Inference of structure ensembles of flexible biomolecules from sparse, averaged data.
Ontology highlight
ABSTRACT:
SUBMITTER: Olsson S
PROVIDER: S-EPMC3820694 | biostudies-literature | 2013
REPOSITORIES: biostudies-literature
Publications
Inference of structure ensembles of flexible biomolecules from sparse, averaged data.
Olsson Simon S Frellsen Jes J Boomsma Wouter W Mardia Kanti V KV Hamelryck Thomas T
PloS one 20131107 11
We present the theoretical foundations of a general principle to infer structure ensembles of flexible biomolecules from spatially and temporally averaged data obtained in biophysical experiments. The central idea is to compute the Kullback-Leibler optimal modification of a given prior distribution τ(x) with respect to the experimental data and its uncertainty. This principle generalizes the successful inferential structure determination method and recently proposed maximum entropy methods. Trac ...[more]
Similar Datasets
Project description:Mounting experimental evidence suggests a role for the spatial organization of chromatin in crucial processes of the cell nucleus such as transcription regulation. Chromosome conformation capture techniques allow us to characterize chromatin structure by mapping contacts between chromosomal loci on a genome-wide scale. The most widespread modality is to measure contact frequencies averaged over a population of cells. Single-cell variants exist, but suffer from low contact numbers and have not yet gained the same resolution as population methods. While intriguing biological insights have already been garnered from ensemble-averaged data, information about three-dimensional (3D) genome organization in the underlying individual cells remains largely obscured because the contact maps show only an average over a huge population of cells. Moreover, computational methods for structure modeling of chromatin have mostly focused on fitting a single consensus structure, thereby ignoring any cell-to-cell variability in the model itself. Here, we propose a fully Bayesian method to infer ensembles of chromatin structures and to determine the optimal number of states in a principled, objective way. We illustrate our approach on simulated data and compute multistate models of chromatin from chromosome conformation capture carbon copy (5C) data. Comparison with independent data suggests that the inferred ensembles represent the underlying sample population faithfully. Harnessing the rich information contained in multistate models, we investigate cell-to-cell variability of chromatin organization into topologically associating domains, thus highlighting the ability of our approach to deliver insights into chromatin organization of great biological relevance.
| S-EPMC7148566 | biostudies-literature
Project description:There is growing interest in analysing high-dimensional count data, which often exhibit quasi-sparsity corresponding to an overabundance of zeros and small nonzero counts. Existing methods for analysing multivariate count data via Poisson or negative binomial log-linear hierarchical models with zero-inflation cannot flexibly adapt to quasi-sparse settings. We develop a new class of continuous local-global shrinkage priors tailored to quasi-sparse counts. Theoretical properties are assessed, including flexible posterior concentration and stronger control of false discoveries in multiple testing. Simulation studies demonstrate excellent small-sample properties relative to competing methods. We use the method to detect rare mutational hotspots in exome sequencing data and to identify North American cities most impacted by terrorism.
| S-EPMC5793680 | biostudies-literature
Project description:NMR restrictions are suitable to specify the geometry of a molecule when a single well-defined global free energy minimum exists that is significantly lower than other local minima. Carbohydrates are quite flexible, and therefore, NMR observables do not always correlate with a single conformer but instead with an ensemble of low free energy conformers that can be accessed by thermal fluctuations. In this communication, we describe a novel procedure to identify and weight the contribution to the ensemble of local minima conformers based on comparison to residual dipolar couplings (RDCs) or other NMR observables, such as scalar couplings. A genetic algorithm is implemented to globally minimize the R factor comparing calculated RDCs to experiment. This is done by optimizing the weights of different conformers derived from the exhaustive local minima conformational search program, fast sugar structure prediction software (FSPS). We apply this framework to six human milk sugars, LND-1, LNF-1, LNF-2, LNF-3, LNnT, and LNT, and are able to determine corresponding population weights for the ensemble of conformers. Interestingly, our results indicate that in all cases the RDCs can be well represented by only a few most important conformers. This confirms that several, but not all of the glycosidic linkages in histo-blood group "epitopes" are quite rigid.
| S-EPMC3183381 | biostudies-literature
Project description:BackgroundComparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles.ResultsThe proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values <0.0001).ConclusionWe have developed a nonlinear mixed effects model that is appropriate for the analysis of sparse metabolic and physiological time profiles. The model permits sound statistical inference procedures, based on ANOVA likelihood ratio tests, for testing the significance of differences between short time course data under different biological perturbations.
| S-EPMC3114728 | biostudies-literature
Project description:Many proteins consist of folded domains connected by regions with higher flexibility. The details of the resulting conformational ensemble play a central role in controlling interactions between domains and with binding partners. Small-Angle Scattering (SAS) is well-suited to study the conformational states adopted by proteins in solution. However, analysis is complicated by the limited information content in SAS data and care must be taken to avoid constructing overly complex ensemble models and fitting to noise in the experimental data. To address these challenges, we developed a method based on Bayesian statistics that infers conformational ensembles from a structural library generated by all-atom Monte Carlo simulations. The first stage of the method involves a fast model selection based on variational Bayesian inference that maximizes the model evidence of the selected ensemble. This is followed by a complete Bayesian inference of population weights in the selected ensemble. Experiments with simulated ensembles demonstrate that model evidence is capable of identifying the correct ensemble and that correct number of ensemble members can be recovered up to high level of noise. Using experimental data, we demonstrate how the method can be extended to include data from Nuclear Magnetic Resonance (NMR) and structural energies of conformers extracted from the all-atom energy functions. We show that the data from SAXS, NMR chemical shifts and energies calculated from conformers can work synergistically to improve the definition of the conformational ensemble.
| S-EPMC6312354 | biostudies-literature
Project description:We present a simple and general approach termed REsemble for quantifying population overlap and structural similarity between ensembles. This approach captures improvements in the quality of ensembles determined using increasing input experimental data--improvements that go undetected when conventional methods for comparing ensembles are used--and reveals unexpected similarities between RNA ensembles determined using NMR and molecular dynamics simulations.
| S-EPMC4041546 | biostudies-literature
Project description:Solution nuclear magnetic resonance (NMR) experiments allow RNA dynamics to be determined in an aqueous environment. However, when a limited number of peaks are assigned, it is difficult to obtain structural information. We here show a protocol based on the combination of experimental data (Nuclear Overhauser Effect, NOE) and molecular dynamics simulations with enhanced sampling methods. This protocol allows to (a) obtain a maximum entropy ensemble compatible with NMR restraints and (b) obtain a minimal set of metastable conformations compatible with the experimental data (maximum parsimony). The method is applied to a hairpin of 29 nt from an inverted SINEB2, which is part of the SINEUP family and has been shown to enhance protein translation. A clustering procedure is introduced where the annotation of base-base interactions and glycosidic bond angles is used as a metric. By reweighting the contributions of the clusters, minimal sets of four conformations could be found which are compatible with the experimental data. A motif search on the structural database showed that some identified low-population states are present in experimental structures of other RNA transcripts. The introduced method can be applied to characterize RNA dynamics in systems where a limited amount of NMR information is available.
| S-EPMC7026608 | biostudies-literature
Project description:BackgroundHigh throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account.ResultsWe propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks.ConclusionSparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform (group lasso approach) as well as structures that involve all data platforms (Elitist lasso approach).AvailabilityThe additional file contains a MATLAB implementation of the sparse simultaneous component method.
| S-EPMC3283562 | biostudies-literature
Project description: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.
| S-EPMC2143983 | biostudies-other
Project description:Temporal analysis of genome-wide data can provide insights into the underlying mechanism of the biological processes in two ways. First, grouping the temporal data provides a richer, more robust representation of the underlying processes that are co-regulated. The net result is a significant dimensional reduction of the genome-wide array data into a smaller set of vocabularies for bioinformatics analysis. Second, the computed set of time-course vocabularies can be interrogated for a potential causal network that can shed light on the underlying interactions. The method is coupled with an experiment for investigating responses to high doses of ionizing radiation with and without a small priming dose. From a computational perspective, inference of a causal network can rapidly become computationally intractable with the increasing number of variables. Additionally, from a bioinformatics perspective, larger networks always hinder interpretation. Therefore, our method focuses on inferring the simplest network that is computationally tractable and interpretable. The method first reduces the number of temporal variables through consensus clustering to reveal a small set of temporal templates. It then enforces simplicity in the network configuration through the sparsity constraint, which is further regularized by requiring continuity between consecutive time points. We present intermediate results for each computational step, and apply our method to a time-course transcriptome dataset for a cell line receiving a challenge dose of ionizing radiation with and without a prior priming dose. Our analyses indicate that (i) the priming dose increases the diversity of the computed templates (e.g., diversity of transcriptome signatures); thus, increasing the network complexity; (ii) as a result of the priming dose, there are a number of unique templates with delayed and oscillatory profiles; and (iii) radiation-induced stress responses are enriched through pathway and subnetwork studies.
| S-EPMC3423420 | biostudies-literature