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.     

On the Importance of the Distance Measures Used to Train and Test Knowledge-Based Potentials for Proteins

Knowledge-based potentials are energy functions derived from the analysis of databases of protein structures and sequences. They can be divided into two classes. Potentials from the first class are based on a direct conversion of the distributions of some geometric properties observed in native protein structures into energy values, while potentials from the second class are trained to mimic quantitatively the geometric differences between incorrectly folded models and native structures. In this paper, we focus on the relationship between energy and geometry when training the second class of knowledge-based potentials. We assume that the difference in energy between a decoy structure and the corresponding native structure is linearly related to the distance between the two structures. We trained two distance-based knowledge-based potentials accordingly, one based on all inter-residue distances (PPD), while the other had the set of all distances filtered to reflect consistency in an ensemble of decoys (PPE). We tested four types of metric to characterize the distance between the decoy and the native structure, two based on extrinsic geometry (RMSD and GTD-TS*), and two based on intrinsic geometry (Q* and MT). The corresponding eight potentials were tested on a large collection of decoy sets. We found that it is usually better to train a potential using an intrinsic distance measure. We also found that PPE outperforms PPD, emphasizing the benefits of capturing consistent information in an ensemble. The relevance of these results for the design of knowledge-based potentials is discussed.     

3dRNAscore: a distance and torsion angle dependent evaluation function of 3D RNA structures

Model evaluation is a necessary step for better prediction and design of 3D RNA structures. For proteins, this has been widely studied and the knowledge-based statistical potential has been proved to be one of effective ways to solve this problem. Currently, a few knowledge-based statistical potentials have also been proposed to evaluate predicted models of RNA tertiary structures. The benchmark tests showed that they can identify the native structures effectively but further improvements are needed to identify near-native structures and those with non-canonical base pairs. Here, we present a novel knowledge-based potential, 3dRNAscore, which combines distance-dependent and dihedral-dependent energies. The benchmarks on different testing datasets all show that 3dRNAscore are more efficient than existing evaluation methods in recognizing native state from a pool of near-native states of RNAs as well as in ranking near-native states of RNA models.     

GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies

Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.     

Dynamic RNA Fitness Landscapes of a Group I Ribozyme during Changes to the Experimental Environment

Fitness landscapes of protein and RNA molecules can be studied experimentally using high-throughput techniques to measure the functional effects of numerous combinations of mutations. The rugged topography of these molecular fitness landscapes is important for understanding and predicting natural and experimental evolution. Mutational effects are also dependent upon environmental conditions, but the effects of environmental changes on fitness landscapes remains poorly understood. Here, we investigate the changes to the fitness landscape of a catalytic RNA molecule while changing a single environmental variable that is critical for RNA structure and function. Using high-throughput sequencing of in vitro selections, we mapped a fitness landscape of the Azoarcus group I ribozyme under eight different concentrations of magnesium ions (1–48 mM MgCl₂). The data revealed the magnesium dependence of 16,384 mutational neighbors, and from this, we investigated the magnesium induced changes to the topography of the fitness landscape. The results showed that increasing magnesium concentration improved the relative fitness of sequences at higher mutational distances while also reducing the ruggedness of the mutational trajectories on the landscape. As a result, as magnesium concentration was increased, simulated populations evolved toward higher fitness faster. Curve-fitting of the magnesium dependence of individual ribozymes demonstrated that deep sequencing of in vitro reactions can be used to evaluate the structural stability of thousands of sequences in parallel. Overall, the results highlight how environmental changes that stabilize structures can also alter the ruggedness of fitness landscapes and alter evolutionary processes.     

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.     

Different combinations of atomic interactions predict protein‐small molecule and protein‐DNA/RNA affinities with similar accuracy

Interactions between proteins and other molecules play essential roles in all biological processes. Although it is widely held that a protein's ligand specificity is determined primarily by its three‐dimensional structure, the general principles by which structure determines ligand binding remain poorly understood. Here we use statistical analyses of a large number of protein?ligand complexes with associated binding‐affinity measurements to quantitatively characterize how combinations of atomic interactions contribute to ligand affinity. We find that there are significant differences in how atomic interactions determine ligand affinity for proteins that bind small chemical ligands, those that bind DNA/RNA and those that interact with other proteins. Although protein‐small molecule and protein‐DNA/RNA binding affinities can be accurately predicted from structural data, models predicting one type of interaction perform poorly on the others. Additionally, the particular combinations of atomic interactions required to predict binding affinity differed between small‐molecule and DNA/RNA data sets, consistent with the conclusion that the structural bases determining ligand affinity differ among interaction types. In contrast to what we observed for small‐molecule and DNA/RNA interactions, no statistical models were capable of predicting protein?protein affinity with >60% correlation. We demonstrate the potential usefulness of protein‐DNA/RNA binding prediction as a possible tool for high‐throughput virtual screening to guide laboratory investigations, suggesting that quantitative characterization of diverse molecular interactions may have practical applications as well as fundamentally advancing our understanding of how molecular structure translates into function. Proteins 2015; 83:2100–2114. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

Interaction cutoff effect on ruggedness of protein-protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.     

Stochastic modeling of noninteracting probes in the protein structure space for construction of knowledge-based potentials for atom-atom interactions

Knowledge-based potentials are extensively used to represent atomic interactions in modeling the protein structure. We consider a number of problems in constructing efficient knowledge-based potentials for biopolymer modeling. We show that some limitations can be overcome by normalizing estimated interactions through the distribution of distances between noninteracting random probes in protein structure space. We demonstrate that knowledge-based potentials thus constructed can be efficiently applied for analysis of the hydration state of proteins atoms. With this approach, one can predict the locations of structural water molecules in a protein globule. We have also succeeded in recognizing the correctly folded protein structure among many misfolded decoys in cases when the interaction with water solvent is dominant for structure formation.     

Energy barriers, pathways, and dynamics during folding of large, multidomain RNAs

Large, multidomain RNA molecules are generally thought to fold following multiple pathways down rugged landscapes populated with intermediates and traps. A challenge to understanding RNA folding reactions is the complex relationships that exist between the structure of the RNA and its folding landscape. The identification of intermediate species that populate folding landscapes and characterization of elements of their structures are the key components to solving the RNA folding problem. This review explores recent studies that characterize the dominant pathways by which RNA folds, structural and dynamic features of intermediates that populate the folding landscape, and the energy barriers that separate the distinct steps of the folding process.     

Discriminative ability with respect to amino acid types: assessing the performance of knowledge-based potentials without threading

We present a novel method designed to analyze the discriminative ability of knowledge-based potentials with respect to the 20 residue types. The method is based on the preference of amino acids for specific types of protein environment, and uses a virtual mutagenesis experiment to estimate how much information a given potential can provide about environments of each amino acid type. This allows one to test and optimize the performance of real potentials at the level of individual amino acids, using actual data on residue environments from a dataset of known protein structures. We have applied our method to long-range and medium-range pairwise distance-dependent potentials. The results of our study indicate that these potentials are only able to discriminate between a very limited number of residue types, and that discriminative ability is extremely sensitive to the choice of parameters used to construct the potentials, and even to the size of the training dataset. We also show that different types of pairwise distance potentials are dominated by different types of interactions. These dominant interactions strongly depend on the type of approximation used to define residue position. For each potential, our methodology is able to identify a potential-specific amino acid distance matrix and a reduced amino acid alphabet of any specified size, which may have implications for sequence alignment and multibody models.     

Extracting stacking interaction parameters for RNA from the data set of native structures

A crucial step in the determination of the three-dimensional native structures of RNA is the prediction of their secondary structures, which are stable independent of the tertiary fold. Accurate prediction of the secondary structure requires context-dependent estimates of the interaction parameters. We have exploited the growing database of natively folded RNA structures in the Protein Data Bank (PDB) to obtain stacking interaction parameters using a knowledge-based approach. Remarkably, the calculated values of the resulting statistical potentials (SPs) are in excellent agreement with the parameters determined using measurements in small oligonucleotides. We validate the SPs by predicting 74% of the base-pairs in a dataset of structures using the ViennaRNA package. Interestingly, this number is similar to that obtained using the measured thermodynamic parameters. We also tested the efficacy of the SP in predicting secondary structure by using gapless threading, which we advocate as an alternative method for rapidly predicting RNA structures. For RNA molecules with less than 700 nucleotides, about 70% of the native base-pairs are correctly predicted. As a further validation of the SPs we calculated Z-scores, which measure the relative stability of the native state with respect to a manifold of higher free energy states. The computed Z-scores agree with estimates made using calorimetric measurements for a few RNA molecules. Structural analysis was used to rationalize the success and failures of SP and experimentally determined parameters. First, from the near perfect linear relationship between the number of native base-pairs and sequence length, we show that nearly 46% of nucleotides are not in stacks. Second, by analyzing the suboptimal structures that are generated in gapless threading we show that the SPs and experimentally determined parameters are most successful in predicting stacks that end in hairpins. These results show that further improvement in secondary structure prediction requires reliable estimates of interaction parameters for loops, bulges, and stacks that do not end in hairpins.     

A knowledge-based forcefield for protein-protein interface design

A distance-dependent knowledge-based potential for protein-protein interactions is derived and tested for application in protein design. Information on residue type specific C(alpha) and C(beta) pair distances is extracted from complex crystal structures in the Protein Data Bank and used in the form of radial distribution functions. The use of only backbone and C(beta) position information allows generation of relative protein-protein orientation poses with minimal sidechain information. Further coarse-graining can be done simply in the same theoretical framework to give potentials for residues of known type interacting with unknown type, as in a one-sided interface design problem. Both interface design via pose generation followed by sidechain repacking and localized protein-protein docking tests are performed on 39 nonredundant antibody-antigen complexes for which crystal structures are available. As reference, Lennard-Jones potentials, unspecific for residue type and biasing toward varying degrees of residue pair separation are used as controls. For interface design, the knowledge-based potentials give the best combination of consistently designable poses, low RMSD to the known structure, and more tightly bound interfaces with no added computational cost. 77% of the poses could be designed to give complexes with negative free energies of binding. Generally, larger interface separation promotes designability, but weakens the binding of the resulting designs. A localized docking test shows that the knowledge-based nature of the potentials improves performance and compares respectably with more sophisticated all-atoms potentials.     

Statistical measures on residue-level protein structural properties

The atomic-level structural properties of proteins, such as bond lengths, bond angles, and torsion angles, have been well studied and understood based on either chemistry knowledge or statistical analysis. Similar properties on the residue-level, such as the distances between two residues and the angles formed by short sequences of residues, can be equally important for structural analysis and modeling, but these have not been examined and documented on a similar scale. While these properties are difficult to measure experimentally, they can be statistically estimated in meaningful ways based on their distributions in known proteins structures. Residue-level structural properties including various types of residue distances and angles are estimated statistically. A software package is built to provide direct access to the statistical data for the properties including some important correlations not previously investigated. The distributions of residue distances and angles may vary with varying sequences, but in most cases, are concentrated in some high probability ranges, corresponding to their frequent occurrences in either α-helices or β-sheets. Strong correlations among neighboring residue angles, similar to those between neighboring torsion angles at the atomic-level, are revealed based on their statistical measures. Residue-level statistical potentials can be defined using the statistical distributions and correlations of the residue distances and angles. Ramachandran-like plots for strongly correlated residue angles are plotted and analyzed. Their applications to structural evaluation and refinement are demonstrated. With the increase in both number and quality of known protein structures, many structural properties can be derived from sets of protein structures by statistical analysis and data mining, and these can even be used as a supplement to the experimental data for structure determinations. Indeed, the statistical measures on various types of residue distances and angles provide more systematic and quantitative assessments on these properties, which can otherwise be estimated only individually and qualitatively. Their distributions and correlations in known protein structures show their importance for providing insights into how proteins may fold naturally to various residue-level structures.     

Structural organization of the RNA-degrading exosome

The RNA exosome participates in the degradation and processing of a wide range of RNA molecules. Recent advances in understanding how the exosome is organized and functions largely stem from structural studies. Crystal structures of archaeal exosomes bound to RNA and of the corresponding nine-subunit human exosome core show that the archaeal and eukaryotic complexes have a similar molecular architecture, but have a diverged catalytic mechanism. The crystal structures of two hydrolytic RNases that associate with the exosome provide the framework for their catalytic activity. Negative-stain EM reconstructions give us a first glimpse of how they associate with the core complex. Together, these structural studies have implications for the mechanism of RNA recruitment and degradation by the exosome complexes.     

Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters

Understanding the function of complex RNA molecules depends critically on understanding their structure. However, creating three-dimensional (3D) structural models of RNA remains a significant challenge. We present a protocol (the nucleic acid simulation tool [NAST]) for RNA modeling that uses an RNA-specific knowledge-based potential in a coarse-grained molecular dynamics engine to generate plausible 3D structures. We demonstrate NAST's capabilities by using only secondary structure and tertiary contact predictions to generate, cluster, and rank structures. Representative structures in the best ranking clusters averaged 8.0 ± 0.3 Å and 16.3 ± 1.0 Å RMSD for the yeast phenylalanine tRNA and the P4-P6 domain of the Tetrahymena thermophila group I intron, respectively. The coarse-grained resolution allows us to model large molecules such as the 158-residue P4-P6 or the 388-residue T. thermophila group I intron. One advantage of NAST is the ability to rank clusters of structurally similar decoys based on their compatibility with experimental data. We successfully used ideal small-angle X-ray scattering data and both ideal and experimental solvent accessibility data to select the best cluster of structures for both tRNA and P4-P6. Finally, we used NAST to build in missing loops in the crystal structures of the Azoarcus and Twort ribozymes, and to incorporate crystallographic data into the Michel–Westhof model of the T. thermophila group I intron, creating an integrated model of the entire molecule. Our software package is freely available at https://simtk.org/home/nast.     

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.     

Towards genome-scale structure prediction for transmembrane proteins

In this paper we briefly review some of the recent progress made by ourselves and others in developing methods for predicting the structures of transmembrane proteins from amino acid sequence. Transmembrane proteins are an important class of proteins involved in many diverse biological functions, many of which have great impact in terms of disease mechanism and drug discovery. Despite their biological importance, it has proven very difficult to solve the structures of these proteins by experimental techniques, and so there is a great deal of pressure to develop effective methods for predicting their structure. The methods we discuss range from methods for transmembrane topology prediction to new methods for low resolution folding simulations in a knowledge-based force field. This potential is designed to reproduce the properties of the lipid bilayer. Our eventual aim is to apply these methods in tandem so that useful three-dimensional models can be built for a large fraction of the transmembrane protein domains in whole proteomes.