Sampling globally and locally correct RNA 3D structures using Ernwin, SPQR and experimental SAXS data.

The determination of the three-dimensional structure of large RNA macromolecules in solution is a challenging task that often requires the use of several experimental and computational techniques. Small-angle X-ray scattering can provide insight into some geometrical properties of the probed molecule, but this data must be properly interpreted in order to generate a three-dimensional model. Here, we propose a multiscale pipeline which introduces SAXS data into modelling the global shape of RNA in solution, which can be hierarchically refined until reaching atomistic precision in explicit solvent. The low-resolution helix model (Ernwin) deals with the exploration of the huge conformational space making use of the SAXS data, while a nucleotide-level model (SPQR) removes clashes and disentangles the proposed structures, leading the structure to an all-atom representation in explicit water. We apply the procedure on four different known pdb structures up to 159 nucleotides with promising results. Additionally, we predict an all-atom structure for the Plasmodium falceparum signal recognition particle ALU RNA based on SAXS data deposited in the SASBDB, which has an alternate conformation and better fit to the SAXS data than the previously published structure based on the same data but other modelling methods.

The Multiscale Ernwin/SPQR RNA Structure Prediction Pipeline.

Aside from the well-known role in protein synthesis, RNA can perform catalytic, regulatory, and other essential biological functions which are determined by its three-dimensional structure. In this regard, a great effort has been made during the past decade to develop computational tools for the prediction of the structure of RNAs from the knowledge of their sequence, incorporating experimental data to refine or guide the modeling process. Nevertheless, this task can become exceptionally challenging when dealing with long noncoding RNAs, constituted by more than 200 nucleotides, due to their large size and the specific interactions involved. In this chapter, we describe a multiscale approach to predict such structures, incorporating SAXS experimental data into a hierarchical procedure which couples two coarse-grained representations: Ernwin, a helix-based approach, which deals with the global arrangement of secondary structure elements, and SPQR, a nucleotide-centered coarse-grained model, which corrects and refines the structures predicted at the coarser level.We describe the methodology through its application on the Braveheart long noncoding RNA, starting from the SAXS and secondary structure data to propose a refined, all-atom structure.

RNA Secondary Structures Regulate Adsorption of Fragments onto Flat Substrates.

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substrate. Within this approach, we study the specific role of stem-hairpin and multibranch RNA secondary structure motifs on its adsorption phenomenology. Our findings identify a dual regime of adsorption for short RNA fragments with and without the secondary structure and underline the adsorption efficiency in both cases as a function of the surface interaction strength. The observed behavior results from an interplay between the number of contacts formed at the surface and the conformational entropy of the RNA molecule. The adsorption phenomenology of RNA seems to persist also for much longer RNAs as qualitatively observed by comparing the trends of our simulations with a theoretical approach based on an ideal semiflexible polymer chain.

Structural 3D Domain Reconstruction of the RNA Genome from Viruses with Secondary Structure Models.

Three-dimensional RNA domain reconstruction is important for the assembly, disassembly and delivery functionalities of a packed proteinaceus capsid. However, to date, the self-association of RNA molecules is still an open problem. Recent chemical probing reports provide, with high reliability, the secondary structure of diverse RNA ensembles, such as those of viral genomes. Here, we present a method for reconstructing the complete 3D structure of RNA genomes, which combines a coarse-grained model with a subdomain composition scheme to obtain the entire genome inside proteinaceus capsids based on secondary structures from experimental techniques. Despite the amount of sampling involved in the folded and also unfolded RNA molecules, advanced microscope techniques can provide points of anchoring, which enhance our model to include interactions between capsid pentamers and RNA subdomains. To test our method, we tackle the satellite tobacco mosaic virus (STMV) genome, which has been widely studied by both experimental and computational communities. We provide not only a methodology to structurally analyze the tertiary conformations of the RNA genome inside capsids, but a flexible platform that allows the easy implementation of features/descriptors coming from both theoretical and experimental approaches.

Brief Comparison between Experimental and Computationally Generated Ensembles of RNA Dinucleotides.

The computational modeling of RNA and its interactions is of crucial importance for the understanding of the wide variety of biological functions it performs. Among these approaches, several coarse-grained models employ structural databases to derive their energy functions or to define scoring functions for structure prediction purposes. In many cases, the parametrization is done by using as a reference a set of experimentally determined structures or data obtained from Molecular Dynamics simulations. Since the two choices are clearly different, we present here a brief comparison of the essential spaces of a set of conformations of two topologically connected nucleotides generated by these means. We find that when the nucleotides are embedded into a duplex, the essential spaces of both ensembles are quite restricted and do not differ substantially. Nevertheless, when the conformational space of a free dinucleoside monophosphate simulation is compared against a similar set obtained from the structural database, the differences of the essential spaces are considerable. In addition, we show a brief comparison of a specific distance between the nucleotides which correlates with the sugar pucker of the first nucleotide and analyze its distribution under similar conditions.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview.

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Effects and limitations of a nucleobase-driven backmapping procedure for nucleic acids using steered molecular dynamics.

Coarse-grained models can be of great help to address the problem of structure prediction in nucleic acids. On one hand they can make the prediction more efficient, while on the other hand they can also help to identify the essential degrees of freedom and interactions for the description of a number of structures. With the aim to provide an all-atom representation in an explicit solvent to the predictions of our SPlit and conQueR (SPQR) coarse-grained model of RNA, we recently introduced a backmapping procedure which enforces the predicted structure into an atomistic one by means of steered molecular dynamics. These simulations minimize the ERMSD, a particular metric which deals exclusively with the relative arrangement of nucleobases, between the atomistic representation and the target structure. In this paper, we explore the effects of this approach on the resulting interaction networks and backbone conformations by applying it on a set of fragments using as a target their native structure. We find that the geometry of the target structures can be reliably recovered, with limitations in the regions with unpaired bases such as bulges. In addition, we observe that the folding pathway can also change depending on the parameters used in the definition of the ERMSD and the use of other metrics such as the RMSD.

A nucleobase-centered coarse-grained representation for structure prediction of RNA motifs.

We introduce the SPlit-and-conQueR (SPQR) model, a coarse-grained (CG) representation of RNA designed for structure prediction and refinement. In our approach, the representation of a nucleotide consists of a point particle for the phosphate group and an anisotropic particle for the nucleoside. The interactions are, in principle, knowledge-based potentials inspired by the $\mathcal {E}$SCORE function, a base-centered scoring function. However, a special treatment is given to base-pairing interactions and certain geometrical conformations which are lost in a raw knowledge-based model. This results in a representation able to describe planar canonical and non-canonical base pairs and base-phosphate interactions and to distinguish sugar puckers and glycosidic torsion conformations. The model is applied to the folding of several structures, including duplexes with internal loops of non-canonical base pairs, tetraloops, junctions and a pseudoknot. For the majority of these systems, experimental structures are correctly predicted at the level of individual contacts. We also propose a method for efficiently reintroducing atomistic detail from the CG representation.

Static and dynamic light scattering by red blood cells: A numerical study.

Light scattering is a well-established experimental technique, which gains more and more popularity in the biological field because it offers the means for non-invasive imaging and detection. However, the interpretation of light-scattering signals remains challenging due to the complexity of most biological systems. Here, we investigate static and dynamic scattering properties of red blood cells (RBCs) using two mesoscopic hydrodynamics simulation methods-multi-particle collision dynamics and dissipative particle dynamics. Light scattering is studied for various membrane shear elasticities, bending rigidities, and RBC shapes (e.g., biconcave and stomatocyte). Simulation results from the two simulation methods show good agreement, and demonstrate that the static light scattering of a diffusing RBC is not very sensitive to the changes in membrane properties and moderate alterations in cell shapes. We also compute dynamic light scattering of a diffusing RBC, from which dynamic properties of RBCs such as diffusion coefficients can be accessed. In contrast to static light scattering, the dynamic measurements can be employed to differentiate between the biconcave and stomatocytic RBC shapes and generally allow the differentiation based on the membrane properties. Our simulation results can be used for better understanding of light scattering by RBCs and the development of new non-invasive methods for blood-flow monitoring.

Single-Molecule FRET Measurements in Additive-Enriched Aqueous Solutions.

The addition of high amounts of chemical denaturants, salts, viscosity enhancers or macro-molecular crowding agents has an impact on the physical properties of buffer solutions. Among others, the (microscopic) viscosity, the refractive index, the dielectric constant, and the ionic strength can be affected. Here, we systematically evaluate the importance of solvent characteristics with respect to single-molecule FRET (smFRET) data. First, we present a confocal based method for the determination of fluorescence quantum yields to facilitate a fast characterization of smFRET-samples at sub-nM-concentrations. As a case study, we analyze smFRET data of structurally rigid, double-stranded DNA-oligonucleotides in aqueous buffer and in buffers with specific amounts of glycerol, guanidine hydrochloride (GdnHCl), and sodium chloride (NaCl) added. We show that the calculation of interdye distances, without taking into account solvent-induced spectral and photophysical changes of the labels, leads to deviations of up to 4 Å from the real interdye distances. Additionally, we demonstrate that electrostatic dye-dye repulsions are negligible for the interdye distance regime considered here (>50 Å). Finally, we use our approach to validate the further compaction of the already unfolded state of phosphoglycerate kinase (PGK) with decreasing denaturant concentrations, a mechanism known as coil-globule transition.

Conformational state distributions and catalytically relevant dynamics of a hinge-bending enzyme studied by single-molecule FRET and a coarse-grained simulation.

Over the last few decades, a view has emerged showing that multidomain enzymes are biological machines evolved to harness stochastic kicks of solvent particles into highly directional functional motions. These intrinsic motions are structurally encoded, and Nature makes use of them to catalyze chemical reactions by means of ligand-induced conformational changes and states redistribution. Such mechanisms align reactive groups for efficient chemistry and stabilize conformers most proficient for catalysis. By combining single-molecule Förster resonance energy transfer measurements with normal mode analysis and coarse-grained mesoscopic simulations, we obtained results for a hinge-bending enzyme, namely phosphoglycerate kinase (PGK), which support and extend these ideas. From single-molecule Förster resonance energy transfer, we obtained insight into the distribution of conformational states and the dynamical properties of the domains. The simulations allowed for the characterization of interdomain motions of a compact state of PGK. The data show that PGK is intrinsically a highly dynamic system sampling a wealth of conformations on timescales ranging from nanoseconds to milliseconds and above. Functional motions encoded in the fold are performed by the PGK domains already in its ligand-free form, and substrate binding is not required to enable them. Compared to other multidomain proteins, these motions are rather fast and presumably not rate-limiting in the enzymatic reaction. Ligand binding slightly readjusts the orientation of the domains and feasibly locks the protein motions along a preferential direction. In addition, the functionally relevant compact state is stabilized by the substrates, and acts as a prestate to reach active conformations by means of Brownian motions.

Inter-dye distance distributions studied by a combination of single-molecule FRET-filtered lifetime measurements and a weighted accessible volume (wAV) algorithm.

Förster resonance energy transfer (FRET) is an important tool for studying the structural and dynamical properties of biomolecules. The fact that both the internal dynamics of the biomolecule and the movements of the biomolecule-attached dyes can occur on similar timescales of nanoseconds is an inherent problem in FRET studies. By performing single-molecule FRET-filtered lifetime measurements, we are able to characterize the amplitude of the motions of fluorescent probes attached to double-stranded DNA standards by means of flexible linkers. With respect to previously proposed experimental approaches, we improved the precision and the accuracy of the inter-dye distance distribution parameters by filtering out the donor-only population with pulsed interleaved excitation. A coarse-grained model is employed to reproduce the experimentally determined inter-dye distance distributions. This approach can easily be extended to intrinsically flexible proteins allowing, under certain conditions, to decouple the macromolecule amplitude of motions from the contribution of the dye linkers.

Hydrodynamics of discrete-particle models of spherical colloids: a multiparticle collision dynamics simulation study.

We investigate the hydrodynamic properties of a spherical colloid model, which is composed of a shell of point particles by hybrid mesoscale simulations, which combine molecular dynamics simulations for the sphere with the multiparticle collision dynamics approach for the fluid. Results are presented for the center-of-mass and angular velocity correlation functions. The simulation results are compared with theoretical results for a rigid colloid obtained as a solution of the Stokes equation with no-slip boundary conditions. Similarly, analytical results of a point-particle model are presented, which account for the finite size of the simulated system. The simulation results agree well with both approaches on appropriative time scales; specifically, the long-time correlations are quantitatively reproduced. Moreover, a procedure is proposed to obtain the infinite-system-size diffusion coefficient based on a combination of simulation results and analytical predictions. In addition, we present the velocity field in the vicinity of the colloid and demonstrate its close agreement with the theoretical prediction. Our studies show that a point-particle model of a sphere is very well suited to describe the hydrodynamic properties of spherical colloids, with a significantly reduced numerical effort.

Structure and dynamics of a compact state of a multidomain protein, the mercuric ion reductase.

The functional efficacy of colocalized, linked protein domains is dependent on linker flexibility and system compaction. However, the detailed characterization of these properties in aqueous solution presents an enduring challenge. Here, we employ a novel, to our knowledge, combination of complementary techniques, including small-angle neutron scattering, neutron spin-echo spectroscopy, and all-atom molecular dynamics and coarse-grained simulation, to identify and characterize in detail the structure and dynamics of a compact form of mercuric ion reductase (MerA), an enzyme central to bacterial mercury resistance. MerA possesses metallochaperone-like N-terminal domains (NmerA) tethered to its catalytic core domain by linkers. The NmerA domains are found to interact principally through electrostatic interactions with the core, leashed by the linkers so as to subdiffuse on the surface over an area close to the core C-terminal Hg(II)-binding cysteines. How this compact, dynamical arrangement may facilitate delivery of Hg(II) from NmerA to the core domain is discussed.

Coupling different levels of resolution in molecular simulations.

Simulation schemes for liquids or strongly fluctuating systems that allow to change the molecular representation in a subvolume of the simulation box while preserving the equilibrium with the surroundings introduce conceptual problems of thermodynamic consistency. In this work we present a general scheme based on thermodynamic arguments which ensures a thermodynamic equilibrium among molecules of different representations. The robustness of the algorithm is tested for two examples, namely, an adaptive resolution simulation, atomistic/coarse grained, for a liquid of tetrahedral molecules, and an adaptive resolution simulation of a binary mixture of tetrahedral molecules and spherical solutes.