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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.  Ab initio folding of proteins using all-atom discrete molecular dynamics 
Structure (London, England : 1993)  2008;16(7):1010-1018.
Summary
Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. Using the replica exchange method, we perform folding simulations of six small proteins (20–60 residues) with distinct native structures. In all cases, native or near-native states are reached in simulations. For three small proteins, multiple folding transitions are observed and the computationally-characterized thermodynamics are in quantitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes, and applied to protein engineering and design of protein-protein interactions.
doi:10.1016/j.str.2008.03.013
PMCID: PMC2533517  PMID: 18611374
ab initio protein folding; environment-dependent hydrogen bond; replica exchange; free energy landscape; conformational sampling
3.  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
4.  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
5.  DNA tri- and tetra-loops and RNA tetra-loops hairpins fold as elastic biopolymer chains in agreement with PDB coordinates 
Nucleic Acids Research  2003;31(3):1086-1096.
The biopolymer chain elasticity (BCE) approach and the new molecular modelling methodology presented previously are used to predict the tri- dimensional backbones of DNA and RNA hairpin loops. The structures of eight remarkably stable DNA or RNA hairpin molecules closed by a mispair, recently determined in solution by NMR and deposited in the PDB, are shown to verify the predicted trajectories by an analysis automated for large numbers of PDB conformations. They encompass: one DNA tetraloop, -GTTA-; three DNA triloops, -AAA- or -GCA-; and four RNA tetraloops, -UUCG-. Folding generates no distortions and bond lengths and bond angles of main atoms of the sugar–phosphate backbone are well restored upon energy refinement. Three different methods (superpositions, distance of main chain atoms to the elastic line and RMSd) are used to show a very good agreement between the trajectories of sugar–phosphate backbones and between entire molecules of theoretical models and of PDB conformations. The geometry of end conditions imposed by the stem is sufficient to dictate the different characteristic DNA or RNA folding shapes. The reduced angular space, consisting of the new parameter, angle Ω, together with the χ angle offers a simple, coherent and quantitative description of hairpin loops.
PMCID: PMC149216  PMID: 12560507
6.  The shape-shifting quasispecies of RNA: One sequence, many functional folds 
Physical Chemistry Chemical Physics  2011;13(24):11524-11537.
E Unus pluribum, or “Of One, Many”, may be at the root of decoding the RNA sequence-structure-function relationship. RNAs embody the large majority of genes in higher eukaryotes and fold in a sequence-directed fashion into three-dimensional structures that perform functions conserved across all cellular life forms, ranging from regulating to executing gene expression. While it is the most important determinant of RNA structure, the nucleotide sequence is generally not sufficient to specify a unique set of secondary and tertiary interactions due to the highly frustrated nature of RNA folding. This frustration results in folding heterogeneity, a common phenomenon wherein a chemically homogeneous population of RNA molecules folds into multiple stable structures. Often, these alternative conformations constitute misfolds, lacking the biological activity of the natively folded RNA. Intriguingly, a number of RNAs have recently been described as capable of adopting multiple distinct conformations that all perform, or contribute to, the same function. Characteristically, these conformations interconvert slowly on the experimental timescale, suggesting that they should be regarded as distinct native states. We discuss how rugged folding free energy landscapes give rise to multiple native states in the Tetrahymena Group I intron ribozyme, hairpin ribozyme, sarcin-ricin loop, ribosome, and an in vitro selected aptamer. We further describe the varying degrees to which folding heterogeneity impacts function in these RNAs, and compare and contrast this impact with that of heterogeneities found in protein folding. Embracing that one sequence can give rise to multiple native folds, we hypothesize that this phenomenon imparts adaptive advantages on any functionally evolving RNA quasispecies.
doi:10.1039/c1cp20576e
PMCID: PMC3359863  PMID: 21603685
7.  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
8.  Robust and Generic RNA Modeling Using Inferred Constraints: A Structure for the Hepatitis C Virus IRES Pseudoknot Domain 
Biochemistry  2010;49(24):4931-4933.
RNA function is dependent on its structure, yet three-dimensional folds for most biologically important RNAs are unknown. We develop a generic discrete molecular dynamics (DMD)-based modeling system that uses long-range constraints inferred from diverse biochemical or bioinformatic analyses to create statistically significant (p < 0.01) native-like folds for RNAs of known structure ranging from 45 to 158 nucleotides. We then predict the unknown structure of the hepatitis C virus IRES pseudoknot domain. The resulting RNA model rationalizes independent solvent accessibility and cryo-electron microscopy structure information. The pseudoknot positions the AUG start codon near the mRNA channel and is tRNA-like, suggesting the IRES employs molecular mimicry as a functional strategy.
doi:10.1021/bi100142y
PMCID: PMC2889920  PMID: 20545364
9.  The high-resolution NMR structure of the early folding intermediate of the Thermus thermophilus ribonuclease H 
Journal of molecular biology  2008;384(2):531-539.
Elucidation of the high-resolution structures of folding intermediates is a necessary but difficult step toward the ultimate understanding of the mechanism of protein folding. Here, using hydrogen exchange-directed protein engineering, we populated the folding intermediate of the T. thermophilus ribonuclease H, which forms before the rate-limiting transition state, by removing the unfolded regions of the intermediate, including an α-helix and two β-strands (51 folded residues). Using multi-dimensional NMR, we solved the structure of this intermediate mimic to an atomic resolution (backbone rmsd 0.51 Å). It has a native-like backbone topology and shows some local deviations from the native structure, revealing that the structure of the folded region of an early folding intermediate can be as well defined as the native structure. The topological parameters calculated from the structures of the intermediate mimic and the native state predict that the intermediate should fold on a millisecond time scale or less and form much faster than the native state. Other factors that may lead to the slow folding of the native state and the accumulation of the intermediate before the rate-limiting transition state are also discussed.
doi:10.1016/j.jmb.2008.09.044
PMCID: PMC2628467  PMID: 18848567
10.  Frnakenstein: multiple target inverse RNA folding 
BMC Bioinformatics  2012;13:260.
Background
RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard.
Results
In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets.
Conclusions
Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.
doi:10.1186/1471-2105-13-260
PMCID: PMC3534541  PMID: 23043260
RNA; Inverse folding; Genetic algorithm; Riboswitch
11.  RNA misfolding and the action of chaperones 
RNA folds to a myriad of three-dimensional structures and performs an equally diverse set of functions. The ability of RNA to fold and function in vivo is all the more remarkable because, in vitro, RNA has been shown to have a strong propensity to adopt misfolded, non-functional conformations. A principal factor underlying the dominance of RNA misfolding is that local RNA structure can be quite stable even in the absence of enforcing global tertiary structure. This property allows non-native structure to persist, and it also allows native structure to form and stabilize non-native contacts or non-native topology. In recent years it has become clear that one of the central reasons for the apparent disconnect between the capabilities of RNA in vivo and its in vitro folding properties is the presence of RNA chaperones, which facilitate conformational transitions of RNA and therefore mitigate the deleterious effects of RNA misfolding. Over the past two decades, it has been demonstrated that several classes of non-specific RNA binding proteins possess profound RNA chaperone activity in vitro and when overexpressed in vivo, and at least some of these proteins appear to function as chaperones in vivo. More recently, it has been shown that certain DExD/H-box proteins function as general chaperones to facilitate folding of group I and group II introns. These proteins are RNA-dependent ATPases and have RNA helicase activity, and are proposed to function by using energy from ATP binding and hydrolysis to disrupt RNA structure and/or to displace proteins from RNA-protein complexes. This review outlines experimental studies that have led to our current understanding of the range of misfolded RNA structures, the physical origins of RNA misfolding, and the functions and mechanisms of putative RNA chaperone proteins.
PMCID: PMC2610265  PMID: 17981525
RNA folding; DEAD-box Proteins; Cold-Shock Proteins; tRNA; group I intron; Review
12.  Folding and Finding RNA Secondary Structure 
SUMMARY
Optimal exploitation of the expanding database of sequences requires rapid finding and folding of RNAs. Methods are reviewed that automate folding and discovery of RNAs with algorithms that couple thermodynamics with chemical mapping, NMR, and/or sequence comparison. New functional noncoding RNAs in genome sequences can be found by combining sequence comparison with the assumption that functional noncoding RNAs will have more favorable folding free energies than other RNAs. When a new RNA is discovered, experiments and sequence comparison can restrict folding space so that secondary structure can be rapidly determined with the help of predicted free energies. In turn, secondary structure restricts folding in three dimensions, which allows modeling of three-dimensional structure. An example from a domain of a retrotransposon is described. Discovery of new RNAs and their structures will provide insights into evolution, biology, and design of therapeutics. Applications to studies of evolution are also reviewed.
Combining sequence comparison and thermodynamic considerations with experimental approaches such as chemical mapping and NMR allows rapid modeling of RNA secondary structure.
doi:10.1101/cshperspect.a003665
PMCID: PMC2982177  PMID: 20685845
13.  Electronic polarization stabilizes tertiary structure prediction of HP-36 
Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.
doi:10.1007/s00894-014-2195-7
PMCID: PMC3996369  PMID: 24715046
Molecular dynamics; Polarization effect; Protein folding; Solvent model
14.  Square-Shaped RNA Particles From Different RNA Folds 
Nano letters  2009;9(3):1270-1277.
The structural information encoding specific conformations of natural RNAs can be implemented within artificial RNA sequences to control both three-dimensional (3D) shape and self-assembling interfaces for nanotechnology and synthetic biology applications. We have identified three natural RNA motifs known to direct helical topology into approximately 90° bends: a five-way tRNA junction, a three-way junction and a two-helix bend. These three motifs, embedded within rationally designed RNAs (tectoRNA), were chosen for generating square-shaped tetrameric RNA nanoparticles (NPs). The ability of each motif to direct the formation of supramolecular assemblies was compared by both native gel assays and atomic force microscopy (AFM). While there are multiple structural solutions for building square-shaped RNA particles, differences in the thermodynamics and molecular dynamics of the 90°-motif can lead to different biophysical behaviors for the resulting supramolecular complexes. We demonstrate via structural assembly programming how the different 90°-motifs can preferentially direct the formation of either 2D or 3D assemblies.
doi:10.1021/nl900261h
PMCID: PMC2664548  PMID: 19239258
15.  Taming free energy landscapes with RNA chaperones 
RNA Biology  2010;7(6):677-686.
Many non-coding RNAs fold into complex three-dimensional structures, yet the self-assembly of RNA structure is hampered by mispairing, weak tertiary interactions, electrostatic barriers, and the frequent requirement that the 5′ and 3′ ends of the transcript interact. This rugged free energy landscape for RNA folding means that some RNA molecules in a population rapidly form their native structure, while many others become kinetically trapped in misfolded conformations. Transient binding of RNA chaperone proteins destabilize misfolded intermediates and lower the transition states between conformations, producing a smoother landscape that increases the rate of folding and the probability that a molecule will find the native structure. DEAD-box proteins couple the chemical potential of ATP hydrolysis with repetitive cycles of RNA binding and release, expanding the range of conditions under which they can refold RNA structures.
doi:10.4161/rna.7.6.13615
PMCID: PMC3073327  PMID: 21045544
RNA folding; kinetic partitioning; ribozyme; RNA chaperone; DEAD-box
16.  Multiple Native States Reveal Persistent Ruggedness of an RNA Folding Landscape 
Nature  2010;463(7281):681-684.
According to the “thermodynamic hypothesis”, the sequence of a biological macromolecule defines its folded, active structure as a global energy minimum on the folding landscape.1,2 But the enormous complexity of folding landscapes of large macromolecules raises a question: Is there indeed a unique global energy minimum corresponding to a unique native conformation, or are there deep local minima corresponding to alternative active conformations?3 Folding of many proteins is well described by two-state models, leading to highly simplified representations of protein folding landscapes with a single native conformation.4,5 Nevertheless, accumulating experimental evidence suggests a more complex topology of folding landscapes with multiple active conformations that can take seconds or longer to interconvert.6,7,8 Here we employ single molecule experiments to demonstrate that an RNA enzyme folds into multiple distinct native states that interconvert much slower than the time scale of catalysis. These data demonstrate that the severe ruggedness of RNA folding landscapes extends into conformational space occupied by native conformations.
doi:10.1038/nature08717
PMCID: PMC2818749  PMID: 20130651
17.  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
18.  Discrete RNA libraries from pseudo-torsional space 
Journal of molecular biology  2012;421(1):6-26.
The discovery that RNA molecules can fold into complex structures and carry out diverse cellular roles has led to interest in developing tools for modeling RNA tertiary structure. While significant progress has been made in establishing that the RNA backbone is rotameric, few libraries of discrete conformations specifically for use in RNA modeling have been validated. Here, we present six libraries of discrete RNA conformations based on a simplified pseudo-torsional notation of the RNA backbone, comparable to phi and psi in the protein backbone. We evaluate the ability of each library to represent single nucleotide backbone conformations and we show how individual library fragments can be assembled into dinucleotides that are consistent with established RNA backbone descriptors spanning from sugar to sugar. We then use each library to build all-atom models of 20 test folds and we show how the composition of a fragment library can limit model quality. Despite the limitations inherent in using discretized libraries, we find that several hundred discrete fragments can rebuild RNA folds up to 174 nucleotides in length with atomic-level accuracy (<1.5Å RMSD). We anticipate the libraries presented here could easily be incorporated into RNA structural modeling, analysis, or refinement tools.
doi:10.1016/j.jmb.2012.03.002
PMCID: PMC3422622  PMID: 22425640
RNA structure; RNA backbone conformation; RNA fragment library; RNA modeling
19.  Coarse-Grained Prediction of RNA Loop Structures 
PLoS ONE  2012;7(11):e48460.
One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.
doi:10.1371/journal.pone.0048460
PMCID: PMC3493578  PMID: 23144887
20.  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
21.  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
22.  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
23.  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
24.  Mapping the Kinetic Barriers of a Large RNA Molecule's Folding Landscape 
PLoS ONE  2014;9(2):e85041.
The folding of linear polymers into discrete three-dimensional structures is often required for biological function. The formation of long-lived intermediates is a hallmark of the folding of large RNA molecules due to the ruggedness of their energy landscapes. The precise thermodynamic nature of the barriers (whether enthalpic or entropic) that leads to intermediate formation is still poorly characterized in large structured RNA molecules. A classic approach to analyzing kinetic barriers are temperature dependent studies analyzed with Eyring's transition state theory. We applied Eyring's theory to time-resolved hydroxyl radical (•OH) footprinting kinetics progress curves collected at eight temperature from 21.5°C to 51°C to characterize the thermodynamic nature of folding intermediate formation for the Mg2+-mediated folding of the Tetrahymena thermophila group I ribozyme. A common kinetic model configuration describes this RNA folding reaction over the entire temperature range studied consisting of primary (fast) transitions to misfolded intermediates followed by much slower secondary transitions, consistent with previous studies. Eyring analysis reveals that the primary transitions are moderate in magnitude and primarily enthalpic in nature. In contrast, the secondary transitions are daunting in magnitude and entropic in nature. The entropic character of the secondary transitions is consistent with structural rearrangement of the intermediate species to the final folded form. This segregation of kinetic control reveals distinctly different molecular mechanisms during the two stages of RNA folding and documents the importance of entropic barriers to defining rugged RNA folding landscapes.
doi:10.1371/journal.pone.0085041
PMCID: PMC3934814  PMID: 24586236
25.  Predicting protein folding pathways at the mesoscopic level based on native interactions between secondary structure elements 
BMC Bioinformatics  2008;9:320.
Background
Since experimental determination of protein folding pathways remains difficult, computational techniques are often used to simulate protein folding. Most current techniques to predict protein folding pathways are computationally intensive and are suitable only for small proteins.
Results
By assuming that the native structure of a protein is known and representing each intermediate conformation as a collection of fully folded structures in which each of them contains a set of interacting secondary structure elements, we show that it is possible to significantly reduce the conformation space while still being able to predict the most energetically favorable folding pathway of large proteins with hundreds of residues at the mesoscopic level, including the pig muscle phosphoglycerate kinase with 416 residues. The model is detailed enough to distinguish between different folding pathways of structurally very similar proteins, including the streptococcal protein G and the peptostreptococcal protein L. The model is also able to recognize the differences between the folding pathways of protein G and its two structurally similar variants NuG1 and NuG2, which are even harder to distinguish. We show that this strategy can produce accurate predictions on many other proteins with experimentally determined intermediate folding states.
Conclusion
Our technique is efficient enough to predict folding pathways for both large and small proteins at the mesoscopic level. Such a strategy is often the only feasible choice for large proteins. A software program implementing this strategy (SSFold) is available at .
doi:10.1186/1471-2105-9-320
PMCID: PMC2527578  PMID: 18651953

Results 1-25 (632170)