Prediction of solution properties and dynamics of RNAs by means of Brownian dynamics simulation of coarse-grained models: Ribosomal 5S RNA and phenylalanine transfer RNA

Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides a Fast but Still Accurate Treatment of Hydrodynamic Interactions in Brownian Dynamics Simulations of Biological Macromolecules

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HIs). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here, we explore the use of an alternative way to accelerate the calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA-RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA-RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast, approximate way of including HIs in BD simulations of intermediate-scale systems.

Modeling the 3D structure and conformational dynamics of very large RNAs using coarse-grained molecular simulations

We describe a computational approach to building and simulating realistic 3D models of very large RNA molecules (>1000 nucleotides) at a resolution of one "bead" per nucleotide. The method starts with a predicted secondary structure and uses several stages of energy minimization and Brownian dynamics (BD) simulation to build 3D models. A key step in the protocol is the temporary addition of a 4 ^th spatial dimension that allows all predicted helical elements to become disentangled from each other in an effectively automated way. We then use the resulting 3D models as input to Brownian dynamics simulations that include hydrodynamic interactions (HIs) that allow the diffusive properties of the RNA to be modelled as well as enabling its conformational dynamics to be simulated. To validate the dynamics part of the method, we first show that when applied to small RNAs with known 3D structures the BD-HI simulation models accurately reproduce their experimental hydrodynamic radii (Rh). We then apply the modelling and simulation protocol to a variety of RNAs for which experimental Rh values have been reported ranging in size from 85 to 3569 nucleotides. We show that the 3D models, when used in BD-HI simulations, produce hydrodynamic radii that are usually in good agreement with experimental estimates for RNAs that do not contain tertiary contacts that persist even under very low salt conditions. Finally, we show that sampling of the conformational dynamics of large RNAs on timescales of 100 µs is computationally feasible with BD-HI simulations.

An Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides A Fast But Still Accurate Treatment Of Hydrodynamic Interactions In Brownian Dynamics Simulations Of Biological Macromolecules

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HI). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here we explore the use of an alternative way to accelerate calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast approximate way of including HIs in BD simulations of intermediate-scale systems.

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.

HullRad: Fast Calculations of Folded and Disordered Protein and Nucleic Acid Hydrodynamic Properties

Hydrodynamic properties are useful parameters for estimating the size and shape of proteins and nucleic acids in solution. The calculation of such properties from structural models informs on the solution properties of these molecules and complements corresponding structural studies. Here we report, to our knowledge, a new method to accurately predict the hydrodynamic properties of molecular structures. This method uses a convex hull model to estimate the hydrodynamic volume of the molecule and is orders of magnitude faster than common methods. It works well for both folded proteins and ensembles of conformationally heterogeneous proteins and for nucleic acids. Because of its simplicity and speed, the method should be useful for the modification of computer-generated, intrinsically disordered protein ensembles and ensembles of flexible, but folded, molecules in which rapid calculation of experimental parameters is needed. The convex hull method is implemented in a Python script called HullRad. The use of the method is facilitated by a web server and the code is freely available for batch applications.

Sedimentation of Reversibly Interacting Macromolecules with Changes in Fluorescence Quantum Yield

Sedimentation velocity analytical ultracentrifugation with fluorescence detection has emerged as a powerful method for the study of interacting systems of macromolecules. It combines picomolar sensitivity with high hydrodynamic resolution, and can be carried out with photoswitchable fluorophores for multicomponent discrimination, to determine the stoichiometry, affinity, and shape of macromolecular complexes with dissociation equilibrium constants from picomolar to micromolar. A popular approach for data interpretation is the determination of the binding affinity by isotherms of weight-average sedimentation coefficients s_w. A prevailing dogma in sedimentation analysis is that the weight-average sedimentation coefficient from the transport method corresponds to the signal- and population-weighted average of all species. We show that this does not always hold true for systems that exhibit significant signal changes with complex formation-properties that may be readily encountered in practice, e.g., from a change in fluorescence quantum yield. Coupled transport in the reaction boundary of rapidly reversible systems can make significant contributions to the observed migration in a way that cannot be accounted for in the standard population-based average. Effective particle theory provides a simple physical picture for the reaction-coupled migration process. On this basis, we develop a more general binding model that converges to the well-known form of s_w with constant signals, but can account simultaneously for hydrodynamic cotransport in the presence of changes in fluorescence quantum yield. We believe this will be useful when studying interacting systems exhibiting fluorescence quenching, enhancement, or Förster resonance energy transfer with transport methods.

Dynamic light scattering: a practical guide and applications in biomedical sciences

Dynamic light scattering (DLS), also known as photon correlation spectroscopy (PCS), is a very powerful tool for studying the diffusion behaviour of macromolecules in solution. The diffusion coefficient, and hence the hydrodynamic radii calculated from it, depends on the size and shape of macromolecules. In this review, we provide evidence of the usefulness of DLS to study the homogeneity of proteins, nucleic acids, and complexes of protein-protein or protein-nucleic acid preparations, as well as to study protein-small molecule interactions. Further, we provide examples of DLS's application both as a complementary method to analytical ultracentrifugation studies and as a screening tool to validate solution scattering models using determined hydrodynamic radii.