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Results for “conformational ensemble”

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PubMed1987

Reevaluation of rotamer populations for 1,6 linkages: reconciliation with potential energy calculations.

Applications of ensemble averaging to the solution conformation of model compounds for N-linked glycans are further investigated. Specifically, the interpretation usually applied to observed values of J5,6', a parameter reflecting the rotameric distribution about C5-C6 bonds (torsion angle omega in 1,6 glycosidic linkages) in 6-O-substituted hexopyranosides, was found to be inconsistent with populations derived from potential energy calculations. However, agreement between observed and calculated, ensemble-averaged values of J5,6' was obtained and the distribution of omega rotamers reinterpreted. Values of J5,6' that were previously interpreted as indicative of equipartition between two rotamers in fact reflect a marked preference for one of them. Additional potential energy terms, previously absent from energy calculations, are introduced and shown to be without effect on interpretations of omega rotamer distributions. From comparisons with both NMR relaxation and scalar coupling constant data, it is concluded that a simple empirical algorithm, HSEA, calculating van der Waals, exo-anomeric, and (as appropriate) hydrogen-bonding terms, is best suited for describing the population distributions in solution for oligosaccharides and N-linked glycans.

Carbohydrate Conformation↗

PubMed2026

One chromatin, many structures: From ensemble contact maps to single-cell 3D organization.

Understanding how chromatin folds in three dimensions remains challenging because most experimental assays capture low-dimensional projections of an underlying, highly heterogeneous polymer. Here, we present an ensemble-based interpretive framework built on the previously introduced Self-Returning Excluded Volume (SR-EV) model, a minimal generator of chromatin conformations using a nucleosome-indexed coarse-grained representation based on stochastic return rules and excluded-volume geometry. Despite its simplicity, SR-EV recapitulates key experimental signatures across scales: heterogeneous nanoscale packing domains resembling ChromEMT and ChromSTEM observations, sparse and highly variable single-configuration contact patterns analogous to single-cell chromosome conformation capture (Hi-C), and robust ensemble-level contact enrichment consistent with topologically associating domains (TADs). In this framework, Hi-C loop and TAD signatures are interpreted as ensemble-level statistical enrichments rather than invariant features of single-cell conformations. SR-EV is explicitly designed to generate large ensembles of complete three-dimensional chromatin configurations that can be projected consistently onto two-dimensional contact maps and one-dimensional genomic profiles. By introducing architectural-protein effects only through ensemble selection rather than explicit forces, SR-EV supports a separation between intrinsic polymer geometry and regulatory bias and suggests that TAD-like features can emerge as statistical enrichments rather than deterministic three-dimensional structures. Coordination number and probe-based accessibility computed directly from SR-EV provide a unified link between three-dimensional packing, two-dimensional contact maps, and one-dimensional genomic profiles. The main contribution of this work is to show, within a single coarse-grained framework, how these multimodal observables arise as linked projections of the same heterogeneous chromatin ensemble through averaging and conditional sampling. Together, these results establish SR-EV as a minimal and geometrically grounded mesoscale reference framework for interpreting how heterogeneous chromatin ensembles give rise to multimodal experimental observables while remaining consistent with the fact that chromatin organization is realized in individual cells.

Chromatin↗

PubMed2005

A structural model for unfolded proteins from residual dipolar couplings and small-angle x-ray scattering.

Natively unfolded proteins play key roles in normal and pathological biochemical processes. Despite their importance for function, this category of proteins remains beyond the reach of classical structural biology because of their inherent conformational heterogeneity. We present a description of the intrinsic conformational sampling of unfolded proteins based on residue-specific /Psi propensities from loop regions of a folded protein database and simple volume exclusion. This approach is used to propose a structural model of the 57-aa, natively disordered region of the nucleocapsid-binding domain of Sendai virus phosphoprotein. Structural ensembles obeying these simple rules of conformational sampling are used to simulate averaged residual dipolar couplings (RDCs) and small-angle x-ray scattering data. This protein is particularly informative because RDC data from the equally sized folded and unfolded domains both report on the unstructured region, allowing a quantitative analysis of the degree of order present in this part of the protein. Close agreement between experimental and simulated RDC and small-angle x-ray scattering data validates this simple model of conformational sampling, providing a precise description of local structure and dynamics and average dimensions of the ensemble of sampled structures. RDC data from two urea-unfolded systems are also closely reproduced. The demonstration that conformational behavior of unfolded proteins can be accurately predicted from the primary sequence by using a simple set of rules has important consequences for our understanding of the structure and dynamics of the unstructured state.

Models, Molecular↗

PubMed2005

A skewed-momenta method to efficiently generate conformational-transition trajectories.

We present a novel computational method, the skewed-momenta method (Skew'M), which applies a bias to the Maxwell distribution of initial momenta used to generate ensembles of trajectories. As a result, conformational transitions are accentuated and kinetic properties are calculated more effectively. The connection to the related puddle jumping method is discussed. A reweighting scheme permits the exact calculation of kinetic properties. Applications are presented for the rapid calculation of rate constants for molecular isomerization, and for the efficient reconstruction of free-energy profiles using a straightforward modification of the Jarzynski identity.

Chemistry, Physical↗

PubMed2005

HOPE: a homotopy optimization method for protein structure prediction.

We use a homotopy optimization method, HOPE, to minimize the potential energy associated with a protein model. The method uses the minimum energy conformation of one protein as a template to predict the lowest energy structure of a query sequence. This objective is achieved by following a path of conformations determined by a homotopy between the potential energy functions for the two proteins. Ensembles of solutions are produced by perturbing conformations along the path, increasing the likelihood of predicting correct structures. Successful results are presented for pairs of homologous proteins, where HOPE is compared to a variant of Newton's method and to simulated annealing.

Algorithms↗

PubMed2002

Distribution of molecular size within an unfolded state ensemble using small-angle X-ray scattering and pulse field gradient NMR techniques.

The size distribution of molecules within an unfolded state of the N-terminal SH3 domain of drk (drkN SH3) has been studied by small-angle X-ray scattering (SAXS) and pulsed-field-gradient NMR (PFG-NMR) methods. An empirical model to describe this distribution in the unfolded state ensemble has been proposed based on (i) the ensemble-averaged radius of gyration and hydrodynamic radius derived from the SAXS and PFG-NMR data, respectively, and (ii) a histogram of the size distribution of structures obtained from preliminary analyses of structural parameters recorded on the unfolded state. Results show that this unfolded state, U(exch), which exists in equilibrium with the folded state, F(exch), under non-denaturing conditions, is relatively compact, with the average size of conformers within the unfolded state ensemble only 30-40% larger than the folded state structure. In addition, the model predicts a significant overlap in the size range of structures comprising the U(exch) state with those in a denatured state obtained by addition of 2 M guanidinium chloride.

Animals↗

PubMed2000

Polymer principles of protein calorimetric two-state cooperativity.

The experimental calorimetric two-state criterion requires the van't Hoff enthalpy DeltaH(vH) around the folding/unfolding transition midpoint to be equal or very close to the calorimetric enthalpy DeltaH(cal) of the entire transition. We use an analytical model with experimental parameters from chymotrypsin inhibitor 2 to elucidate the relationship among several different van't Hoff enthalpies used in calorimetric analyses. Under reasonable assumptions, the implications of these DeltaH(vH)'s being approximately equal to DeltaH(cal) are equivalent: Enthalpic variations among denatured conformations in real proteins are much narrower than some previous lattice-model estimates, suggesting that the energy landscape theory "folding to glass transition temperature ratio" T(f) /T(g) may exceed 6.0 for real calorimetrically two-state proteins. Several popular three-dimensional lattice protein models, with different numbers of residue types in their alphabets, are found to fall short of the high experimental standard for being calorimetrically two-state. Some models postulate a multiple-conformation native state with substantial pre-denaturational energetic fluctuations well below the unfolding transition temperature, or predict a significant post-denaturational continuous conformational expansion of the denatured ensemble at temperatures well above the transition point, or both. These scenarios either disagree with experiments on protein size and dynamics, or are inconsistent with conventional interpretation of calorimetric data. However, when empirical linear baseline subtractions are employed, the resulting DeltaH(vH)/DeltaH(cal)'s for some models can be increased to values closer to unity, and baseline subtractions are found to correspond roughly to an operational definition of native-state conformational diversity. These results necessitate a re-assessment of theoretical models and experimental interpretations.

Calorimetry↗

PubMed2003

Hybrid global optimization algorithms for protein structure prediction: alternating hybrids.

Hybrid global optimization methods attempt to combine the beneficial features of two or more algorithms, and can be powerful methods for solving challenging nonconvex optimization problems. In this paper, novel classes of hybrid global optimization methods, termed alternating hybrids, are introduced for application as a tool in treating the peptide and protein structure prediction problems. In particular, these new optimization methods take the form of hybrids between a deterministic global optimization algorithm, the alphaBB, and a stochastically based method, conformational space annealing (CSA). The alphaBB method, as a theoretically proven global optimization approach, exhibits consistency, as it guarantees convergence to the global minimum for twice-continuously differentiable constrained nonlinear programming problems, but can benefit from computationally related enhancements. On the other hand, the independent CSA algorithm is highly efficient, though the method lacks theoretical guarantees of convergence. Furthermore, both the alphaBB method and the CSA method are found to identify ensembles of low-energy conformers, an important feature for determining the true free energy minimum of the system. The proposed hybrid methods combine the desirable features of efficiency and consistency, thus enabling the accurate prediction of the structures of larger peptides. Computational studies for met-enkephalin and melittin, employing sequential and parallel computing frameworks, demonstrate the promise for these proposed hybrid methods.

Algorithms↗

PubMed2001

Calculation of ensembles of structures representing the unfolded state of an SH3 domain.

The N-terminal SH3 domain of drk (drkN SH3 domain) exists in equilibrium between a folded (F(exch)) and an unfolded (U(exch)) form under non-denaturing conditions. In order to further our previous descriptions of the U(exch) state, we have developed a protocol for calculating ensembles of structures, based on experimental spectroscopic data, which broadly represent the unfolded state. A large number of unfolding trajectories were generated, starting from the folded state structure of the protein, in order to provide a reasonable sampling of the conformational space accessible to this sequence. Unfolded state ensembles have been "calculated" using a newly developed program ENSEMBLE, which optimizes the population weights assigned to each structure based on experimental properties of the U(exch) state. Pseudo-energy terms for nuclear Overhauser effects, J-coupling constants, (13)C chemical shifts, translational diffusion coefficients and tryptophan ring burial based on NMR and fluorescence data have been implemented. The population weight assignment procedure was performed for different starting ensembles. Small numbers of structures (<60) dominate the final ensembles compared to the total number in the starting ensembles, suggesting that the drkN SH3 domain U(exch) state can be described by a limited number of lower-energy conformations. The calculated U(exch) state ensembles are much more compact than a "random coil" chain, with significant native-like residual structure observed. In particular, a sizable population of conformers having the n-src loop and distal beta-hairpin structures exist in the calculated U(exch) state ensembles, and Trp36 is involved in a large number of interactions, both native and non-native.

Animals↗

PubMed2004

Existence of specific "folds" in polyproline II ensembles of an "unfolded"alanine peptide detected by molecular dynamics.

Equilibrium ensembles of octaalanine (Ac-Ala8-NHMe) in water, prepared with MD, are analyzed for contributing microstates with an RMSD-based conformational clustering algorithm. The extracted ensemble-averaged properties are in excellent agreement with numerous spectroscopic measurements reported with small alanine model peptides in water. However, the dominantly polyproline II-like ensemble of the peptide is found to be populated with a handful of highly position-specific "folds", including beta-turns, beta-hairpins, and helix nuclei, which could be the "seeds" that initiate proteins along their folding pathways.

Dipeptides↗

PubMed1998

Molecular modeling of the Abeta1-42 peptide from Alzheimer's disease.

The three-dimensional structure of the Alzheimer's disease Abeta1-42 peptide was predicted by sequence homology, threading approaches and by experimental observations. The Abeta molecule displayed a Greek key motif with four antiparallel beta-strands. To shield thermodynamically unfavorable domains, two Abeta molecules interact with each other to generate a beta-barrel structure with a hydrophilic surface and a hydrophobic core. The N-terminal domains of the dimer form crevices into which the non-polar C-termini are accommodated to yield a globular structure 27x32 A in diameter. Alternatively, the C-terminal domains of two opposing dimers could be extended to form an antiparallel beta-sheet. The stacking of these building blocks generates a helical protofilament. To create a thermodynamically more favorable structure, three protofilaments associate into a right-handed triple helix with a hydrophobic beta-sheet completely surrounded by the hydrophilic beta-barrels made of residues 1-28. Two triple helical strands can further associate into a right-handed amyloid filament. Although our model did not meet all the expected criteria, it nevertheless exhibited a series of naturally disposed structural features, revealed by other biophysical studies utilizing synthetic Abeta peptides. These characteristics are of functional significance in terms of Abeta-topology, fibril formation and cytotoxicity. The model also suggests that Abeta may not exist in a thermodynamically stable conformation, but rather as an ensemble of metastable dimeric structures some of which are capable of generating an extended C-terminal antiparallel beta-sheet essential in the promotion of fibrillogenesis.

Alzheimer Disease↗

PubMedDate not supplied

[Modeling of the 3D structure of the HIV-Haiti immunodominant epitope].

The 3D structure for the HIV-Haiti immunodominant epitope was computed in terms of NMR spectroscopy data using the theoretical procedure including a probabilistic approach in conjunction with molecular mechanics algorithms and quantum chemical methods. The immunogenic crown of the virus protein gp120 was shown to form in solution a prevalent conformation whose geometric parameters match the double beta-turn IV-IV. Two structures observed in crystal were found in the ensemble of the best-energy conformations of the HIV-Haiti principal neutralizing epitope. From a comparison of simulated structures with those computed previously for the HIV-Thailand and HIV-MN isolates, it was concluded that the immunogenic tip of gp120 gives rise to similar spatial backbone forms in different HIV-1 strains but has some inherent conformational flexibility of its individual amino acid residues. The differences in local fragment structures revealed in three isolates of HIV-1 are supposed to be important for the specificity of its binding with neutralizing antibodies.

Computational Biology↗

PubMed1998

Solution structure of the C-terminal SH2 domain of the p85 alpha regulatory subunit of phosphoinositide 3-kinase.

Heterodimeric class IA phosphoinositide 3-kinase (PI 3-kinase) plays a crucial role in a variety of cellular signalling events downstream of a number of cell-surface receptor tyrosine kinases. Activation of the enzyme is effected in part by the binding of two Src homology-2 domains (SH2) of the 85 kDa regulatory subunit to specific phosphotyrosine-containing peptide motifs within activated cytoplasmic receptor domains. The solution structure of the uncomplexed C-terminal SH2 (C-SH2) domain of the p85 alpha subunit of PI 3-kinase has been determined by means of multinuclear, double and triple-resonance NMR experiments and restrained molecular-dynamics simulated-annealing calculations. The solution structure clearly indicates that the uncomplexed C-SH2 domain conforms to the consensus polypeptide fold exhibited by other SH2 domains, with an additional short helical element at the N terminus. In particular, the C-SH2 structure is very similar to both the p85 alpha N-terminal SH2 domain (N-SH2) and the Src SH2 domain with a root mean square difference (rmsd) for 44 C alpha atoms of 1.09 and 0.89 A, respectively. The canonical BC, EF and BG loops are less well-defined by the experimental restraints and show greater variability in the ensemble of C-SH2 conformers. The lower level of definition in these regions may reflect the presence of conformational disorder, an interpretation supported by the absence or broadening of backbone and side-chain NMR resonances for some of these residues. NMR experiments were performed, where C-SH2 was titrated with phosphotyrosine-containing peptides corresponding to p85 alpha recognition sites in the cytoplasmic domain of the platelet-derived growth-factor receptor. The ligand-induced chemical-shift perturbations indicate the amino-acid residues in C-SH2 involved in peptide recognition follow the pattern predicted from homologous complexes. A series of C-SH2 mutants was generated and tested for phosphotyrosine peptide binding by surface plasmon resonance. Mutation of the invariant Arg36 (beta B5) to Met completely abolishes phosphopeptide binding. Mutation of each of Ser38, Ser39 or Lys40 in the BC loop to Ala reduces the affinity of C-SH2 for a cognate phosphopeptide, as does mutation of His93 (BG5) to Asn. These effects are consistent with the involvement of the BC loop and BG loops regions in ligation of phosphopeptide ligands. Mutation of Cys57 (beta D5) in C-SH2 to Ile, the corresponding residue type in the p85 alpha N-SH2 domain, results in a change in peptide binding selectivity of C-SH2 towards that demonstrated by p85 alpha N-SH2. This pattern of p85 alpha phosphopeptide binding specificity is interpreted in terms of a model of the p85 alpha/PDGF-receptor interaction.

Amino Acid Sequence↗

PubMed1998

Molecular dynamic simulations of environment and sequence dependent DNA conformations: the development of the BMS nucleic acid force field and comparison with experimental results.

Molecular dynamic (MD) simulations using the BMS nucleic acid force field produce environment and sequence dependent DNA conformations that closely mimic experimentally derived structures. The parameters were initially developed to reproduce the potential energy surface, as defined by quantum mechanics, for a set of small molecules that can be used as the building blocks for nucleic acid macromolecules (dimethyl phosphate, cyclopentane, tetrahydrofuran, etc.). Then the dihedral parameters were fine tuned using a series of condensed phase MD simulations of DNA and RNA (in zero added salt, 4M NaCl, and 75% ethanol solutions). In the tuning process the free energy surface for each dihedral was derived from the MD ensemble and fitted to the conformational distributions and populations observed in 87 A- and B-DNA x-ray and 17 B-DNA NMR structures. Over 41 nanoseconds of MD simulations are presented which demonstrate that the force field is capable of producing stable trajectories, in the correct environments, of A-DNA, double stranded A-form RNA, B-DNA, Z-DNA, and a netropsin-DNA complex that closely reproduce the experimentally determined and/or canonical DNA conformations. Frequently the MD averaged structure is closer to the experimentally determined structure than to the canonical DNA conformation. MD simulations of A- to B- and B- to A-DNA transitions are also shown. A-DNA simulations in a low salt environment cleanly convert into the B-DNA conformation and converge into the RMS space sampled by a low salt simulation of the same sequence starting from B-DNA. In MD simulations using the BMS force field the B-form of d(GGGCCC)2 in a 75% ethanol solution converts into the A-form. Using the same methodology, parameters, and conditions the A-form of d(AAATTT)2 correctly converts into the B-DNA conformation. These studies demonstrate that the force field is capable of reproducing both environment and sequence dependent DNA structures. The 41 nanoseconds (nsec) of MD simulations presented in this paper paint a global picture which suggests that the DNA structures observed in low salt solutions are largely due to the favorable internal energy brought about by the nearly uniform screening of the DNA electrostatics. While the conformations sampled in high salt or mixed solvent environments occur from selective and asymmetric screening of the phosphate groups and DNA grooves, respectively, brought about by sequence induced ion and solvent packing.

Adenine↗

PubMed2000

Role of phosphorylation in the conformation of tau peptides implicated in Alzheimer's disease.

A series of peptides corresponding to isolated regions of Tau (tau) protein have been synthesized and their conformations determined by (1)H NMR spectroscopy. Immunodominant peptides corresponding to tau(224-240) and a bisphosphorylated derivative in which a single Thr and a single Ser are phosphorylated at positions 231 and 235 respectively, and which are recognized by an Alzheimer's disease-specific monoclonal antibody, were the main focus of the study. The nonphosphorylated peptide adopts essentially a random coil conformation in aqueous solution, but becomes slightly more ordered into beta-type structure as the hydrophobicity of the solvent is increased by adding up to 50% trifluoroethanol (TFE). Similar trends are observed for the bisphosphorylated peptide, with a somewhat stronger tendency to form an extended structure. There is tentative NMR evidence for a small population of species containing a turn at residues 229-231 in the phosphorylated peptide, and this is strongly supported by CD spectroscopy. A proposal that the selection of a bioactive conformation from a disordered solution ensemble may be an important step (in either tubulin binding or in the formation of PHF) is supported by kinetic data on Pro isomerization. A recent study showed that Thr231 phosphorylation affected the rate of prolyl isomerization and abolished tubulin binding. This binding was restored by the action of the prolyl isomerase Pin1. In the current study, we find evidence for the existence of both trans and cis forms of tau peptides in solution but no difference in the equilibrium distribution of cis-trans isomers upon phosphorylation. Increasing hydrophobicity decreases the prevalence of cis forms and increases the major trans conformation of each of the prolines present in these molecules. We also synthesized mutant peptides containing Tyr substitutions preceding the Pro residues and found that phosphorylation of Tyr appears to have an effect on the equilibrium ratio of cis-trans isomerization and decreases the cis content.

Alzheimer Disease↗

PubMed2007

Application of single molecule Förster resonance energy transfer to protein folding.

Protein folding is a process characterized by a large degree of conformational heterogeneity. In such cases, classical experimental methods yield only mean values, averaged over large ensembles of molecules. The microscopic distributions of conformations, trajectories, or sequences of events often remain unknown, and with them the underlying molecular mechanisms. Signal averaging can be avoided by observing individual molecules. A particularly versatile method is highly sensitive fluorescence detection. In combination with Förster resonance energy transfer, distances and conformational dynamics can be investigated in single molecules. This chapter introduces the practical aspects of applying this method to protein folding.

Chromatography, High Pressure Liquid↗

PubMed1996

Conformational analysis of blood group A trisaccharide in solution and in the binding site of Dolichos biflorus lectin using transient and transferred nuclear Overhauser enhancement (NOE) and rotating-frame NOE experiments.

The present study is concerned with the elucidation of the conformation of the blood group A trisaccharide (alpha-D-GalNAc(1-3)[alpha-L-Fuc(1-->2)] beta-D-Gal-O-R) in the combining site of Dolichos biflorus seed lectin by use of 400-MHz and 600-MHz NMR spectroscopy. D. biflorus lectin displays a unique specificity for GalNAc residues. It occurs in solution as a tetrameric assembly having a molecular mass of 110 kDa, with two carbohydrate-binding sites per molecule. First, NOE build-up curves were obtained for the free blood group A trisaccharide from one-dimensional transient NOE experiments. Simulated NOE build-up curves were constructed from an ensemble of low-energy conformers derived from previous investigations. The comparison of theoretical and experimental data indicates that an equilibrium between two families of low-energy conformers most likely reflects the solution behavior of the trisaccharide in solution. Two-dimensional transferred NOE and rotating-frame enhancements (ROE) were subsequently measured for the trisaccharide complexed with the D. biflorus seed lectin. In addition to the NOEs observed for the free trisaccharide, the transferred NOESY spectrum showed several new NOEs that were identified as spin diffusion using a rotating-frame NOESY (ROESY) experiment. Experimental interglycosidic transferred nuclear Overhauser effect (TRNOE) build-up curves were compared to theoretical curves calculated for both low-energy conformers located in the D. biflorus lectin-binding site. Calculations of theoretical TRNOE were performed using a combination of the full relaxation matrix and the protein-ligand exchange matrix. Comparison between experimental and simulated TRNOE volumes leads to the conclusion that one conformation of blood group A trisaccharide is selected upon binding by D. biflorus lectin.

ABO Blood-Group System↗

PubMed1996

Energy functions that discriminate X-ray and near native folds from well-constructed decoys.

This study generates ensembles of decoy or test structures for eight small proteins with a variety of different folds. Between 35,000 and 200,000 decoys were generated for each protein using our four-state off-lattice model together with a novel relaxation method. These give compact self-avoiding conformations each constrained to have native secondary structure. Ensembles of these decoy conformations were used to test the ability of several types of empirical contact, surface area and distance-dependent energy functions to distinguish between correct and incorrect conformations. These tests have shown that none of the functions is able to distinguish consistently either the X-ray conformation or the near-native conformations from others which are incorrect. Certain combinations of two of these energy functions were able, however, consistently to identify X-ray structures from amongst the decoy conformations. These same combinations are better also at identifying near-native conformations, consistently finding them with a hundred-fold higher frequency than chance. The fact that these combination energy functions perform better than generally accepted energy functions suggests their future use in folding simulations and perhaps threading predictions.

Crystallography, X-Ray↗