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PubMed2005

[Use of ensemble structural descriptors for increasing the efficiency of QSAR study].

A new concept of describing the dependence of the mutagenic activity of a chemical substance on its structure (QSAR analysis) is presented. It involves ensemble descriptors, which are combinations of unrelated fragments of molecular structure. Software has been developed to generate various structural fragments of molecules and their combinations (ensembles) and select ensemble descriptors of statistical significance for the biological activity of a chemical. By examples of univocal ensemble descriptors consisting of two structural fragments and present only in active or only in inactive compounds, it has been shown that the efficiency of QSAR study can be increased fourfold or more. The approach has been applied to a set of 105 compounds whose mutagenic effect on rodent sex cells is known.

Animals↗

PubMed1998

A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells.

The problem of predicting the position of a freely foraging rat based on the ensemble firing patterns of place cells recorded from the CA1 region of its hippocampus is used to develop a two-stage statistical paradigm for neural spike train decoding. In the first, or encoding stage, place cell spiking activity is modeled as an inhomogeneous Poisson process whose instantaneous rate is a function of the animal's position in space and phase of its theta rhythm. The animal's path is modeled as a Gaussian random walk. In the second, or decoding stage, a Bayesian statistical paradigm is used to derive a nonlinear recursive causal filter algorithm for predicting the position of the animal from the place cell ensemble firing patterns. The algebra of the decoding algorithm defines an explicit map of the discrete spike trains into the position prediction. The confidence regions for the position predictions quantify spike train information in terms of the most probable locations of the animal given the ensemble firing pattern. Under our inhomogeneous Poisson model position was a three to five times stronger modulator of the place cell spiking activity than theta phase in an open circular environment. For animal 1 (2) the median decoding error based on 34 (33) place cells recorded during 10 min of foraging was 8.0 (7.7) cm. Our statistical paradigm provides a reliable approach for quantifying the spatial information in the ensemble place cell firing patterns and defines a generally applicable framework for studying information encoding in neural systems.

Action Potentials↗

PubMed2026

Reinforcement learning-based dynamic ensemble for missense variant effect prediction and tiered prioritization of VUS.

BACKGROUND: Accurate classification of missense variants remains a challenging task despite major advances in genomics. Numerous computational models have been developed to assist in variant classification, but often require repeated integration and benchmarking efforts. Ensemble methods have been proposed to overcome the limitations of single predictors, but mostly rely on fixed, predefined weights that constrain their ability to capture interactions among predictive signals. METHODS: We present GenixRL, a dynamic ensemble framework that reformulates model fusion as a reinforcement learning optimization problem. GenixRL uses a Q-learning agent to learn a policy that dynamically weights the probabilistic outputs of complementary predictors, including BayesDel (addAF and noAF), ClinPred, and MetaRNN. Replacing static weighting with policy learning allows GenixRL to adaptively identify optimal weightings and substantially improve classification accuracy. RESULTS: In benchmark evaluation against 25 state-of-the-art predictors, GenixRL achieved an AUROC of 0.9644 on an independent ClinVar dataset. On saturation genome editing assays for BRCA1 and BRCA2, GenixRL achieved the best performance and ranked highest on 14 of 17 clinically significant genes in a zero-shot evaluation. Applied to uncertain and conflicting ClinVar variants, GenixRL enabled tiered, evidence-based prioritization of hundreds of thousands of variants as likely pathogenic or pathogenic with high confidence, supported by orthogonal population evidence from gnomAD. CONCLUSION: GenixRL advances pathogenicity prediction for missense variants and provides an adaptive ensemble that sorts variants of uncertain significance into tiered candidates for expert curation and functional validation.

Mutation, Missense↗

PubMed1998

Small structural ensembles for a 17-nucleotide mimic of the tRNA T psi C-loop via fitting dipolar relaxation rates with the quadratic programming algorithm.

Solution structures are typically average structures determined with the help of nmr-derived distance and torsion angle information. However, when a biomolecule populates significantly different conformations, the average structure might be prone to artifacts, and other refinement strategies are necessary. For example, when experimental restraints are used in molecular dynamics simulations in a time-averaged fashion (MDtar), the experimental structural information does no longer need to be satisfied at each step of the simulation; instead, the whole trajectory must agree with the restraints. However, the resulting structural ensembles are large and not unique and it is not trivial to extract the essential dynamic features for a system. Here we demonstrate that large MDtar ensembles can be simplified substantially by reducing the number of members to just a few on the basis of adjusting the individual probabilities of the members with the PDQPRO program [N. B. Ulyanov et al. Biophysical Journal (1995), Vol. 68, p. 13]. This algorithm finds the global minimum for a search function that represents the best match of a given ensemble with the experimental dipolar interproton relaxation rates. We have applied this strategy to a 17-residue RNA hairpin, whose loop exhibited considerable flexibility evident from nmr data. This 17mer is a mimic of the T psi C-loop of tRNA, where nucleotide 54 is usually a ribosylthymidine. The methylation of U54, which is completely buried in transfer ribonucleic acid, is administered by tRNA (m5 U54)-methyltransferase (RUMT). Since the 17mer is a good substrate for RUMT, we previously concluded that the flexibility of the 17mer's loop is a key to how RUMT gains access to the methylation site [L. J. Yao et al. Journal of Biomolecular NMR (1996) Vol. 9. p. 229]. Application of the PDQPRO algorithm to the previously acquired MDtar trajectories allowed us to reduce the number of conformations from several hundred to one major and five or six minor conformations with individual populations from approximately 5% to approximately 50% without any deterioration in the match with the experimental data. The major conformation exhibits a continuation of A-form helicity through part of the loop, involving C60 and U59. In this and most other conformations the methylation site in U54 is no longer buried.

Algorithms↗

PubMed1999

NMR characterization of partially folded and unfolded conformational ensembles of proteins.

Studies of unfolded and partially folded proteins provide important insight into the initiation and process of protein folding. This review focuses on the use of nmr in characterization of ensembles of proteins that model the early stages of folding. Analysis of an ensemble includes description of the number of conformations, their structure, relative populations, interconversion rates, and dynamics of subconformations. A chemically synthesized analogue of bovine pancreatic trypsin inhibitor (BPTI), [14-38](Abu), has provided a rare system for characterization of multiple partially folded conformations in slow exchange at near physiological conditions. Multidimensional nmr techniques coupled with selective labeling were used to probe different segments of the polypeptide chain. At each labeled site, there is evidence of slow interconversion between two families of partially folded conformations that in themselves are ensembles of rapidly interconverting conformers. All these conformers display significantly more order in the core relative to the rest of the molecule. For other variants of BPTI that are unfolded at equilibrium, the most ordered structure is also favored in the hydrophobic core residues of the native protein. This is consistent with the hypothesis that the residues that are the first to fold go on to form the most stable, structure-determining part of the protein.

Animals↗

PubMed2003

Rigid-body dynamics in the isothermal-isobaric ensemble: a test on the accuracy and computational efficiency.

We have developed a time-reversible rigid-body (rRB) molecular dynamics algorithm in the isothermal-isobaric (NPT) ensemble. The algorithm is an extension of rigid-body dynamics [Matubayasi and Nakahara, J Chem Phys 1999, 110, 3291] to the NPT ensemble on the basis of non-Hamiltonian statistical mechanics [Martyna, G. J. et al., J Chem Phys 1994, 101, 4177]. A series of MD simulations of water as well as fully hydrated lipid bilayer systems have been undertaken to investigate the accuracy and efficiency of the algorithm. The rRB algorithm was shown to be superior to the state-of-the-art constraint-dynamics algorithm SHAKE/RATTLE/ROLL, with respect to computational efficiency. However, it was revealed that both algorithms produced accurate trajectories of molecules in the NPT as well as NVT ensembles, as long as a reasonably short time step was used. A couple of multiple time-step (MTS) integration schemes were also examined. The advantage of the rRB algorithm for computational efficiency increased when the MD simulation was carried out using MTS on parallel processing computer systems; total computer time for MTS-MD of a lipid bilayer using 64 processors was reduced by about 40% using rRB instead of SHAKE/RATTLE/ROLL.

Journal Article↗

PubMed2006

Visualization of ensemble activity patterns of mechanosensory afferents in the cricket cercal sensory system with calcium imaging.

The cercal sensory system of the cricket mediates the detection and analysis of low velocity air currents in the animal's immediate environment, and is implemented around an internal representation of air current direction that demonstrates the essential features of a continuous neural map. Previous neurophysiological and anatomical studies have yielded predictions of the global spatio-temporal patterns of activity that should be evoked in the sensory afferent map by air current stimuli of different directions. We tested those predictions by direct visualization of ensemble afferent activity patterns using Ca2+ -sensitive indicators. The AM ester of the fluorescent Ca2+ indicator (Oregon Green 488 BAPTA-1 AM) was injected under the sheath of a cercal sensory nerve containing all of the mechanosensory afferent axons from one cercus. Optical signals were recorded with a digital intensified CCD camera. Control experiments using direct electrical stimulation of stained and unstained nerves demonstrated that the observed Ca2+ signals within the terminal abdominal ganglion (TAG) were due to activation of the dye-loaded sensory afferent neurons. To visualize the spatial patterns of air-current-evoked ensemble activity, unidirectional air currents were applied repeatedly from eight different directions, and the optically recorded responses from each direction were averaged. The dispersion of the optical signals by the ganglion limited the spatial resolution with which these ensemble afferent activity patterns could be observed. However, resolution was adequate to demonstrate that different directional stimuli induced different spatial patterns of Ca2+ elevation in the terminal arbors of afferents within the TAG. These coarsely- resolved, optically-recorded patterns were consistent with the anatomy-based predictions.

Air Movements↗

PubMed1992

Assembly of polypeptide and protein backbone conformations from low energy ensembles of short fragments: development of strategies and construction of models for myoglobin, lysozyme, and thymosin beta 4.

Recently we developed methods for the construction of knowledge-based mean fields from a data base of known protein structures. As shown previously, this approach can be used to calculate ensembles of probable conformations for short fragments of polypeptide chains. Here we develop procedures for the assembly of short fragments to complete three-dimensional models of polypeptide chains. The amino acid sequence of a given protein is decomposed into all possible overlapping fragments of a given length, and an ensemble of probable conformations is calculated for each fragment. The fragments are assembled to a complete model by choosing appropriate conformations from the individual ensembles and by averaging over equivalent angles. Finally a consistent model is obtained by rebuilding the conformation from the average angles. From the average angles the local variability of the structure can be calculated, which is a useful criterion for the reliability of the model. The procedure is applied to the calculation of the local backbone conformations of myoglobin and lysozyme whose structures have been solved by X-ray analysis and thymosin beta 4, a polypeptide of 43 amino acid residues whose structure was recently investigated by NMR spectroscopy. We demonstrate that substantial fractions of the calculated local backbone conformations are similar to the experimentally determined structures.

Amino Acid Sequence↗

PubMed1996

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.

Kinetics↗

PubMed1998

Flexible ligand docking using conformational ensembles.

Molecular docking algorithms suggest possible structures for molecular complexes. They are used to model biological function and to discover potential ligands. A present challenge for docking algorithms is the treatment of molecular flexibility. Here, the rigid body program, DOCK, is modified to allow it to rapidly fit multiple conformations of ligands. Conformations of a given molecule are pre-calculated in the same frame of reference, so that each conformer shares a common rigid fragment with all other conformations. The ligand conformers are then docked together, as an ensemble, into a receptor binding site. This takes advantage of the redundancy present in differing conformers of the same molecule. The algorithm was tested using three organic ligand protein systems and two protein-protein systems. Both the bound and unbound conformations of the receptors were used. The ligand ensemble method found conformations that resembled those determined in X-ray crystal structures (RMS values typically less than 1.5 A). To test the method's usefulness for inhibitor discovery, multi-compound and multi-conformer databases were screened for compounds known to bind to dihydrofolate reductase and compounds known to bind to thymidylate synthase. In both cases, known inhibitors and substrates were identified in conformations resembling those observed experimentally. The ligand ensemble method was 100-fold faster than docking a single conformation at a time and was able to screen a database of over 34 million conformations from 117,000 molecules in one to four CPU days on a workstation.

Algorithms↗

PubMed2002

Dynamic and structural analysis of isotropically distributed molecular ensembles.

An efficient new method is presented for the characterization of motional correlations derived from a set of protein structures without requiring the separation of overall and internal motion. In this method, termed isotropically distributed ensemble (IDE) analysis, each structure is represented by an ensemble of isotropically distributed replicas corresponding to the situation found in an isotropic protein solution. This leads to a covariance matrix of the cartesian atomic positions with elements proportional to the ensemble average of scalar products of the position vectors with respect to the center of mass. Diagonalization of the covariance matrix yields eigenmodes and amplitudes that describe concerted motions of atoms, including overall rotational and intramolecular dynamics. It is demonstrated that this covariance matrix naturally distinguishes between "rigid" and "mobile" parts without necessitating a priori selection of a reference structure and an atom set for the orientational alignment process. The method was applied to the analysis of a 5-ns molecular dynamics trajectory of native ubiquitin and a 40-ns trajectory of a partially folded state of ubiquitin. The results were compared with essential dynamics analysis. By taking advantage of the spherical symmetry of the IDE covariance matrix, more than a 10-fold speed up is achieved for the computation of eigenmodes and mode amplitudes. IDE analysis is particularly suitable for studying the correlated dynamics of flexible and large molecules.

Computer Simulation↗

PubMed2003

Ab initio construction of polypeptide fragments: efficient generation of accurate, representative ensembles.

We describe a novel method to generate ensembles of conformations of the main-chain atoms [N, C(alpha), C, O, Cbeta] for a sequence of amino acids within the context of a fixed protein framework. Each conformation satisfies fundamental stereo-chemical restraints such as idealized geometry, favorable phi/psi angles, and excluded volume. The ensembles include conformations both near and far from the native structure. Algorithms for effective conformational sampling and constant time overlap detection permit the generation of thousands of distinct conformations in minutes. Unlike previous approaches, our method samples dihedral angles from fine-grained phi/psi state sets, which we demonstrate is superior to exhaustive enumeration from coarse phi/psi sets. Applied to a large set of loop structures, our method samples consistently near-native conformations, averaging 0.4, 1.1, and 2.2 A main-chain root-mean-square deviations for four, eight, and twelve residue long loops, respectively. The ensembles make ideal decoy sets to assess the discriminatory power of a selection method. Using these decoy sets, we conclude that quality of anchor geometry cannot reliably identify near-native conformations, though the selection results are comparable to previous loop prediction methods. In a subsequent study (de Bakker et al.: Proteins 2003;51:21-40), we demonstrate that the AMBER forcefield with the Generalized Born solvation model identifies near-native conformations significantly better than previous methods.

Algorithms↗

PubMed2005

Clustering algorithms for identifying core atom sets and for assessing the precision of protein structure ensembles.

An important open question in the field of NMR-based biomolecular structure determination is how best to characterize the precision of the resulting ensemble of structures. Typically, the RMSD, as minimized in superimposing the ensemble of structures, is the preferred measure of precision. However, the presence of poorly determined atomic coordinates and multiple "RMSD-stable domains"--locally well-defined regions that are not aligned in global superimpositions--complicate RMSD calculations. In this paper, we present a method, based on a novel, structurally defined order parameter, for identifying a set of core atoms to use in determining superimpositions for RMSD calculations. In addition we present a method for deciding whether to partition that core atom set into "RMSD-stable domains" and, if so, how to determine partitioning of the core atom set. We demonstrate our algorithm and its application in calculating statistically sound RMSD values by applying it to a set of NMR-derived structural ensembles, superimposing each RMSD-stable domain (or the entire core atom set, where appropriate) found in each protein structure under consideration. A parameter calculated by our algorithm using a novel, kurtosis-based criterion, the epsilon-value, is a measure of precision of the superimposition that complements the RMSD. In addition, we compare our algorithm with previously described algorithms for determining core atom sets. The methods presented in this paper for biomolecular structure superimposition are quite general, and have application in many areas of structural bioinformatics and structural biology.

Algorithms↗

PubMed2000

Acid phosphatase reaction with peroxyl radicals: inactivation mechanism and behavior of the partially modified ensemble.

Acid phosphatase (AP) is readily inactivated when exposed to the free radicals generated in the pyrolysis of 2, 2'-azobis(2-amidinopropane) hydrochloride (AAPH) under aerobic conditions. On average, a large number of tryptophan groups are modified by each protein molecule that loses its catalytic activity. In spite of this, the enzyme inactivation takes place without induction times, a result that indicates either that damage is progressive or that damage of a critical target is needed to inactivate the enzyme (all-or-nothing mechanism). A Lineweaver-Burk plot of the enzyme activity measured at pH 4.8 is not compatible with an all-or-nothing mechanism, showing that after exposure of the native protein ensemble to the free radical source there are partially damaged molecules whose affinity for the substrate is widely different from that of the native molecules. On the other hand, the partially damaged ensemble shows a normal Michaelis-Menten behavior when the activity is measured at pH 7.0, with only a reduced value of V(M), relative to that of the unmodified ensemble. These results show that the native protein and modified proteins that remain active constitute different populations, with different responses to pH changes. Comparative heat denaturation studies of the native and pretreated proteins support this proposal.

Acid Phosphatase↗

PubMed1997

Characterization of long-range structure in the denatured state of staphylococcal nuclease. II. Distance restraints from paramagnetic relaxation and calculation of an ensemble of structures.

Structural analysis of delta131delta, a fragment model of the denatured state of staphylococcal nuclease, has been extended by obtaining long-range distance restraints between chain segments by paramagnetic relaxation enhancement. Fourteen unique PROXYL spin labels were introduced at sites that are solvent-exposed in the native state, and the resulting enhancements of T2 for the amide protons were measured by NMR spectroscopy. When these data were combined with either measured or estimated correlation times tau(c), the r(-6)-weighted, time and ensemble-averaged distance between the spin label and 30 to 60 amide protons could be calculated for each spin-labeled protein. On the basis of approximately 700 such loose distance restraints, ensembles of compatible structures were generated by a combined distance geometry/molecular dynamics approach. Because of the large uncertainty in the physical basis of these distance restraints, a number of calculations were carried out to establish the sensitivity of the calculated structures to systematic errors in these restraints. Overall, the structural features reflected in the paramagnetic relaxation data were robust; large variations in tau(c), in the bounds window of allowed distances, or in the number of restraint distances used had small effects on the general features common to all calculated structures. The global topology of this denatured form of staphylococcal nuclease, as described by an ensemble of conformations consistent with the data, is strikingly similar to that of the native state, the major difference being the segregation of two hydrophobic segments that form a beta hairpin in the native state. These findings suggest that the topology of a protein's fold is established in the denatured state in the absence of cooperative interactions involving tight packing or stable hydrogen bonding. Hydrophobic interactions alone may encode global topology.

Algorithms↗

PubMed2000

Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins.

Recent experimental results suggest that the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble, at least for small, fast-folding proteins. To investigate the extent of the topological control of the folding process, we studied the folding of simplified models of five small globular proteins constructed using a Go-like potential to retain the information about the native structures but drastically reduce the energetic frustration and energetic heterogeneity among residue-residue native interactions. By comparing the structure of the transition state ensemble (experimentally determined by Phi-values) and of the intermediates with those obtained using our models, we show that these energetically unfrustrated models can reproduce the global experimentally known features of the transition state ensembles and "en-route" intermediates, at least for the analyzed proteins. This result clearly indicates that, as long as the protein sequence is sufficiently minimally frustrated, topology plays a central role in determining the folding mechanism.

Bacterial Proteins↗

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↗

PubMed2003

Statistical formulae of the energy distribution among a globular protein structure ensemble.

In prediction of a protein main-chain structure into which a query sequence of amino acids folds, one evaluates the relative stability of a candidate structure against reference structures. We developed a statistical theory for calculating the energy distribution over a main-chain structure ensemble, only with an amino acid composition given as a single argument. Then, we obtained a statistical formulae of the ensemble mean and ensemble variance V[E] of the reference structural energies, as explicit functions of the amino acid composition. The mean and the variance V[E] calculated from the formulae were well or roughly consistent with those resulting from a gapless threading simulation. We can use the formulae not only to perform the high-through-put screening of sequences in the inverse folding problem, but also to handle the problem analytically.

Animals↗