Methods for SAXS-based structure determination of biomolecular complexes

Using AlphaFold and Symmetrical Docking to Predict Protein-Protein Interactions for Exploring Potential Crystallization Conditions

Protein crystallization remains a major bottleneck in X-ray crystallography due to difficulties in achieving favorable molecular arrangements within the crystal lattice. While protein-protein interactions at molecular packing interfaces are crucial for determining crystallization conditions, methods for predicting crystal packing interfaces and systematically exploring crystallization conditions remain limited. In this study, we present MASCL (Molecular Assembly Simulation in Crystal Lattice), a novel approach that integrates AlphaFold with symmetrical docking to simulate crystal packing. To evaluate packing quality, we introduced PackQ, a stringent metric based on the DockQ framework, where models with scores above 0.36 are considered successful. In benchmark tests on P41212 and P43212 space groups, MASCL successfully predicted packing interfaces for 26.8% and 30.1% of targets within the top 100 models. When focusing on models with successfully predicted initial crystallographic dimeric assemblies (DockQ ≥ 0.23), success rates improved to 57.9% and 39.8% within the top 25 models, respectively. Additionally, we developed AAI-PatchBag, a patch-based method using physicochemical descriptors to assess molecular interface similarity. Compared to conventional condition-searching strategies like sequence alignment, structure superposition, and shape comparison, AAI-PatchBag reduced the number of trials required to identify potential crystallization conditions. Applied to lysozyme crystallization, AAI-PatchBag efficiently identified conditions yielding crystals with the desired packing. Overall, MASCL and AAI-PatchBag advance the prediction of protein-protein interactions within the crystal lattice and facilitate the identification of potential crystallization conditions through molecular packing interface similarity, contributing to a deeper understanding of protein crystallization.

The sequence-structure-function relationship of intrinsic ERα disorder

The oestrogen receptor (ER or ERα), a nuclear hormone receptor that drives most breast cancer1, is commonly activated by phosphorylation at serine 118 within its intrinsically disordered N-terminal transactivation domain2,3. Although this modification enables oestrogen-independent ER function, its mechanism has remained unclear despite ongoing clinical trials of kinase inhibitors targeting this region4-6. By integration of small-angle X-ray scattering and nuclear magnetic resonance spectroscopy with functional studies, we show that serine 118 phosphorylation triggers an unexpected expansion of the disordered domain and disrupts specific hydrophobic clustering between two aromatic-rich regions. Mutations mimicking this disruption rescue ER transcriptional activity, target-gene expression and cell growth impaired by a phosphorylation-deficient S118A mutation. These findings, driven by hydrophobic interactions, extend beyond electrostatic models and provide mechanistic insights into intrinsically disordered proteins7, with implications for other nuclear receptors8. This fundamental sequence-structure-function relationship advances our understanding of intrinsic ER disorder, crucial for developing targeted breast cancer therapeutics.

Small-Angle X-ray Scattering (SAXS) Combined with SAXS-Driven Molecular Dynamics for Structural Analysis of Multistranded RNA Assemblies

Nucleic acids (RNA and DNA) play crucial roles in all living organisms and find wide utility in clinical settings. The convergence of rationally designed nucleic acid multistranded assemblies with embedded therapeutic properties has led to the development of a platform based on nucleic acid nanoparticles (NANPs). NANPs incorporate various functional moieties to deliver their combinations to diseased cells in a highly controlled manner. Given that the structure and composition of NANPs can also influence their immunorecognition and biological activities, thorough verification of all designs is essential. We introduce an experimental pipeline for small-angle X-ray scattering (SAXS) to gather structural details about the solution-state NANPs assembled from up to 12 RNA strands. To the best of our knowledge, this study represents the largest multistranded RNA nanoassemblies characterized in this manner to date. We show that synchronized implementation of SAXS-driven molecular dynamics simulations reveals the diverse conformational landscape inhabited by these assemblies and provides insights into their immunorecognition. The developed strategy expands the capabilities of therapeutic nucleic acids and emerging nucleic acid nanotechnologies.

Equivariant Flexible Modeling of the Protein-Ligand Binding Pose with Geometric Deep Learning

Flexible modeling of the protein-ligand complex structure is a fundamental challenge for in silico drug development. Recent studies have improved commonly used docking tools by incorporating extra-deep learning-based steps. However, such strategies limit their accuracy and efficiency because they retain massive sampling pressure and lack consideration for flexible biomolecular changes. In this study, we propose FlexPose, a geometric graph network capable of direct flexible modeling of complex structures in Euclidean space without the following conventional sampling and scoring strategies. Our model adopts two key designs: scalar-vector dual feature representation and SE(3)-equivariant network, to manage dynamic structural changes, as well as two strategies: conformation-aware pretraining and weakly supervised learning, to boost model generalizability in unseen chemical space. Benefiting from these paradigms, our model dramatically outperforms all tested popular docking tools and recently advanced deep learning methods, especially in tasks involving protein conformation changes. We further investigate the impact of protein and ligand similarity on the model performance with two conformation-aware strategies. Moreover, FlexPose provides an affinity estimation and model confidence for postanalysis.

Biophysical and Integrative Characterization of Protein Intrinsic Disorder as a Prime Target for Drug Discovery

Protein intrinsic disorder is increasingly recognized for its biological and disease-driven functions. However, it represents significant challenges for biophysical studies due to its high conformational flexibility. In addressing these challenges, we highlight the complementary and distinct capabilities of a range of experimental and computational methods and further describe integrative strategies available for combining these techniques. Integrative biophysics methods provide valuable insights into the sequence–structure–function relationship of disordered proteins, setting the stage for protein intrinsic disorder to become a promising target for drug discovery. Finally, we briefly summarize recent advances in the development of new small molecule inhibitors targeting the disordered N-terminal domains of three vital transcription factors.

Incorporation of D2O-Induced Fluorine Chemical Shift Perturbations into Ensemble-Structure Characterization of the ERalpha Disordered Region

Structural characterization of intrinsically disordered proteins (IDPs) requires a concerted effort between experiments and computations by accounting for their conformational heterogeneity. Given the diversity of experimental tools providing local and global structural information, constructing an experimental restraint-satisfying structural ensemble remains challenging. Here, we use the disordered N-terminal domain (NTD) of the estrogen receptor alpha (ERalpha) as a model system to combine existing small-angle X-ray scattering (SAXS) and hydroxyl radical protein footprinting (HRPF) data and newly acquired solvent accessibility data via D2O-induced fluorine chemical shifting (DFCS) measurements. A new set of DFCS data for the solvent exposure of a set of 12 amino acid positions were added to complement previously acquired HRPF measurements for the solvent exposure of the other 16 nonoverlapping amino acids, thereby improving the NTD ensemble characterization considerably. We also found that while choosing an initial ensemble of structures generated from a different atomic-level force field or sampling/modeling method can lead to distinct contact maps even when the same sets of experimental measurements were used for ensemble-fitting, comparative analyses from these initial ensembles reveal commonly recurring structural features in their ensemble-averaged contact map. Specifically, nonlocal or long-range transient interactions were found consistently between the N-terminal segments and the central region, sufficient to mediate the conformational ensemble and regulate how the NTD interacts with its coactivator proteins.

An overview of structural approaches to study therapeutic RNAs

RNAs provide considerable opportunities as therapeutic agent to expand the plethora of classical therapeutic targets, from extracellular and surface proteins to intracellular nucleic acids and its regulators, in a wide range of diseases. RNA versatility can be exploited to recognize cell types, perform cell therapy, and develop new vaccine classes. Therapeutic RNAs (aptamers, antisense nucleotides, siRNA, miRNA, mRNA and CRISPR-Cas9) can modulate or induce protein expression, inhibit molecular interactions, achieve genome editing as well as exon-skipping. A common RNA thread, which makes it very promising for therapeutic applications, is its structure, flexibility, and binding specificity. Moreover, RNA displays peculiar structural plasticity compared to proteins as well as to DNA. Here we summarize the recent advances and applications of therapeutic RNAs, and the experimental and computational methods to analyze their structure, by biophysical techniques (liquid-state NMR, scattering, reactivity, and computational simulations), with a focus on dynamic and flexibility aspects and to binding analysis. This will provide insights on the currently available RNA therapeutic applications and on the best techniques to evaluate its dynamics and reactivity.

SAXS-guided unbiased coarse-grained Monte Carlo simulation for identification of self-assembly nanostructures and dimensions

Recent studies have shown that solvated amphiphiles can form nanostructured self-assemblies called dynamic binary complexes (DBCs) in the presence of ions. Since the nanostructures of DBCs are directly related to their viscoelastic properties, it is important to understand how the nanostructures change under different solution conditions. However, it is challenging to obtain a three-dimensional molecular description of these nanostructures by utilizing conventional experimental characterization techniques or thermodynamic models. To this end, we combined the structural data from small angle X-ray scattering (SAXS) experiments and thermodynamic knowledge from coarse-grained Monte Carlo (CGMC) simulations to identify the detailed three-dimensional nanostructure of DBCs. Specifically, unbiased CGMC simulations are performed with SAXS-guided initial conditions, which aids us to sample accurate nanostructures in a computationally efficient fashion. As a result, an elliptical bilayer nanostructure is obtained as the most probable nanostructure of DBCs whose dimensions are validated by scanning electron microscope (SEM) images. Then, utilizing the obtained molecular model of DBCs, we could also explain the pH tunability of the system. Overall, our results from SAXS-guided unbiased CGMC simulations highlight that using potential energy combined with SAXS data, we can distinguish otherwise degenerate nanostructures resulting from the inherent ambiguity of SAXS patterns.

Unravelling the molecular interaction of diselenodipropionic acid (DSePA) with human serum albumin (HSA)

DSePA, a pharmacologically efficient selenium compound shows strong binding with extracellular carrier protein, Human Serum Albumin.

Fabrication of Transparent Polymer Optical Device Combined with Selective Visible-Light Transmission and Zero-Birefringence

The formation of optical products using the traditional molten processing methods is a direct and extensive application of optical fields, and it suffers from intrinsic birefringence and optical distortion due to polymer orientation and residual stress. Here, a unique concept is proposed by assembling photonic crystal nanospheres without orientation in a rubbery state to realize transparent optical devices with zero-birefringence and high transparency. By developing fabrication techniques for transparent zero-birefringence optical devices, certain outstanding performances are realized, including no optical distortion and excellent mechanical properties. Simultaneously, by controlling the particle size of the photonic crystal, one has successfully obtained transparent optical devices with the visible light selective transmission are successfully obtained. The transparent zero-birefringence optical devices are promising candidates for potential applications for fine optical devices. The work opens up an exciting new fabrication route for zero-birefringence and highly transparent polymer devices that have been difficult to create using traditional methods.

Integrative structural modeling of a multidomain polo-like kinase

Polo-like kinase 1 (PLK1) is a key regulator and coordinator for mitotic signaling that contains two major functional units of a kinase domain (KD) and a polo-box domain (PBD). While individual domain structures of the KD and the PBD are known, how they interact and assemble into a functional complex remains an open question. The structural model from the KD-PBD-Map205PBM heterotrimeric crystal structure of zebrafish PLK1 represents a major step in understanding the KD and the PBD interactions. However, how these two domains interact when connected by a linker in the full length PLK1 needs further investigation. By integrating different sources of structural data from small-angle X-ray scattering, hydroxyl radical protein footprinting, and computational sampling, here we report an overall architecture for PLK1 multidomain assembly between the KD and the PBD. Our model revealed that the KD uses its C-lobe to interact with the PBD via the site near the phosphopeptide binding site in its auto-inhibitory state in solution. Disruption of this auto-inhibition via site-directed mutagenesis at the KD-PBD interface increases its kinase activity, supporting the functional role of KD-PBD interactions predicted for regulating the PLK1 kinase function. Our results indicate that the full length human PLK1 takes dynamic structures with a variety of domain-domain interfaces in solution.

Quantitative comparison between sub-millisecond time resolution single-molecule FRET measurements and 10-second molecular simulations of a biosensor protein

Molecular Dynamics (MD) simulations seek to provide atomic-level insights into conformationally dynamic biological systems at experimentally relevant time resolutions, such as those afforded by single-molecule fluorescence measurements. However, limitations in the time scales of MD simulations and the time resolution of single-molecule measurements have challenged efforts to obtain overlapping temporal regimes required for close quantitative comparisons. Achieving such overlap has the potential to provide novel theories, hypotheses, and interpretations that can inform idealized experimental designs that maximize the detection of the desired reaction coordinate. Here, we report MD simulations at time scales overlapping with in vitro single-molecule Förster (fluorescence) resonance energy transfer (smFRET) measurements of the amino acid binding protein LIV-BP^SS at sub-millisecond resolution. Computationally efficient all-atom structure-based simulations, calibrated against explicit solvent simulations, were employed for sampling multiple cycles of LIV-BP^SS clamshell-like conformational changes on the time scale of seconds, examining the relationship between these events and those observed by smFRET. The MD simulations agree with the smFRET measurements and provide valuable information on local dynamics of fluorophores at their sites of attachment on LIV-BP^SS and the correlations between fluorophore motions and large-scale conformational changes between LIV-BP^SS domains. We further utilize the MD simulations to inform the interpretation of smFRET data, including Förster radius (R₀) and fluorophore orientation factor (κ²) determinations. The approach we describe can be readily extended to distinct biochemical systems, allowing for the interpretation of any FRET system conjugated to protein or ribonucleoprotein complexes, including those with more conformational processes, as well as those implementing multi-color smFRET.

Förster (fluorescence) resonance energy transfer (FRET) has been used extensively by biophysicists as a molecular-scale ruler that yields fundamental structural and kinetic insights into transient processes including complex formation and conformational rearrangements required for biological function. FRET techniques require the identification of informative fluorophore labeling sites, spaced at defined distances to inform on a reaction coordinate of interest and consideration of noise sources that have the potential to obscure quantitative interpretations. Here, we describe an approach to leverage advancements in computationally efficient all-atom structure-based molecular dynamics simulations in which structural dynamics observed via FRET can be interpreted in full atomistic detail on commensurate time scales. We demonstrate the potential of this approach using a model FRET system, the amino acid binding protein LIV-BP^SS conjugated to self-healing organic fluorophores. LIV-BP^SS exhibits large scale, sub-millisecond clamshell-like conformational changes between open and closed conformations associated with ligand unbinding and binding, respectively. Our findings inform on the molecular basis of the dynamics observed by smFRET and on strategies to optimize fluorophore labeling sites, the manner of fluorophore attachment, and fluorophore composition.

Birefringence- and Optical Distortion-Free Isotropic Polymer Lens Assisted by Photonic Microspheres

Development of low-cost and light polymer optical devices to substitute for inorganic materials is a major trend. Traditional molten processing methods are direct and have been extensively applied in optical product manufacturing. However, the inevitable intrinsic birefringence and optical distortion due to polymer molecular chain anisotropy limit their application in high-end optical devices. Here, we report a novel thermocompression strategy for isotropic polymer lens fabrication, in which a cross-linked photonic crystal (PC) consisting of closely stacked polymer microspheres is used as a precursor and then heated and pressed under the rubbery state. A polymethyl methacrylate microsphere-based PC is used as a demonstration, and the obtained isotropic lenses exhibit superior performance compared to the traditional counterpart, which are birefringence-free (Δn < 1 × 10^-5) and optical distortion-free and have excellent mechanical properties (hardness reaches 0.28 GPa), and the hidden mechanism is carefully studied. These properties enable the isotropic lens to be applied in precision optical components such as the lens of spectacles, microscope, telescope and endoscope, industrial camera, and astronaut helmet, and the proposed general method can extend to various polymers and provide new opportunities for the development of three-dimensional PCs.

ClusPro in rounds 38 to 45 of CAPRI: Toward combining template-based methods with free docking

Targets in the protein docking experiment CAPRI (Critical Assessment of Predicted Interactions) generally present new challenges and contribute to new developments in methodology. In rounds 38 to 45 of CAPRI, most targets could be effectively predicted using template-based methods. However, the server ClusPro required structures rather than sequences as input, and hence we had to generate and dock homology models. The available templates also provided distance restraints that were directly used as input to the server. We show here that such an approach has some advantages. Free docking with template-based restraints using ClusPro reproduced some interfaces suggested by weak or ambiguous templates while not reproducing others, resulting in correct server predicted models. More recently we developed the fully automated ClusPro TBM server that performs template-based modeling and thus can use sequences rather than structures of component proteins as input. The performance of the server, freely available for noncommercial use at https://tbm.cluspro.org, is demonstrated by predicting the protein-protein targets of rounds 38 to 45 of CAPRI.

Exploring the mechanism of pullulan delay potato starch long-term retrogradation from the viewpoint of amylopectin chain motion

Starch retrogradation is an inevitable process in the natural state caused by movement of starch chains. Therefore, the objective of this study was to explore the essence of starch long-term retrogradation from the viewpoint of amylopectin chain motion. The radius of gyration (R_g) and form factor (ρ) values of potato starch (PS) and PS with pullulan (PS-PUL) gradually increased during the retrogradation process. Furthermore, the conformation of molecular chains evolved from spherical to ellipsoidal to rod-like during starch retrogradation. Based on the analysis of condensed matter theory, these results illustrated that starch chains from gelatinization to retrogradation experienced shrinkage to extension. The values of R_g and ρ of PS-PUL were lower than PS, and the evolution of conformations showed that PUL delayed the long-term retrogradation of PS by decreasing the motion of amylopectin molecular chains to increase chain flexibility, and decrease the degree of entanglement and crosslinking. This study provides a novel method for characterizing starch retrogradation on the molecular level.

Structural Characterization of Protein-Protein Interactions with pyDockSAXS

Structural characterization of protein-protein interactions can provide essential details to understand biological functions at the molecular level and to facilitate their manipulation for biotechnological and biomedical purposes. Unfortunately, the 3D structure is available for only a small fraction of all possible protein-protein interactions, due to the technical limitations of high-resolution structural determination methods. In this context, low-resolution structural techniques, such as small-angle X-ray scattering (SAXS), can be combined with computational docking to provide structural models of protein-protein interactions at large scale. In this chapter, we describe the pyDockSAXS web server ( https://life.bsc.es/pid/pydocksaxs ), which uses pyDock docking and scoring to provide structural models that optimally satisfy the input SAXS data. This server, which is freely available to the scientific community, provides an automatic pipeline to model the structure of a protein-protein complex from SAXS data.

Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images

BACKGROUND

Atomic Force Microscopy (AFM) is an experimental technique to study structure-function relationship of biomolecules. AFM provides images of biomolecules at nanometer resolution. High-speed AFM experiments produce a series of images following dynamics of biomolecules. To further understand biomolecular functions, information on three-dimensional (3D) structures is beneficial.

METHOD

We aim to recover 3D information from an AFM image by computational modeling. The AFM image includes only low-resolution representation of a molecule; therefore we represent the structures by a coarse grained model (Gaussian mixture model). Using Monte-Carlo sampling, candidate models are generated to increase similarity between AFM images simulated from the models and target AFM image.

RESULTS

The algorithm was tested on two proteins to model their conformational transitions. Using a simulated AFM image as reference, the algorithm can produce a low-resolution 3D model of the target molecule. Effect of molecular orientations captured in AFM images on the 3D modeling performance was also examined and it is shown that similar accuracy can be obtained for many orientations.

CONCLUSIONS

The proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail.

GENERAL SIGNIFICANCE

High-speed AFM experiments allow us to directly observe biomolecules in action, which provides insights on biomolecular function through dynamics. However, as only partial structural information can be obtained from AFM data, this new AFM based hybrid modeling method would be useful to retrieve 3D information of the entire biomolecule.

Small-Angle Scattering as a Structural Probe for Nucleic Acid Nanoparticles (NANPs) in a Dynamic Solution Environment

Nucleic acid-based technologies are an emerging research focus area for pharmacological and biological studies because they are biocompatible and can be designed to produce a variety of scaffolds at the nanometer scale. The use of nucleic acids (ribonucleic acid (RNA) and/or deoxyribonucleic acid (DNA)) as building materials in programming the assemblies and their further functionalization has recently established a new exciting field of RNA and DNA nanotechnology, which have both already produced a variety of different functional nanostructures and nanodevices. It is evident that the resultant architectures require detailed structural and functional characterization and that a variety of technical approaches must be employed to promote the development of the emerging fields. Small-angle X-ray and neutron scattering (SAS) are structural characterization techniques that are well placed to determine the conformation of nucleic acid nanoparticles (NANPs) under varying solution conditions, thus allowing for the optimization of their design. SAS experiments provide information on the overall shapes and particle dimensions of macromolecules and are ideal for following conformational changes of the molecular ensemble as it behaves in solution. In addition, the inherent differences in the neutron scattering of nucleic acids, lipids, and proteins, as well as the different neutron scattering properties of the isotopes of hydrogen, combined with the ability to uniformly label biological macromolecules with deuterium, allow one to characterize the conformations and relative dispositions of the individual components within an assembly of biomolecules. This article will review the application of SAS methods and provide a summary of their successful utilization in the emerging field of NANP technology to date, as well as share our vision on its use in complementing a broad suite of structural characterization tools with some simulated results that have never been shared before.

SAXS-guided Enhanced Unbiased Sampling for Structure Determination of Proteins and Complexes

Molecular simulations can be utilized to predict protein structure ensembles and dynamics, though sufficient sampling of molecular ensembles and identification of key biologically relevant conformations remains challenging. Low-resolution experimental techniques provide valuable structural information on biomolecule at near-native conditions, which are often combined with molecular simulations to determine and refine protein structural ensembles. In this study, we demonstrate how small angle x-ray scattering (SAXS) information can be incorporated in Markov state model-based adaptive sampling strategy to enhance time efficiency of unbiased MD simulations and identify functionally relevant conformations of proteins and complexes. Our results show that using SAXS data combined with additional information, such as thermodynamics and distance restraints, we are able to distinguish otherwise degenerate structures due to the inherent ambiguity of SAXS pattern. We further demonstrate that adaptive sampling guided by SAXS and hybrid information can significantly reduce the computation time required to discover target structures. Overall, our findings demonstrate the potential of this hybrid approach in predicting near-native structures of proteins and complexes. Other low-resolution experimental information can be incorporated in a similar manner to collectively enhance unbiased sampling and improve the accuracy of structure prediction from simulation.

Multidomain architecture of estrogen receptor reveals interfacial cross-talk between its DNA-binding and ligand-binding domains

Human estrogen receptor alpha (hERα) is a hormone-responsive nuclear receptor (NR) involved in cell growth and survival that contains both a DNA-binding domain (DBD) and a ligand-binding domain (LBD). Functionally relevant inter-domain interactions between the DBD and LBD have been observed in several other NRs, but for hERα, the detailed structural architecture of the complex is unknown. By utilizing integrated complementary techniques of small-angle X-ray scattering, hydroxyl radical protein footprinting and computational modeling, here we report an asymmetric L-shaped “boot” structure of the multidomain hERα and identify the specific sites on each domain at the domain interface involved in DBD–LBD interactions. We demonstrate the functional role of the proposed DBD–LBD domain interface through site-specific mutagenesis altering the hERα interfacial structure and allosteric signaling. The L-shaped structure of hERα is a distinctive DBD–LBD organization of NR complexes and more importantly, reveals a signaling mechanism mediated by inter-domain crosstalk that regulates this receptor’s allosteric function.

The human estrogen receptor alpha (hERα) is a hormone-responsive transcription factor. Here the authors combine small-angle X-ray scattering, hydroxyl radical protein footprinting and computational modeling and show that multidomain hERα adopts an L-shaped boot-like architecture revealing a cross-talk between its DNA-binding domain and Ligand-binding domain.

Dummy-atom modelling of stacked and helical nanostructures from solution scattering data

The availability of dummy-atom modelling programs to determine the shape of monodisperse globular particles from small-angle solution scattering data has led to outstanding scientific advances. However, there is no equivalent procedure that allows modelling of stacked, seemingly endless structures, such as helical systems. This work presents a bead-modelling algorithm that reconstructs the structural motif of helical and rod-like systems. The algorithm is based on a 'projection scheme': by exploiting the recurrent nature of stacked systems, such as helices, the full structure is reduced to a single building-block motif. This building block is fitted by allowing random dummy-atom movements without an underlying grid. The proposed method is verified using a variety of analytical models, and examples are presented of successful shape reconstruction from experimental data sets. To make the algorithm available to the scientific community, it is implemented in a graphical computer program that encourages user interaction during the fitting process and also includes an option for shape reconstruction of globular particles.

Reduction of small-angle scattering profiles to finite sets of structural invariants

This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters called Kn which are related to the shape of the object of study. These Kn, together with a radius R, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and the Dmax parameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

Healing X-ray scattering images

X-ray scattering images contain numerous gaps and defects arising from detector limitations and experimental configuration. We present a method to heal X-ray scattering images, filling gaps in the data and removing defects in a physically meaningful manner. Unlike generic inpainting methods, this method is closely tuned to the expected structure of reciprocal-space data. In particular, we exploit statistical tests and symmetry analysis to identify the structure of an image; we then copy, average and interpolate measured data into gaps in a way that respects the identified structure and symmetry. Importantly, the underlying analysis methods provide useful characterization of structures present in the image, including the identification of diffuse versus sharp features, anisotropy and symmetry. The presented method leverages known characteristics of reciprocal space, enabling physically reasonable reconstruction even with large image gaps. The method will correspondingly fail for images that violate these underlying assumptions. The method assumes point symmetry and is thus applicable to small-angle X-ray scattering (SAXS) data, but only to a subset of wide-angle data. Our method succeeds in filling gaps and healing defects in experimental images, including extending data beyond the original detector borders.

The ClusPro web server for protein-protein docking

The ClusPro server (https://cluspro.org) is a widely used tool for protein-protein docking. The server provides a simple home page for basic use, requiring only two files in Protein Data Bank (PDB) format. However, ClusPro also offers a number of advanced options to modify the search; these include the removal of unstructured protein regions, application of attraction or repulsion, accounting for pairwise distance restraints, construction of homo-multimers, consideration of small-angle X-ray scattering (SAXS) data, and location of heparin-binding sites. Six different energy functions can be used, depending on the type of protein. Docking with each energy parameter set results in ten models defined by centers of highly populated clusters of low-energy docked structures. This protocol describes the use of the various options, the construction of auxiliary restraints files, the selection of the energy parameters, and the analysis of the results. Although the server is heavily used, runs are generally completed in <4 h.

Thermodynamics of Hydrophobic Amino Acids in Solution: A Combined Experimental-Computational Study

We present a joint experimental-computational study to quantitatively describe the thermodynamics of hydrophobic leucine amino acids in aqueous solution. X-ray scattering data were acquired at a series of solute and salt concentrations to effectively measure interleucine interactions, indicating that a major scattering peak is observed consistently at q = 0.83 Å^-1. Atomistic molecular dynamics simulations were then performed and compared with the scattering data, achieving high consistency at both small and wider scattering angles (q = 0-1.5 Å^-1). This experimental-computational consistence enables a first glimpse of the leucine-leucine interacting landscape, where two leucine molecules are aligned mostly in a parallel fashion, as opposed to antiparallel, but also allows us to derive effective leucine-leucine interactions in solution. Collectively, this combined approach of employing experimental scattering and molecular simulation enables quantitative characterization of effective intermolecular interactions of hydrophobic amino acids, critical for protein function and dynamics such as protein folding.

Bayesian inference of protein ensembles from SAXS data

The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble.

The ClusPro web server for protein-protein docking

The ClusPro server (https://cluspro.org) is a widely used tool for protein-protein docking. The server provides a simple home page for basic use, requiring only two files in Protein Data Bank (PDB) format. However, ClusPro also offers a number of advanced options to modify the search; these include the removal of unstructured protein regions, application of attraction or repulsion, accounting for pairwise distance restraints, construction of homo-multimers, consideration of small-angle X-ray scattering (SAXS) data, and location of heparin-binding sites. Six different energy functions can be used, depending on the type of protein. Docking with each energy parameter set results in ten models defined by centers of highly populated clusters of low-energy docked structures. This protocol describes the use of the various options, the construction of auxiliary restraints files, the selection of the energy parameters, and the analysis of the results. Although the server is heavily used, runs are generally completed in <4 h.

New additions to the ClusPro server motivated by CAPRI

The heavily used protein-protein docking server ClusPro performs three computational steps as follows: (1) rigid body docking, (2) RMSD based clustering of the 1000 lowest energy structures, and (3) the removal of steric clashes by energy minimization. In response to challenges encountered in recent CAPRI targets, we added three new options to ClusPro. These are (1) accounting for small angle X-ray scattering data in docking; (2) considering pairwise interaction data as restraints; and (3) enabling discrimination between biological and crystallographic dimers. In addition, we have developed an extremely fast docking algorithm based on 5D rotational manifold FFT, and an algorithm for docking flexible peptides that include known sequence motifs. We feel that these developments will further improve the utility of ClusPro. However, CAPRI emphasized several shortcomings of the current server, including the problem of selecting the right energy parameters among the five options provided, and the problem of selecting the best models among the 10 generated for each parameter set. In addition, results convinced us that further development is needed for docking homology models. Finally, we discuss the difficulties we have encountered when attempting to develop a refinement algorithm that would be computationally efficient enough for inclusion in a heavily used server. Proteins 2017; 85:435-444. © 2016 Wiley Periodicals, Inc.

A Practical Guide to iSPOT Modeling: An Integrative Structural Biology Platform

Integrative structure modeling is an emerging method for structural determination of protein-protein complexes that are challenging for conventional structural techniques. Here, we provide a practical protocol for implementing our integrated iSPOT platform by integrating three different biophysical techniques: small-angle X-ray scattering (SAXS), hydroxyl radical footprinting, and computational docking simulations. Specifically, individual techniques are described from experimental and/or computational perspectives, and complementary structural information from these different techniques are integrated for accurate characterization of the structures of large protein-protein complexes.

Theoretical modeling of multiprotein complexes by iSPOT: Integration of small-angle X-ray scattering, hydroxyl radical footprinting, and computational docking

Structural determination of protein-protein complexes such as multidomain nuclear receptors has been challenging for high-resolution structural techniques. Here, we present a combined use of multiple biophysical methods, termed iSPOT, an integration of shape information from small-angle X-ray scattering (SAXS), protection factors probed by hydroxyl radical footprinting, and a large series of computationally docked conformations from rigid-body or molecular dynamics (MD) simulations. Specifically tested on two model systems, the power of iSPOT is demonstrated to accurately predict the structures of a large protein-protein complex (TGFβ-FKBP12) and a multidomain nuclear receptor homodimer (HNF-4α), based on the structures of individual components of the complexes. Although neither SAXS nor footprinting alone can yield an unambiguous picture for each complex, the combination of both, seamlessly integrated in iSPOT, narrows down the best-fit structures that are about 3.2Å and 4.2Å in RMSD from their corresponding crystal structures, respectively. Furthermore, this proof-of-principle study based on the data synthetically derived from available crystal structures shows that the iSPOT-using either rigid-body or MD-based flexible docking-is capable of overcoming the shortcomings of standalone computational methods, especially for HNF-4α. By taking advantage of the integration of SAXS-based shape information and footprinting-based protection/accessibility as well as computational docking, this iSPOT platform is set to be a powerful approach towards accurate integrated modeling of many challenging multiprotein complexes.

Accurate optimization of amino acid form factors for computing small-angle X-ray scattering intensity of atomistic protein structures

Structure modelling via small-angle X-ray scattering (SAXS) data generally requires intensive computations of scattering intensity from any given biomolecular structure, where the accurate evaluation of SAXS profiles using coarse-grained (CG) methods is vital to improve computational efficiency. To date, most CG SAXS computing methods have been based on a single-bead-per-residue approximation but have neglected structural correlations between amino acids. To improve the accuracy of scattering calculations, accurate CG form factors of amino acids are now derived using a rigorous optimization strategy, termed electron-density matching (EDM), to best fit electron-density distributions of protein structures. This EDM method is compared with and tested against other CG SAXS computing methods, and the resulting CG SAXS profiles from EDM agree better with all-atom theoretical SAXS data. By including the protein hydration shell represented by explicit CG water molecules and the correction of protein excluded volume, the developed CG form factors also reproduce the selected experimental SAXS profiles with very small deviations. Taken together, these EDM-derived CG form factors present an accurate and efficient computational approach for SAXS computing, especially when higher molecular details (represented by the q range of the SAXS data) become necessary for effective structure modelling.

Bridging the gap between in vitro and in vivo RNA folding

Deciphering the folding pathways and predicting the structures of complex three-dimensional biomolecules is central to elucidating biological function. RNA is single-stranded, which gives it the freedom to fold into complex secondary and tertiary structures. These structures endow RNA with the ability to perform complex chemistries and functions ranging from enzymatic activity to gene regulation. Given that RNA is involved in many essential cellular processes, it is critical to understand how it folds and functions in vivo. Within the last few years, methods have been developed to probe RNA structures in vivo and genome-wide. These studies reveal that RNA often adopts very different structures in vivo and in vitro, and provide profound insights into RNA biology. Nonetheless, both in vitro and in vivo approaches have limitations: studies in the complex and uncontrolled cellular environment make it difficult to obtain insight into RNA folding pathways and thermodynamics, and studies in vitro often lack direct cellular relevance, leaving a gap in our knowledge of RNA folding in vivo. This gap is being bridged by biophysical and mechanistic studies of RNA structure and function under conditions that mimic the cellular environment. To date, most artificial cytoplasms have used various polymers as molecular crowding agents and a series of small molecules as cosolutes. Studies under such in vivo-like conditions are yielding fresh insights, such as cooperative folding of functional RNAs and increased activity of ribozymes. These observations are accounted for in part by molecular crowding effects and interactions with other molecules. In this review, we report milestones in RNA folding in vitro and in vivo and discuss ongoing experimental and computational efforts to bridge the gap between these two conditions in order to understand how RNA folds in the cell.

Sampling Enrichment toward Target Structures Using Hybrid Molecular Dynamics-Monte Carlo Simulations

Sampling enrichment toward a target state, an analogue of the improvement of sampling efficiency (SE), is critical in both the refinement of protein structures and the generation of near-native structure ensembles for the exploration of structure-function relationships. We developed a hybrid molecular dynamics (MD)-Monte Carlo (MC) approach to enrich the sampling toward the target structures. In this approach, the higher SE is achieved by perturbing the conventional MD simulations with a MC structure-acceptance judgment, which is based on the coincidence degree of small angle x-ray scattering (SAXS) intensity profiles between the simulation structures and the target structure. We found that the hybrid simulations could significantly improve SE by making the top-ranked models much closer to the target structures both in the secondary and tertiary structures. Specifically, for the 20 mono-residue peptides, when the initial structures had the root-mean-squared deviation (RMSD) from the target structure smaller than 7 Å, the hybrid MD-MC simulations afforded, on average, 0.83 Å and 1.73 Å in RMSD closer to the target than the parallel MD simulations at 310K and 370K, respectively. Meanwhile, the average SE values are also increased by 13.2% and 15.7%. The enrichment of sampling becomes more significant when the target states are gradually detectable in the MD-MC simulations in comparison with the parallel MD simulations, and provide >200% improvement in SE. We also performed a test of the hybrid MD-MC approach in the real protein system, the results showed that the SE for 3 out of 5 real proteins are improved. Overall, this work presents an efficient way of utilizing solution SAXS to improve protein structure prediction and refinement, as well as the generation of near native structures for function annotation.

SAXS studies of RNA: structures, dynamics, and interactions with partners

Small-angle X-ray scattering, SAXS, is a powerful and easily employed experimental technique that provides solution structures of macromolecules. The size and shape parameters derived from SAXS provide global structural information about these molecules in solution and essentially complement data acquired by other biophysical methods. As applied to protein systems, SAXS is a relatively mature technology: sophisticated tools exist to acquire and analyze data, and to create structural models that include dynamically flexible ensembles. Given the expanding appreciation of RNA's biological roles, there is a need to develop comparable tools to characterize solution structures of RNA, including its interactions with important biological partners. We review the progress toward achieving this goal, focusing on experimental and computational innovations. The use of multiphase modeling, absolute calibration and contrast variation methods, among others, provides new and often unique ways of visualizing this important biological molecule and its essential partners: ions, other RNAs, or proteins. WIREs RNA 2016, 7:512-526. doi: 10.1002/wrna.1349 For further resources related to this article, please visit the WIREs website.

Accounting for observed small angle X-ray scattering profile in the protein-protein docking server ClusPro

The protein-protein docking server ClusPro is used by thousands of laboratories, and models built by the server have been reported in over 300 publications. Although the structures generated by the docking include near-native ones for many proteins, selecting the best model is difficult due to the uncertainty in scoring. Small angle X-ray scattering (SAXS) is an experimental technique for obtaining low resolution structural information in solution. While not sufficient on its own to uniquely predict complex structures, accounting for SAXS data improves the ranking of models and facilitates the identification of the most accurate structure. Although SAXS profiles are currently available only for a small number of complexes, due to its simplicity the method is becoming increasingly popular. Since combining docking with SAXS experiments will provide a viable strategy for fairly high-throughput determination of protein complex structures, the option of using SAXS restraints is added to the ClusPro server. © 2015 Wiley Periodicals, Inc.