Emerging structural themes in large RNA molecules

Extensive networks of tertiary interactions give rise to unique, highly organized domain architectures that characterize the three-dimensional structure of large RNA molecules. Formed by stacked layers of a near-planar arrangement of contiguous coaxial helices, large RNA molecules are relatively flat in overall shape. The functional core of these molecules is stabilized by a diverse set of tertiary interaction motifs that often bring together distant regions of conserved nucleotides. Although homologous RNAs from different organisms can be structurally diverse, they adopt a structurally conserved functional core that includes preassembled active and/or substrate binding sites. These findings broaden our understanding of RNA folding and tertiary structure stabilization, illustrating how large, complex RNAs assemble into unique structures to perform recognition and catalysis.     

Evaluating mixture models for building RNA knowledge-based potentials

Ribonucleic acid (RNA) molecules play important roles in a variety of biological processes. To properly function, RNA molecules usually have to fold to specific structures, and therefore understanding RNA structure is vital in comprehending how RNA functions. One approach to understanding and predicting biomolecular structure is to use knowledge-based potentials built from experimentally determined structures. These types of potentials have been shown to be effective for predicting both protein and RNA structures, but their utility is limited by their significantly rugged nature. This ruggedness (and hence the potential's usefulness) depends heavily on the choice of bin width to sort structural information (e.g. distances) but the appropriate bin width is not known a priori. To circumvent the binning problem, we compared knowledge-based potentials built from inter-atomic distances in RNA structures using different mixture models (Kernel Density Estimation, Expectation Minimization and Dirichlet Process). We show that the smooth knowledge-based potential built from Dirichlet process is successful in selecting native-like RNA models from different sets of structural decoys with comparable efficacy to a potential developed by spline-fitting - a commonly taken approach - to binned distance histograms. The less rugged nature of our potential suggests its applicability in diverse types of structural modeling.     

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.     

Prediction of structural stability of short beta-hairpin peptides by molecular dynamics and knowledge-based potentials

Background  

The structural stability of peptides in solution strongly affects their binding affinities and specificities. Thus, in peptide biotechnology, an increase in the structural stability is often desirable. The present work combines two orthogonal computational techniques, Molecular Dynamics and a knowledge-based potential, for the prediction of structural stability of short peptides (< 20 residues) in solution.     

Coarse-grained molecular simulations of large biomolecules

Recently, we saw a dramatic increase in the number of researches that rely on coarse-grained (CG) simulations for large biomolecules. Here, first, we briefly describe recently developed and used CG models for proteins and nucleic acids. Balance between structure-based and physico-chemical terms is a key issue. We also discuss the multiscale algorithms used to derive CG parameters. Next, we comment on the dynamics used in CG simulations with an emphasis on the importance of hydrodynamic interactions. We then discuss the pros and cons of CG simulations. Finally, we overview recent exciting applications of CG simulations. Publicly available tools and software for CG simulations are also summarized.     

Coarse-grained modeling of mucus barrier properties

We designed a simple coarse-grained model of the glycocalyx layer, or adhesive mucus layer (AML), covered by mucus gel (luminal mucus layer) using a polymer lattice model and stochastic sampling (replica exchange Monte Carlo) for canonical ensemble simulations. We assumed that mucin MUC16 is responsible for the structural properties of the AML. Other mucins that are much smaller in size and less relevant for layer structure formation were not included. We further assumed that the system was in quasi-equilibrium. For systems with surface coverage and concentrations of model mucins mimicking physiological conditions, we determined the equilibrium distribution of inert nanoparticles within the mucus layers using an efficient replica exchange Monte Carlo sampling procedure. The results show that the two mucus layers penetrate each other only marginally, and the bilayer imposes a strong barrier for nanoparticles, with the AML layer playing a crucial role in the mucus barrier.     

On the occurrence of the T-loop RNA folding motif in large RNA molecules

The T-loop RNA folding motif may be considered as a five-nucleotide motif composed of a U-turn flanked by a noncanonical base pair. It was recently proposed that the flanking noncanonical base pair is always a UA trans Watson-Crick/Hoogsteen base pair stacked on a Watson-Crick base pair on one side. Here we show that structural analysis of several large RNA molecules, including the recently solved crystal structure of the specificity domain of Bacillus subtilis RNase P, combined with sequence analysis, indicates a broader sequence consensus for the motif. Additionally, we show that the flanking base pair does not necessarily stack on a Watson-Crick base pair and the 3' terminus of the five-nucleotide motif is often followed by a sharp turn in the phosphate backbone rather than just a bulged base or bases.     

Predicting transmembrane helix pair configurations with knowledge-based distance-dependent pair potentials

As a first step toward a novel de novo structure prediction approach for alpha-helical membrane proteins, we developed coarse-grained knowledge-based potentials to score the mutual configuration of transmembrane (TM) helices. Using a comprehensive database of 71 known membrane protein structures, pairwise potentials depending solely on amino acid types and distances between C(alpha)-atoms were derived. To evaluate the potentials, they were used as an objective function for the rigid docking of 442 TM helix pairs. This is by far the largest test data set reported to date for that purpose. After clustering 500 docking runs for each pair and considering the largest cluster, we found solutions with a root mean squared (RMS) deviation <2 A for about 30% of all helix pairs. Encouragingly, if only clusters that contain at least 20% of all decoys are considered, a success rate >71% (with a RMS deviation <2 A) is obtained. The cluster size thus serves as a measure of significance to identify good docking solutions. In a leave-one-protein-family-out cross-validation study, more than 2/3 of the helix pairs were still predicted with an RMS deviation <2.5 A (if only clusters that contain at least 20% of all decoys are considered). This demonstrates the predictive power of the potentials in general, although it is advisable to further extend the knowledge base to derive more robust potentials in the future. When compared to the scoring function of Fleishman and Ben-Tal, a comparable performance is found by our cross-validated potentials. Finally, well-predicted "anchor helix pairs" can be reliably identified for most of the proteins of the test data set. This is important for an extension of the approach towards TM helix bundles because these anchor pairs will act as "nucleation sites" to which more helices will be added subsequently, which alleviates the sampling problem.     

Potentials 'R'Us web-server for protein energy estimations with coarse-grained knowledge-based potentials

Background  

Knowledge-based potentials have been widely used in the last 20 years for fold recognition, protein structure prediction from amino acid sequence, ligand binding, protein design, and many other purposes. However generally these are not readily accessible online.     

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.     

Ligand-supported homology modelling of protein binding-sites using knowledge-based potentials

A new approach, MOBILE, is presented that models protein binding-sites including bound ligand molecules as restraints. Initially generated, homology models of the target protein are refined iteratively by including information about bioactive ligands as spatial restraints and optimising the mutual interactions between the ligands and the binding-sites. Thus optimised models can be used for structure-based drug design and virtual screening. In a first step, ligands are docked into an averaged ensemble of crude homology models of the target protein. In the next step, improved homology models are generated, considering explicitly the previously placed ligands by defining restraints between protein and ligand atoms. These restraints are expressed in terms of knowledge-based distance-dependent pair potentials, which were compiled from crystallographically determined protein-ligand complexes. Subsequently, the most favourable models are selected by ranking the interactions between the ligands and the generated pockets using these potentials. Final models are obtained by selecting the best-ranked side-chain conformers from various models, followed by an energy optimisation of the entire complex using a common force-field. Application of the knowledge-based pair potentials proved efficient to restrain the homology modelling process and to score and optimise the modelled protein-ligand complexes. For a test set of 46 protein-ligand complexes, taken from the Protein Data Bank (PDB), the success rate of producing near-native binding-site geometries (rmsd<2.0A) with MODELLER is 70% when the ligand restrains the homology modelling process in its native orientation. Scoring these complexes with the knowledge-based potentials, in 66% of the cases a pose with rmsd <2.0A is found on rank 1. Finally, MOBILE has been applied to two case studies modelling factor Xa based on trypsin and aldose reductase based on aldehyde reductase.     

Analysis of knowledge-based protein-ligand potentials using a self-consistent method

We propose a self-consistent approach to analyze knowledge-based atom-atom potentials used to calculate protein-ligand binding energies. Ligands complexed to actual protein structures were first built using the SMoG growth procedure (DeWitte & Shakhnovich, 1996) with a chosen input potential. These model protein-ligand complexes were used to construct databases from which knowledge-based protein-ligand potentials were derived. We then tested several different modifications to such potentials and evaluated their performance on their ability to reconstruct the input potential using the statistical information available from a database composed of model complexes. Our data indicate that the most significant improvement resulted from properly accounting for the following key issues when estimating the reference state: (1) the presence of significant nonenergetic effects that influence the contact frequencies and (2) the presence of correlations in contact patterns due to chemical structure. The most successful procedure was applied to derive an atom-atom potential for real protein-ligand complexes. Despite the simplicity of the model (pairwise contact potential with a single interaction distance), the derived binding free energies showed a statistically significant correlation (approximately 0.65) with experimental binding scores for a diverse set of complexes.     

Recurring features of local tertiary structural elements in RNA molecules exemplified by hepatitis D virus RNA

Elements of local tertiary structure in RNA molecules are important in understanding structure-function relationships. The loop E motif, first identified in several eukaryotic RNAs at functional sites which share an exceptional propensity for UV crosslinking between specific bases, was subsequently shown to have a characteristic tertiary structure. Common sequences and secondary structures have allowed other examples of the E-loop motif to be recognized in a number of RNAs at sites of protein binding or other biological function. We would like to know if more elements of local tertiary structure, in addition to the E-loop, can be identified by such common features. The highly structured circular RNA genome of the hepatitis D virus (HDV) provides an ideal test molecule because it has extensive internal structure, a UV-crosslinkable tertiary element, and specific sites for functional interactions with proteins including host PKR. We have now found a UV-crosslinkable element of local tertiary structure in antigenomic HDV RNA which, although differing from the E-loop, has a very similar pattern of sequence and secondary structure to the UV-crosslinkable element found in the genomic strand. Despite the fact that the two structures map close to one another, the sequences comprising them are not the templates for each other. Instead, the template regions for each element are additional sites for potential higher order structure on their respective complementary strands. This wealth of recurring sequences interspersed with base-paired stems provides a context to examine other RNA species for such features and their correlations with biological function.     

Coarse-grained modeling of the actin filament derived from atomistic-scale simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.     

Evolutionary potentials: structure specific knowledge-based potentials exploiting the evolutionary record of sequence homologs

We introduce a new type of knowledge-based potentials for protein structure prediction, called 'evolutionary potentials', which are derived using a single experimental protein structure and all three-dimensional models of its homologous sequences. The new potentials have been benchmarked against other knowledge-based potentials, resulting in a significant increase in accuracy for model assessment. In contrast to standard knowledge-based potentials, we propose that evolutionary potentials capture key determinants of thermodynamic stability and specific sequence constraints required for fast folding.     

Chemical probing of conformation in large RNA molecules. Analysis of 16 S ribosomal RNA using diethylpyrocarbonate

Peattie & Gilbert (1980) have described an accurate and rapid gel method for assessing conformation of individual nucleotides in RNA, based on chemical modification of bases and aniline-induced strand scission. In order to extend this approach to analysis of large RNA molecules, we introduce the use of hybridization of modified RNA with DNA restriction fragments to generate RNA fragments of defined length. In principle, this permits chemical probing of conformation at any position of any RNA molecule for which a cloned DNA coding sequence is available. To illustrate the utility of this method, we use diethylpyrocarbonate to probe the reactivities of adenine residues in Escherichia coli 16 S rRNA under "native" (80 mM-potassium cacodylate (pH 7.0), 20 mM-MgCl2, 300 mM-KCl) and "quasi-secondary" (80 mM-potassium cacodylate (pH 7.0), 1 mM-EDTA) conditions. This study shows that: (1) there is generally good agreement between diethylpyrocarbonate reactivities of adenine residues in naked 16 S rRNA and a secondary structure model based on comparative sequence analysis; of 309 adenine residues probed under native conditions, only four strongly reactive residues are found in helices in the model. (2) Candidates for possible tertiary interactions are identified as adenine residues that are unpaired in the model and unreactive toward diethylpyrocarbonate under native conditions but reactive under quasi-secondary conditions. (3) An unexpectedly stable structure has been identified in the region between positions 109 and 279, where many adenine residues remain unreactive even at 90 degrees C in 80 mM-potassium cacodylate, 1 mM-EDTA. This may correspond to a structural "core" that is important for early events in ribosome assembly.