be modified for cases where the pitch is not constant. Using the analogy of the bending of a beam, we took the tilt angle to change linearly with distance along the major helix and the pitch of a motif to be affected by neighboring motifs depending on the rigidity of the alpha-helical strands. We tested our approach by fitting the two-, three-, and four-stranded noncanonical coiled coils of GrpE, hemagglutinin, and tetrabrachion. The backbone atoms of the model and crystal structures agreed with root mean square deviations of <1.1 A.     

Historical review: another 50th anniversary--new periodicities in coiled coils

In 1953, Francis Crick and Linus Pauling both proposed models of supercoiled helices (‘coiled coils’) for the structure of keratin. These were the first attempts at modelling the tertiary structure of a protein. Crick emphasized the packing mode of the side-chains (‘knobs-into-holes’), which required a periodicity of seven residues over two helical turns (7/2) and a supercoil in the opposite sense of the constituent helices. By contrast, Pauling envisaged a broader set of periodicities (4/1, 7/2, 18/5, 15/4, 11/3) and supercoils of both senses. Crick's model became canonical and the ‘heptad repeat’ essentially synonymous with coiled coils, but 50 years later new crystal structures and protein sequences show that the less common periodicities envisaged by Pauling also occur in coiled coils, adding a variant packing mode (‘knobs-to-knobs’) to the standard model. Pauling's laboratory notebooks suggest that he searched unsuccessfully for this packing mode in 1953.     

Core side-chain packing and backbone conformation in Lpp-56 coiled-coil mutants

Native proteins exhibit precise geometric packing of atoms in their hydrophobic interiors. Nonetheless, controversy remains about the role of core side-chain packing in specifying and stabilizing the folded structures of proteins. Here we investigate the role of core packing in determining the conformation and stability of the Lpp-56 trimerization domain. The X-ray crystal structures of Lpp-56 mutants with alanine substitutions at two and four interior core positions reveal trimeric coiled coils in which the twist of individual helices and the helix-helix spacing vary significantly to achieve the most favored superhelical packing arrangement. Introduction of each alanine "layer" into the hydrophobic core destabilizes the superhelix by 1.4 kcal mol(-1). Although the methyl groups of the alanine residues pack at their optimum van der Waals contacts in the coiled-coil trimer, they provide a smaller component of hydrophobic interactions than bulky hydrophobic side-chains to the thermodynamic stability. Thus, specific side-chain packing in the hydrophobic core of coiled coils are important determinants of protein main-chain conformation and stability.     

Open-and-shut cases in coiled-coil assembly: alpha-sheets and alpha-cylinders

The coiled coil is a ubiquitous protein-folding motif. It generally is accepted that coiled coils are characterized by sequence patterns known as heptad repeats. Such patterns direct the formation and assembly of amphipathic alpha-helices, the hydrophobic faces of which interface in a specific manner first proposed by Crick and termed "knobs-into-holes packing". We developed software, SOCKET, to recognize this packing in protein structures. As expected, in a trawl of the protein data bank, we found examples of canonical coiled coils with a single contiguous heptad repeat. In addition, we identified structures with multiple, overlapping heptad repeats. This observation extends Crick's original postulate: Multiple, offset heptad repeats help explain assemblies with more than two helices. Indeed, we have found that the sequence offset of the multiple heptad repeats is related to the coiled-coil oligomer state. Here we focus on one particular sequence motif in which two heptad repeats are offset by two residues. This offset sets up two hydrophobic faces separated by approximately 150 degrees -160 degrees around the alpha-helix. In turn, two different combinations of these faces are possible. Either similar or opposite faces can interface, which leads to open or closed multihelix assemblies. Accordingly, we refer to these two forms as alpha-sheets and alpha-cylinders. We illustrate these structures with our own predictions and by reference to natural variants on these designs that have recently come to light.     

Antiparallel four-stranded coiled coil specified by a 3-3-1 hydrophobic heptad repeat

Coiled-coil sequences in proteins commonly share a seven-amino acid repeat with nonpolar side chains at the first (a) and fourth (d) positions. We investigate here the role of a 3-3-1 hydrophobic repeat containing nonpolar amino acids at the a, d, and g positions in determining the structures of coiled coils using mutants of the GCN4 leucine zipper dimerization domain. When three charged residues at the g positions in the parental sequence are replaced by nonpolar alanine or valine side chains, stable four-helix structures result. The X-ray crystal structures of the tetramers reveal antiparallel, four-stranded coiled coils in which the a, d, and g side chains interlock in a combination of knobs-into-knobs and knobs-into-holes packing. Interfacial interactions in a coiled coil can therefore be prescribed by hydrophobic-polar patterns beyond the canonical 3-4 heptad repeat. The results suggest that the conserved, charged residues at the g positions in the GCN4 leucine zipper can impart a negative design element to disfavor thermodynamically more stable, antiparallel tetramers.     

Probing designability via a generalized model of helical bundle geometry

Because the space of folded protein structures is highly degenerate, with recurring secondary and tertiary motifs, methods for representing protein structure in terms of collective physically relevant coordinates are of great interest. By collapsing structural diversity to a handful of parameters, such methods can be used to delineate the space of designable structures (i.e., conformations that can be stabilized with a large number of sequences)—a crucial task for de novo protein design. We first demonstrate this on natural α-helical coiled coils using the Crick parameterization. We show that over 95% of known coiled-coil structures are within  1-Å C_α root mean square deviation of a Crick-ideal backbone. Derived parameters show that natural geometric space of coiled coils is highly restricted and can be represented by “allowed” conformations amidst a potential continuum of conformers. Allowed structures have (1) restricted axial offsets between helices, which differ starkly between parallel and anti-parallel structures; (2) preferred superhelical radii, which depend linearly on the oligomerization state; (3) pronounced radius-dependent a- and d-position amino acid propensities; and (4) discrete angles of rotation of helices about their axes, which are surprisingly independent of oligomerization state or orientation. In all, we estimate the space of designable coiled-coil structures to be reduced at least 160-fold relative to the space of geometrically feasible structures. To extend the benefits of structural parameterization to other systems, we developed a general mathematical framework for parameterizing arbitrary helical structures, which reduces to the Crick parameterization as a special case. The method is successfully validated on a set of non-coiled-coil helical bundles, frequent in channels and transporter proteins, which show significant helix bending but not supercoiling. Programs for coiled-coil parameter fitting and structure generation are provided via a web interface at http://www.gevorggrigoryan.com/cccp/, and code for generalized helical parameterization is available upon request.     

Conformational specificity of the lac repressor coiled-coil tetramerization domain

Predictive understanding of how the folded, functional shape of a native protein is encoded in the linear sequence of its amino acid residues remains an unsolved challenge in modern structural biology. Antiparallel four-stranded coiled coils are relatively simple protein structures that embody a heptad sequence repeat and rich diversity for tertiary packing of alpha-helices. To explore specific sequence determinants of the lac repressor coiled-coil tetramerization domain, we have engineered a set of buried nonpolar side chains at the a-, d-, and e-positions into the hydrophobic interior of the dimeric GCN4 leucine zipper. Circular dichroism and equilibrium ultracentrifugation studies show that this core variant (GCN4-pAeLV) forms a stable tetrameric structure with a reversible and highly cooperative thermal unfolding transition. The X-ray crystal structure at 1.9 A reveals that GCN4-pAeLV is an antiparallel four-stranded coiled coil of the lac repressor type in which the a, d, and e side chains associate by means of combined knobs-against-knobs and knobs-into-holes packing with a characteristic interhelical offset of 0.25 heptad. Comparison of the side chain shape and packing in the antiparallel tetramers shows that the burial of alanine residues at the e positions between the neighboring helices of GCN4-pAeLV dictates both the antiparallel orientation and helix offset. This study fills in a gap in our knowledge of the determinants of structural specificity in antiparallel coiled coils and improves our understanding of how specific side chain packing forms the teritiary structure of a functional protein.     

A parallel coiled-coil tetramer with offset helices

Specific helix-helix interactions are fundamental in assembling the native state of proteins and in protein-protein interfaces. Coiled coils afford a unique model system for elucidating principles of molecular recognition between alpha helices. The coiled-coil fold is specified by a characteristic seven amino acid repeat containing hydrophobic residues at the first (a) and fourth (d) positions. Nonpolar side chains spaced three and four residues apart are referred to as the 3-4 hydrophobic repeat. The presence of apolar amino acids at the e or g positions (corresponding to a 3-3-1 hydrophobic repeat) can provide new possibilities for close-packing of alpha-helices that includes examples such as the lac repressor tetramerization domain. Here we demonstrate that an unprecedented coiled-coil interface results from replacement of three charged residues at the e positions in the dimeric GCN4 leucine zipper by nonpolar valine side chains. Equilibrium circular dichroism and analytical ultracentrifugation studies indicate that the valine-containing mutant forms a discrete alpha-helical tetramer with a significantly higher stability than the parent leucine-zipper molecule. The 1.35 A resolution crystal structure of the tetramer reveals a parallel four-stranded coiled coil with a three-residue interhelical offset. The local packing geometry of the three hydrophobic positions in the tetramer conformation is completely different from that seen in classical tetrameric structures yet bears resemblance to that in three-stranded coiled coils. These studies demonstrate that distinct van der Waals interactions beyond the a and d side chains can generate a diverse set of helix-helix interfaces and three-dimensional supercoil structures.     

Packing and hydrophobicity effects on protein folding and stability: effects of beta-branched amino acids, valine and isoleucine, on the formation and stability of two-stranded alpha-helical coiled coils/leucine zippers.

The aim of this study was to examine the differences between hydrophobicity and packing effects in specifying the three-dimensional structure and stability of proteins when mutating hydrophobes in the hydrophobic core. In DNA-binding proteins (leucine zippers), Leu residues are conserved at positions "d," and beta-branched amino acids, Ile and Val, often occur at positions "a" in the hydrophobic core. In order to discern what effect this selective distribution of hydrophobes has on the formation and stability of two-stranded alpha-helical coiled coils/leucine zippers, three Val or three Ile residues were simultaneously substituted for Leu at either positions "a" (9, 16, and 23) or "d" (12, 19, and 26) in both chains of a model coiled coil. The stability of the resulting coiled coils was monitored by CD in the presence of Gdn.HCl. The results of the mutations of Ile to Val at either positions "a" or "d" in the reduced or oxidized coiled coils showed a significant hydrophobic effect with the additional methylene group in Ile stabilizing the coiled coil (delta delta G values range from 0.45 to 0.88 kcal/mol/mutation). The results of mutations of Leu to Ile or Val at positions "a" in the reduced or oxidized coiled coils showed a significant packing effect in stabilizing the coiled coil (delta delta G values range from 0.59 to 1.03 kcal/mol/mutation). Our results also indicate the subtle control hydrophobic packing can have not only on protein stability but on the conformation adopted by the amphipathic alpha-helices. These structural findings correlate with the observation that in DNA-binding proteins, the conserved Leu residues at positions "d" are generally less tolerant of amino acid substitutions than the hydrophobic residues at positions "a."     

Restraint-driven formation of alpha-helical coiled coils in molecular dynamics simulations.

The alpha-helical coiled coil motif is among the first characterized and widely found architecture of protein structures. We report here a fast and reliable approach of simulated annealing molecular dynamics (SA/MD) for predicting the three-dimensional structures of various alpha-helical coiled coils of heptad repeat. One key element of our simulation involves a geometric restraint requiring residues occupying the first and fourth positions of the heptad to orient to the angle of their respective statistical average derived from a survey of coiled-coil structures deposited in the Protein Data Bank. Another is the incorporation of subunit rotation and inversion operations for generating symmetrized protein assemblies during the dynamics simulations. The procedure is fully automated and can be applied to different oligomerization states of identical subunits, as well as both parallel and antiparallel arrangements. Despite simplicity, the formation of five coiled-coil prototype systems driven by the restraint-based SA/MD approach shows that the level of prediction accuracy achieved previously by more elaborate procedures can be retained. The present work thus provides validation of a simulation approach that can be employed to utilize a wide variety of knowledge-based geometric restraints for structural prediction of symmetrical or pseudo-symmetrical protein systems.     

28 The study of tRNA modifications by molecular dynamics

Modified nucleosides are prevalent in tRNA. Experimental studies reveal that modifications play an important role in tuning tRNA activity. In this study, molecular dynamics (MD) simulations were used to investigate how modifications alter tRNA structure and dynamics. The X-ray crystal structures of tRNA-Asp, tRNA-Phe, and tRNA-iMet, both with and without modifications, were used as initial structures for 333-ns time-scale MD trajectories with AMBER. For each tRNA molecule, three independent trajectory calculations were performed. Force field parameters were built using the RESP procedure of Cieplak et al. for 17 nonstandard tRNA residues. The global root-mean-square deviations (RMSDs) of atomic positions show that modifications only introduce significant rigidity to tRNA-Phe’s global structure. Interestingly, regional RMSDs of anticodon stem-loop suggest that modified tRNA has more rigid structure compared to the unmodified tRNA in this domain. The anticodon RMSDs of the modified tRNAs, however, are higher than those of corresponding unmodified tRNAs. These findings suggest that rigidity of the anticodon arm is essential for tRNA translocation in the ribosome complex, and, on the other hand, flexibility of anticodon might be critical for anticodon–codon recognition. We also measure the angle between the 3D L-shaped arms of tRNA; backbone atoms of acceptor stem and TψC stem loop are selected to indicate one vector, and backbone atoms of anticodon stem and D stem loop are selected to indicate the other vector. By measuring the angle between two vectors, we find that the initiator tRNA has a narrower range of hinge motion compared to tRNA-Asp and tRNA-Phe, which are elongator tRNA. This suggests that elongator tRNAs, which might require significant flexibility in this hinge to transition from the A–to-P site in the ribosome, have evolved to specifically accommodate this need.     

Buried polar residues in coiled-coil interfaces

Coiled coils, estimated to constitute 3-5% of the encoded residues in most genomes, are characterized by a heptad repeat, (abcdefg)(n), where the buried a and d positions form the interface between multiple alpha-helices. Although generally hydrophobic, a substantial fraction ( approximately 20%) of these a- and d-position residues are polar or charged. We constructed variants of the well-characterized coiled coil GCN4-p1 with a single polar residue (Asn, Gln, Ser, or Thr) at either an a or a d position. The stability and oligomeric specificity of each variant were measured, and crystal structures of coiled-coil trimers with threonine or serine at either an a or a d position were determined. The structures show how single polar residues in the interface affect not only local packing, but also overall coiled-coil geometry as seen by changes in the Crick supercoil parameters and core cavity volumes.     

Influence of a heptad repeat stutter on the pH‐dependent conformational behavior of the central coiled‐coil from influenza hemagglutinin HA2

The coiled‐coil is one of the most common protein structural motifs. Amino acid sequences of regions that participate in coiled‐coils contain a heptad repeat in which every third then forth residue is occupied by a hydrophobic residue. Here we examine the consequences of a “stutter,” a deviation of the idealized heptad repeat that is found in the central coiled‐coil of influenza hemagluttinin HA2. Characterization of a peptide containing the native stutter‐containing HA2 sequence, as well as several variants in which the stutter was engineered out to restore an idealized heptad repeat pattern, revealed that the stutter is important for allowing coiled‐coil formation in the WT HA2 at both neutral and low pH (7.1 and 4.5). By contrast, all variants that contained idealized heptad repeats exhibited marked pH‐dependent coiled‐coil formation with structures forming much more stably at low pH. A crystal structure of one variant containing an idealized heptad repeat, and comparison to the WT HA2 structure, suggest that the stutter distorts the optimal interhelical core packing arrangement, resulting in unwinding of the coiled‐coil superhelix. Interactions between acidic side chains, in particular E69 and E74 (present in all peptides studied), are suggested to play a role in mediating these pH‐dependent conformational effects. This conclusion is partially supported by studies on HA2 variant peptides in which these positions were altered to aspartic acid. These results provide new insight into the structural role of the heptad repeat stutter in HA2. Proteins 2014; 82:2220–2228. © 2014 Wiley Periodicals, Inc.     

Fast detection of common geometric substructure in proteins.

We consider the problem of identifying common three-dimensional substructures between proteins. Our method is based on comparing the shape of the alpha-carbon backbone structures of the proteins in order to find three-dimensional (3D) rigid motions that bring portions of the geometric structures into correspondence. We propose a geometric representation of protein backbone chains that is compact yet allows for similarity measures that are robust against noise and outliers. This representation encodes the structure of the backbone as a sequence of unit vectors, defined by each adjacent pair of alpha-carbons. We then define a measure of the similarity of two protein structures based on the root mean squared (RMS) distance between corresponding orientation vectors of the two proteins. Our measure has several advantages over measures that are commonly used for comparing protein shapes, such as the minimum RMS distance between the 3D positions of corresponding atoms in two proteins. A key advantage is that this new measure behaves well for identifying common substructures, in contrast with position-based measures where the nonmatching portions of the structure dominate the measure. At the same time, it avoids the quadratic space and computational difficulties associated with methods based on distance matrices and contact maps. We show applications of our approach to detecting common contiguous substructures in pairs of proteins, as well as the more difficult problem of identifying common protein domains (i.e., larger substructures that are not necessarily contiguous along the protein chain).     

Pitch diversity in α-helical coiled coils

Two complementary methods for measuring local pitch based on heptad position in α-helical coiled coils are described and applied to six crystal structures. The results reveal a diversity of pitch values: two-stranded coiled coils appear to have pitch values near 150 Å the values for three- and four-stranded coiled coils range closer to 200 Å. The methods also provide a rapid and sensitive gauge of local coiled-coil conformation. Polar or charged residues in the apolar interface between coiled-coil helices markedly affect local pitch values, suggesting a connection between pitch uniformity and coiled-coil stability. Moreover, the identification of a skip residue (heptad frame shift) in the hemaglutinin glycoprotein of influenza virus (HA) allows interpretation of local pitch changes. These results on relatively short coiled-coil structures have relevance for the much longer fibrous proteins (many of which have skip residues) whose detailed structures are not yet established. We also show that local pitch values from molecular dynamics predictions of the GCN4 leucine zipper are in striking agreement with the high-resolution crystal structure—a result not readily discerned by direct comparison of atomic coordinates. Taken together, these methods reveal specific aspects of coiled-coil structure which may escape detection by global analyses of pitch. © 1993 Wiley-Liss, Inc.     

A procedure for refining a coiled coil protein structure using x-ray fiber diffraction and modeling

We describe a combined use of experimental and simulation techniques to configure side chains in a coiled coil structure. As already demonstrated in a previous work, x-ray diffraction patterns from hard alpha-keratin fibers in the 5.15 A meridian zone reflect the global configuration of the chi(1) dihedral angle of the coiled coil side chains. Molecular simulations, such as energy minimization and molecular dynamics, and rotameric representation in the PDB, are used here on a heterodimeric coiled coil to investigate the dihedral angle distribution along the sequence. Different procedures have been used to build the structure, the quality assessment was based on the agreement between the simulated diffraction patterns and the experimental ones in the fingerprint region of coiled coils (5.15 A). The best one for building a realistic coiled coil structure consists of placing the side chains using molecular dynamics (MD) simulations, followed by side chain positioning using SMD or SCWRL procedures. The side chains and the backbone are equilibrated during the MD until they reach an equilibrium state for the t/g(+) ratio. Positioning the side chains on the resulting backbone, using the above procedures, gives rise to a well-defined 5.15 A meridian reflection.     

Effects of charged amino acids at b and c heptad positions on specificity and stability of four-chain coiled coils

An understanding of the balance of chemical forces responsible for protein stability and specificity of structure is essential for the success of efforts in protein design. Specifically, electrostatic interactions between charged amino acids have been explored extensively to understand the contribution of this force to protein stability. Much research on the importance of electrostatic interactions as specificity and stability determinants in two-stranded coiled coils has been done, but there remains significant controversy about the magnitude of the attractive forces using such systems. We have developed a four-stranded coiled-coil system with charged residues incorporated at b and c heptad positions to explore the role of charge interactions. Here, we test quantitatively the effects of varying sidechain length on the magnitude of such electrostatic interactions. We synthesized peptides containing either aspartate or ornithine at both b and c heptad positions and tested their ability to self-associate and to hetero-associate with one another and with peptides containing glutamate or lysine at the same positions. We find that interactions between glutamate and either lysine or ornithine are more favorable than the corresponding interactions involving aspartate. In each case, charged interactions provide additional stability to coiled coils, although helix propensity effects may play a significant role in determining the overall stability of these structures.