Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.     

De novo protein structure prediction by dynamic fragment assembly and conformational space annealing

Ab initio protein structure prediction is a challenging problem that requires both an accurate energetic representation of a protein structure and an efficient conformational sampling method for successful protein modeling. In this article, we present an ab initio structure prediction method which combines a recently suggested novel way of fragment assembly, dynamic fragment assembly (DFA) and conformational space annealing (CSA) algorithm. In DFA, model structures are scored by continuous functions constructed based on short- and long-range structural restraint information from a fragment library. Here, DFA is represented by the full-atom model by CHARMM with the addition of the empirical potential of DFIRE. The relative contributions between various energy terms are optimized using linear programming. The conformational sampling was carried out with CSA algorithm, which can find low energy conformations more efficiently than simulated annealing used in the existing DFA study. The newly introduced DFA energy function and CSA sampling algorithm are implemented into CHARMM. Test results on 30 small single-domain proteins and 13 template-free modeling targets of the 8th Critical Assessment of protein Structure Prediction show that the current method provides comparable and complementary prediction results to existing top methods.     

A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction

Background

Elucidating the native structure of a protein molecule from its sequence of amino acids, a problem known as de novo structure prediction, is a long standing challenge in computational structural biology. Difficulties in silico arise due to the high dimensionality of the protein conformational space and the ruggedness of the associated energy surface. The issue of multiple minima is a particularly troublesome hallmark of energy surfaces probed with current energy functions. In contrast to the true energy surface, these surfaces are weakly-funneled and rich in comparably deep minima populated by non-native structures. For this reason, many algorithms seek to be inclusive and obtain a broad view of the low-energy regions through an ensemble of low-energy (decoy) conformations. Conformational diversity in this ensemble is key to increasing the likelihood that the native structure has been captured.

Methods

We propose an evolutionary search approach to address the multiple-minima problem in decoy sampling for de novo structure prediction. Two population-based evolutionary search algorithms are presented that follow the basic approach of treating conformations as individuals in an evolving population. Coarse graining and molecular fragment replacement are used to efficiently obtain protein-like child conformations from parents. Potential energy is used both to bias parent selection and determine which subset of parents and children will be retained in the evolving population. The effect on the decoy ensemble of sampling minima directly is measured by additionally mapping a conformation to its nearest local minimum before considering it for retainment. The resulting memetic algorithm thus evolves not just a population of conformations but a population of local minima.

Results and conclusions

Results show that both algorithms are effective in terms of sampling conformations in proximity of the known native structure. The additional minimization is shown to be key to enhancing sampling capability and obtaining a diverse ensemble of decoy conformations, circumventing premature convergence to sub-optimal regions in the conformational space, and approaching the native structure with proximity that is comparable to state-of-the-art decoy sampling methods. The results are shown to be robust and valid when using two representative state-of-the-art coarse-grained energy functions.

     

Sampling realistic protein conformations using local structural bias

The prediction of protein structure from sequence remains a major unsolved problem in biology. The most successful protein structure prediction methods make use of a divide-and-conquer strategy to attack the problem: a conformational sampling method generates plausible candidate structures, which are subsequently accepted or rejected using an energy function. Conceptually, this often corresponds to separating local structural bias from the long-range interactions that stabilize the compact, native state. However, sampling protein conformations that are compatible with the local structural bias encoded in a given protein sequence is a long-standing open problem, especially in continuous space. We describe an elegant and mathematically rigorous method to do this, and show that it readily generates native-like protein conformations simply by enforcing compactness. Our results have far-reaching implications for protein structure prediction, determination, simulation, and design.     

Enhanced sampling near the native conformation using statistical potentials for local side-chain and backbone interactions

In the preceding article in this issue of Proteins, an empirical energy function consisting of 4 statistical potentials that quantify local side-chain-backbone and side-chain-side-chain interactions has been demonstrated to successfully identify the native conformations of short sequence fragments and the native structure within large sets of high-quality decoys. Because this energy function consists entirely of interactions between residues separated by fewer than 5 positions, it can be used at the earliest stage of ab initio structure prediction to enhance the efficiency of conformational search. In this article, protein fragments are generated de novo by recombining very short segments of protein structures (2, 4, or 6 residues), either selected at random or optimized with respect this local energy function. When local energy is optimized in selected fragments, more efficient sampling of conformational space near the native conformation is consistently observed for 450 randomly selected single turn fragments, with turn lengths varying from 3 to 12 residues and all 4 combinations of flanking secondary structure. These results further demonstrate the energetic significance of local interactions in protein conformations. When used in combination with longer range energy functions, application of these potentials should lead to more accurate prediction of protein structure.     

Force field based conformational analysis of RNA structural motifs: GNRA tetraloops and their pyrimidine relatives

The protocol of conformational analysis applied here to ribonucleotide oligomers combines conformational search in the space of torsion angles and energy minimization using the AMBER4.1 force field with a continuum treatment of electrostatic solute-solvent interactions. RNA fragments with 5′-GGGCGNNAGCCU-3′ sequences commonly fold into hairpins with four-membered loops. The combinatorial search for acceptable conformations using the MC-SYM program was restricted to loop nucleotides and yielded roughly 1500 structures being compatible with a double-stranded stem. After energy minimization by the JUMNA program (without applying any experimental constraints), these structures converged into an ensemble of 74 different conformers including 26 structures which contained the sheared G-A base pair observed in experimental studies of GNRA tetraloops. Energetic analysis shows that inclusion of solvent electrostatic effects is critically important for the selection of conformers that agree with experimentally determined structures. The continuum model accounts for solvent polarization by means of the electrostatic reaction field. In the case of GNRA loop sequences, the contributions of the reaction field shift relative stabilities towards conformations showing most of the structural features derived from NMR studies. The agreement of computed conformations with the experimental structures of GAAA, GCAA, and GAGA tetraloops suggests that the continuum treatment of the solvent represents a definitive improvement over methods using simple damping models in electrostatic energy calculations. Application of the procedure described here to the evaluation of the relative stabilities of conformers resulting from searching the conformational space of RNA structural motifs provides some progress in (non-homology based) RNA 3D-structure prediction. Received: 20 January 1999 / Revised version: 4 June 1999 / Accepted: 10 June 1999     

Improved prediction of RNA tertiary structure with insights into native state dynamics

The importance of RNA tertiary structure is evident from the growing number of published high resolution NMR and X-ray crystallographic structures of RNA molecules. These structures provide insights into function and create a knowledge base that is leveraged by programs such as Assemble, ModeRNA, RNABuilder, NAST, FARNA, Mc-Sym, RNA2D3D, and iFoldRNA for tertiary structure prediction and design. While these methods sample native-like RNA structures during simulations, all struggle to capture the native RNA conformation after scoring. We propose RSIM, an improved RNA fragment assembly method that preserves RNA global secondary structure while sampling conformations. This approach enhances the quality of predicted RNA tertiary structure, provides insights into the native state dynamics, and generates a powerful visualization of the RNA conformational space. RSIM is available for download from http://www.github.com/jpbida/rsim.     

Protein local conformations arise from a mixture of Gaussian distributions

The classical approaches for protein structure prediction rely either on homology of the protein sequence with a template structure or on ab initio calculations for energy minimization. These methods suffer from disadvantages such as the lack of availability of homologous template structures or intractably large conformational search space, respectively. The recently proposed fragment library based approaches first predict the local structures,which can be used in conjunction with the classical approaches of protein structure prediction. The accuracy of the predictions is dependent on the quality of the fragment library. In this work, we have constructed a library of local conformation classes purely based on geometric similarity. The local conformations are represented using Geometric Invariants, properties that remain unchanged under transformations such as translation and rotation, followed by dimension reduction via principal component analysis. The local conformations are then modeled as a mixture of Gaussian probability distribution functions (PDF). Each one of the Gaussian PDF's corresponds to a conformational class with the centroid representing the average structure of that class. We find 46 classes when we use an octapeptide as a unit of local conformation. The protein 3-D structure can now be described as a sequence of local conformational classes. Further, it was of interest to see whether the local conformations can be predicted from the amino acid sequences. To that end,we have analyzed the correlation between sequence features and the conformational classes.     

Modeling of the structure in aqueous solution of the exopolysaccharide produced by Lactobacillus helveticus 766.

A method is described for constructing a conformational model in water of a heteropolysaccharide built up from repeating units, and is applied to the exopolysaccharide produced by Lactobacillus helveticus 766. The molecular modeling method is based on energy minima, obtained from molecular mechanics calculations of each of the constituting disaccharide fragments of the repeating unit in vacuo, as starting points. Subsequently, adaptive umbrella sampling of the potential of mean force is applied to extract rotamer populations of glycosidic dihedral angles of oligosaccharide fragments in solution. From these analyses, the most probable conformations are constructed for the hexasaccharide-repeating unit of the polysaccharide. After exploring the conformational space of each of the individual structures by molecular dynamics simulations, the different repeating unit conformations are used as building blocks for the generation of oligo- and polysaccharide models, by using a polysaccharide building program. The created models of the exopolysaccharide produced by L. helveticus 766 exhibit a flexible twisted secondary structure and tend to adopt a random coil conformation as tertiary structure.     

Protein local conformations arise from a mixture of Gaussian distributions

The classical approaches for protein structure prediction rely either on homology of the protein sequence with a template structure or on ab initio calculations for energy minimization. These methods suffer from disadvantages such as the lack of availability of homologous template structures or intractably large conformational search space, respectively. The recently proposed fragment library based approaches first predict the local structures, which can be used in conjunction with the classical approaches of protein structure prediction. The accuracy of the predictions is dependent on the quality of the fragment library. In this work, we have constructed a library of local conformation classes purely based on geometric similarity. The local conformations are represented using Geometric Invariants, properties that remain unchanged under transformations such as translation and rotation, followed by dimension reduction via principal component analysis. The local conformations are then modeled as a mixture of Gaussian probability distribution functions (PDF). Each one of the Gaussian PDF’s corresponds to a conformational class with the centroid representing the average structure of that class. We find 46 classes when we use an octapeptide as a unit of local conformation. The protein 3-D structure can now be described as a sequence of local conformational classes. Further, it was of interest to see whether the local conformations can be predicted from the amino acid sequences. To that end, we have analyzed the correlation between sequence features and the conformational classes.     

Validating a Coarse-Grained Potential Energy Function through Protein Loop Modelling

Coarse-grained (CG) methods for sampling protein conformational space have the potential to increase computational efficiency by reducing the degrees of freedom. The gain in computational efficiency of CG methods often comes at the expense of non-protein like local conformational features. This could cause problems when transitioning to full atom models in a hierarchical framework. Here, a CG potential energy function was validated by applying it to the problem of loop prediction. A novel method to sample the conformational space of backbone atoms was benchmarked using a standard test set consisting of 351 distinct loops. This method used a sequence-independent CG potential energy function representing the protein using -carbon positions only and sampling conformations with a Monte Carlo simulated annealing based protocol. Backbone atoms were added using a method previously described and then gradient minimised in the Rosetta force field. Despite the CG potential energy function being sequence-independent, the method performed similarly to methods that explicitly use either fragments of known protein backbones with similar sequences or residue-specific /-maps to restrict the search space. The method was also able to predict with sub-Angstrom accuracy two out of seven loops from recently solved crystal structures of proteins with low sequence and structure similarity to previously deposited structures in the PDB. The ability to sample realistic loop conformations directly from a potential energy function enables the incorporation of additional geometric restraints and the use of more advanced sampling methods in a way that is not possible to do easily with fragment replacement methods and also enable multi-scale simulations for protein design and protein structure prediction. These restraints could be derived from experimental data or could be design restraints in the case of computational protein design. C++ source code is available for download from http://www.sbg.bio.ic.ac.uk/phyre2/PD2/.     

Coarse-Grained Prediction of RNA Loop Structures

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.     

Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

RNA molecules play integral roles in gene regulation, and understanding their structures gives us important insights into their biological functions. Despite recent developments in template-based and parameterized energy functions, the structure of RNA--in particular the nonhelical regions--is still difficult to predict. Knowledge-based potentials have proven efficient in protein structure prediction. In this work, we describe two differentiable knowledge-based potentials derived from a curated data set of RNA structures, with all-atom or coarse-grained representation, respectively. We focus on one aspect of the prediction problem: the identification of native-like RNA conformations from a set of near-native models. Using a variety of near-native RNA models generated from three independent methods, we show that our potential is able to distinguish the native structure and identify native-like conformations, even at the coarse-grained level. The all-atom version of our knowledge-based potential performs better and appears to be more effective at discriminating near-native RNA conformations than one of the most highly regarded parameterized potential. The fully differentiable form of our potentials will additionally likely be useful for structure refinement and/or molecular dynamics simulations.     

Predicting Peptide Structures in Native Proteins from Physical Simulations of Fragments

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.     

Backrub-like backbone simulation recapitulates natural protein conformational variability and improves mutant side-chain prediction

Incorporation of effective backbone sampling into protein simulation and design is an important step in increasing the accuracy of computational protein modeling. Recent analysis of high-resolution crystal structures has suggested a new model, termed backrub, to describe localized, hinge-like alternative backbone and side-chain conformations observed in the crystal lattice. The model involves internal backbone rotations about axes between C-alpha atoms. Based on this observation, we have implemented a backrub-inspired sampling method in the Rosetta structure prediction and design program. We evaluate this model of backbone flexibility using three different tests. First, we show that Rosetta backrub simulations recapitulate the correlation between backbone and side-chain conformations in the high-resolution crystal structures upon which the model was based. As a second test of backrub sampling, we show that backbone flexibility improves the accuracy of predicting point-mutant side-chain conformations over fixed backbone rotameric sampling alone. Finally, we show that backrub sampling of triosephosphate isomerase loop 6 can capture the millisecond/microsecond oscillation between the open and closed states observed in solution. Our results suggest that backrub sampling captures a sizable fraction of localized conformational changes that occur in natural proteins. Application of this simple model of backbone motions may significantly improve both protein design and atomistic simulations of localized protein flexibility.     

Protein structure prediction based on fragment assembly and parameter optimization

We propose a novel method for ab-initio prediction of protein tertiary structures based on the fragment assembly and global optimization. Fifteen residue long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full-length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low-lying local minima of the energy. Then in order to enhance the performance of the prediction method, we optimize the linear parameters of the energy function, so that the native-like conformations become energetically more favorable than the non-native ones for proteins with known structures. We test the feasibility of the parameter optimization procedure by applying it to the training set consisting of three proteins: the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd), a designed protein betanova, and 1fsd.     

A conditional random fields method for RNA sequence-structure relationship modeling and conformation sampling

Accurate tertiary structures are very important for the functional study of non-coding RNA molecules. However, predicting RNA tertiary structures is extremely challenging, because of a large conformation space to be explored and lack of an accurate scoring function differentiating the native structure from decoys. The fragment-based conformation sampling method (e.g. FARNA) bears shortcomings that the limited size of a fragment library makes it infeasible to represent all possible conformations well. A recent dynamic Bayesian network method, BARNACLE, overcomes the issue of fragment assembly. In addition, neither of these methods makes use of sequence information in sampling conformations. Here, we present a new probabilistic graphical model, conditional random fields (CRFs), to model RNA sequence-structure relationship, which enables us to accurately estimate the probability of an RNA conformation from sequence. Coupled with a novel tree-guided sampling scheme, our CRF model is then applied to RNA conformation sampling. Experimental results show that our CRF method can model RNA sequence-structure relationship well and sequence information is important for conformation sampling. Our method, named as TreeFolder, generates a much higher percentage of native-like decoys than FARNA and BARNACLE, although we use the same simple energy function as BARNACLE. CONTACT: zywang@ttic.edu; j3xu@ttic.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Strategies for dealing with conformational sampling in structural calculations of flexible or kinked transmembrane peptides.

Peptides corresponding to transmembrane (TM) segments from membrane proteins provide a potential route for the determination of membrane protein structure. We have determined that 2 functionally critical TM segments from the mammalian Na+/H+ exchanger display well converged structure in regions separated by break points. The flexibility of these break points results in conformational sampling in solution. A brief review of available NMR structures of helical membrane proteins demonstrates that there are a number of published structures showing similar properties. Such flexibility is likely indicative of kinks in the full-length protein. This minireview focuses on methods and protocols for NMR structure calculation and analysis of peptide structures under conditions of conformational sampling. The methods outlined allow the identification and analysis of structured peptides containing break points owing to conformational sampling and the differentiation between oligomerization and ensemble-averaged observation of multiple peptide conformations.     

Synergistic SHAPE/Single-Molecule Deconvolution of RNA Conformation under Physiological Conditions

Structural RNA domains are widely involved in the regulation of biological functions, such as gene expression, gene modification, and gene repair. Activity of these dynamic regions depends sensitively on the global fold of the RNA, in particular, on the binding affinity of individual conformations to effector molecules in solution. Consequently, both the 1) structure and 2) conformational dynamics of noncoding RNAs prove to be essential in understanding the coupling that results in biological function. Toward this end, we recently reported observation of three conformational states in the metal-induced folding pathway of the tRNA-like structure domain of Brome Mosaic Virus, via single-molecule fluorescence resonance energy transfer studies. We report herein selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE)-directed structure predictions as a function of metal ion concentrations ([Mⁿ⁺]) to confirm the three-state folding model, as well as test 2° structure models from the literature. Specifically, SHAPE reactivity data mapped onto literature models agrees well with the secondary structures observed at 0–10 mM [Mg²⁺], with only minor discrepancies in the E hairpin domain at low [Mg²⁺]. SHAPE probing and SHAPE-directed structure predictions further confirm the stepwise unfolding pathway previously observed in our single-molecule studies. Of special relevance, this means that reduction in the metal-ion concentration unfolds the 3′ pseudoknot interaction before unfolding the long-range stem interaction. This work highlights the synergistic power of combining 1) single-molecule Förster resonance energy transfer and 2) SHAPE-directed structure-probing studies for detailed analysis of multiple RNA conformational states. In particular, single-molecule guided deconvolution of the SHAPE reactivities permits 2° structure predictions of isolated RNA conformations, thereby substantially improving on traditional limitations associated with current structure prediction algorithms.