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1.  iFoldRNA: Three-dimensional RNA Structure Prediction and Folding 
Bioinformatics (Oxford, England)  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 nucleotides) 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 Angstrom root mean square deviations from corresponding experimentally derived structures. RNA folding parameters including specific heat, contact maps, simulation trajectories, gyration radii, root mean square deviations 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.
doi:10.1093/bioinformatics/btn328
PMCID: PMC2559968  PMID: 18579566
2.  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
3.  Can molecular dynamics simulations help in discriminating correct from erroneous protein 3D models? 
BMC Bioinformatics  2008;9:6.
Background
Recent approaches for predicting the three-dimensional (3D) structure of proteins such as de novo or fold recognition methods mostly rely on simplified energy potential functions and a reduced representation of the polypeptide chain. These simplifications facilitate the exploration of the protein conformational space but do not permit to capture entirely the subtle relationship that exists between the amino acid sequence and its native structure. It has been proposed that physics-based energy functions together with techniques for sampling the conformational space, e.g., Monte Carlo or molecular dynamics (MD) simulations, are better suited to the task of modelling proteins at higher resolutions than those of models obtained with the former type of methods. In this study we monitor different protein structural properties along MD trajectories to discriminate correct from erroneous models. These models are based on the sequence-structure alignments provided by our fold recognition method, FROST. We define correct models as being built from alignments of sequences with structures similar to their native structures and erroneous models from alignments of sequences with structures unrelated to their native structures.
Results
For three test sequences whose native structures belong to the all-α, all-β and αβ classes we built a set of models intended to cover the whole spectrum: from a perfect model, i.e., the native structure, to a very poor model, i.e., a random alignment of the test sequence with a structure belonging to another structural class, including several intermediate models based on fold recognition alignments. We submitted these models to 11 ns of MD simulations at three different temperatures. We monitored along the corresponding trajectories the mean of the Root-Mean-Square deviations (RMSd) with respect to the initial conformation, the RMSd fluctuations, the number of conformation clusters, the evolution of secondary structures and the surface area of residues. None of these criteria alone is 100% efficient in discriminating correct from erroneous models. The mean RMSd, RMSd fluctuations, secondary structure and clustering of conformations show some false positives whereas the residue surface area criterion shows false negatives. However if we consider these criteria in combination it is straightforward to discriminate the two types of models.
Conclusion
The ability of discriminating correct from erroneous models allows us to improve the specificity and sensitivity of our fold recognition method for a number of ambiguous cases.
doi:10.1186/1471-2105-9-6
PMCID: PMC2245900  PMID: 18179702
4.  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
5.  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
6.  Vfold: A Web Server for RNA Structure and Folding Thermodynamics Prediction 
PLoS ONE  2014;9(9):e107504.
Background
The ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies.
Results
The Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization.
Conclusions
The Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at “http://rna.physics.missouri.edu”.
doi:10.1371/journal.pone.0107504
PMCID: PMC4162592  PMID: 25215508
7.  Crumple: A Method for Complete Enumeration of All Possible Pseudoknot-Free RNA Secondary Structures 
PLoS ONE  2012;7(12):e52414.
The diverse landscape of RNA conformational space includes many canyons and crevices that are distant from the lowest minimum free energy valley and remain unexplored by traditional RNA structure prediction methods. A complete description of the entire RNA folding landscape can facilitate identification of biologically important conformations. The Crumple algorithm rapidly enumerates all possible non-pseudoknotted structures for an RNA sequence without consideration of thermodynamics while filtering the output with experimental data. The Crumple algorithm provides an alternative approach to traditional free energy minimization programs for RNA secondary structure prediction. A complete computation of all non-pseudoknotted secondary structures can reveal structures that would not be predicted by methods that sample the RNA folding landscape based on thermodynamic predictions. The free energy minimization approach is often successful but is limited by not considering RNA tertiary and protein interactions and the possibility that kinetics rather than thermodynamics determines the functional RNA fold. Efficient parallel computing and filters based on experimental data make practical the complete enumeration of all non-pseudoknotted structures. Efficient parallel computing for Crumple is implemented in a ring graph approach. Filters for experimental data include constraints from chemical probing of solvent accessibility, enzymatic cleavage of paired or unpaired nucleotides, phylogenetic covariation, and the minimum number and lengths of helices determined from crystallography or cryo-electron microscopy. The minimum number and length of helices has a significant effect on reducing conformational space. Pairing constraints reduce conformational space more than single nucleotide constraints. Examples with Alfalfa Mosaic Virus RNA and Trypanosome brucei guide RNA demonstrate the importance of evaluating all possible structures when pseduoknots, RNA-protein interactions, and metastable structures are important for biological function. Crumple software is freely available at http://adenosine.chem.ou.edu/software.html.
doi:10.1371/journal.pone.0052414
PMCID: PMC3531468  PMID: 23300665
8.  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
9.  DEAD-Box Helicase Proteins Disrupt RNA Tertiary Structure Through Helix Capture 
PLoS Biology  2014;12(10):e1001981.
Single-molecule fluorescence experiments reveal how DEAD-box proteins unfold structured RNAs to promote conformational transitions and refolding to the native functional state.
DEAD-box helicase proteins accelerate folding and rearrangements of highly structured RNAs and RNA–protein complexes (RNPs) in many essential cellular processes. Although DEAD-box proteins have been shown to use ATP to unwind short RNA helices, it is not known how they disrupt RNA tertiary structure. Here, we use single molecule fluorescence to show that the DEAD-box protein CYT-19 disrupts tertiary structure in a group I intron using a helix capture mechanism. CYT-19 binds to a helix within the structured RNA only after the helix spontaneously loses its tertiary contacts, and then CYT-19 uses ATP to unwind the helix, liberating the product strands. Ded1, a multifunctional yeast DEAD-box protein, gives analogous results with small but reproducible differences that may reflect its in vivo roles. The requirement for spontaneous dynamics likely targets DEAD-box proteins toward less stable RNA structures, which are likely to experience greater dynamic fluctuations, and provides a satisfying explanation for previous correlations between RNA stability and CYT-19 unfolding efficiency. Biologically, the ability to sense RNA stability probably biases DEAD-box proteins to act preferentially on less stable misfolded structures and thereby to promote native folding while minimizing spurious interactions with stable, natively folded RNAs. In addition, this straightforward mechanism for RNA remodeling does not require any specific structural environment of the helicase core and is likely to be relevant for DEAD-box proteins that promote RNA rearrangements of RNP complexes including the spliceosome and ribosome.
Author Summary
In addition to carrying genetic information from DNA to protein, RNAs function in many essential cellular processes. This often requires the RNA to form a specific three-dimensional structure, and some functions require cycling between multiple structures. However, RNAs have a strong propensity to become trapped in nonfunctional, misfolded structures. Due to the intrinsic stability of local structure for RNA, these misfolded species can be long-lived and therefore accumulate. ATP-dependent RNA chaperone proteins called DEAD-box proteins are known to promote native RNA folding by disrupting misfolded structures. Although these proteins can unwind short RNA helices, the mechanism by which they act upon higher order tertiary contacts is unknown. Our current work shows that DEAD-box proteins capture transiently exposed RNA helices, preventing any tertiary contacts from reforming and potentially destabilizing the global RNA architecture. Helix unwinding by the DEAD-box protein then allows the product RNA strands to form new contacts. This helix capture mechanism for manipulation of RNA tertiary structure does not require a specific binding motif or structural environment and may be general for DEAD-box helicase proteins that act on structured RNAs.
doi:10.1371/journal.pbio.1001981
PMCID: PMC4211656  PMID: 25350280
10.  Ab initio modeling of small proteins by iterative TASSER simulations 
BMC Biology  2007;5:17.
Background
Predicting 3-dimensional protein structures from amino-acid sequences is an important unsolved problem in computational structural biology. The problem becomes relatively easier if close homologous proteins have been solved, as high-resolution models can be built by aligning target sequences to the solved homologous structures. However, for sequences without similar folds in the Protein Data Bank (PDB) library, the models have to be predicted from scratch. Progress in the ab initio structure modeling is slow. The aim of this study was to extend the TASSER (threading/assembly/refinement) method for the ab initio modeling and examine systemically its ability to fold small single-domain proteins.
Results
We developed I-TASSER by iteratively implementing the TASSER method, which is used in the folding test of three benchmarks of small proteins. First, data on 16 small proteins (< 90 residues) were used to generate I-TASSER models, which had an average Cα-root mean square deviation (RMSD) of 3.8Å, with 6 of them having a Cα-RMSD < 2.5Å. The overall result was comparable with the all-atomic ROSETTA simulation, but the central processing unit (CPU) time by I-TASSER was much shorter (150 CPU days vs. 5 CPU hours). Second, data on 20 small proteins (< 120 residues) were used. I-TASSER folded four of them with a Cα-RMSD < 2.5Å. The average Cα-RMSD of the I-TASSER models was 3.9Å, whereas it was 5.9Å using TOUCHSTONE-II software. Finally, 20 non-homologous small proteins (< 120 residues) were taken from the PDB library. An average Cα-RMSD of 3.9Å was obtained for the third benchmark, with seven cases having a Cα-RMSD < 2.5Å.
Conclusion
Our simulation results show that I-TASSER can consistently predict the correct folds and sometimes high-resolution models for small single-domain proteins. Compared with other ab initio modeling methods such as ROSETTA and TOUCHSTONE II, the average performance of I-TASSER is either much better or is similar within a lower computational time. These data, together with the significant performance of automated I-TASSER server (the Zhang-Server) in the 'free modeling' section of the recent Critical Assessment of Structure Prediction (CASP)7 experiment, demonstrate new progresses in automated ab initio model generation. The I-TASSER server is freely available for academic users .
doi:10.1186/1741-7007-5-17
PMCID: PMC1878469  PMID: 17488521
11.  An Evolution-Based Approach to De Novo Protein Design and Case Study on Mycobacterium tuberculosis 
PLoS Computational Biology  2013;9(10):e1003298.
Computational protein design is a reverse procedure of protein folding and structure prediction, where constructing structures from evolutionarily related proteins has been demonstrated to be the most reliable method for protein 3-dimensional structure prediction. Following this spirit, we developed a novel method to design new protein sequences based on evolutionarily related protein families. For a given target structure, a set of proteins having similar fold are identified from the PDB library by structural alignments. A structural profile is then constructed from the protein templates and used to guide the conformational search of amino acid sequence space, where physicochemical packing is accommodated by single-sequence based solvation, torsion angle, and secondary structure predictions. The method was tested on a computational folding experiment based on a large set of 87 protein structures covering different fold classes, which showed that the evolution-based design significantly enhances the foldability and biological functionality of the designed sequences compared to the traditional physics-based force field methods. Without using homologous proteins, the designed sequences can be folded with an average root-mean-square-deviation of 2.1 Å to the target. As a case study, the method is extended to redesign all 243 structurally resolved proteins in the pathogenic bacteria Mycobacterium tuberculosis, which is the second leading cause of death from infectious disease. On a smaller scale, five sequences were randomly selected from the design pool and subjected to experimental validation. The results showed that all the designed proteins are soluble with distinct secondary structure and three have well ordered tertiary structure, as demonstrated by circular dichroism and NMR spectroscopy. Together, these results demonstrate a new avenue in computational protein design that uses knowledge of evolutionary conservation from protein structural families to engineer new protein molecules of improved fold stability and biological functionality.
Author Summary
The goal of computational protein design is to create new protein sequences of desirable structure and biological function. Most protein design methods are developed to search for sequences with the lowest free-energy based on physics-based force fields following Anfinsen's thermodynamic hypothesis. A major obstacle of such approaches is the inaccuracy of the force-field design, which cannot accurately describe atomic interactions or correctly recognize protein folds. We propose a novel method which uses evolutionary information, in the form of sequence profiles from structure families, to guide the sequence design. Since sequence profiles are generally more accurate than physics-based potentials in protein fold recognition, a unique advantage lies on that it targets the design procedure to a family of protein sequence profiles to enhance the robustness of designed sequences. The method was tested on 87 proteins and the designed sequences can be folded by I-TASSER to models with an average RMSD 2.1 Å. As a case study of large-scale application, the method is extended to redesign all structurally resolved proteins in the human pathogenic bacteria, Mycobacterium tuberculosis. Five sequences varying in fold and sizes were characterized by circular dichroism and NMR spectroscopy experiments and three were shown to have ordered tertiary structure.
doi:10.1371/journal.pcbi.1003298
PMCID: PMC3812052  PMID: 24204234
12.  Optimal contact definition for reconstruction of Contact Maps 
BMC Bioinformatics  2010;11:283.
Background
Contact maps have been extensively used as a simplified representation of protein structures. They capture most important features of a protein's fold, being preferred by a number of researchers for the description and study of protein structures. Inspired by the model's simplicity many groups have dedicated a considerable amount of effort towards contact prediction as a proxy for protein structure prediction. However a contact map's biological interest is subject to the availability of reliable methods for the 3-dimensional reconstruction of the structure.
Results
We use an implementation of the well-known distance geometry protocol to build realistic protein 3-dimensional models from contact maps, performing an extensive exploration of many of the parameters involved in the reconstruction process. We try to address the questions: a) to what accuracy does a contact map represent its corresponding 3D structure, b) what is the best contact map representation with regard to reconstructability and c) what is the effect of partial or inaccurate contact information on the 3D structure recovery. Our results suggest that contact maps derived from the application of a distance cutoff of 9 to 11Å around the Cβ atoms constitute the most accurate representation of the 3D structure. The reconstruction process does not provide a single solution to the problem but rather an ensemble of conformations that are within 2Å RMSD of the crystal structure and with lower values for the pairwise average ensemble RMSD. Interestingly it is still possible to recover a structure with partial contact information, although wrong contacts can lead to dramatic loss in reconstruction fidelity.
Conclusions
Thus contact maps represent a valid approximation to the structures with an accuracy comparable to that of experimental methods. The optimal contact definitions constitute key guidelines for methods based on contact maps such as structure prediction through contacts and structural alignments based on maximum contact map overlap.
doi:10.1186/1471-2105-11-283
PMCID: PMC3583236  PMID: 20507547
13.  SimulFold: Simultaneously Inferring RNA Structures Including Pseudoknots, Alignments, and Trees Using a Bayesian MCMC Framework 
PLoS Computational Biology  2007;3(8):e149.
Computational methods for predicting evolutionarily conserved rather than thermodynamic RNA structures have recently attracted increased interest. These methods are indispensable not only for elucidating the regulatory roles of known RNA transcripts, but also for predicting RNA genes. It has been notoriously difficult to devise them to make the best use of the available data and to predict high-quality RNA structures that may also contain pseudoknots. We introduce a novel theoretical framework for co-estimating an RNA secondary structure including pseudoknots, a multiple sequence alignment, and an evolutionary tree, given several RNA input sequences. We also present an implementation of the framework in a new computer program, called SimulFold, which employs a Bayesian Markov chain Monte Carlo method to sample from the joint posterior distribution of RNA structures, alignments, and trees. We use the new framework to predict RNA structures, and comprehensively evaluate the quality of our predictions by comparing our results to those of several other programs. We also present preliminary data that show SimulFold's potential as an alignment and phylogeny prediction method. SimulFold overcomes many conceptual limitations that current RNA structure prediction methods face, introduces several new theoretical techniques, and generates high-quality predictions of conserved RNA structures that may include pseudoknots. It is thus likely to have a strong impact, both on the field of RNA structure prediction and on a wide range of data analyses.
Author Summary
Not only is the prediction of evolutionarily conserved RNA structures important for elucidating the potential functions of RNA sequences and the mechanisms by which these functions are exerted, but it also lies at the core of RNA gene prediction. To get an accurate prediction of the conserved RNA structure, we need a high-quality sequence alignment and an evolutionary tree relating several evolutionarily related sequences. These are two strong requirements that are typically difficult to fulfill unless the encoded RNA structure is already known. We present what is to our knowledge the first method that solves this chicken-and-egg problem by co-estimating all three quantities simultaneously. We show that our novel method, called SimulFold, can be successfully applied over a wide range of sequence similarities to detect conserved RNA structures, including those with pseudoknots. We also show its potential as an alignment and phylogeny prediction method. Our method overcomes several significant limitations of existing methods and has the potential to be used for a very diverse range of tasks.
doi:10.1371/journal.pcbi.0030149
PMCID: PMC1941756  PMID: 17696604
14.  Computing the Partition Function for Kinetically Trapped RNA Secondary Structures 
PLoS ONE  2011;6(1):e16178.
An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in time and space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1) the number of locally optimal structures is far fewer than the total number of structures – indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2) the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3) the (modified) maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model) can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected accuracy. Web server and source code available at http://bioinformatics.bc.edu/clotelab/RNAlocopt/.
doi:10.1371/journal.pone.0016178
PMCID: PMC3030561  PMID: 21297972
15.  Physics-based de novo prediction of RNA 3D structures 
The journal of physical chemistry. B  2011;115(14):4216-4226.
Current experiments on structural determination cannot keep up the pace with the steadily emerging RNA sequences and new functions. This underscores the request for an accurate model for RNA three-dimensional (3D) structural prediction. Although considerable progress has been made in mechanistic studies, accurate prediction for RNA tertiary folding from sequence remains an unsolved problem. The first and most important requirement for the prediction of RNA structure from physical principles is an accurate free energy model. A recently developed three-vector virtual bond-based RNA folding model (“Vfold”) has allowed us to compute the chain entropy and predict folding free energies and structures for RNA secondary structures and simple pseudoknots. Here we develop a free energy-based method to predict larger more complex RNA tertiary folds. The approach is based on a multiscaling strategy: from the nucleotide sequence, we predict the two-dimensional (2D) structures (defined by the base pairs and tertiary contacts); based on the 2D structure, we construct a 3D scaffold; with the 3D scaffold as the initial state, we combine AMBER energy minimization and PDB-based fragment search to predict the all-atom structure. A key advantage of the approach is the statistical mechanical calculation for the conformational entropy of RNA structures, including those with cross-linked loops. Benchmark tests show that the model leads to significant improvements in RNA 3D structure prediction.
doi:10.1021/jp112059y
PMCID: PMC3072456  PMID: 21413701
Energy landscape; RNA folding; Structural prediction; Tertiary structure
16.  Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity 
Journal of molecular biology  2007;367(3):909-924.
Using a combined master equation and kinetic cluster approach, we investigate RNA pseudoknot folding and unfolding kinetics. The energetic parameters are computed from a recently developed Vfold model for RNA secondary structure and pseudoknot folding thermodynamics. The folding kinetics theory is based on the complete conformational ensemble, including all the native-like and non-native states. The predicted folding and unfolding pathways, activation barriers, Arrhenius plots, and rate-limiting steps lead to several findings. First, for the PK5 pseudoknot, a misfolded 5′ hairpin emerges as a stable kinetic trap in the folding process, and the detrapping from this misfolded state is the rate-limiting step for the overall folding process. The calculated rate constant and activation barrier agree well with the experimental data. Second, as an application of the model, we investigate the kinetic folding pathways for hTR (human Telomerase RNA) pseudoknot. The predicted folding and unfolding pathways not only support the proposed role of conformational switch between hairpin and pseudoknot in hTR activity, but also reveal molecular mechanism for the conformational switch. Furthermore, for an experimentally studied hTR mutation, whose hairpin intermediate is destabilized, the model predicts a long-lived transient hairpin structure, and the switch between the transient hairpin intermediate and the native pseudoknot may be responsible for the observed hTR activity. Such finding would help resolve the apparent contradiction between the observed hTR activity and the absence of a stable hairpin.
doi:10.1016/j.jmb.2007.01.006
PMCID: PMC1995092  PMID: 17276459
Kinetics; RNA pseudoknot; Activation energy; Misfolded state; Telomerase
17.  BCL::Fold - De Novo Prediction of Complex and Large Protein Topologies by Assembly of Secondary Structure Elements 
PLoS ONE  2012;7(11):e49240.
Computational de novo protein structure prediction is limited to small proteins of simple topology. The present work explores an approach to extend beyond the current limitations through assembling protein topologies from idealized α-helices and β-strands. The algorithm performs a Monte Carlo Metropolis simulated annealing folding simulation. It optimizes a knowledge-based potential that analyzes radius of gyration, β-strand pairing, secondary structure element (SSE) packing, amino acid pair distance, amino acid environment, contact order, secondary structure prediction agreement and loop closure. Discontinuation of the protein chain favors sampling of non-local contacts and thereby creation of complex protein topologies. The folding simulation is accelerated through exclusion of flexible loop regions further reducing the size of the conformational search space. The algorithm is benchmarked on 66 proteins with lengths between 83 and 293 amino acids. For 61 out of these proteins, the best SSE-only models obtained have an RMSD100 below 8.0 Å and recover more than 20% of the native contacts. The algorithm assembles protein topologies with up to 215 residues and a relative contact order of 0.46. The method is tailored to be used in conjunction with low-resolution or sparse experimental data sets which often provide restraints for regions of defined secondary structure.
doi:10.1371/journal.pone.0049240
PMCID: PMC3500284  PMID: 23173050
18.  RNA folding on the 3D triangular lattice 
BMC Bioinformatics  2009;10:369.
Background
Difficult problems in structural bioinformatics are often studied in simple exact models to gain insights and to derive general principles. Protein folding, for example, has long been studied in the lattice model. Recently, researchers have also begun to apply the lattice model to the study of RNA folding.
Results
We present a novel method for predicting RNA secondary structures with pseudoknots: first simulate the folding dynamics of the RNA sequence on the 3D triangular lattice, next extract and select a set of disjoint base pairs from the best lattice conformation found by the folding simulation. Experiments on sequences from PseudoBase show that our prediction method outperforms the HotKnot algorithm of Ren, Rastegari, Condon and Hoos, a leading method for RNA pseudoknot prediction. Our method for RNA secondary structure prediction can be adapted into an efficient reconstruction method that, given an RNA sequence and an associated secondary structure, finds a conformation of the sequence on the 3D triangular lattice that realizes the base pairs in the secondary structure. We implemented a suite of computer programs for the simulation and visualization of RNA folding on the 3D triangular lattice. These programs come with detailed documentation and are accessible from the companion website of this paper at http://www.cs.usu.edu/~mjiang/rna/DeltaIS/.
Conclusion
Folding simulation on the 3D triangular lattice is effective method for RNA secondary structure prediction and lattice conformation reconstruction. The visualization software for the lattice conformations of RNA structures is a valuable tool for the study of RNA folding and is a great pedagogic device.
doi:10.1186/1471-2105-10-369
PMCID: PMC2780420  PMID: 19891777
19.  Six Rossmannoid folds, including the Class I aminoacyl-tRNA synthetases, share a partial core with the anti-codon-binding domain of a Class II aminoacyl-tRNA synthetase 
Bioinformatics  2010;26(6):709-714.
Motivation: Similarities in core residue packing provide evidence for divergence or convergence not reported using other methods.
Results: We apply a new method for rapid structure comparison based on Simplicial Neighborhood Analysis of Protein Packing (SNAPP) to the diverse structural classification of proteins (SCOP) α/β-class of protein folds. The procedure identifies inter-residue packing motifs shared by protein pairs from different folds. A threshold of 0.67 Å RMSD for all atoms of corresponding residues ensures inclusion of only highly significant similarities comparable with those observed for identical catalytic residues in homologues. Many tertiary packing motifs are shared among the three classical Rossmannoid folds, as well as thousands of other motifs that occur in at least two distinct folds. Merging of neighboring packing motifs facilitated recognition of larger, recurrent substructures or cores. The anti-codon-binding domain of an archeal aminoacyl-tRNA synthetase (aaRS) was discovered to possess a packed core in which eight identical amino acid residues are within 0.55 Å RMSD of the comparable structure in the FixJ receiver, a member of the Rossmannoid family that also includes the CheY signaling protein and flavodoxin-like proteins. Further investigation identified close variants of this core in five other Rossmannoid folds, including a functionally relevant core in Class Ia aminoacyl-tRNA synthetases. Although it is possible that the two essentially identical cores in the ProRS anti-codon-binding domain and the FixJ receiver converged to the same structure, the consensus core obtained from the structural and sequence alignments suggests that all the implicated protein folds descended from a simpler ancestral protein in which this core provided nucleotide binding and proto-allosteric functions.
Availability: Programs are available at http://staff.vbi.vt.edu/cammer/snapp/download/
Implementation: Programs were written in Perl and c and run under Linux.
Contact: cammer@vbi.vt.edu
doi:10.1093/bioinformatics/btq039
PMCID: PMC2852213  PMID: 20130031
20.  Gaia: automated quality assessment of protein structure models 
Bioinformatics  2011;27(16):2209-2215.
Motivation: Increasing use of structural modeling for understanding structure–function relationships in proteins has led to the need to ensure that the protein models being used are of acceptable quality. Quality of a given protein structure can be assessed by comparing various intrinsic structural properties of the protein to those observed in high-resolution protein structures.
Results: In this study, we present tools to compare a given structure to high-resolution crystal structures. We assess packing by calculating the total void volume, the percentage of unsatisfied hydrogen bonds, the number of steric clashes and the scaling of the accessible surface area. We assess covalent geometry by determining bond lengths, angles, dihedrals and rotamers. The statistical parameters for the above measures, obtained from high-resolution crystal structures enable us to provide a quality-score that points to specific areas where a given protein structural model needs improvement.
Availability and Implementation: We provide these tools that appraise protein structures in the form of a web server Gaia (http://chiron.dokhlab.org). Gaia evaluates the packing and covalent geometry of a given protein structure and provides quantitative comparison of the given structure to high-resolution crystal structures.
Contact: dokh@unc.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btr374
PMCID: PMC3150034  PMID: 21700672
21.  Extended structures in RNA folding intermediates are due to non-native interactions rather than electrostatic repulsion 
Journal of molecular biology  2010;397(5):1298-1306.
RNA folding occurs via a series of transitions between metastable intermediate states for Mg2+ concentrations below those needed to fold the native structure. In general, these folding intermediates are considerably less compact than their respective native states. Our previous work demonstrates that the major equilibrium intermediate of the 154 residue specificity domain (S-domain) of the B. subtilis RNase P RNA is more extended than its native structure. We now investigate two models with falsifiable predictions regarding the origins of the extended intermediate structures in the S-domains of the B. subtilis and the E. coli RNase P RNA that belong to different classes P RNA and have distinct native structures. The first model explores the contribution of electrostatic repulsion, while the second model probes specific interactions in the core of the folding intermediate. Using small-angle X-ray scattering (SAXS) and Langevin Dynamics (LD) simulations, we show that electrostatics only plays a minor role, whereas specific interactions largely accounts for the extended nature of the intermediate. Structural contacts in the core, including a non-native base-pair, help to stabilize the intermediate conformation. We conclude that RNA folding intermediates adopt extended conformations due to short-range, non-native interactions rather than generic electrostatic repulsion of helical domains. These principles apply to other ribozymes and riboswitches that undergo functionally relevant conformational changes.
doi:10.1016/j.jmb.2010.02.025
PMCID: PMC2873146  PMID: 20188108
Langevin dynamics; P RNA; S-domain
22.  Native structure-based modeling and simulation of biomolecular systems per mouse click 
BMC Bioinformatics  2014;15(1):292.
Background
Molecular dynamics (MD) simulations provide valuable insight into biomolecular systems at the atomic level. Notwithstanding the ever-increasing power of high performance computers current MD simulations face several challenges: the fastest atomic movements require time steps of a few femtoseconds which are small compared to biomolecular relevant timescales of milliseconds or even seconds for large conformational motions. At the same time, scalability to a large number of cores is limited mostly due to long-range interactions. An appealing alternative to atomic-level simulations is coarse-graining the resolution of the system or reducing the complexity of the Hamiltonian to improve sampling while decreasing computational costs. Native structure-based models, also called Gō-type models, are based on energy landscape theory and the principle of minimal frustration. They have been tremendously successful in explaining fundamental questions of, e.g., protein folding, RNA folding or protein function. At the same time, they are computationally sufficiently inexpensive to run complex simulations on smaller computing systems or even commodity hardware. Still, their setup and evaluation is quite complex even though sophisticated software packages support their realization.
Results
Here, we establish an efficient infrastructure for native structure-based models to support the community and enable high-throughput simulations on remote computing resources via GridBeans and UNICORE middleware. This infrastructure organizes the setup of such simulations resulting in increased comparability of simulation results. At the same time, complete workflows for advanced simulation protocols can be established and managed on remote resources by a graphical interface which increases reusability of protocols and additionally lowers the entry barrier into such simulations for, e.g., experimental scientists who want to compare their results against simulations. We demonstrate the power of this approach by illustrating it for protein folding simulations for a range of proteins.
Conclusions
We present software enhancing the entire workflow for native structure-based simulations including exception-handling and evaluations. Extending the capability and improving the accessibility of existing simulation packages the software goes beyond the state of the art in the domain of biomolecular simulations. Thus we expect that it will stimulate more individuals from the community to employ more confidently modeling in their research.
Electronic supplementary material
The online version of this article (doi:10.1186/1471-2105-15-292) contains supplementary material, which is available to authorized users.
doi:10.1186/1471-2105-15-292
PMCID: PMC4162935  PMID: 25176255
Protein folding; RNA folding; Native structure-based model; Molecular dynamics; GridBeans
23.  Differences between cotranscriptional and free riboswitch folding 
Nucleic Acids Research  2013;42(4):2687-2696.
Riboswitches are part of noncoding regions of messenger RNA (mRNA) that act as RNA sensors regulating gene expression of the downstream gene. Typically, one out of two distinct conformations is formed depending on ligand binding when the transcript leaves RNA polymerase (RNAP). Elongation of the RNA chain by RNAP, folding and binding all occurs simultaneously and interdependently on the seconds’ timescale. To investigate the effect of transcript elongation velocity on folding for the S-adenosylmethionine (SAM)-I and adenine riboswitches we employ two complementary coarse-grained in silico techniques. Native structure-based molecular dynamics simulations provide a 3D, atomically resolved model of folding with homogenous energetics. Energetically more detailed kinetic Monte Carlo simulations give access to longer timescale by describing folding on the secondary structure level and feature the incorporation of competing aptamer conformations and a ligand-binding model. Depending on the extrusion scenarios, we observe and quantify different pathways in structure formation with robust agreements between the two techniques. In these scenarios, free-folding riboswitches exhibit different folding characteristics compared with transcription-rate limited folding. The critical transcription rate distinguishing these cases is higher than physiologically relevant rates. This result suggests that in vivo folding of the analyzed SAM-I and adenine riboswitches is transcription-rate limited.
doi:10.1093/nar/gkt1213
PMCID: PMC3936736  PMID: 24275497
24.  Self Containment, a Property of Modular RNA Structures, Distinguishes microRNAs 
PLoS Computational Biology  2008;4(8):e1000150.
RNA molecules will tend to adopt a folded conformation through the pairing of bases on a single strand; the resulting so-called secondary structure is critical to the function of many types of RNA. The secondary structure of a particular substring of functional RNA may depend on its surrounding sequence. Yet, some RNAs such as microRNAs retain their specific structures during biogenesis, which involves extraction of the substructure from a larger structural context, while other functional RNAs may be composed of a fusion of independent substructures. Such observations raise the question of whether particular functional RNA substructures may be selected for invariance of secondary structure to their surrounding nucleotide context. We define the property of self containment to be the tendency for an RNA sequence to robustly adopt the same optimal secondary structure regardless of whether it exists in isolation or is a substring of a longer sequence of arbitrary nucleotide content. We measured degree of self containment using a scoring method we call the self-containment index and found that miRNA stem loops exhibit high self containment, consistent with the requirement for structural invariance imposed by the miRNA biogenesis pathway, while most other structured RNAs do not. Further analysis revealed a trend toward higher self containment among clustered and conserved miRNAs, suggesting that high self containment may be a characteristic of novel miRNAs acquiring new genomic contexts. We found that miRNAs display significantly enhanced self containment compared to other functional RNAs, but we also found a trend toward natural selection for self containment in most functional RNA classes. We suggest that self containment arises out of selection for robustness against perturbations, invariance during biogenesis, and modular composition of structural function. Analysis of self containment will be important for both annotation and design of functional RNAs. A Python implementation and Web interface to calculate the self-containment index are available at http://kim.bio.upenn.edu/software/.
Author Summary
An RNA molecule is made up of a linear sequence of nucleotides, which form pairwise interactions that define its folded three-dimensional structure; the particular structure largely depends on the specific sequence. These base-pairing interactions are stabilizing, and the RNA will tend to fold in a particular way to maximize stability. Consider some nucleotide sequence that optimally folds into some structure in isolation; if this sequence is now embedded inside a larger sequence, then either the original structure will be a robust subcomponent of the larger folded structure, or it will be disrupted due to new interactions between the original sequence and the surrounding sequence. We explore this property of context robustness of structure and in particular define the property of “self containment” to describe intrinsic context robustness—i.e., the tendency for certain sequences to be structurally robust in many different sequence contexts. Self containment turns out to be a strong characteristic of a class of RNAs called microRNAs, whose biogenesis process depends on the maintenance of structural robustness. This finding will be useful in future efforts to characterize novel miRNAs, as well as in understanding the regulation and evolution of noncoding functional RNAs as modular units.
doi:10.1371/journal.pcbi.1000150
PMCID: PMC2517099  PMID: 18725951
25.  Predicting RNA pseudoknot folding thermodynamics 
Nucleic Acids Research  2006;34(9):2634-2652.
Based on the experimentally determined atomic coordinates for RNA helices and the self-avoiding walks of the P (phosphate) and C4 (carbon) atoms in the diamond lattice for the polynucleotide loop conformations, we derive a set of conformational entropy parameters for RNA pseudoknots. Based on the entropy parameters, we develop a folding thermodynamics model that enables us to compute the sequence-specific RNA pseudoknot folding free energy landscape and thermodynamics. The model is validated through extensive experimental tests both for the native structures and for the folding thermodynamics. The model predicts strong sequence-dependent helix-loop competitions in the pseudoknot stability and the resultant conformational switches between different hairpin and pseudoknot structures. For instance, for the pseudoknot domain of human telomerase RNA, a native-like and a misfolded hairpin intermediates are found to coexist on the (equilibrium) folding pathways, and the interplay between the stabilities of these intermediates causes the conformational switch that may underlie a human telomerase disease.
doi:10.1093/nar/gkl346
PMCID: PMC1463895  PMID: 16709732

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