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.     

Monte carlo simulations of protein folding. II. Application to protein A,ROP, and crambin

The hierarchy of lattice Monte Carlo models described in the accompanying paper (Kolinski, A., Skolnick, J. Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Proteins 18:338–352, 1994) is applied to the simulation of protein folding and the prediction of 3-dimensional structure. Using sequence information alone, three proteins have been successfully folded: the B domain of staphylococcal protein A, a 120 residue, monomeric version of ROP dimer, and crambin. Starting from a random expanded conformation, the model proteins fold along relatively well-defined folding pathways. These involve a collection of early intermediates, which are followed by the final (and rate-determining) transition from compact intermediates closely resembling the molten globule state to the native-like state. The predicted structures are rather unique, with native-like packing of the side chains. The accuracy of the predicted native conformations is better than those obtained in previous folding simulations. The best (but by no means atypical) folds of protein A have a coordinate rms of 2.25 Å from the native Cα trace, and the best coordinate rms from crambin is 3.18 Å. For ROP monomer, the lowest coordinate rms from equivalent Cαs of ROP dimer is 3.65 Å. Thus, for two simple helical proteins and a small α/β protein, the ability to predict protein structure from sequence has been demonstrated. © 1994 John Wiley & Sons, Inc.     

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.     

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.     

Molecular dynamics simulations of hydrophobic collapse of ubiquitin.

Nine nonnative conformations of ubiquitin, generated during two different thermal denaturation trajectories, were simulated under nearly native conditions (62 degrees C). The simulations included all protein and solvent atoms explicitly, and simulation times ranged from 1-2.4 ns. The starting structures had alpha-carbon root-mean-square deviations (RMSDs) from the crystal structure of 4-12 A and radii of gyration as high as 1.3 times that of the native state. In all but one case, the protein collapsed when the temperature was lowered and sampled conformations as compact as those reached in a control simulation beginning from the crystal structure. In contrast, the protein did not collapse when simulated in a 60% methanol:water mixture. The behavior of the protein depended on the starting structure: during simulation of the most native-like starting structures (<5 A RMSD to the crystal structure) the RMSD decreased, the number of native hydrogen bonds increased, and the secondary and tertiary structure increased. Intermediate starting structures (5-10 A RMSD) collapsed to the radius of gyration of the control simulation, hydrophobic residues were preferentially buried, and the protein acquired some native contacts. However, the protein did not refold. The least native starting structures (10-12 A RMSD) did not collapse as completely as the more native-like structures; instead, they experienced large fluctuations in radius of gyration and went through cycles of expansion and collapse, with improved burial of hydrophobic residues in successive collapsed states.     

A Probabilistic Model of RNA Conformational Space

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.     

Estimating the Contributions of Selection and Self-Organization in RNA Secondary Structure

In addition to characteristic structural properties imposed by evolutionary modification, evolved, single-stranded RNAs also display characteristic structural properties imposed by intrinsic physical constraints on RNA polymer folding. The balance of intrinsic and functionally selected characters in the folded conformation of evolved secondary structures was determined by comparing the predicted secondary structures of evolved and unevolved (random) RNA sequences. Though evolved conformations are significantly more ordered than conformations of random-sequence RNA, this analysis demonstrates that the majority of conformational order within evolved structures results not from evolutionary optimization but from constraints imposed by rules intrinsic to RNA polymer folding. Received: 25 November 1998 / Accepted: 12 February 1999     

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.     

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.     

Predicting RNA pseudoknot folding thermodynamics

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.     

Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains

Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.     

Contact order and ab initio protein structure prediction

Although much of the motivation for experimental studies of protein folding is to obtain insights for improving protein structure prediction, there has been relatively little connection between experimental protein folding studies and computational structural prediction work in recent years. In the present study, we show that the relationship between protein folding rates and the contact order (CO) of the native structure has implications for ab initio protein structure prediction. Rosetta ab initio folding simulations produce a dearth of high CO structures and an excess of low CO structures, as expected if the computer simulations mimic to some extent the actual folding process. Consistent with this, the majority of failures in ab initio prediction in the CASP4 (critical assessment of structure prediction) experiment involved high CO structures likely to fold much more slowly than the lower CO structures for which reasonable predictions were made. This bias against high CO structures can be partially alleviated by performing large numbers of additional simulations, selecting out the higher CO structures, and eliminating the very low CO structures; this leads to a modest improvement in prediction quality. More significant improvements in predictions for proteins with complex topologies may be possible following significant increases in high-performance computing power, which will be required for thoroughly sampling high CO conformations (high CO proteins can take six orders of magnitude longer to fold than low CO proteins). Importantly for such a strategy, simulations performed for high CO structures converge much less strongly than those for low CO structures, and hence, lack of simulation convergence can indicate the need for improved sampling of high CO conformations. The parallels between Rosetta simulations and folding in vivo may extend to misfolding: The very low CO structures that accumulate in Rosetta simulations consist primarily of local up-down beta-sheets that may resemble precursors to amyloid formation.     

Cooperative folding mechanism of a beta-hairpin peptide studied by a multicanonical replica-exchange molecular dynamics simulation

G-peptide is a 16-residue peptide of the C-terminal end of streptococcal protein G B1 domain, which is known to fold into a specific beta-hairpin within 6 micros. Here, we study molecular mechanism on the stability and folding of G-peptide by performing a multicanonical replica-exchange (MUCAREM) molecular dynamics simulation with explicit solvent. Unlike the preceding simulations of the same peptide, the simulation was started from an unfolded conformation without any experimental information on the native conformation. In the 278-ns trajectory, we observed three independent folding events. Thus MUCAREM can be estimated to accelerate the folding reaction more than 60 times than the conventional molecular dynamics simulations. The free-energy landscape of the peptide at room temperature shows that there are three essential subevents in the folding pathway to construct the native-like beta-hairpin conformation: (i) a hydrophobic collapse of the peptide occurs with the side-chain contacts between Tyr45 and Phe52, (ii) then, the native-like turn is formed accompanying with the hydrogen-bonded network around the turn region, and (iii) finally, the rest of the backbone hydrogen bonds are formed. A number of stable native hydrogen bonds are formed cooperatively during the second stage, suggesting the importance of the formation of the specific turn structure. This is also supported by the accumulation of the nonnative conformations only with the hydrophobic cluster around Tyr45 and Phe52. These simulation results are consistent with high phi-values of the turn region observed by experiment.     

Structure and stability of RNA/RNA kissing complex: with application to HIV dimerization initiation signal

We develop a statistical mechanical model to predict the structure and folding stability of the RNA/RNA kissing-loop complex. One of the key ingredients of the theory is the conformational entropy for the RNA/RNA kissing complex. We employ the recently developed virtual bond-based RNA folding model (Vfold model) to evaluate the entropy parameters for the different types of kissing loops. A benchmark test against experiments suggests that the entropy calculation is reliable. As an application of the model, we apply the model to investigate the structure and folding thermodynamics for the kissing complex of the HIV-1 dimerization initiation signal. With the physics-based energetic parameters, we compute the free energy landscape for the HIV-1 dimer. From the energy landscape, we identify two minimal free energy structures, which correspond to the kissing-loop dimer and the extended-duplex dimer, respectively. The results support the two-step dimerization process for the HIV-1 replication cycle. Furthermore, based on the Vfold model and energy minimization, the theory can predict the native structure as well as the local minima in the free energy landscape. The root-mean-square deviations (RMSDs) for the predicted kissing-loop dimer and extended-duplex dimer are ∼3.0 Å. The method developed here provides a new method to study the RNA/RNA kissing complex.     

Predicting the structures of 18 peptides using Geocore

We describe an extensive test of Geocore, an ab initio peptide folding algorithm. We studied 18 short molecules for which there are structures in the Protein Data Bank; chains are up to 31 monomers long. Except for the very shortest peptides, an extremely simple energy function is sufficient to discriminate the true native state from more than 10(8) lowest energy conformations that are searched explicitly for each peptide. A high incidence of native-like structures is found within the best few hundred conformations generated by Geocore for each amino acid sequence. Predictions improve when the number of discrete phi/psi choices is increased.     

Beta-sheet folding of fragment (16-36) of bovine pancreatic trypsin inhibitor as predicted by Monte Carlo simulated annealing.

A tertiary structure prediction is described using Monte Carlo simulated annealing for the peptide fragment corresponding to residues 16-36 of bovine pancreatic trypsin inhibitor (BPTI). The simulation starts with randomly chosen initial conformations and is performed without imposing experimental constraints using energy functions given for generic interatomic interactions. Out of 20 simulation trials, seven conformations show a sheet-like structure--two strands connected by a turn--although this sheet-like structure is not as rigid as that observed in native BPTI. It is also shown that these conformations are mostly looped and exhibit a native-like right-handed twist. Unlike the case with the C-peptide of RNase A, no conspicuous alpha-helical structure is found in any of the final conformations obtained in the simulation. However, the lowest-energy conformation does not resemble exactly the native structure. This indicates that the rigid beta-sheet conformation of native BPTI merely corresponds to a local minimum of the energy function if the fragment with residues 16-36 is isolated from the native protein. A statistical analysis of all 20 final conformations suggests that the tendency for the peptide segments to form extended beta-strands is strong for those with residues 18-24, and moderate for those with residues 30-35. The segment of residues 25-29 does not tend to form any definite structure. In native BPTI, the former segments are involved in the beta-sheet and the latter in the turn. A folding scenario is also speculated from this analysis.     

Efficient identification of near‐native conformations in ab initio protein structure prediction using structural profiles

One of the major bottlenecks in many ab initio protein structure prediction methods is currently the selection of a small number of candidate structures for high‐resolution refinement from large sets of low‐resolution decoys. This step often includes a scoring by low‐resolution energy functions and a clustering of conformations by their pairwise root mean square deviations (RMSDs). As an efficient selection is crucial to reduce the overall computational cost of the predictions, any improvement in this direction can increase the overall performance of the predictions and the range of protein structures that can be predicted. We show here that the use of structural profiles, which can be predicted with good accuracy from the amino acid sequences of proteins, provides an efficient means to identify good candidate structures. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

A NMR strategy to unambiguously distinguish nucleic acid hairpin and duplex conformations applied to a Xist RNA A-repeat

All RNA sequences that fold into hairpins possess the intrinsic potential to form intermolecular duplexes because of their high self-complementarity. The thermodynamically more stable duplex conformation is favored under high salt conditions and at high RNA concentrations, posing a challenging problem for structural studies of small RNA hairpin conformations. We developed and applied a novel approach to unambiguously distinguish RNA hairpin and duplex conformations for the structural analysis of a Xist RNA A-repeat. Using a combination of a quantitative HNN-COSY experiment and an optimized double isotope-filtered NOESY experiment we could define the conformation of the 26-mer A-repeat RNA. In contrast to a previous secondary structure prediction of a double hairpin structure, the NMR data show that only the first predicted hairpin is formed, while the second predicted hairpin mediates dimerization of the A-repeat by duplex formation with a second A-repeat. The strategy employed here will be generally applicable to identify and quantify populations of hairpin and duplex conformations and to define RNA folding topology from inter- and intra-molecular base-pairing patterns.