A first principle particle mesh method for solution SAXS of large bio-molecular systems

Reweighting of molecular simulations with explicit-solvent SAXS restraints elucidates ion-dependent RNA ensembles

Small-angle X-ray scattering (SAXS) experiments are increasingly used to probe RNA structure. A number of forward models that relate measured SAXS intensities and structural features, and that are suitable to model either explicit-solvent effects or solute dynamics, have been proposed in the past years. Here, we introduce an approach that integrates atomistic molecular dynamics simulations and SAXS experiments to reconstruct RNA structural ensembles while simultaneously accounting for both RNA conformational dynamics and explicit-solvent effects. Our protocol exploits SAXS pure-solute forward models and enhanced sampling methods to sample an heterogenous ensemble of structures, with no information towards the experiments provided on-the-fly. The generated structural ensemble is then reweighted through the maximum entropy principle so as to match reference SAXS experimental data at multiple ionic conditions. Importantly, accurate explicit-solvent forward models are used at this reweighting stage. We apply this framework to the GTPase-associated center, a relevant RNA molecule involved in protein translation, in order to elucidate its ion-dependent conformational ensembles. We show that (a) both solvent and dynamics are crucial to reproduce experimental SAXS data and (b) the resulting dynamical ensembles contain an ion-dependent fraction of extended structures.

Structural insights into the membrane receptor ShuA in DDM micelles and in a model of gram-negative bacteria outer membrane as seen by SAXS and MD simulations

Successful crystallization of membrane proteins in detergent micelles depends on key factors such as conformational stability of the protein in micellar assemblies, the protein-detergent complex (PDC) monodispersity and favorable protein crystal contacts by suitable shielding of the protein hydrophobic surface by the detergent belt. With the aim of studying the influence of amphiphilic environment on membrane protein structure, stability and crystallizability, we combine molecular dynamics (MD) simulations with SEC-MALLS and SEC-SAXS (Size Exclusion Chromatography in line with Multi Angle Laser Light Scattering or Small Angle X-ray Scattering) experiments to describe the protein-detergent interactions that could help to rationalize PDC crystallization. In this context, we compare the protein-detergent interactions of ShuA from Shigella dysenteriae in n-Dodecyl-β-D-Maltopyranoside (DDM) with ShuA inserted in a realistic model of gram-negative bacteria outer membrane (OM) containing a mixture of bacterial lipopolysaccharide and phospholipids. To evaluate the quality of the PDC models, we compute the corresponding SAXS curves from the MD trajectories and compare with the experimental ones. We show that computed SAXS curves obtained from the MD trajectories reproduce better the SAXS obtained from the SEC-SAXS experiments for ShuA surrounded by 268 DDM molecules. The MD results show that the DDM molecules form around ShuA a closed belt whose the hydrophobic thickness appears slightly smaller (~22 Å) than the hydrophobic transmembrane domain of the protein (24.6 Å) suggested by Orientations of Proteins in Membranes (OPM) database. The simulations also show that ShuA transmembrane domain is remarkably stable in all the systems except for the extracellular and periplasmic loops that exhibit larger movements due to specific molecular interactions with lipopolysaccharides (LPS). We finally point out that this detergent behavior may lead to the occlusion of the periplasmic hydrophilic surface and poor crystal contacts leading to difficulties in crystallization of ShuA in DDM.

Martini bead form factors for nucleic acids and their application in the refinement of protein–nucleic acid complexes against SAXS data

The use of small-angle X-ray scattering (SAXS) in combination with molecular dynamics simulation is hampered by its heavy computational cost. The calculation of SAXS from atomic structures can be speeded up by using a coarse-grain representation of the structure. Following the work of Niebling, Björling & Westenhoff [J. Appl. Cryst. (2014), 47, 1190–1198], the Martini bead form factors for nucleic acids have been derived and then implemented, together with those previously determined for proteins, in the publicly available PLUMED library. A hybrid multi-resolution strategy has also been implemented to perform SAXS restrained simulations at atomic resolution by calculating the virtual positions of the Martini beads on the fly and using them for the calculation of SAXS. The accuracy and efficiency of the method are demonstrated by refining the structure of two protein–nucleic acid complexes. Instrumental for this result is the use of metainference, which allows the consideration and alleviation of the approximations at play in the present SAXS calculations.

Hybrid Methods for Modeling Protein Structures Using Molecular Dynamics Simulations and Small-Angle X-Ray Scattering Data

Small-angle X-ray scattering (SAXS) is an efficient experimental tool to measure the overall shape of macromolecular structures in solution. However, due to the low resolution of SAXS data, high-resolution data obtained from X-ray crystallography or NMR and computational methods such as molecular dynamics (MD) simulations are complementary to SAXS data for understanding protein functions based on their structures at atomic resolution. Because MD simulations provide a physicochemically proper structural ensemble for flexible proteins in solution and a precise description of solvent effects, the hybrid analysis of SAXS and MD simulations is a promising method to estimate reasonable solution structures and structural ensembles in solution. Here, we review typical and useful in silico methods for modeling three dimensional protein structures, calculating theoretical SAXS profiles, and analyzing ensemble structures consistent with experimental SAXS profiles. We also review two examples of the hybrid analysis, termed MD-SAXS method in which MD simulations are carried out without any knowledge of experimental SAXS data, and the experimental SAXS data are used only to assess the consistency of the solution model from MD simulations with those observed in experiments. One example is an investigation of the intrinsic dynamics of EcoO109I using the computational method to obtain a theoretical profile from the trajectory of an MD simulation. The other example is a structural investigation of the vitamin D receptor ligand-binding domain using snapshots generated by MD simulations and assessment of the snapshots by experimental SAXS data.