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1.  A conditional neural fields model for protein threading 
Bioinformatics  2012;28(12):i59-i66.
Motivation: Alignment errors are still the main bottleneck for current template-based protein modeling (TM) methods, including protein threading and homology modeling, especially when the sequence identity between two proteins under consideration is low (<30%).
Results: We present a novel protein threading method, CNFpred, which achieves much more accurate sequence–template alignment by employing a probabilistic graphical model called a Conditional Neural Field (CNF), which aligns one protein sequence to its remote template using a non-linear scoring function. This scoring function accounts for correlation among a variety of protein sequence and structure features, makes use of information in the neighborhood of two residues to be aligned, and is thus much more sensitive than the widely used linear or profile-based scoring function. To train this CNF threading model, we employ a novel quality-sensitive method, instead of the standard maximum-likelihood method, to maximize directly the expected quality of the training set. Experimental results show that CNFpred generates significantly better alignments than the best profile-based and threading methods on several public (but small) benchmarks as well as our own large dataset. CNFpred outperforms others regardless of the lengths or classes of proteins, and works particularly well for proteins with sparse sequence profiles due to the effective utilization of structure information. Our methodology can also be adapted to protein sequence alignment.
Contact: j3xu@ttic.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/bts213
PMCID: PMC3371845  PMID: 22689779
2.  A Probabilistic Model of RNA Conformational Space 
PLoS Computational Biology  2009;5(6):e1000406.
The increasing importance of non-coding RNA in biology and medicine has led to a growing interest in the problem of RNA 3-D structure prediction. As is the case for proteins, RNA 3-D structure prediction methods require two key ingredients: an accurate energy function and a conformational sampling procedure. Both are only partly solved problems. Here, we focus on the problem of conformational sampling. The current state of the art solution is based on fragment assembly methods, which construct plausible conformations by stringing together short fragments obtained from experimental structures. However, the discrete nature of the fragments necessitates the use of carefully tuned, unphysical energy functions, and their non-probabilistic nature impairs unbiased sampling. We offer a solution to the sampling problem that removes these important limitations: a probabilistic model of RNA structure that allows efficient sampling of RNA conformations in continuous space, and with associated probabilities. We show that the model captures several key features of RNA structure, such as its rotameric nature and the distribution of the helix lengths. Furthermore, the model readily generates native-like 3-D conformations for 9 out of 10 test structures, solely using coarse-grained base-pairing information. In conclusion, the method provides a theoretical and practical solution for a major bottleneck on the way to routine prediction and simulation of RNA structure and dynamics in atomic detail.
Author Summary
The importance of RNA in biology and medicine has increased immensely over the last several years, due to the discovery of a wide range of important biological processes that are under the guidance of non-coding RNA. As is the case with proteins, the function of an RNA molecule is encoded in its three-dimensional (3-D) structure, which in turn is determined by the molecule's sequence. Therefore, interest in the computational prediction of the 3-D structure of RNA from sequence is great. One of the main bottlenecks in routine prediction and simulation of RNA structure and dynamics is sampling, the efficient generation of RNA-like conformations, ideally in a mathematically and physically sound way. Current methods require the use of unphysical energy functions to amend the shortcomings of the sampling procedure. We have developed a mathematical model that describes RNA's conformational space in atomic detail, without the shortcomings of other sampling methods. As an illustration of its potential, we describe a simple yet efficient method to sample conformations that are compatible with a given secondary structure. An implementation of the sampling method, called BARNACLE, is freely available.
doi:10.1371/journal.pcbi.1000406
PMCID: PMC2691987  PMID: 19543381
3.  Fragment-free approach to protein folding using conditional neural fields 
Bioinformatics  2010;26(12):i310-i317.
Motivation: One of the major bottlenecks with ab initio protein folding is an effective conformation sampling algorithm that can generate native-like conformations quickly. The popular fragment assembly method generates conformations by restricting the local conformations of a protein to short structural fragments in the PDB. This method may limit conformations to a subspace to which the native fold does not belong because (i) a protein with really new fold may contain some structural fragments not in the PDB and (ii) the discrete nature of fragments may prevent them from building a native-like fold. Previously we have developed a conditional random fields (CRF) method for fragment-free protein folding that can sample conformations in a continuous space and demonstrated that this CRF method compares favorably to the popular fragment assembly method. However, the CRF method is still limited by its capability of generating conformations compatible with a sequence.
Results: We present a new fragment-free approach to protein folding using a recently invented probabilistic graphical model conditional neural fields (CNF). This new CNF method is much more powerful than CRF in modeling the sophisticated protein sequence-structure relationship and thus, enables us to generate native-like conformations more easily. We show that when coupled with a simple energy function and replica exchange Monte Carlo simulation, our CNF method can generate decoys much better than CRF on a variety of test proteins including the CASP8 free-modeling targets. In particular, our CNF method can predict a correct fold for T0496_D1, one of the two CASP8 targets with truly new fold. Our predicted model for T0496 is significantly better than all the CASP8 models.
Contact: jinboxu@gmail.com
doi:10.1093/bioinformatics/btq193
PMCID: PMC2881378  PMID: 20529922
4.  A Probabilistic and Continuous Model of Protein Conformational Space for Template-Free Modeling 
Journal of Computational Biology  2010;17(6):783-798.
Abstract
One of the major challenges with protein template-free modeling is an efficient sampling algorithm that can explore a huge conformation space quickly. The popular fragment assembly method constructs a conformation by stringing together short fragments extracted from the Protein Data Base (PDB). The discrete nature of this method may limit generated conformations to a subspace in which the native fold does not belong. Another worry is that a protein with really new fold may contain some fragments not in the PDB. This article presents a probabilistic model of protein conformational space to overcome the above two limitations. This probabilistic model employs directional statistics to model the distribution of backbone angles and 2nd-order Conditional Random Fields (CRFs) to describe sequence-angle relationship. Using this probabilistic model, we can sample protein conformations in a continuous space, as opposed to the widely used fragment assembly and lattice model methods that work in a discrete space. We show that when coupled with a simple energy function, this probabilistic method compares favorably with the fragment assembly method in the blind CASP8 evaluation, especially on alpha or small beta proteins. To our knowledge, this is the first probabilistic method that can search conformations in a continuous space and achieves favorable performance. Our method also generated three-dimensional (3D) models better than template-based methods for a couple of CASP8 hard targets. The method described in this article can also be applied to protein loop modeling, model refinement, and even RNA tertiary structure prediction.
doi:10.1089/cmb.2009.0235
PMCID: PMC3203516  PMID: 20583926
conditional random fields (CRFs); directional statistics; fragment assembly; lattice model; protein structure prediction; template-free modeling
5.  Near-Native Protein Loop Sampling Using Nonparametric Density Estimation Accommodating Sparcity 
PLoS Computational Biology  2011;7(10):e1002234.
Unlike the core structural elements of a protein like regular secondary structure, template based modeling (TBM) has difficulty with loop regions due to their variability in sequence and structure as well as the sparse sampling from a limited number of homologous templates. We present a novel, knowledge-based method for loop sampling that leverages homologous torsion angle information to estimate a continuous joint backbone dihedral angle density at each loop position. The φ,ψ distributions are estimated via a Dirichlet process mixture of hidden Markov models (DPM-HMM). Models are quickly generated based on samples from these distributions and were enriched using an end-to-end distance filter. The performance of the DPM-HMM method was evaluated against a diverse test set in a leave-one-out approach. Candidates as low as 0.45 Å RMSD and with a worst case of 3.66 Å were produced. For the canonical loops like the immunoglobulin complementarity-determining regions (mean RMSD <2.0 Å), the DPM-HMM method performs as well or better than the best templates, demonstrating that our automated method recaptures these canonical loops without inclusion of any IgG specific terms or manual intervention. In cases with poor or few good templates (mean RMSD >7.0 Å), this sampling method produces a population of loop structures to around 3.66 Å for loops up to 17 residues. In a direct test of sampling to the Loopy algorithm, our method demonstrates the ability to sample nearer native structures for both the canonical CDRH1 and non-canonical CDRH3 loops. Lastly, in the realistic test conditions of the CASP9 experiment, successful application of DPM-HMM for 90 loops from 45 TBM targets shows the general applicability of our sampling method in loop modeling problem. These results demonstrate that our DPM-HMM produces an advantage by consistently sampling near native loop structure. The software used in this analysis is available for download at http://www.stat.tamu.edu/~dahl/software/cortorgles/.
Author Summary
A protein's structure consists of elements of regular secondary structure connected by less regular stretches of loop segments. The irregularity of the loop structure makes loop modeling quite challenging. More accurate sampling of these loop conformations has a direct impact on protein modeling, design, function classification, as well as protein interactions. A method has been developed that extends a more comprehensive knowledge-based approach to producing models of the loop regions of protein structure. Most physical models cannot adequately sample the large conformational space, while the more discrete knowledge based libraries are conformationally limited. To address both of these problems, we introduce a novel statistical method that produces a continuous yet weighted estimation of loop conformational space from a discrete library of structures by using a Dirichlet process mixture of hidden Markov models (DPM-HMM). Applied to loop structure sampling, the results of a number of tests demonstrate that our approach quickly generates large numbers of candidates with near native loop conformations. Most significantly, in the cases where the template sampling is sparse and/or far from native conformations, the DPM-HMM method samples close to the native space and produces a population of accurate loop structures.
doi:10.1371/journal.pcbi.1002234
PMCID: PMC3197639  PMID: 22028638
6.  Protein structure prediction by all-atom free-energy refinement 
Background
The reliable prediction of protein tertiary structure from the amino acid sequence remains challenging even for small proteins. We have developed an all-atom free-energy protein forcefield (PFF01) that we could use to fold several small proteins from completely extended conformations. Because the computational cost of de-novo folding studies rises steeply with system size, this approach is unsuitable for structure prediction purposes. We therefore investigate here a low-cost free-energy relaxation protocol for protein structure prediction that combines heuristic methods for model generation with all-atom free-energy relaxation in PFF01.
Results
We use PFF01 to rank and cluster the conformations for 32 proteins generated by ROSETTA. For 22/10 high-quality/low quality decoy sets we select near-native conformations with an average Cα root mean square deviation of 3.03 Å/6.04 Å. The protocol incorporates an inherent reliability indicator that succeeds for 78% of the decoy sets. In over 90% of these cases near-native conformations are selected from the decoy set. This success rate is rationalized by the quality of the decoys and the selectivity of the PFF01 forcefield, which ranks near-native conformations an average 3.06 standard deviations below that of the relaxed decoys (Z-score).
Conclusion
All-atom free-energy relaxation with PFF01 emerges as a powerful low-cost approach toward generic de-novo protein structure prediction. The approach can be applied to large all-atom decoy sets of any origin and requires no preexisting structural information to identify the native conformation. The study provides evidence that a large class of proteins may be foldable by PFF01.
doi:10.1186/1472-6807-7-12
PMCID: PMC1832197  PMID: 17371594
7.  A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction 
BMC Structural Biology  2013;13(Suppl 1):S4.
Background
Elucidating the native structure of a protein molecule from its sequence of amino acids, a problem known as de novo structure prediction, is a long standing challenge in computational structural biology. Difficulties in silico arise due to the high dimensionality of the protein conformational space and the ruggedness of the associated energy surface. The issue of multiple minima is a particularly troublesome hallmark of energy surfaces probed with current energy functions. In contrast to the true energy surface, these surfaces are weakly-funneled and rich in comparably deep minima populated by non-native structures. For this reason, many algorithms seek to be inclusive and obtain a broad view of the low-energy regions through an ensemble of low-energy (decoy) conformations. Conformational diversity in this ensemble is key to increasing the likelihood that the native structure has been captured.
Methods
We propose an evolutionary search approach to address the multiple-minima problem in decoy sampling for de novo structure prediction. Two population-based evolutionary search algorithms are presented that follow the basic approach of treating conformations as individuals in an evolving population. Coarse graining and molecular fragment replacement are used to efficiently obtain protein-like child conformations from parents. Potential energy is used both to bias parent selection and determine which subset of parents and children will be retained in the evolving population. The effect on the decoy ensemble of sampling minima directly is measured by additionally mapping a conformation to its nearest local minimum before considering it for retainment. The resulting memetic algorithm thus evolves not just a population of conformations but a population of local minima.
Results and conclusions
Results show that both algorithms are effective in terms of sampling conformations in proximity of the known native structure. The additional minimization is shown to be key to enhancing sampling capability and obtaining a diverse ensemble of decoy conformations, circumventing premature convergence to sub-optimal regions in the conformational space, and approaching the native structure with proximity that is comparable to state-of-the-art decoy sampling methods. The results are shown to be robust and valid when using two representative state-of-the-art coarse-grained energy functions.
doi:10.1186/1472-6807-13-S1-S4
PMCID: PMC3953177  PMID: 24565020
8.  Alignment of distantly related protein structures: algorithm, bound and implications to homology modeling 
Bioinformatics  2011;27(18):2537-2545.
Motivation: Building an accurate alignment of a large set of distantly related protein structures is still very challenging.
Results: This article presents a novel method 3DCOMB that can generate a multiple structure alignment (MSA) with not only as many conserved cores as possible, but also high-quality pairwise alignments. 3DCOMB is unique in that it makes use of both local and global structure environments, combined by a statistical learning method, to accurately identify highly similar fragment blocks (HSFBs) among all proteins to be aligned. By extending the alignments of these HSFBs, 3DCOMB can quickly generate an accurate MSA without using progressive alignment. 3DCOMB significantly excels others in aligning distantly related proteins. 3DCOMB can also generate correct alignments for functionally similar regions among proteins of very different structures while many other MSA tools fail. 3DCOMB is useful for many real-world applications. In particular, it enables us to find out that there is still large improvement room for multiple template homology modeling while several other MSA tools fail to do so.
Availability: 3DCOMB is available at http://ttic.uchicago.edu/~jinbo/software.htm.
Contact: jinboxu@gmail.com
Supplementary Information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btr432
PMCID: PMC3167051  PMID: 21791532
9.  A Correspondence Between Solution-State Dynamics of an Individual Protein and the Sequence and Conformational Diversity of its Family 
PLoS Computational Biology  2009;5(5):e1000393.
Conformational ensembles are increasingly recognized as a useful representation to describe fundamental relationships between protein structure, dynamics and function. Here we present an ensemble of ubiquitin in solution that is created by sampling conformational space without experimental information using “Backrub” motions inspired by alternative conformations observed in sub-Angstrom resolution crystal structures. Backrub-generated structures are then selected to produce an ensemble that optimizes agreement with nuclear magnetic resonance (NMR) Residual Dipolar Couplings (RDCs). Using this ensemble, we probe two proposed relationships between properties of protein ensembles: (i) a link between native-state dynamics and the conformational heterogeneity observed in crystal structures, and (ii) a relation between dynamics of an individual protein and the conformational variability explored by its natural family. We show that the Backrub motional mechanism can simultaneously explore protein native-state dynamics measured by RDCs, encompass the conformational variability present in ubiquitin complex structures and facilitate sampling of conformational and sequence variability matching those occurring in the ubiquitin protein family. Our results thus support an overall relation between protein dynamics and conformational changes enabling sequence changes in evolution. More practically, the presented method can be applied to improve protein design predictions by accounting for intrinsic native-state dynamics.
Author Summary
Knowledge of protein properties is essential for enhancing the understanding and engineering of biological functions. One key property of proteins is their flexibility—their intrinsic ability to adopt different conformations. This flexibility can be measured experimentally but the measurements are indirect and computational models are required to interpret them. Here we develop a new computational method for interpreting these measurements of flexibility and use it to create a model of flexibility of the protein ubiquitin. We apply our results to show relationships between the flexibility of one protein and the diversity of structures and amino acid sequences of the protein's evolutionary family. Thus, our results show that more accurate computational modeling of protein flexibility is useful for improving prediction of a broader range of amino acid sequences compatible with a given protein. Our method will be helpful for advancing methods to rationally engineer protein functions by enabling sampling of conformational and sequence diversity similar to that of a protein's evolutionary family.
doi:10.1371/journal.pcbi.1000393
PMCID: PMC2682763  PMID: 19478996
10.  Discriminative learning for protein conformation sampling 
Proteins  2008;73(1):228-240.
Protein structure prediction without using templates (i.e., ab initio folding) is one of the most challenging problems in structural biology. In particular, conformation sampling poses as a major bottleneck of ab initio folding. This article presents CRFSampler, an extensible protein conformation sampler, built on a probabilistic graphical model Conditional Random Fields (CRFs). Using a discriminative learning method, CRFSampler can automatically learn more than ten thousand parameters quantifying the relationship among primary sequence, secondary structure, and (pseudo) backbone angles. Using only compactness and self-avoiding constraints, CRFSampler can efficiently generate protein-like conformations from primary sequence and predicted secondary structure. CRFSampler is also very flexible in that a variety of model topologies and feature sets can be defined to model the sequence-structure relationship without worrying about parameter estimation. Our experimental results demonstrate that using a simple set of features, CRFSampler can generate decoys with much higher quality than the most recent HMM model.
doi:10.1002/prot.22057
PMCID: PMC2826217  PMID: 18412258
protein conformation sampling; conditional random fields (CRFs); discriminative learning
11.  RNA Structure Determination Using SAXS Data 
The journal of physical chemistry. B  2010;114(31):10039-10048.
Exploiting the experimental information from small-angle x-ray solution scattering (SAXS) in conjunction with structure prediction algorithms can be advantageous in the case of ribonucleic acids (RNA), where global restraints on the 3D fold are often lacking. Traditional usage of SAXS data often starts by attempting to reconstruct the molecular shape ab initio, which is subsequently used to assess the quality of model Here, an alternative strategy is explored whereby the models from a very large decoy set are directly sorted according to their fit to the SAXS data is developed. For rapid computation of SAXS patterns, the method developed here makes use of a coarse-grained representation of RNA. It also accounts for the explicit treatment of the contribution to the scattering of water molecules and ions surrounding the RNA. The method, called Fast-SAXS-RNA, is first calibrated using a transfer RNA (tRNA-val) and then tested on the P4-P6 fragment of group I intron (P4-P6). Fast-SAXS-RNA is then used as a filter for decoy models generated by the MC-Fold and MC-Sym pipeline, a suite of RNA 3D all-atoms structure algorithms that encode and exploit RNA 3D architectural principles. The ability of Fast-SAXS-RNA to discriminate native folds is tested against three widely used RNA molecules in molecular modeling benchmarks: the tRNA, the P4-P6, and a synthetic hairpin suspected to assemble into a homodimer. For each molecule, a large pool of decoys are generated, scored, and ranked using Fast-SAXS-RNA. The method is able to identify low-RMSD models among top ranking structures, for both tRNA and P4-P6. For the hairpin, the approach correctly identifies the dimeric state as the solution structure over the monomeric state and alternative secondary structures. The method offers a powerful strategy for recognizing native RNA conformations as well as multimeric assemblies and alternative secondary structures, thus enabling high-throughput RNA structure determination using SAXS data.
doi:10.1021/jp1057308
PMCID: PMC3164809  PMID: 20684627
12.  Improved protein structure selection using decoy-dependent discriminatory functions 
Background
A key component in protein structure prediction is a scoring or discriminatory function that can distinguish near-native conformations from misfolded ones. Various types of scoring functions have been developed to accomplish this goal, but their performance is not adequate to solve the structure selection problem. In addition, there is poor correlation between the scores and the accuracy of the generated conformations.
Results
We present a simple and nonparametric formula to estimate the accuracy of predicted conformations (or decoys). This scoring function, called the density score function, evaluates decoy conformations by performing an all-against-all Cα RMSD (Root Mean Square Deviation) calculation in a given decoy set. We tested the density score function on 83 decoy sets grouped by their generation methods (4state_reduced, fisa, fisa_casp3, lmds, lattice_ssfit, semfold and Rosetta). The density scores have correlations as high as 0.9 with the Cα RMSDs of the decoy conformations, measured relative to the experimental conformation for each decoy.
We previously developed a residue-specific all-atom probability discriminatory function (RAPDF), which compiles statistics from a database of experimentally determined conformations, to aid in structure selection. Here, we present a decoy-dependent discriminatory function called self-RAPDF, where we compiled the atom-atom contact probabilities from all the conformations in a decoy set instead of using an ensemble of native conformations, with a weighting scheme based on the density scores. The self-RAPDF has a higher correlation with Cα RMSD than RAPDF for 76/83 decoy sets, and selects better near-native conformations for 62/83 decoy sets. Self-RAPDF may be useful not only for selecting near-native conformations from decoy sets, but also for fold simulations and protein structure refinement.
Conclusions
Both the density score and the self-RAPDF functions are decoy-dependent scoring functions for improved protein structure selection. Their success indicates that information from the ensemble of decoy conformations can be used to derive statistical probabilities and facilitate the identification of near-native structures.
doi:10.1186/1472-6807-4-8
PMCID: PMC449718  PMID: 15207004
13.  Fast and accurate search for non-coding RNA pseudoknot structures in genomes 
Bioinformatics  2008;24(20):2281-2287.
Motivation: Searching genomes for non-coding RNAs (ncRNAs) by their secondary structure has become an important goal for bioinformatics. For pseudoknot-free structures, ncRNA search can be effective based on the covariance model and CYK-type dynamic programming. However, the computational difficulty in aligning an RNA sequence to a pseudoknot has prohibited fast and accurate search of arbitrary RNA structures. Our previous work introduced a graph model for RNA pseudoknots and proposed to solve the structure–sequence alignment by graph optimization. Given k candidate regions in the target sequence for each of the n stems in the structure, we could compute a best alignment in time O(ktn) based upon a tree width t decomposition of the structure graph. However, to implement this method to programs that can routinely perform fast yet accurate RNA pseudoknot searches, we need novel heuristics to ensure that, without degrading the accuracy, only a small number of stem candidates need to be examined and a tree decomposition of a small tree width can always be found for the structure graph.
Results: The current work builds on the previous one with newly developed preprocessing algorithms to reduce the values for parameters k and t and to implement the search method into a practical program, called RNATOPS, for RNA pseudoknot search. In particular, we introduce techniques, based on probabilistic profiling and distance penalty functions, which can identify for every stem just a small number k (e.g. k ≤ 10) of plausible regions in the target sequence to which the stem needs to align. We also devised a specialized tree decomposition algorithm that can yield tree decomposition of small tree width t (e.g. t ≤ 4) for almost all RNA structure graphs. Our experiments show that with RNATOPS it is possible to routinely search prokaryotic and eukaryotic genomes for specific RNA structures of medium to large sizes, including pseudoknots, with high sensitivity and high specificity, and in a reasonable amount of time.
Availability: The source code in C++ for RNATOPS is available at www.uga.edu/RNA-Informatics/software/rnatops/
Contact: cai@cs.uga.edu
Supplementary information: The online Supplementary Material contains all illustrative figures and tables referenced by this article.
doi:10.1093/bioinformatics/btn393
PMCID: PMC2562014  PMID: 18687694
14.  A Probabilistic Fragment-Based Protein Structure Prediction Algorithm 
PLoS ONE  2012;7(7):e38799.
Conformational sampling is one of the bottlenecks in fragment-based protein structure prediction approaches. They generally start with a coarse-grained optimization where mainchain atoms and centroids of side chains are considered, followed by a fine-grained optimization with an all-atom representation of proteins. It is during this coarse-grained phase that fragment-based methods sample intensely the conformational space. If the native-like region is sampled more, the accuracy of the final all-atom predictions may be improved accordingly. In this work we present EdaFold, a new method for fragment-based protein structure prediction based on an Estimation of Distribution Algorithm. Fragment-based approaches build protein models by assembling short fragments from known protein structures. Whereas the probability mass functions over the fragment libraries are uniform in the usual case, we propose an algorithm that learns from previously generated decoys and steers the search toward native-like regions. A comparison with Rosetta AbInitio protocol shows that EdaFold is able to generate models with lower energies and to enhance the percentage of near-native coarse-grained decoys on a benchmark of proteins. The best coarse-grained models produced by both methods were refined into all-atom models and used in molecular replacement. All atom decoys produced out of EdaFold’s decoy set reach high enough accuracy to solve the crystallographic phase problem by molecular replacement for some test proteins. EdaFold showed a higher success rate in molecular replacement when compared to Rosetta. Our study suggests that improving low resolution coarse-grained decoys allows computational methods to avoid subsequent sampling issues during all-atom refinement and to produce better all-atom models. EdaFold can be downloaded from http://www.riken.jp/zhangiru/software/.
doi:10.1371/journal.pone.0038799
PMCID: PMC3400640  PMID: 22829868
15.  Recombination Pattern Reanalysis of Some HIV-1 Circulating Recombination Forms Suggest the Necessity and Difficulty of Revision 
PLoS ONE  2014;9(9):e107349.
Background
Recombination is one of the major mechanisms underlying the generation of HIV-1 variability. Currently 61 circulating recombinant forms of HIV-1 have been identified. With the development of recombination detection techniques and accumulation of HIV-1 reference stains, more accurate mosaic structures of circulating recombinant forms (CRFs), like CRF04 and CRF06, have undergone repeated analysis and upgrades. Such revisions may also be necessary for other CRFs. Unlike previous studies, whose results are based primarily on a single recombination detection program, the current study was based on multiple recombination analysis, which may have produced more impartial results.
Methods
Representative references of 3 categories of intersubtype recombinants were selected, including BC recombinants (CRF07 and CRF08), BG recombinants (CRF23 and CRF24), and BF recombinants (CRF38 and CRF44). They were reanalyzed in detail using both the jumping profile hidden Markov model and RDP3.
Results
The results indicate that revisions and upgrades are very necessary and the entire re-analysis suggested 2 types of revision: (i) length of inserted fragments; and (ii) number of inserted fragments. The reanalysis also indicated that determination of small regions of about 200 bases or fewer should be performed with more caution.
Conclusion
Results indicated that the involvement of multiple recombination detection programs is very necessary. Additionally, results suggested two major challenges, one involving the difficulty of accurately determining the locations of breakpoints and the second involving identification of small regions of about 200 bases or fewer with greater caution. Both indicate the complexity of HIV-1 recombination. The resolution would depend critically on development of a recombination analysis algorithm, accumulation of HIV-1 stains, and a higher sequencing quality. With the changes in recombination pattern, phylogenetic relationships of some CRFs may also change. All these results may be critical to understand the role of recombination in a complex and dynamic HIV evolution.
doi:10.1371/journal.pone.0107349
PMCID: PMC4159329  PMID: 25203725
16.  PubChem3D: Conformer generation 
Background
PubChem, an open archive for the biological activities of small molecules, provides search and analysis tools to assist users in locating desired information. Many of these tools focus on the notion of chemical structure similarity at some level. PubChem3D enables similarity of chemical structure 3-D conformers to augment the existing similarity of 2-D chemical structure graphs. It is also desirable to relate theoretical 3-D descriptions of chemical structures to experimental biological activity. As such, it is important to be assured that the theoretical conformer models can reproduce experimentally determined bioactive conformations. In the present study, we investigate the effects of three primary conformer generation parameters (the fragment sampling rate, the energy window size, and force field variant) upon the accuracy of theoretical conformer models, and determined optimal settings for PubChem3D conformer model generation and conformer sampling.
Results
Using the software package OMEGA from OpenEye Scientific Software, Inc., theoretical 3-D conformer models were generated for 25,972 small-molecule ligands, whose 3-D structures were experimentally determined. Different values for primary conformer generation parameters were systematically tested to find optimal settings. Employing a greater fragment sampling rate than the default did not improve the accuracy of the theoretical conformer model ensembles. An ever increasing energy window did increase the overall average accuracy, with rapid convergence observed at 10 kcal/mol and 15 kcal/mol for model building and torsion search, respectively; however, subsequent study showed that an energy threshold of 25 kcal/mol for torsion search resulted in slightly improved results for larger and more flexible structures. Exclusion of coulomb terms from the 94s variant of the Merck molecular force field (MMFF94s) in the torsion search stage gave more accurate conformer models at lower energy windows. Overall average accuracy of reproduction of bioactive conformations was remarkably linear with respect to both non-hydrogen atom count ("size") and effective rotor count ("flexibility"). Using these as independent variables, a regression equation was developed to predict the RMSD accuracy of a theoretical ensemble to reproduce bioactive conformations. The equation was modified to give a minimum RMSD conformer sampling value to help ensure that 90% of the sampled theoretical models should contain at least one conformer within the RMSD sampling value to a "bioactive" conformation.
Conclusion
Optimal parameters for conformer generation using OMEGA were explored and determined. An equation was developed that provides an RMSD sampling value to use that is based on the relative accuracy to reproduce bioactive conformations. The optimal conformer generation parameters and RMSD sampling values determined are used by the PubChem3D project to generate theoretical conformer models.
doi:10.1186/1758-2946-3-4
PMCID: PMC3042967  PMID: 21272340
17.  Novel HIV-1 Recombinants Spreading across Multiple Risk Groups in the United Kingdom: The Identification and Phylogeography of Circulating Recombinant Form (CRF) 50_A1D 
PLoS ONE  2014;9(1):e83337.
Background
An increase in non-B HIV-1 infections among men who have sex with men (MSM) in the United Kingdom (UK) has created opportunities for novel recombinants to arise and become established. We used molecular mapping to characterize the importance of such recombinants to the UK HIV epidemic, in order to gain insights into transmission dynamics that can inform control strategies.
Methods and Results
A total of 55,556 pol (reverse transcriptase and protease) sequences in the UK HIV Drug Resistance Database were analyzed using Subtype Classification Using Evolutionary Algorithms (SCUEAL). Overall 72 patients shared the same A1/D recombination breakpoint in pol, comprising predominantly MSM but also heterosexuals and injecting drug users (IDUs). In six MSM, full-length single genome amplification of plasma HIV-1 RNA was performed in order to characterize the A1/D recombinant. Subtypes and recombination breakpoints were identified using sliding window and jumping profile hidden markov model approaches. Global maximum likelihood trees of gag, pol and env genes were drawn using FastTree version 2.1. Five of the six strains showed the same novel A1/D recombinant (8 breakpoints), which has been classified as CRF50_A1D. The sixth strain showed a complex CRF50_A1D/B/U structure. Divergence dates and phylogeographic inferences were determined using Bayesian Evolutionary Analysis using Sampling Trees (BEAST). This estimated that CRF50_A1D emerged in the UK around 1992 in MSM, with subsequent transmissions to heterosexuals and IDUs. Analysis of CRF50_A1D/B/U demonstrated that around the year 2000 CRF50_A1D underwent recombination with a subtype B strain.
Conclusions
We report the identification of CRF50_A1D, a novel circulating recombinant that emerged in UK MSM around 1992, with subsequent onward transmission to heterosexuals and IDUs, and more recent recombination with subtype B. These findings highlight the changing dynamics of HIV transmission in the UK and the converging of the two previously distinct MSM and heterosexual epidemics.
doi:10.1371/journal.pone.0083337
PMCID: PMC3893077  PMID: 24454702
18.  Predicting Peptide Structures in Native Proteins from Physical Simulations of Fragments 
PLoS Computational Biology  2009;5(2):e1000281.
It has long been proposed that much of the information encoding how a protein folds is contained locally in the peptide chain. Here we present a large-scale simulation study designed to examine the extent to which conformations of peptide fragments in water predict native conformations in proteins. We perform replica exchange molecular dynamics (REMD) simulations of 872 8-mer, 12-mer, and 16-mer peptide fragments from 13 proteins using the AMBER 96 force field and the OBC implicit solvent model. To analyze the simulations, we compute various contact-based metrics, such as contact probability, and then apply Bayesian classifier methods to infer which metastable contacts are likely to be native vs. non-native. We find that a simple measure, the observed contact probability, is largely more predictive of a peptide's native structure in the protein than combinations of metrics or multi-body components. Our best classification model is a logistic regression model that can achieve up to 63% correct classifications for 8-mers, 71% for 12-mers, and 76% for 16-mers. We validate these results on fragments of a protein outside our training set. We conclude that local structure provides information to solve some but not all of the conformational search problem. These results help improve our understanding of folding mechanisms, and have implications for improving physics-based conformational sampling and structure prediction using all-atom molecular simulations.
Author Summary
Proteins must fold to unique native structures in order to perform their functions. To do this, proteins must solve a complicated conformational search problem, the details of which remain difficult to study experimentally. Predicting folding pathways and the mechanisms by which proteins fold is thus central to understanding how proteins work. One longstanding question is the extent to which proteins solve the search problem locally, by folding into sub-structures that are dictated primarily by local sequence. Here, we address this question by conducting a large-scale molecular dynamics simulation study of protein fragments in water. The simulation data was then used to optimize a statistical model that predicted native and non-native contacts. The performance of the resulting model suggests that local structuring provides some but not all of the information to solve the folding problem, and that molecular dynamics simulation of fragments can be useful for protein structure prediction and design.
doi:10.1371/journal.pcbi.1000281
PMCID: PMC2629132  PMID: 19197352
19.  Improving predicted protein loop structure ranking using a Pareto-optimality consensus method 
Background
Accurate protein loop structure models are important to understand functions of many proteins. Identifying the native or near-native models by distinguishing them from the misfolded ones is a critical step in protein loop structure prediction.
Results
We have developed a Pareto Optimal Consensus (POC) method, which is a consensus model ranking approach to integrate multiple knowledge- or physics-based scoring functions. The procedure of identifying the models of best quality in a model set includes: 1) identifying the models at the Pareto optimal front with respect to a set of scoring functions, and 2) ranking them based on the fuzzy dominance relationship to the rest of the models. We apply the POC method to a large number of decoy sets for loops of 4- to 12-residue in length using a functional space composed of several carefully-selected scoring functions: Rosetta, DOPE, DDFIRE, OPLS-AA, and a triplet backbone dihedral potential developed in our lab. Our computational results show that the sets of Pareto-optimal decoys, which are typically composed of ~20% or less of the overall decoys in a set, have a good coverage of the best or near-best decoys in more than 99% of the loop targets. Compared to the individual scoring function yielding best selection accuracy in the decoy sets, the POC method yields 23%, 37%, and 64% less false positives in distinguishing the native conformation, indentifying a near-native model (RMSD < 0.5A from the native) as top-ranked, and selecting at least one near-native model in the top-5-ranked models, respectively. Similar effectiveness of the POC method is also found in the decoy sets from membrane protein loops. Furthermore, the POC method outperforms the other popularly-used consensus strategies in model ranking, such as rank-by-number, rank-by-rank, rank-by-vote, and regression-based methods.
Conclusions
By integrating multiple knowledge- and physics-based scoring functions based on Pareto optimality and fuzzy dominance, the POC method is effective in distinguishing the best loop models from the other ones within a loop model set.
doi:10.1186/1472-6807-10-22
PMCID: PMC2914074  PMID: 20642859
20.  A method for probing the mutational landscape of amyloid structure 
Bioinformatics  2011;27(13):i34-i42.
Motivation: Proteins of all kinds can self-assemble into highly ordered β-sheet aggregates known as amyloid fibrils, important both biologically and clinically. However, the specific molecular structure of a fibril can vary dramatically depending on sequence and environmental conditions, and mutations can drastically alter amyloid function and pathogenicity. Experimental structure determination has proven extremely difficult with only a handful of NMR-based models proposed, suggesting a need for computational methods.
Results: We present AmyloidMutants, a statistical mechanics approach for de novo prediction and analysis of wild-type and mutant amyloid structures. Based on the premise of protein mutational landscapes, AmyloidMutants energetically quantifies the effects of sequence mutation on fibril conformation and stability. Tested on non-mutant, full-length amyloid structures with known chemical shift data, AmyloidMutants offers roughly 2-fold improvement in prediction accuracy over existing tools. Moreover, AmyloidMutants is the only method to predict complete super-secondary structures, enabling accurate discrimination of topologically dissimilar amyloid conformations that correspond to the same sequence locations. Applied to mutant prediction, AmyloidMutants identifies a global conformational switch between Aβ and its highly-toxic ‘Iowa’ mutant in agreement with a recent experimental model based on partial chemical shift data. Predictions on mutant, yeast-toxic strains of HET-s suggest similar alternate folds. When applied to HET-s and a HET-s mutant with core asparagines replaced by glutamines (both highly amyloidogenic chemically similar residues abundant in many amyloids), AmyloidMutants surprisingly predicts a greatly reduced capacity of the glutamine mutant to form amyloid. We confirm this finding by conducting mutagenesis experiments.
Availability: Our tool is publically available on the web at http://amyloid.csail.mit.edu/.
Contact: lindquist_admin@wi.mit.edu; bab@csail.mit.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btr238
PMCID: PMC3117379  PMID: 21685090
21.  Sampling Realistic Protein Conformations Using Local Structural Bias 
PLoS Computational Biology  2006;2(9):e131.
The prediction of protein structure from sequence remains a major unsolved problem in biology. The most successful protein structure prediction methods make use of a divide-and-conquer strategy to attack the problem: a conformational sampling method generates plausible candidate structures, which are subsequently accepted or rejected using an energy function. Conceptually, this often corresponds to separating local structural bias from the long-range interactions that stabilize the compact, native state. However, sampling protein conformations that are compatible with the local structural bias encoded in a given protein sequence is a long-standing open problem, especially in continuous space. We describe an elegant and mathematically rigorous method to do this, and show that it readily generates native-like protein conformations simply by enforcing compactness. Our results have far-reaching implications for protein structure prediction, determination, simulation, and design.
Synopsis
Protein structure prediction is one of the main unsolved problems in computational biology today. A common way to tackle the problem is to generate plausible protein conformations using a fairly inaccurate but fast method, and to evaluate the conformations using an accurate but slow method. The main bottleneck lies in the first step, that is, efficiently exploring protein conformational space. Currently, the best way to do this is to construct plausible structures by stringing together fragments from experimentally determined protein structures, a method called fragment assembly. Hamelryck, Kent, and Krogh present a new method that can efficiently generate protein conformations that are compatible with a given protein sequence. Unlike for existing methods, the generated conformations cover a continuous range and come with an associated probability. The method shows great promise for use in protein structure prediction, determination, simulation, and design.
doi:10.1371/journal.pcbi.0020131
PMCID: PMC1570370  PMID: 17002495
22.  iFoldRNA: three-dimensional RNA structure prediction and folding 
Bioinformatics  2008;24(17):1951-1952.
Summary: Three-dimensional RNA structure prediction and folding is of significant interest in the biological research community. Here, we present iFoldRNA, a novel web-based methodology for RNA structure prediction with near atomic resolution accuracy and analysis of RNA folding thermodynamics. iFoldRNA rapidly explores RNA conformations using discrete molecular dynamics simulations of input RNA sequences. Starting from simplified linear-chain conformations, RNA molecules (<50 nt) fold to native-like structures within half an hour of simulation, facilitating rapid RNA structure prediction. All-atom reconstruction of energetically stable conformations generates iFoldRNA predicted RNA structures. The predicted RNA structures are within 2–5 Å root mean squre deviations (RMSDs) from corresponding experimentally derived structures. RNA folding parameters including specific heat, contact maps, simulation trajectories, gyration radii, RMSDs from native state, fraction of native-like contacts are accessible from iFoldRNA. We expect iFoldRNA will serve as a useful resource for RNA structure prediction and folding thermodynamic analyses.
Availability: http://iFoldRNA.dokhlab.org.
Contact: dokh@med.unc.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btn328
PMCID: PMC2559968  PMID: 18579566
23.  Characterization and frequency of a newly identified HIV-1 BF1 intersubtype circulating recombinant form in São Paulo, Brazil 
Virology Journal  2010;7:74.
Background
HIV circulating recombinant forms (CRFs) play an important role in the global and regional HIV epidemics, particularly in regions where multiple subtypes are circulating. To date, several (>40) CRFs are recognized worldwide with five currently circulating in Brazil. Here, we report the characterization of near full-length genome sequences (NFLG) of six phylogenetically related HIV-1 BF1 intersubtype recombinants (five from this study and one from other published sequences) representing CRF46_BF1.
Methods
Initially, we selected 36 samples from 888 adult patients residing in São Paulo who had previously been diagnosed as being infected with subclade F1 based on pol subgenomic fragment sequencing. Proviral DNA integrated in peripheral blood mononuclear cells (PBMC) was amplified from the purified genomic DNA of all 36-blood samples by five overlapping PCR fragments followed by direct sequencing. Sequence data were obtained from the five fragments that showed identical genomic structure and phylogenetic trees were constructed and compared with previously published sequences. Genuine subclade F1 sequences and any other sequences that exhibited unique mosaic structures were omitted from further analysis
Results
Of the 36 samples analyzed, only six sequences, inferred from the pol region as subclade F1, displayed BF1 identical mosaic genomes with a single intersubtype breakpoint identified at the nef-U3 overlap (HXB2 position 9347-9365; LTR region). Five of these isolates formed a rigid cluster in phylogentic trees from different subclade F1 fragment regions, which we can now designate as CRF46_BF1. According to our estimate, the new CRF accounts for 0.56% of the HIV-1 circulating strains in São Paulo. Comparison with previously published sequences revealed an additional five isolates that share an identical mosaic structure with those reported in our study. Despite sharing a similar recombinant structure, only one sequence appeared to originate from the same CRF46_BF1 ancestor.
Conclusion
We identified a new circulating recombinant form with a single intersubtype breakpoint identified at the nef-LTR U3 overlap and designated CRF46_BF1. Given the biological importance of the LTR U3 region, intersubtype recombination in this region could play an important role in HIV evolution with critical consequences for the development of efficient genetic vaccines.
doi:10.1186/1743-422X-7-74
PMCID: PMC2859377  PMID: 20398371
24.  Sampled ensemble neutrality as a feature to classify potential structured RNAs 
BMC Genomics  2015;16(1):35.
Background
Structured RNAs have many biological functions ranging from catalysis of chemical reactions to gene regulation. Yet, many homologous structured RNAs display most of their conservation at the secondary or tertiary structure level. As a result, strategies for structured RNA discovery rely heavily on identification of sequences sharing a common stable secondary structure. However, correctly distinguishing structured RNAs from surrounding genomic sequence remains challenging, especially during de novo discovery. RNA also has a long history as a computational model for evolution due to the direct link between genotype (sequence) and phenotype (structure). From these studies it is clear that evolved RNA structures, like protein structures, can be considered robust to point mutations. In this context, an RNA sequence is considered robust if its neutrality (extent to which single mutant neighbors maintain the same secondary structure) is greater than that expected for an artificial sequence with the same minimum free energy structure.
Results
In this work, we bring concepts from evolutionary biology to bear on the structured RNA de novo discovery process. We hypothesize that alignments corresponding to structured RNAs should consist of neutral sequences. We evaluate several measures of neutrality for their ability to distinguish between alignments of structured RNA sequences drawn from Rfam and various decoy alignments. We also introduce a new measure of RNA structural neutrality, the structure ensemble neutrality (SEN). SEN seeks to increase the biological relevance of existing neutrality measures in two ways. First, it uses information from an alignment of homologous sequences to identify a conserved biologically relevant structure for comparison. Second, it only counts base-pairs of the original structure that are absent in the comparison structure and does not penalize the formation of additional base-pairs.
Conclusion
We find that several measures of neutrality are effective at separating structured RNAs from decoy sequences, including both shuffled alignments and flanking genomic sequence. Furthermore, as an independent feature classifier to identify structured RNAs, SEN yields comparable performance to current approaches that consider a variety of features including stability and sequence identity. Finally, SEN outperforms other measures of neutrality at detecting mutational robustness in bacterial regulatory RNA structures.
Electronic supplementary material
The online version of this article (doi:10.1186/s12864-014-1203-8) contains supplementary material, which is available to authorized users.
doi:10.1186/s12864-014-1203-8
PMCID: PMC4333902  PMID: 25649229
RNA structural robustness; RNA de novo discovery; RNA structural ensemble; Mutational robustness
25.  NCACO-score: An effective main-chain dependent scoring function for structure modeling 
BMC Bioinformatics  2011;12:208.
Background
Development of effective scoring functions is a critical component to the success of protein structure modeling. Previously, many efforts have been dedicated to the development of scoring functions. Despite these efforts, development of an effective scoring function that can achieve both good accuracy and fast speed still presents a grand challenge.
Results
Based on a coarse-grained representation of a protein structure by using only four main-chain atoms: N, Cα, C and O, we develop a knowledge-based scoring function, called NCACO-score, that integrates different structural information to rapidly model protein structure from sequence. In testing on the Decoys'R'Us sets, we found that NCACO-score can effectively recognize native conformers from their decoys. Furthermore, we demonstrate that NCACO-score can effectively guide fragment assembly for protein structure prediction, which has achieved a good performance in building the structure models for hard targets from CASP8 in terms of both accuracy and speed.
Conclusions
Although NCACO-score is developed based on a coarse-grained model, it is able to discriminate native conformers from decoy conformers with high accuracy. NCACO is a very effective scoring function for structure modeling.
doi:10.1186/1471-2105-12-208
PMCID: PMC3123610  PMID: 21612673

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