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Bayesian model based clustering analysis: application to a molecular dynamics trajectory of the HIV-1 integrase catalytic core.

This work describes the application of a Bayesian method for clustering protein conformations sampled during a molecular dynamics simulation of the HIV-1 integrase catalytic core. A clustering analysis is carried out under the assumption of normal distribution without fixing the number of clusters in advance. Some performance measures, such as posterior probability and class cross entropy, are used to determine the most probable set of clusters. The Bayesian clustering method results in meaningful groups identifying transitions between conformational ensembles. The dihedral angles involved in such transitions are also examined in detail. The conformations in high dimensional space are projected into 3D space employing a multidimensional scaling technique to provide a visual inspection.

Algorithms↗

Studying the folding process of the acylphosphatase from Sulfolobus solfataricus. A comparative analysis with other proteins from the same superfamily.

The folding process of the acylphosphatase from Sulfolobus solfataricus (Sso AcP) has been followed, starting from the fully unfolded state, using a variety of spectroscopic probes, including intrinsic fluorescence, circular dichroism, and ANS binding. The results indicate that an ensemble of partially folded or misfolded species form rapidly on the submillisecond time scale after initiation of folding. This conformational ensemble produces a pronounced downward curvature in the Chevron plot, appears to possess a content of secondary structure similar to that of the native state, as revealed by far-UV circular dichroism, and appears to have surface-exposed hydrophobic clusters, as indicated by the ability of this ensemble to bind to 8-anilino-1-naphthalenesulfonic acid (ANS). Sso AcP folds from this conformational state with a rate constant of ca. 5 s(-1) at pH 5.5 and 37 degrees C. A minor slow exponential phase detected during folding (rate constant of 0.2 s(-1) under these conditions) is accelerated by cyclophilin A and is absent in a mutant of Sso AcP in which alanine replaces the proline residue at position 50. This indicates that for a lower fraction of Sso AcP molecules the folding process is rate-limited by the cis-trans isomerism of the peptide bond preceding Pro50. A comparative analysis with four other homologous proteins from the acylphosphatase superfamily shows that sequence hydrophobicity is an important determinant of the conformational stability of partially folded states that may accumulate during folding of a protein. A low net charge and a high propensity to form alpha-helical structure also emerge as possibly important determinants of the stability of partially folded states. A significant correlation is also observed between folding rate and hydrophobic content of the sequence within this superfamily, lending support to the idea that sequence hydrophobicity, in addition to relative contact order and conformational stability of the native state, is a key determinant of folding rate.

Acid Anhydride Hydrolases↗

Molecular flexibility in protein-DNA interactions.

In living cells protein-DNA interactions are fundamental processes. Here, we compare the 3D structures of several DNA-binding proteins frequently determined with and without attached DNA. We studied the global structure (backbone-traces) as well as the local structure (binding sites) by comparing pair-wise the related atoms. The DNA-interaction sites of uncomplexed proteins show conspicuously high local structural flexibility. Binding to DNA results in specific local conformations, which are clearly distinct from the unbound states. The adaptation of the protein's binding site to DNA can never be described by the lock and key model but in all cases by the induced fit model. Conformational changes in the seven protein backbone traces take place in different ways. Two of them dock onto DNA without a significant change, while the other five proteins are characterized by a backbone conformation change caused by DNA docking. In the case of three proteins of the latter group the DNA-complexed conformation also occurs in a few uncomplexed structures. This behavior can be described by a conformational ensemble, which is narrowed down by DNA docking until only one single DNA-complexed conformation occurs. Different docking models are discussed and each of the seven proteins is assigned to one of them.

Binding Sites↗

Calculation of protein ionization equilibria with conformational sampling: pK(a) of a model leucine zipper, GCN4 and barnase.

The use of conformational ensembles provided by nuclear magnetic resonance (NMR) experiments or generated by molecular dynamics (MD) simulations has been regarded as a useful approach to account for protein motions in the context of pK(a) calculations, yet the idea has been tested occasionally. This is the first report of systematic comparison of pK(a) estimates computed from long multiple MD simulations and NMR ensembles. As model systems, a synthetic leucine zipper, the naturally occurring coiled coil GCN4, and barnase were used. A variety of conformational averaging and titration curve-averaging techniques, or combination thereof, was adopted and/or modified to investigate the effect of extensive global conformational sampling on the accuracy of pK(a) calculations. Clustering of coordinates is proposed as an approach to reduce the vast diversity of MD ensembles to a few structures representative of the average electrostatic properties of the system in solution. Remarkable improvement of the accuracy of pK(a) predictions was achieved by the use of multiple MD simulations. By using multiple trajectories the absolute error in pK(a) predictions for the model leucine zipper was reduced to as low as approximately 0.25 pK(a) units. The validity, advantages, and limitations of explicit conformational sampling by MD, compared with the use of an average structure and a high internal protein dielectric value as means to improve the accuracy of pK(a) calculations, are discussed.

Bacterial Proteins↗

Motional dynamics of residues in a beta-hairpin peptide measured by 13C-NMR relaxation.

Structurally characterizing partially folded peptides is problematic given the nature of their transient conformational states. 13C-NMR relaxation data can provide information on the geometry of bond rotations, motional restrictions, and correlated bond rotations of the backbone and side chains and, therefore, is one approach that is useful to assess the presence of folded structure within a conformational ensemble. A peptide 12mer, R1GITVNG7KTYGR12, has been shown to partially fold in a relatively stable beta-hairpin conformation centered at NG. Here, five residues, G2, V5, G7, Y10, G11, were selectively 13C-enriched, and 13C-NMR relaxation experiments were performed to obtain auto- and cross-correlation motional order parameters, correlation times, bond rotation angular variances, and bond rotational correlation coefficients. Our results indicate that, of the three glycines, G7 within the hairpin beta-turn displays the most correlated phi(t),psi(t) rotations with its axis of rotation bisecting the angle defined by the H-C-H bonds. These positively correlated bond rotations give rise to "twisting" type motions of the HCH group. V5 and Y10 phi,psi bond rotations are also positively correlated, with their CbetaCalphaH groups undergoing similar "twisting" type motions. Motions of near-terminal residues G2 and G11 are less restricted and less correlated and are best described as wobbling-in-a-cone. V5 and Y10 side-chain motions, aside from being highly restricted, were found to be correlated with phi,psi bond rotations. At 303 K, where the hairpin is considered "unfolded," the peptide exists in a transient, collapsed state because backbone and side-chain motions of V5, G7, and Y10 remain relatively restricted, unlike their counterparts in GXG-based tripeptides. These results provide unique information toward understanding conformational variability in the unfolded state of proteins, which is necessary to solve the protein folding problem.

Hot Temperature↗

Stabilization of a type VI turn in a family of linear peptides in water solution.

The sources of the stability of a type VI turn formed with high population in the cis isomeric form of an unblocked six residue peptide, Ser1-Tyr2-Pro3-Tyr4-Asp5-Val6 (SYPYDV), were investigated by making extensive amino acid substitutions at residues 2, 4 and 5. Several NMR parameters indicate the presence of the turn, including significant upfield shifts of the proton resonances of the cis proline, a small 3JHN alpha coupling constant for residue 2, a cross-turn d alpha N(i,i+2) from residue 2 to residue 4 and in increased mole fraction of the cis form in the conformational ensemble. By these criteria, a number of peptides were found to contain significant populations of type VI turn conformers in the cis form of the peptide. The NMR parameters are highly dependent on the sequence of the peptide, and are strongly correlated with each other and with the population of type VI turn. The greatest populations of turn conformations were observed for peptides of the general form AA-Ar-Pro-Ar-Hp, where AA represents any amino acid, Ar an aromatic residue and Hp a small hydrophilic residue. There is no evidence in the form of lowered amide proton temperature coefficients for direct hydrogen bonding as a primary source of turn stability. Instead, the major stabilizing factor, indicated by the strong dependence of the turn population on the presence of aromatic (not hydrophobic) residues at positions 2 and 4, is the stacking of the aromatic and proline rings. A measurable preference for deprotonated aspartate at position 5, which is not part of the turn itself, and the destabilization of the turn at high and low pH, indicate that electrostatic interactions between the unblocked N terminus and the aspartate carboxyl group also act to stabilize the turn conformation when the Ar-Pro-Ar sequence is present. Implications for stabilization of local elements of secondary structure during the earliest events in protein folding are discussed.

Amino Acid Sequence↗

Ensemble modulation as an origin of denaturant-independent hydrogen exchange in proteins.

Native state hydrogen exchange (HX) has become a powerful tool for the analysis of conformational states that exist under native conditions. However, the interpretation of HX data in terms of conformational fluctuations is still controversial. In particular, it has been shown that many residues display exchange behavior that is independent of denaturant concentration. It has been postulated that this lack of denaturant dependence results from local fluctuations that do not expose appreciable amounts of buried surface area. Here, we use a general thermodynamic description of HX to explore the different possibilities for this behavior. We find that the denaturant dependence seen in HX experiments under native conditions is not a de facto indication of the amount of surface area exposure required for exchange. Instead, this behavior results from the relatively homogenous character of the conformational ensemble that exists under native conditions and the non-specific nature of denaturant effects. Furthermore, a comparison of the HX behavior from a stabilized mutant of Staphylococcal nuclease (SNase) with that predicted for the wild-type SNase from the COREX algorithm suggests that denaturant-independent exchange of many residues is consistent with significant (approximately 10 %) surface area exposure for this protein.

Algorithms↗

Representation of target-bound drugs by computed conformers: implications for conformational libraries.

BACKGROUND: The increasing number of known protein structures provides valuable information about pharmaceutical targets. Drug binding sites are identifiable and suitable lead compounds can be proposed. The flexibility of ligands is a critical point for the selection of potential drugs. Since computed 3D structures of millions of compounds are available, the knowledge of their binding conformations would be a great benefit for the development of efficient screening methods. RESULTS: Integration of two public databases allowed superposition of conformers for 193 approved drugs with 5507 crystallised target-bound counterparts. The generation of 9600 drug conformers using an atomic force field was carried out to obtain an optimal coverage of the conformational space. Bioactive conformations are best described by a conformational ensemble: half of all drugs exhibit multiple active states, distributed over the entire range of the reachable energy and conformational space.A number of up to 100 conformers per drug enabled us to reproduce the bound states within a similarity threshold of 1.0 angstroms in 70% of all cases. This fraction rises to about 90% for smaller or average sized drugs. CONCLUSION: Single drugs adopt multiple bioactive conformations if they interact with different target proteins. Due to the structural diversity of binding sites they adopt conformations that are distributed over a broad conformational space and wide energy range. Since the majority of drugs is well represented by a predefined low number of conformers (up to 100) this procedure is a valuable method to compare compounds by three-dimensional features or for fast similarity searches starting with pharmacophores. The underlying 9600 generated drug conformers are downloadable from the Super Drug Web site 1. All superpositions are visualised at the same source. Additional conformers (110,000) of 2400 classified WHO-drugs are also available.

Amino Acid Sequence↗

Assessing the performance of OMEGA with respect to retrieving bioactive conformations.

OMEGA is a rule-based program which rapidly generates conformational ensembles of small molecules. We have varied the parameters which control the nature of the ensembles generated by OMEGA in a statistical fashion (D-optimal) with the aim of increasing the probability of generating bioactive conformations. Thirty-six drug-like ligands from different ligand-protein complexes determined by high-resolution (< or =2.0A) X-ray crystallography have been analyzed. Statistically significant models (Q(2)> or =0.75) confirm that one can increase the performance of OMEGA by modifying the parameters. Twenty-eight of the bioactive conformations were retrieved when using a low-energy cut-off (5 kcal/mol), a low RMSD value (0.6A) for duplicate removal, and a maximum of 1000 output conformations. All of those that were not retrieved had eight or more rotatable bonds. The duplicate removal parameter was found to have the largest impact on retrieval of bioactive conformations, and the maximum number of conformations also affected the results considerably. The input conformation was found to influence the results largely because certain bond angles can prevent the bioactive conformation from being generated as a low-energy conformation. Pre-optimizing the input structures with MMFF94s improved the results significantly. We also investigated the performance of OMEGA in connection with database searching. The shape-matching program Rapid Overlay of Chemical Structures (ROCS) was used as search tool. Two multi-conformational databases were built from the MDDR database plus the 36 compounds; one large (maximum 1000 conformations/mol) and one small (maximum 100 conformations/mol). Both databases provided satisfactory results in terms of retrieval. ROCS was able to rank 35 out of 36 X-ray structures among the top 500 hits from the large database.

Algorithms↗

Origins of helix-coil switching in a light-sensitive peptide.

Intramolecular cross-linking of peptides by the light-sensitive compound diiodoacetamideazobenzene has been shown to permit reversible photocontrol of the helix-coil transition. Cross-linking between Cys residues spaced at i and i + 7 positions with the trans form of the linker was found to produce a decreased helix content compared to that of the non-cross-linked peptide. Photoisomerization to the cis form of the linker led to substantially higher helix content than in the non-cross-linked peptide. Detailed conformational analysis of the system leads to the conclusion that photocontrol of helix content does not involve specific interactions between the linker and the peptide. Instead, the change in peptide helix content caused by photoisomerization can be predicted by comparing the length ranges of the cis and trans forms of the linker with the expected distance distribution of the Cys attachment points in the intrinsic conformational ensemble of the peptide. The analysis presented here should help to guide the use of these and related linkers for the conformational control of a variety of peptide and protein systems.

Amino Acid Sequence↗

Discovery of nonpeptide, peptidomimetic peptidase inhibitors that target alternate enzyme active site conformations.

Structure-generating programs provide rational methods to rapidly design novel scaffolds targeting the biologic receptor of choice. Recent research has demonstrated proteins equilibrate between families of conformations (ensembles) for which drug design may target. New methods are currently being developed utilizing structure-generating programs to target alternate enzyme conformations in an attempt to overcome the challenge of developing therapeutically useful molecules. These new methods provide the potential to overcome bioavailability problems encountered with peptide and peptide-like molecules by identifying novel small molecule scaffolds.

Binding Sites↗

RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case.

Nuclear magnetic resonance (NMR) provides structural and dynamic information reflecting an average, often non-linear, of multiple solution-state conformations. Therefore, a single optimized structure derived from NMR refinement may be misleading if the NMR data actually result from averaging of distinct conformers. It is hypothesized that a conformational ensemble generated by a valid molecular dynamics (MD) simulation should be able to improve agreement with the NMR data set compared with the single optimized starting structure. Using a model system consisting of two sequence-related self-complementary ribonucleotide octamers for which NMR data was available, 0.3 ns particle mesh Ewald MD simulations were performed in the AMBER force field in the presence of explicit water and counterions. Agreement of the averaged properties of the molecular dynamics ensembles with NMR data such as homonuclear proton nuclear Overhauser effect (NOE)-based distance constraints, homonuclear proton and heteronuclear (1)H-(31)P coupling constant (J) data, and qualitative NMR information on hydrogen bond occupancy, was systematically assessed. Despite the short length of the simulation, the ensemble generated from it agreed with the NMR experimental constraints more completely than the single optimized NMR structure. This suggests that short unrestrained MD simulations may be of utility in interpreting NMR results. As expected, a 0.5 ns simulation utilizing a distance dependent dielectric did not improve agreement with the NMR data, consistent with its inferior exploration of conformational space as assessed by 2-D RMSD plots. Thus, ability to rapidly improve agreement with NMR constraints may be a sensitive diagnostic of the MD methods themselves.

Hydrogen Bonding↗

Molecular dynamics simulations of peptide fragments from hen lysozyme: insight into non-native protein conformations.

Molecular dynamics simulations of four peptides taken from the hen lysozyme sequence have been used to generate models for non-native protein conformations. Comparisons between the different peptides and with experimental data for denatured lysozyme and peptide fragments provides insight into the characteristics of the conformational ensembles populated in these non-native states and the dependence of their structural features on the amino acid sequence. For the denatured conformers populated local contacts dominate in determining the properties observed in the trajectories, all four peptides showing similar characteristics. These include a significant increase in the number of main-chain O(i)-NH(i+2) hydrogen bonds and hydrogen bonds involving side-chain groups, this increase compensating to a large extent for the loss of hydrogen bonds involved in helical or beta-sheet secondary structure in the native fold, and the generation of a population of collapsed states with local clusterings of hydrophobic groups. The hydrophobic clusters enable at least partial burial of many side-chains exposed by the loss of tertiary contacts on denaturation and provide models that may explain the experimentally observed protection of amides from hydrogen exchange and the existence of residual secondary structure in non-native species of lysozyme. The results suggest that this approach has an important role to play in aiding the interpretation of experimental data for conformationally disordered non-native states of proteins.

Animals↗

Cortical cartography using the discrete conformal approach of circle packings.

Cortical flattening algorithms are becoming more widely used to assist in visualizing the convoluted cortical gray matter sheet of the brain. Metric-based approaches are the most common but suffer from high distortions. Conformal, or angle-based algorithms, are supported by a comprehensive mathematical theory. The conformal approach that uses circle packings is versatile in the manipulation and display of results. In addition, it offers some new and interesting metrics that may be useful in neuroscientific analysis and are not available through numerical partial differential equation conformal methods. In this paper, we begin with a brief description of cortical "flat" mapping, from data acquisition to map displays, including a brief review of past flat mapping approaches. We then describe the mathematics of conformal geometry and key elements of conformal mapping. We introduce the mechanics of circle packing and discuss its connections with conformal geometry. Using a triangulated surface representing a cortical hemisphere, we illustrate several manipulations available using circle packing methods and describe the associated "ensemble conformal features" (ECFs). We conclude by discussing current and potential uses of conformal methods in neuroscience and computational anatomy.

Algorithms↗

Formation of native and non-native interactions in ensembles of denatured ACBP molecules from paramagnetic relaxation enhancement studies.

Paramagnetic relaxation enhancement measurements in the denatured state of ACBP have provided distance restraints that have been used in computer simulations to determine the conformational ensembles representing the denatured states of ACBP under a variety of conditions. A detailed comparison of the residual structure in the denatured state of ACBP under these different conditions has enabled us to infer that regions in the N and C-terminal parts of the protein sequence have a high tendency to interact in the unfolded state under physiological conditions. By comparing the structural features in the denatured states with those in the transition state for folding we also provided new insights into the mechanism of formation of the native state of this protein.

Animals↗

Is allostery an intrinsic property of all dynamic proteins?

Allostery involves coupling of conformational changes between two widely separated binding sites. The common view holds that allosteric proteins are symmetric oligomers, with each subunit existing in "at least" two conformational states with a different affinity for ligands. Recent observations such as the allosteric behavior of myoglobin, a classical example of a nonallosteric protein, call into question the existing allosteric dogma. Here we argue that all (nonfibrous) proteins are potentially allosteric. Allostery is a consequence of re-distributions of protein conformational ensembles. In a nonallosteric protein, the binding site shape may not show a concerted second-site change and enzyme kinetics may not reflect an allosteric transition. Nevertheless, appropriate ligands, point mutations, or external conditions may facilitate a population shift, leading a presumably nonallosteric protein to behave allosterically. In principle, practically any potential drug binding to the protein surface can alter the conformational redistribution. The question is its effectiveness in the redistribution of the ensemble, affecting the protein binding sites and its function. Here, we review experimental observations validating this view of protein allostery.

Allosteric Regulation↗

MIMUMBA revisited: torsion angle rules for conformer generation derived from X-ray structures.

A method has been developed which automatically generates SMARTS patterns for four-atomic torsional fragments, searches experimental structures in the Cambridge Crystallographic Database, and obtains rules for preferred torsion angles in drug-size molecules. These rules can be used for exhaustive conformational analysis using the popular conformer generator OMEGA. This approach results in an overall improvement of quality and coverage of conformational space when comparing conformer ensembles generated by this method with results obtained by using the default OMEGA setup. In particular, the percentage of structures with at least one conformation closer than 0.5 A to the X-ray structure improves from 84% to 92% in a test set of 11 027 experimental structures from the CSD. Moreover, the average RMS distance of the closest conformation to the X-ray structure improves from 0.30 to 0.22 A.

Chemistry↗

The glycine residue in cyclic lactam analogues of galanin(1-16)-NH2 is important for stabilizing an N-terminal helix.

The neuropeptide galanin is a 29- or 30-residue peptide whose physiological functions are mediated by G-protein-coupled receptors. Galanin's agonist activity has been shown to be associated with the N-terminal sequence, galanin(1-16). Conformational investigations previously carried out on full-length galanin have, furthermore, indicated the presence of a helical conformation in the neuropeptide's N-terminal domain. Several cyclic lactam analogues of galanin(1-16)-NH2 were prepared in an attempt to stabilize an N-terminal helix in the peptide. Here we describe and compare the solution conformational properties of these analogues in the presence of SDS micelles as determined by NMR, CD, and fluorescence spectroscopy. Differences in CD spectral profiles were observed among the compounds that were studied. Both c[D4, K8]Gal(1-16)-NH2 and c[D4,K8]Gal(1-12)-NH2 adopted stable helical conformations in the micelle solution. On the basis of the analyses of their respective alpha H chemical shifts and NOE patterns, this helix was localized to the first 10 residues. The distance between the aromatic rings of Trp2 and Tyr9 in c[D4, K8]Gal(1-16)-NH2 was determined to be 10.8 +/- 3 A from fluorescence resonance energy transfer measurements. This interchromophore spacing was found to be more consistent with a helical structure than an extended one. Removal of the Gly1 residue in compounds c[D4,K8]Gal(1-16)-NH2 and c[D4, K8]Gal(1-12)-NH2 resulted in a loss of helical conformation and a concomitant reduction in binding potency at the GalR1 receptor but not at the GalR2 receptor. The nuclear Overhauser enhancements obtained for the Gly1 deficient analogues did, however, reveal the presence of nascent helical structures within the N-terminal sequence. Decreasing the ring structure size in c[D4, K8]Gal(1-16)-NH2 by replacing Lys8 with an ornithine residue or by changing the position of the single lysine residue from eight to seven was accompanied by a complete loss of helical structure and dramatically reduced receptor affinity. It is concluded from the data obtained for the series of cyclic galanin(1-16)-NH2 analogues that both the ring structure size and the presence of an N-terminal glycine residue are important for stabilizing an N-terminal helix in these compounds. However, although an N-terminal helix constitutes a predominant portion of the conformational ensemble for compounds c[D4,K8]Gal(1-16)-NH2 and c[D4, K8]Gal(1-12)-NH2, these peptides nevertheless are able to adopt other conformations in solution. Consequently, the correlation between the ability of the cyclic galanin analogues to adopt an N-terminal helix and bind to the GalR1 receptor may be considered as a working hypothesis.

Alanine↗