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.     

The building of protein structures from alpha-carbon coordinates

A procedure for the construction of complete protein structures from only alpha-carbon coordinates is described. This involves building the backbone by sequential addition of Pro, Gly, or Ala residues. This main chain structure is then refined using molecular dynamics. Side chains are constructed by sequential addition of atoms with intermediate molecular dynamics refinement. For alpha lytic protease (a structure that is mostly beta sheet) a backbone root mean square deviation (RMSD) of 0.19 A and an overall RMSD of 1.24 A from the crystallographic coordinates are attained. For troponin C (67% alpha-helix), where the coordinates are available only for the alpha-carbons, a backbone RMSD of 0.41 A and an overall RMSD of 1.68 A are attained (fits kindly provided by Dr. Michael James and Natalie Strynadka). For flavodoxin a backbone RMSD of 0.49 A and an overall RMSD of 1.64 A were attained.     

Solution structure and proposed domain domain recognition interface of an acyl carrier protein domain from a modular polyketide synthase

Polyketides are a medicinally important class of natural products. The architecture of modular polyketide synthases (PKSs), composed of multiple covalently linked domains grouped into modules, provides an attractive framework for engineering novel polyketide-producing assemblies. However, impaired domain-domain interactions can compromise the efficiency of engineered polyketide biosynthesis. To facilitate the study of these domain-domain interactions, we have used nuclear magnetic resonance (NMR) spectroscopy to determine the first solution structure of an acyl carrier protein (ACP) domain from a modular PKS, 6-deoxyerythronolide B synthase (DEBS). The tertiary fold of this 10-kD domain is a three-helical bundle; an additional short helix in the second loop also contributes to the core helical packing. Superposition of residues 14-94 of the ensemble on the mean structure yields an average atomic RMSD of 0.64 +/- 0.09 Angstrom for the backbone atoms (1.21 +/- 0.13 Angstrom for all non-hydrogen atoms). The three major helices superimpose with a backbone RMSD of 0.48 +/- 0.10 Angstrom (0.99 +/- 0.11 Angstrom for non-hydrogen atoms). Based on this solution structure, homology models were constructed for five other DEBS ACP domains. Comparison of their steric and electrostatic surfaces at the putative interaction interface (centered on helix II) suggests a model for protein-protein recognition of ACP domains, consistent with the previously observed specificity. Site-directed mutagenesis experiments indicate that two of the identified residues influence the specificity of ACP recognition.     

Comparison of the transmembrane helices of bovine rhodopsin in the crystal structure and the C α template based on cryo-electron microscopy maps and sequence analysis of the G protein-coupled receptors

G protein-coupled receptors (GPCR) are activated by a diverse array of extracellular signals, ranging from light to polypeptide molecules. The receptors propagate these signals intracellularly using G protein secondary messenger pathways. A common feature in the architecture of these receptors is their seven transmembrane domains. The first crystal structure of a GPCR, bovine rhodopsin, has recently been solved at 2.8 Å. We compared the seven membrane-spanning helices (TMH) from the crystal structure of bovine rhodopsin with those from the low-resolution model of bovine rhodopsin based on the cryo-electron microscopy structure of frog rhodopsin developed by Dr Joyce Baldwin. The model developed by Baldwin used a consensus sequence approach to predict the rotational position of each helix with respect to the other six helices. Superposition of the entire helix bundle of the Baldwin model with the crystal structure gave a RMS difference (RMSD) of 3.2 Å for the 198 C f atoms which suggests a high level of similarity in the arrangement of the helices. Except for TMH IV (RMSD of 4.0 Å), the position of corresponding helices within the helix bundle overlapped well. The superposition of individual helices showed that the RMSD values over 3 Å in the global superposition were largely due to one or more of the following: (i) differences in the unraveling and kinks for these helices, (ii) translation of TMH perpendicular to the membrane and (iii) rotation of helices up to 31°, except for TMH IV in which an additional contribution to the RMSD came from the aforementioned observation. As other crystal structures of GPCRs become available, a comparison with the Baldwin consensus model may reveal larger differences than those observed here.     

FoldGPCR: Structure prediction protocol for the transmembrane domain of G protein‐coupled receptors from class A

Building reliable structural models of G protein‐coupled receptors (GPCRs) is a difficult task because of the paucity of suitable templates, low sequence identity, and the wide variety of ligand specificities within the superfamily. Template‐based modeling is known to be the most successful method for protein structure prediction. However, refinement of homology models within 1–3 Å Cα RMSD of the native structure remains a major challenge. Here, we address this problem by developing a novel protocol (foldGPCR) for modeling the transmembrane (TM) region of GPCRs in complex with a ligand, aimed to accurately model the structural divergence between the template and target in the TM helices. The protocol is based on predicted conserved inter‐residue contacts between the template and target, and exploits an all‐atom implicit membrane force field. The placement of the ligand in the binding pocket is guided by biochemical data. The foldGPCR protocol is implemented by a stepwise hierarchical approach, in which the TM helical bundle and the ligand are assembled by simulated annealing trials in the first step, and the receptor‐ligand complex is refined with replica exchange sampling in the second step. The protocol is applied to model the human β₂‐adrenergic receptor (β₂AR) bound to carazolol, using contacts derived from the template structure of bovine rhodopsin. Comparison with the X‐ray crystal structure of the β₂AR shows that our protocol is particularly successful in accurately capturing helix backbone irregularities and helix‐helix packing interactions that distinguish rhodopsin from β₂AR. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

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     

Robust Driving Forces for Transmembrane Helix Packing

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

The use of side-chain packing methods in modeling bacteriophage repressor and cro proteins.

In recent years, it has been repeatedly demonstrated that the coordinates of the main-chain atoms alone are sufficient to determine the side-chain conformations of buried residues of compact proteins. Given a perfect backbone, the side-chain packing method can predict the side-chain conformations to an accuracy as high as 1.2 Å RMS deviation (RMSD) with greater than 80% of the χ angles correct. However, similarly rigorous studies have not been conducted to determine how well these apply, if at all, to the more important problem of homology modeling per se. Specifically, if the available backbone is imperfect, as expected for practical application of homology modeling, can packing constraints alone achieve sufficiently accurate predictions to be useful? Here, by systematically applying such methods to the pairwise modeling of two repressor and two cro proteins from the closely related bacteriophages 434 and P22, we find that when the backbone RMSD is 0.8 Å, the prediction on buried side chain is accurate with an RMS error of 1.8 Å and approximately 70% of the χ angles correctly predicted. When the backbone RMSD is larger, in the range of 1.6–1.8 Å, the prediction quality is still significantly better than random, with RMS error at 2.2 Å on the buried side chains and 60% accuracy on χ angles. Together these results suggest the following rules-of-thumb for homology modeling of buried side chains. When the sequence identity between the modeled sequence and the template sequence is >50% (or, equivalently, the expected backbone RMSD is <1 Å), side-chain packing methods work well. When sequence identity is between 30–50%, reflecting a backbone RMS error of 1–2 Å, it is still valid to use side-chain packing methods to predict the buried residues, albeit with care. When sequence identity is below 30% (or backbone RMS error greater than 2 Å), the backbone constraint alone is unlikely to produce useful models. Other methods, such as those involving the use of database fragments to reconstruct a template backbone, may be necessary as a complementary guide for modeling.     

Improving prediction of helix–helix packing in membrane proteins using predicted contact numbers as restraints

One of the challenging problems in tertiary structure prediction of helical membrane proteins (HMPs) is the determination of rotation of α‐helices around the helix normal. Incorrect prediction of helix rotations substantially disrupts native residue–residue contacts while inducing only a relatively small effect on the overall fold. We previously developed a method for predicting residue contact numbers (CNs), which measure the local packing density of residues within the protein tertiary structure. In this study, we tested the idea of incorporating predicted CNs as restraints to guide the sampling of helix rotation. For a benchmark set of 15 HMPs with simple to rather complicated folds, the average contact recovery (CR) of best‐sampled models was improved for all targets, the likelihood of sampling models with CR greater than 20% was increased for 13 targets, and the average RMSD100 of best‐sampled models was improved for 12 targets. This study demonstrated that explicit incorporation of CNs as restraints improves the prediction of helix–helix packing. Proteins 2017; 85:1212–1221. © 2017 Wiley Periodicals, Inc.     

Identification of Helical Packing Motifs Common to Bacteriorhodopsin and G Protein-Coupled Receptors

A sequence analysis and comparison of transmembrane helices in bacteriorhodopsin (BR) and G protein-coupled receptors (GPCRs) is presented to identify potential regions of homology across protein families. The results show a common pattern of residues is conserved within the interhelical contact regions of BR that fit a knob-into-hole structural motif previously postulated for globular proteins and photosynthetic reaction centers. Based on an alignment of conserved prolines in transmembrane helices, it is inferred that analogous helix packing arrangements are possible in the rhodopsin-like GPCRs. Molecular models of GPCR helices V and VI indicate these interactions occur between aromatic and hydrophobic residues flanking the highly conserved prolines in these sequences. A similar packing arrangement is shown to occur in the X-ray structure of the melittin which also displays a unique pairing of proline-linked helices. The contact pattern identified is further applied to predict the packing of pairs of proline-containing helices in the pheromone-like and cAMP GPCRs. A potential role in stabilizing structure formation is also suggested for the contacts. The results and conclusions are supported by recent biophysical studies of zinc binding to kappa-opioid receptor mutants.     

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.     

Identification of Helical Packing Motifs Common to Bacteriorhodopsin and G Protein-Coupled Receptors

A sequence analysis and comparison of transmembrane helices in bacteriorhodopsin (BR) and G protein-coupled receptors (GPCRs) is presented to identify potential regions of homology across protein families. The results show a common pattern of residues is conserved within the interhelical contact regions of BR that fit a knob-into-hole structural motif previously postulated for globular proteins and photosynthetic reaction centers. Based on an alignment of conserved prolines in transmembrane helices, it is inferred that analogous helix packing arrangements are possible in the rhodopsin-like GPCRs. Molecular models of GPCR helices V and VI indicate these interactions occur between aromatic and hydrophobic residues flanking the highly conserved prolines in these sequences. A similar packing arrangement is shown to occur in the X-ray structure of the melittin which also displays a unique pairing of proline-linked helices. The contact pattern identified is further applied to predict the packing of pairs of proline-containing helices in the pheromone-like and cAMP GPCRs. A potential role in stabilizing structure formation is also suggested for the contacts. The results and conclusions are supported by recent biophysical studies of zinc binding to kappa-opioid receptor mutants.     

A large data set comparison of protein structures determined by crystallography and NMR: statistical test for structural differences and the effect of crystal packing

The existence of a large number of proteins for which both nuclear magnetic resonance (NMR) and X-ray crystallographic coordinates have been deposited into the Protein Data Bank (PDB) makes the statistical comparison of the corresponding crystal and NMR structural models over a large data set possible, and facilitates the study of the effect of the crystal environment and other factors on structure. We present an approach for detecting statistically significant structural differences between crystal and NMR structural models which is based on structural superposition and the analysis of the distributions of atomic positions relative to a mean structure. We apply this to a set of 148 protein structure pairs (crystal vs NMR), and analyze the results in terms of methodological and physical sources of structural difference. For every one of the 148 structure pairs, the backbone root-mean-square distance (RMSD) over core atoms of the crystal structure to the mean NMR structure is larger than the average RMSD of the members of the NMR ensemble to the mean, with 76% of the structure pairs having an RMSD of the crystal structure to the mean more than a factor of two larger than the average RMSD of the NMR ensemble. On average, the backbone RMSD over core atoms of crystal structure to the mean NMR is approximately 1 A. If non-core atoms are included, this increases to 1.4 A due to the presence of variability in loops and similar regions of the protein. The observed structural differences are only weakly correlated with the age and quality of the structural model and differences in conditions under which the models were determined. We examine steric clashes when a putative crystalline lattice is constructed using a representative NMR structure, and find that repulsive crystal packing plays a minor role in the observed differences between crystal and NMR structures. The observed structural differences likely have a combination of physical and methodological causes. Stabilizing attractive interactions arising from intermolecular crystal contacts which shift the equilibrium of the crystal structure relative to the NMR structure is a likely physical source which can account for some of the observed differences. Methodological sources of apparent structural difference include insufficient sampling or other issues which could give rise to errors in the estimates of the precision and/or accuracy.     

Solution structure of the catalytic domain of human stromelysin complexed with a hydrophobic inhibitor.

Stromelysin, a representative matrix metalloproteinase and target of drug development efforts, plays a prominent role in the pathological proteolysis associated with arthritis and secondarily in that of cancer metastasis and invasion. To provide a structural template to aid the development of therapeutic inhibitors, we have determined a medium-resolution structure of a 20-kDa complex of human stromelysin's catalytic domain with a hydrophobic peptidic inhibitor using multinuclear, multidimensional NMR spectroscopy. This domain of this zinc hydrolase contains a mixed beta-sheet comprising one antiparallel strand and four parallel strands, three helices, and a methionine-containing turn near the catalytic center. The ensemble of 20 structures was calculated using, on average, 8 interresidue NOE restraints per residue for the 166-residue protein fragment complexed with a 4-residue substrate analogue. The mean RMS deviation (RMSD) to the average structure for backbone heavy atoms is 0.91 A and for all heavy atoms is 1.42 A. The structure has good stereochemical properties, including its backbone torsion angles. The beta-sheet and alpha-helices of the catalytic domains of human stromelysin (NMR model) and human fibroblast collagenase (X-ray crystallographic model of Lovejoy B et al., 1994b, Biochemistry 33:8207-8217) superimpose well, having a pairwise RMSD for backbone heavy atoms of 2.28 A when three loop segments are disregarded. The hydroxamate-substituted inhibitor binds across the hydrophobic active site of stromelysin in an extended conformation. The first hydrophobic side chain is deeply buried in the principal S'1 subsite, the second hydrophobic side chain is located on the opposite side of the inhibitor backbone in the hydrophobic S'2 surface subsite, and a third hydrophobic side chain (P'3) lies at the surface.     

Packing of α-helices: Geometrical constraints and contact areas

The helical packing in sperm whale myoglobin has been examined. Using cylindrical co-ordinates based on each helix axis in turn, the overlap of the side-chain atoms of a helix with the surrounding atoms from other parts of the structure was 2.3 Å, but the distribution was not at all uniform and severe overlap occurred in at least one location for each helix. Simple axial translations or rotations of any helix in the native structure are not permitted motions. Translation perpendicular to the helix axis in at least one direction is not restricted by interlocking side-chains.The approach of two helices along the contact normal connecting their axes produces solvent exclusion effects at a distance of about 6 Å from the final position. The solvent-excluded area found in such interaction sites is equivalent to a large hydrophobic contribution to the free energy of association. The six principal sites correspond by themselves to 40% of the total area change in going from the extended sausage model to the native structure. The mean atom-packing densities for these sites and the standard deviations of these values are similar and are equal to that found for the protein as a whole.Helices of close-packed spheres form useful approximations to actual peptide helices. The helix of index number four corresponds closely to an α-helix. The required sphere size corresponds in volume to residues such as leucine or methionine. The predicted packing scheme for such helices corresponds to the three general classes of interactions actually seen.Making use of the geometry implied by the close-packed sphere helix, an algorithm is proposed for picking potentially strong helix-helix interaction sites in peptide chains of known sequence. When combined with preliminary secondary structure predictions, it is suggested that this algorithm might usefully restrict the search for these specific types of contact in the docking portion of a general folding program.     

Folding of Globular Proteins by Energy Minimization and Monte Carlo Simulations with Hydrophobic Surface Area Potentials

We describe an efficient method to calculate analytically the solvent accessible surface areas and their gradients in proteins for empirical force field calculations on serial and parallel computers. In an application to the small three helix bundle protein Er-10, energy minimizations and Monte Carlo simulations were performed with the empirical ECEPP/2 force field, which was extended by a protein solvent interaction term. We show that the NMR structure is stable when refined with the force field including the protein solvent interaction term, but large structural deviations are observed in energy minimization in vacuo. When we started from random structures with preformed helices and maintained the helical segments by dihedral angle constraints, the final structures with the lowest energies resembled the native form. The root-mean-square deviations for the backbone atoms of the three helices compared to the experimentally determined structure was 3 Å to 4 Å.     

Assembly of transmembrane helices of simple polytopic membrane proteins from sequence conservation patterns

The transmembrane (TM) domains of most membrane proteins consist of helix bundles. The seemingly simple task of TM helix bundle assembly has turned out to be extremely difficult. This is true even for simple TM helix bundle proteins, i.e., those that have the simple form of compact TM helix bundles. Herein, we present a computational method that is capable of generating native-like structural models for simple TM helix bundle proteins having modest numbers of TM helices based on sequence conservation patterns. Thus, the only requirement for our method is the presence of more than 30 homologous sequences for an accurate extraction of sequence conservation patterns. The prediction method first computes a number of representative well-packed conformations for each pair of contacting TM helices, and then a library of tertiary folds is generated by overlaying overlapping TM helices of the representative conformations. This library is scored using sequence conservation patterns, and a subsequent clustering analysis yields five final models. Assuming that neighboring TM helices in the sequence contact each other (but not that TM helices A and G contact each other), the method produced structural models of Calpha atom root-mean-square deviation (CA RMSD) of 3-5 A from corresponding crystal structures for bacteriorhodopsin, halorhodopsin, sensory rhodopsin II, and rhodopsin. In blind predictions, this type of contact knowledge is not available. Mimicking this, predictions were made for the rotor of the V-type Na(+)-adenosine triphosphatase without such knowledge. The CA RMSD between the best model and its crystal structure is only 3.4 A, and its contact accuracy reaches 55%. Furthermore, the model correctly identifies the binding pocket for sodium ion. These results demonstrate that the method can be readily applied to ab initio structure prediction of simple TM helix bundle proteins having modest numbers of TM helices.     

Crystal structure of the B-DNA hexamer d(CTCGAG): model for an A-to-B transition.

The crystal structure of the B-DNA hexamer d(CTCGAG) has been solved at 1.9 A resolution by iterative single isomorphous replacement, using the brominated derivative d(CG5BrCGAG), and refined to an R-factor of 18.6% for 120 nonhydrogen nucleic acid atoms and 32 water molecules. Although the central four base pairs form a typical B-form helix, several parameters suggest a transition to an A-like conformation at the termini. Based on this observation, a B-to-A transition was modeled, maintaining efficient base stacking across the junction. The wide minor groove (approximately 6.9 A) is reminiscent of that in the side-by-side double drug-DNA complexes and hosts a double spine of hydration. The global helix axes of the pseudo-continuous helices are at an acute angle of 60 degrees. The pseudocontinuous stacking is reinforced by the minor groove water structure extending between the two duplexes. The crossover point of two pairs of stacked duplexes is at the stacking junction, unlike that observed in the B-DNA decamers and dodecamers. This arrangement may have implications for the structure of a four-way DNA junction. The duplexes are arranged around a large (approximately 20 A diameter) channel centered on a 6(2) screw axis.