Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.     

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.     

Validating and improving elastic network models with molecular dynamics simulations

Elastic network models (ENMs) are a class of simple models intended to represent the collective motions of proteins. In contrast to all‐atom molecular dynamics simulations, the low computational investment required to use an ENM makes them ideal for speculative hypothesis‐testing situations. Historically, ENMs have been validated via comparison to crystallographic B‐factors, but this comparison is relatively low‐resolution and only tests the predictions of relative flexibility. In this work, we systematically validate and optimize a number of ENM‐type models by quantitatively comparing their predictions to microsecond‐scale all‐atom simulations of three different G protein coupled receptors. We show that, despite their apparent simplicity, well‐optimized ENMs perform remarkably well, reproducing the protein fluctuations with an accuracy comparable to what one would expect from all‐atom simulations run for several hundred nanoseconds. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins

While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.     

Validation of X-ray Crystal Structure Ensemble Representations of SARS-CoV-2 Main Protease by Solution NMR Residual Dipolar Couplings

Considerable debate has focused on whether sampling of molecular dynamics trajectories restrained by crystallographic data can be used to develop realistic ensemble models for proteins in their natural, solution state. For the SARS-CoV-2 main protease, M^pro, we evaluated agreement between solution residual dipolar couplings (RDCs) and various recently reported multi-conformer and dynamic-ensemble crystallographic models. Although Phenix-derived ensemble models showed only small improvements in crystallographic R_free, substantially improved RDC agreement over fits to a conventionally refined 1.2-Å X-ray structure was observed, in particular for residues with above average disorder in the ensemble. For a set of six lower resolution (1.55–2.19 Å) M^pro X-ray ensembles, obtained at temperatures ranging from 100 to 310 K, no significant improvement over conventional two-conformer representations was found. At the residue level, large differences in motions were observed among these ensembles, suggesting high uncertainties in the X-ray derived dynamics. Indeed, combining the six ensembles from the temperature series with the two 1.2-Å X-ray ensembles into a single 381-member “super ensemble” averaged these uncertainties and substantially improved agreement with RDCs. However, all ensembles showed excursions that were too large for the most dynamic fraction of residues. Our results suggest that further improvements to X-ray ensemble refinement are feasible, and that RDCs provide a sensitive benchmark in such endeavors. Remarkably, a weighted ensemble of 350 PDB M^pro X-ray structures provided slightly better cross-validated agreement with RDCs than any individual ensemble refinement, implying that differences in lattice confinement also limit the fit of RDCs to X-ray coordinates.     

Coupling between Catalytic Loop Motions and Enzyme Global Dynamics

Catalytic loop motions facilitate substrate recognition and binding in many enzymes. While these motions appear to be highly flexible, their functional significance suggests that structure-encoded preferences may play a role in selecting particular mechanisms of motions. We performed an extensive study on a set of enzymes to assess whether the collective/global dynamics, as predicted by elastic network models (ENMs), facilitates or even defines the local motions undergone by functional loops. Our dataset includes a total of 117 crystal structures for ten enzymes of different sizes and oligomerization states. Each enzyme contains a specific functional/catalytic loop (10–21 residues long) that closes over the active site during catalysis. Principal component analysis (PCA) of the available crystal structures (including apo and ligand-bound forms) for each enzyme revealed the dominant conformational changes taking place in these loops upon substrate binding. These experimentally observed loop reconfigurations are shown to be predominantly driven by energetically favored modes of motion intrinsically accessible to the enzyme in the absence of its substrate. The analysis suggests that robust global modes cooperatively defined by the overall enzyme architecture also entail local components that assist in suitable opening/closure of the catalytic loop over the active site.     

How do proteins recognize specific RNA sites? New clues from autogenously regulated ribosomal proteins

Some ribosomal proteins which bind specifically to ribosomal RNA also act as translational repressors and recognize their encoding messenger RNAs. The messenger- and ribosomal-RNA binding sites for four of these proteins are now well defined, and striking similarities in primary and secondary structure are apparent in most cases. These 'consensus' structures are useful clues to the features proteins use to recognize specific RNAs.     

Global Motions of the Nuclear Pore Complex: Insights from Elastic Network Models

The nuclear pore complex (NPC) is the gate to the nucleus. Recent determination of the configuration of proteins in the yeast NPC at ∼5 nm resolution permits us to study the NPC global dynamics using coarse-grained structural models. We investigate these large-scale motions by using an extended elastic network model (ENM) formalism applied to several coarse-grained representations of the NPC. Two types of collective motions (global modes) are predicted by the ENMs to be intrinsically favored by the NPC architecture: global bending and extension/contraction from circular to elliptical shapes. These motions are shown to be robust against tested variations in the representation of the NPC, and are largely captured by a simple model of a toroid with axially varying mass density. We demonstrate that spoke multiplicity significantly affects the accessible number of symmetric low-energy modes of motion; the NPC-like toroidal structures composed of 8 spokes have access to highly cooperative symmetric motions that are inaccessible to toroids composed of 7 or 9 spokes. The analysis reveals modes of motion that may facilitate macromolecular transport through the NPC, consistent with previous experimental observations.     

FebRNA: An automated fragment-ensemble-based model for building RNA 3D structures

Knowledge of RNA three-dimensional (3D) structures is critical to understanding the important biological functions of RNAs. Although various structure prediction models have been developed, the high-accuracy predictions of RNA 3D structures are still limited to the RNAs with short lengths or with simple topology. In this work, we proposed a new model, namely FebRNA, for building RNA 3D structures through fragment assembly based on coarse-grained (CG) fragment ensembles. Specifically, FebRNA is composed of four processes: establishing the library of different types of non-redundant CG fragment ensembles regardless of the sequences, building CG 3D structure ensemble through fragment assembly, identifying top-scored CG structures through a specific CG scoring function, and rebuilding the all-atom structures from the top-scored CG ones. Extensive examination against different types of RNA structures indicates that FebRNA consistently gives the reliable predictions on RNA 3D structures, including pseudoknots, three-way junctions, four-way and five-way junctions, and RNAs in the RNA-Puzzles. FebRNA is available on the Web site: https://github.com/Tan-group/FebRNA.     

Subtle functional collective motions in pancreatic-like ribonucleases: from ribonuclease A to angiogenin

The analysis of the dynamic behavior of enzymes is fundamental to structural biology. A direct relationship between protein flexibility and biological function has been shown for bovine pancreatic ribonuclease (RNase A) (Rasmussen et al., Nature 1992;357:423-424). More recently, crystallographic studies have shown that functional motions in RNase A involve the enzyme beta-sheet regions that move concertedly on substrate binding and release (Vitagliano et al., Proteins 2002;46:97-104). These motions have been shown to correspond to intrinsic dynamic properties of the native enzyme by molecular dynamics (MD) simulations. To unveil the occurrence of these collective motions in other members of pancreatic-like superfamily, we carried out MD simulations on human angiogenin (Ang). Essential dynamics (ED) analyses performed on the trajectories reveal that Ang exhibits collective motions similar to RNase A, despite the limited sequence identity (33%) of the two proteins. Furthermore, we show that these collective motions are also present in ensembles of experimentally determined structures of both Ang and RNase A. Finally, these subtle concerted beta-sheet motions were also observed for other two members of the pancreatic-like superfamily by comparing the ligand-bound and ligand-free structures of these enzymes. Taken together, these findings suggest that pancreatic-like ribonucleases share an evolutionary conserved dynamic behavior consisting of subtle beta-sheet motions, which are essential for substrate binding and release.     

Focused Functional Dynamics of Supramolecules by Use of a Mixed-Resolution Elastic Network Model

The mixed-resolution elastic network model was introduced previously for computing the motions of a structure, which is described at different levels of detail in different parts, for example, with atomistic and residue-level regions. This method has proved to be an efficient tool to explore the collective dynamics of proteins with some atomistic details, which would be difficult to obtain with either conventional full-atom approaches or fully coarse-grained models. Understanding function often requires atomic detail, but not necessarily for the entire structure. In this study, the calculation of the interaction forces between different resolution regions for the hierarchical levels of coarse-graining is further elaborated on in the new approach by considering explicitly the atomic contacts in the crystal structure. The collective dynamics of the enzyme triosephosphate isomerase and its active site together with loop 6 motions are considered in detail. The supramolecular assemblage ribosome and local atomic motions in its “interesting” functional part—the decoding center—are investigated for the low frequency range of the spectrum with high computational efficiency. This new atom-based mixed coarse-graining approach can be effectively used to generate realistic high-resolution conformations of extremely large protein-DNA or RNA complexes by performing energy minimization on structures deformed along the normal modes of the elastic network model. The new model permits focusing on specific functional parts that move in coordination and response to the remainder of the entire structure.     

Constraints imposed by the membrane selectively guide the alternating access dynamics of the glutamate transporter GltPh

Substrate transport in sodium-coupled amino acid symporters involves a large-scale conformational change that shifts the access to the substrate-binding site from one side of the membrane to the other. The structural change is particularly substantial and entails a unique piston-like quaternary rearrangement in glutamate transporters, as evidenced by the difference between the outward-facing and inward-facing structures resolved for the archaeal aspartate transporter Glt(Ph). These structural changes occur over time and length scales that extend beyond the reach of current fully atomic models, but are regularly explored with the use of elastic network models (ENMs). Despite their success with other membrane proteins, ENM-based approaches for exploring the collective dynamics of Glt(Ph) have fallen short of providing a plausible mechanism. This deficiency is attributed here to the anisotropic constraints imposed by the membrane, which are not incorporated into conventional ENMs. Here we employ two novel (to our knowledge) ENMs to demonstrate that one can largely capture the experimentally observed structural change using only the few lowest-energy modes of motion that are intrinsically accessible to the transporter, provided that the surrounding lipid molecules are incorporated into the ENM. The presence of the membrane reduces the overall energy of the transition compared with conventional models, showing that the membrane not only guides the selected mechanism but also acts as a facilitator. Finally, we show that the dynamics of Glt(Ph) is biased toward transitions of individual subunits of the trimer rather than cooperative transitions of all three subunits simultaneously, suggesting a mechanism of transport that exploits the intrinsic dynamics of individual subunits. Our software is available online at http://www.membranm.csb.pitt.edu.     

Vibrational Dynamics of Icosahedrally Symmetric Biomolecular Assemblies Compared with Predictions Based on Continuum Elasticity

Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses.     

Pre-existing soft modes of motion uniquely defined by native contact topology facilitate ligand binding to proteins

Modeling protein flexibility constitutes a major challenge in accurate prediction of protein-ligand and protein-protein interactions in docking simulations. The lack of a reliable method for predicting the conformational changes relevant to substrate binding prevents the productive application of computational docking to proteins that undergo large structural rearrangements. Here, we examine how coarse-grained normal mode analysis has been advantageously applied to modeling protein flexibility associated with ligand binding. First, we highlight recent studies that have shown that there is a close agreement between the large-scale collective motions of proteins predicted by elastic network models and the structural changes experimentally observed upon ligand binding. Then, we discuss studies that have exploited the predicted soft modes in docking simulations. Two general strategies are noted: pregeneration of conformational ensembles that are then utilized as input for standard fixed-backbone docking and protein structure deformation along normal modes concurrent to docking. These studies show that the structural changes apparently "induced" upon ligand binding occur selectively along the soft modes accessible to the protein prior to ligand binding. They further suggest that proteins offer suitable means of accommodating/facilitating the recognition and binding of their ligand, presumably acquired by evolutionary selection of the suitable three-dimensional structure.     

In silico investigation of conformational motions in superfamily 2 helicase proteins

Helicases are motor proteins that play a central role in the metabolism of DNA and RNA in biological cells. Using the energy of ATP molecules, they are able to translocate along the nucleic acids and unwind their duplex structure. They have been extensively characterized in the past and grouped into superfamilies based on structural similarities and sequential motifs. However, their functional aspects and the mechanism of their operation are not yet well understood. Here, we consider three helicases from the major superfamily 2--Hef, Hel308 and XPD--and study their conformational dynamics by using coarse-grained relaxational elastic network models. Specifically, their responses to mechanical perturbations are analyzed. This enables us to identify robust and ordered conformational motions which may underlie the functional activity of these proteins. As we show, such motions are well-organized and have large amplitudes. Their possible roles in the processing of nucleic substrate are discussed.     

Essential spaces defined by NMR structure ensembles and molecular dynamics simulation show significant overlap

Large concerted motions of proteins which span its “essential space,” are an important component of protein dynamics. We investigate to what extent structure ensembles generated with standard structure calculation techniques such as simulated annealing can capture these motions by comparing them to long-time molecular dynamics (MD) trajectories. The motions are analyzed by principal component analysis and compared using inner products of eigenvectors of the respective covariance matrices. Two very different systems are studied, the β-spectrin PH domain and the single-stranded DNA binding protein (ssDBP) from the filamentous phage Pf3. A comparison of the ensembles from NMR and MD shows significant overlap of the essential spaces, which in the case of ssDBP is extraordinarily high. The influence of variations in the specifications of distance restraints is investigated. We also study the influence of the selection criterion for the final structure ensemble on the definition of mobility. The results suggest a modified criterion that improves conformational sampling in terms of amplitudes of correlated motion. Proteins 31:370–382, 1998. © 1998 Wiley-Liss, Inc.     

Highly sampled tetranucleotide and tetraloop motifs enable evaluation of common RNA force fields

Recent modifications and improvements to standard nucleic acid force fields have attempted to fix problems and issues that have been observed as longer timescale simulations have become routine. Although previous work has shown the ability to fold the UUCG stem–loop structure, until now no group has attempted to quantify the performance of current force fields using highly converged structural populations of the tetraloop conformational ensemble. In this study, we report the use of multiple independent sets of multidimensional replica exchange molecular dynamics (M-REMD) simulations with different initial conditions to generate well-converged conformational ensembles for the tetranucleotides r(GACC) and r(CCCC), as well as the larger UUCG tetraloop motif. By generating what is to our knowledge the most complete RNA structure ensembles reported to date for these systems, we remove the coupling between force field errors and errors due to incomplete sampling, providing a comprehensive comparison between current top-performing MD force fields for RNA. Of the RNA force fields tested in this study, none demonstrate the ability to correctly identify the most thermodynamically stable structure for all three systems. We discuss the deficiencies present in each potential function and suggest areas where improvements can be made. The results imply that although “short” (nsec-μsec timescale) simulations may stay close to their respective experimental structures and may well reproduce experimental observables, inevitably the current force fields will populate alternative incorrect structures that are more stable than those observed via experiment.