A rapid coarse residue-based computational method for x-ray solution scattering characterization of protein folds and multiple conformational states of large protein complexes

Brewing COFFEE: A Sequence-Specific Coarse-Grained Energy Function for Simulations of DNA-Protein Complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription and gene expression to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse-grained Force Field for Energy Estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the self-organized polymer model with side-chains for proteins and the three interaction site model for DNA in a modular fashion, without recalibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a data set of high-resolution crystal structures. The only parameter in COFFEE is the strength (λDNAPRO) of the DNA-protein contact potential. For an optimal choice of λDNAPRO, the crystallographic B-factors for DNA-protein complexes with varying sizes and topologies are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts scattering profiles that are in quantitative agreement with small-angle X-ray scattering experiments, as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which do not alter the balance of electrostatic interactions but affect chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

Fitting high-resolution electron density maps from atomic models to solution scattering data

Solution scattering techniques, such as small- and wide-angle X-ray scattering (SWAXS), provide valuable insights into the structure and dynamics of biological macromolecules in solution. In this study, we present an approach to accurately predict solution X-ray scattering profiles at wide angles from atomic models by generating high-resolution electron density maps. Our method accounts for the excluded volume of bulk solvent by calculating unique adjusted atomic volumes directly from the atomic coordinates. This approach eliminates the need for one of the free fitting parameters commonly used in existing algorithms, resulting in improved accuracy of the calculated SWAXS profile. An implicit model of the hydration shell is generated that uses the form factor of water. Two parameters, namely the bulk solvent density and the mean hydration shell contrast, are adjusted to best fit the data. Results using eight publicly available SWAXS profiles show high-quality fits to the data. In each case, the optimized parameter values show small adjustments demonstrating that the default values are close to the true solution. Disabling parameter optimization produces significantly more accurate predicted scattering profiles compared to the leading software. The algorithm is computationally efficient, comparable to the leading software and up to 10 times faster for large molecules. The algorithm is encoded in a command line script called denss.pdb2mrc.py and is available open source as part of the DENSS v1.7.0 software package. In addition to improving the ability to compare atomic models to experimental SWAXS data, these developments pave the way for increasing the accuracy of modeling algorithms using SWAXS data and decreasing the risk of overfitting.

Accurate and Efficient SAXS/SANS Implementation Including Solvation Layer Effects Suitable for Molecular Simulations

Small-angle X-ray and neutron scattering (SAXS/SANS) provide valuable insights into the structure and dynamics of biomolecules in solution, complementing a wide range of structural techniques, including molecular dynamics simulations. As contrast-based methods, they are sensitive not only to structural properties but also to solvent-solute interactions. Their use in molecular dynamics simulations requires a forward model that should be as fast and accurate as possible. In this work, we demonstrate the feasibility of calculating SAXS and SANS intensities using a coarse-grained representation consisting of one bead per amino acid and three beads per nucleic acid, with form factors that can be corrected on the fly to account for solvation effects at no additional computational cost. By coupling this forward model with molecular dynamics simulations restrained with SAS data, it is possible to determine conformational ensembles or refine the structure and dynamics of proteins and nucleic acids in agreement with the experimental results. To assess the robustness of this approach, we applied it to gelsolin, for which we acquired SAXS data on its closed state, and to a UP1-microRNA complex, for which we used previously collected measurements. Our hybrid-resolution small-angle scattering (hySAS) implementation, being distributed in PLUMED, can be used with atomistic and coarse-grained simulations using diverse restraining strategies.

Brewing COFFEE: A sequence-specific coarse-grained energy function for simulations of DNA-protein complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription, gene expression, to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse grained force field for energy estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the Self-Organized Polymer model with Side Chains for proteins and the Three Interaction Site model for DNA in a modular fashion, without re-calibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a dataset of high-resolution crystal structures. The only parameter in COFFEE is the strength (λ D N A P R O ) of the DNA-protein contact potential. For an optimal choice of λ D N A P R O , the crystallographic B-factors for DNA-protein complexes, with varying sizes and topologies, are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts the scattering profiles that are in quantitative agreement with SAXS experiments as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which does not alter the balance of electrostatic interactions, but affects chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

Fitting high-resolution electron density maps from atomic models to solution scattering data

Solution scattering techniques, such as small and wide-angle X-ray scattering (SWAXS), provide valuable insights into the structure and dynamics of biological macromolecules in solution. In this study, we present an approach to accurately predict solution X-ray scattering profiles at wide angles from atomic models by generating high-resolution electron density maps. Our method accounts for the excluded volume of bulk solvent by calculating unique adjusted atomic volumes directly from the atomic coordinates. This approach eliminates the need for a free fitting parameter commonly used in existing algorithms, resulting in improved accuracy of the calculated SWAXS profile. An implicit model of the hydration shell is generated which uses the form factor of water. Two parameters, namely the bulk solvent density and the mean hydration shell contrast, are adjusted to best fit the data. Results using eight publicly available SWAXS profiles show high quality fits to the data. In each case, the optimized parameter values show small adjustments demonstrating that the default values are close to the true solution. Disabling parameter optimization results in a significant improvement of the calculated scattering profiles compared to the leading software. The algorithm is computationally efficient, showing more than tenfold reduction in execution time compared to the leading software. The algorithm is encoded in a command line script called denss.pdb2mrc.py and is available open source as part of the DENSS v1.7.0 software package (https://github.com/tdgrant1/denss). In addition to improving the ability to compare atomic models to experimental SWAXS data, these developments pave the way for increasing the accuracy of modeling algorithms utilizing SWAXS data while decreasing the risk of overfitting.

Biasing RNA Coarse-Grained Folding Simulations with Small-Angle X-ray Scattering Data

RNA molecules can easily adopt alternative structures in response to different environmental conditions. As a result, a molecule's energy landscape is rough and can exhibit a multitude of deep basins. In the absence of a high-resolution structure, small-angle X-ray scattering data (SAXS) can narrow down the conformational space available to the molecule and be used in conjunction with physical modeling to obtain high-resolution putative structures to be further tested by experiments. Because of the low resolution of these data, it is natural to implement the integration of SAXS data into simulations using a coarse-grained representation of the molecule, allowing for much wider searches and faster evaluation of SAXS theoretical intensity curves than with atomistic models. We present here the theoretical framework and the implementation of a simulation approach based on our coarse-grained model HiRE-RNA combined with SAXS evaluations "on-the-fly" leading the simulation toward conformations agreeing with the scattering data, starting from partially folded structures as the ones that can easily be obtained from secondary structure prediction-based tools. We show on three benchmark systems how our approach can successfully achieve high-resolution structures with remarkable similarity with the native structure recovering not only the overall shape, as imposed by SAXS data, but also the details of initially missing base pairs.

Dynamic particle swarm optimization of biomolecular simulation parameters with flexible objective functions

Molecular simulations are a powerful tool to complement and interpret ambiguous experimental data on biomolecules to obtain structural models. Such data-assisted simulations often rely on parameters, the choice of which is highly non-trivial and crucial to performance. The key challenge is weighting experimental information with respect to the underlying physical model. We introduce FLAPS, a self-adapting variant of dynamic particle swarm optimization, to overcome this parameter selection problem. FLAPS is suited for the optimization of composite objective functions that depend on both the optimization parameters and additional, a priori unknown weighting parameters, which substantially influence the search-space topology. These weighting parameters are learned at runtime, yielding a dynamically evolving and iteratively refined search-space topology. As a practical example, we show how FLAPS can be used to find functional parameters for small-angle X-ray scattering-guided protein simulations.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Comment on the Optimal Parameters to Derive Intrinsically Disordered Protein Conformational Ensembles from Small-Angle X-ray Scattering Data Using the Ensemble Optimization Method

The Ensemble Optimization Method (EOM) is a popular approach to describe small-angle X-ray scattering (SAXS) data from highly disordered proteins. The EOM algorithm selects subensembles of coexisting states from large pools of randomized conformations to fit the SAXS data. Based on the unphysical bimodal radius of gyration (R_g) distribution of conformations resulting from the EOM analysis, a recent article (Fagerberg et al. J. Chem. Theory Comput. 2019, 15 (12), 6968-6983) concluded that this approach inadequately described the SAXS data measured for human Histatin 5 (Hst5), a peptide with antifungal properties. Using extensive experimental and synthetic data, we explored the origin of this observation. We found that the one-bead-per-residue coarse-grained representation with averaged scattering form factors (provided in the EOM as an add-on to represent disordered missing loops or domains) may not be appropriate for EOM analyses of scattering data from short (below 50 residues) proteins/peptides. The method of choice for these proteins is to employ atomistic models (e.g., from molecular dynamics simulations) to sample the protein conformational landscape. As a convenient alternative, we have also improved the coarse-grained approach by introducing amino acid specific form factors in the calculations. We also found that, for small proteins, the search for relatively large subensembles of 20-50 conformers (as implemented in the original EOM version) more adequately describes the conformational space sampled in solution than the procedures optimizing the ensemble size. Our observations have been added as recommendations into the information for EOM users to promote the proper utilization of the program for ensemble-based modeling of SAXS data for all types of disordered systems.

Structure and Dynamics of N-Glycosylated Human Ribonuclease 1

Glycosylation is a common modification that can endow proteins with altered physical and biological properties. Ribonuclease 1 (RNase 1), which is the human homologue of the archetypal enzyme RNase A, undergoes N-linked glycosylation at asparagine residues 34, 76, and 88. We have produced the three individual glycoforms that display the core heptasaccharide, Man₅GlcNAc₂, and analyzed the structure of each glycoform by using small-angle X-ray scattering along with molecular dynamics simulations. The glycan on Asn34 is relatively compact and rigid, donates hydrogen bonds that "cap" the carbonyl groups at the C-terminus of an α-helix, and enhances protein thermostability. In contrast, the glycan on Asn88 is flexible and can even enter the enzymic active site, hindering catalysis. The N-glycosylation of Asn76 has less pronounced consequences. These data highlight the diverse behaviors of Man₅GlcNAc₂ pendants and provide a structural underpinning to the functional consequences of protein glycosylation.

Integrating solvation shell structure in experimentally driven molecular dynamics using x-ray solution scattering data

In the past few decades, prediction of macromolecular structures beyond the native conformation has been aided by the development of molecular dynamics (MD) protocols aimed at exploration of the energetic landscape of proteins. Yet, the computed structures do not always agree with experimental observables, calling for further development of the MD strategies to bring the computations and experiments closer together. Here, we report a scalable, efficient MD simulation approach that incorporates an x-ray solution scattering signal as a driving force for the conformational search of stable structural configurations outside of the native basin. We further demonstrate the importance of inclusion of the hydration layer effect for a precise description of the processes involving large changes in the solvent exposed area, such as unfolding. Utilization of the graphics processing unit allows for an efficient all-atom calculation of scattering patterns on-the-fly, even for large biomolecules, resulting in a speed-up of the calculation of the associated driving force. The utility of the methodology is demonstrated on two model protein systems, the structural transition of lysine-, arginine-, ornithine-binding protein and the folding of deca-alanine. We discuss how the present approach will aid in the interpretation of dynamical scattering experiments on protein folding and association.

Protein Footprinting: Auxiliary Engine to Power the Structural Biology Revolution

Structural biology is entering an exciting time where many new high-resolution structures of large complexes and membrane proteins are determined regularly. These advances have been driven by over fifteen years of technology advancements, first in macromolecular crystallography, and recently in Cryo-electron microscopy. These structures are allowing detailed questions about functional mechanisms of the structures, and the biology enabled by these structures, to be addressed for the first time. At the same time, mass spectrometry technologies for protein structure analysis, "footprinting" studies, have improved their sensitivity and resolution dramatically and can provide detailed sub-peptide and residue level information for validating structures and interactions or understanding the dynamics of structures in the context of ligand binding or assembly. In this perspective, we review the use of protein footprinting to extend our understanding of macromolecular systems, particularly for systems challenging for analysis by other techniques, such as intrinsically disordered proteins, amyloidogenic proteins, and other proteins/complexes so far recalcitrant to existing methods. We also illustrate how the availability of high-resolution structural information can be a foundation for a suite of hybrid approaches to divine structure-function relationships beyond what individual techniques can deliver.

Glycine substitution in SH3-SH2 connector of Hck tyrosine kinase causes population shift from assembled to disassembled state

A combination of small angle X-ray scattering (SAXS) and molecular dynamics (MD) simulations based on a coarse grained model is used to examine the effect of glycine substitutions in the short connector between the SH3 and SH2 domains of Hck, a member of the Src-family kinases. It has been shown previously that the activity of cSrc kinase is upregulated by substitution of 3 residues by glycine in the SH3-SH2 connector. Here, analysis of SAXS data indicates that the population of Hck in the disassembled state increases from 25% in the wild type kinase to 76% in the glycine mutant. This is consistent with the results of free energy perturbation calculations showing that the mutation in the connector shifts the equilibrium from the assembled to the disassembled state. This study supports the notion that the SH3-SH2 connector helps to regulate the activity of tyrosine kinases by shifting the population of the active state of the multidomain protein independent of C-terminal phosphorylation.

Determination of Protein Structural Ensembles by Hybrid-Resolution SAXS Restrained Molecular Dynamics

Small-angle X-ray scattering (SAXS) experiments provide low-resolution but valuable information about the dynamics of biomolecular systems, which could be ideally integrated into molecular dynamics (MD) simulations to accurately determine conformational ensembles of flexible proteins. The applicability of this strategy is hampered by the high computational cost required to calculate scattering intensities from three-dimensional structures. We previously presented a hybrid resolution method that makes atomistic SAXS-restrained MD simulation feasible by adopting a coarse-grained approach to efficiently back-calculate scattering intensities; here, we extend this technique, applying it in the framework of metainference with the aim to investigate the dynamical behavior of flexible biomolecules. The efficacy of the method is assessed on the K63-diubiquitin, showing that the inclusion of SAXS restraints is effective in generating a reliable conformational ensemble, improving the agreement with independent experimental data.

Combination of coarse-grained molecular dynamics simulations and small-angle X-ray scattering experiments

The combination of molecular dynamics (MD) simulations and small-angle X-ray scattering (SAXS), called the MD-SAXS method, is efficient for investigating protein dynamics. To overcome the time-scale limitation of all-atom MD simulations, coarse-grained (CG) representations are often utilized for biomolecular simulations. In this study, we propose a method to combine CG MD simulations with SAXS, termed the CG-MD-SAXS method. In the CG-MD-SAXS method, the scattering factors of CG particles for proteins and nucleic acids are evaluated using high-resolution structural data in the Protein Data Bank, and the excluded volume and the hydration shell are modeled using two adjustable parameters to incorporate solvent effects. To avoid overfitting, only the two parameters are adjusted for an entire structure ensemble. To verify the developed method, theoretical SAXS profiles for various proteins, DNA/RNA, and a protein-RNA complex are compared with both experimental profiles and theoretical profiles obtained by the all-atom representation. In the present study, we applied the CG-MD-SAXS method to the Swi5-Sfr1 complex and three types of nucleosomes to obtain reliable ensemble models consistent with the experimental SAXS data.

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.

Rapid interpretation of small-angle X-ray scattering data

The fundamental aim of structural analyses in biophysics is to reveal a mutual relation between a molecule’s dynamic structure and its physiological function. Small-angle X-ray scattering (SAXS) is an experimental technique for structural characterization of macromolecules in solution and enables time-resolved analysis of conformational changes under physiological conditions. As such experiments measure spatially averaged low-resolution scattering intensities only, the sparse information obtained is not sufficient to uniquely reconstruct a three-dimensional atomistic model. Here, we integrate the information from SAXS into molecular dynamics simulations using computationally efficient native structure-based models. Dynamically fitting an initial structure towards a scattering intensity, such simulations produce atomistic models in agreement with the target data. In this way, SAXS data can be rapidly interpreted while retaining physico-chemical knowledge and sampling power of the underlying force field. We demonstrate our method’s performance using the example of three protein systems. Simulations are faster than full molecular dynamics approaches by more than two orders of magnitude and consistently achieve comparable accuracy. Computational demands are reduced sufficiently to run the simulations on commodity desktop computers instead of high-performance computing systems. These results underline that scattering-guided structure-based simulations provide a suitable framework for rapid early-stage refinement of structures towards SAXS data with particular focus on minimal computational resources and time.

Proteins are the molecular nanomachines in biological cells and thus vital to any known form of life. From the evolutionary perspective, viable protein structure emerges on the basis of a ‘form-follows-function’ principle. A protein’s designated function is inextricably linked to dynamic conformational changes, which can be observed by small-angle X-ray scattering. Intensities from SAXS contain low-resolution information on the protein’s shape at different steps of its functional cycle. We are interested in directly getting an atomistic model of this encoded structure. One powerful approach is to include the experimental data into computational simulations of the protein’s function-related physical motions. We combine scattering intensities with coarse-grained native structure-based models. These models are computationally highly efficient yet describe the system’s dynamics realistically. Here, we present our method for rapid interpretation of scattering intensities from SAXS to derive structural models, using minimal computational resources and time.

Improving Coarse-Grained Protein Force Fields with Small-Angle X-ray Scattering Data

Small-angle X-ray scattering (SAXS) experiments provide valuable structural data for biomolecules in solution. We develop a highly efficient maximum entropy approach to fit SAXS data by introducing minimal biases to a coarse-grained protein force field, the associative memory, water mediated, structure, and energy model (AWSEM). We demonstrate that the resulting force field, AWSEM-SAXS, succeeds in reproducing scattering profiles and models protein structures with shapes that are in much better agreement with experimental results. Quantitative metrics further reveal a modest, but consistent, improvement in the accuracy of modeled structures when SAXS data are incorporated into the force field. Additionally, when applied to a multiconformational protein, we find that AWSEM-SAXS is able to recover the population of different protein conformations from SAXS data alone. We, therefore, conclude that the maximum entropy approach is effective in fine-tuning the force field to better characterize both protein structure and conformational fluctuation.

Inferring Structural Ensembles of Flexible and Dynamic Macromolecules Using Bayesian, Maximum Entropy, and Minimal-Ensemble Refinement Methods

The flexible and dynamic nature of biomolecules and biomolecular complexes is essential for many cellular functions in living organisms but poses a challenge for experimental methods to determine high-resolution structural models. To meet this challenge, experiments are combined with molecular simulations. The latter propose models for structural ensembles, and the experimental data can be used to steer these simulations and to select ensembles that most likely underlie the experimental data. Here, we explain in detail how the "Bayesian Inference Of ENsembles" (BioEn) method can be used to refine such ensembles using a wide range of experimental data. The "Ensemble Refinement of SAXS" (EROS) method is a special case of BioEn, inspired by the Gull-Daniell formulation of maximum entropy image processing and focused originally on X-ray solution scattering experiments (SAXS) and then extended to integrative structural modeling. We also briefly sketch the "minimum ensemble method," a maximum-parsimony refinement method that seeks to represent an ensemble with a minimal number of representative structures.

Predicting X-ray solution scattering from flexible macromolecules

Wide-angle X-ray solution scattering (WAXS) patterns contain substantial information about the structure and dynamics of a protein. Solution scattering from a rigid protein can be predicted from atomic coordinate sets to within experimental error. However, structural fluctuations of proteins in solution can lead to significant changes in the observed intensities. The magnitude and form of these changes contain information about the nature and spatial extent of structural fluctuations in the protein. Molecular dynamics (MD) simulations based on a crystal structure and selected force field generate models for protein internal motions, and here we demonstrate that they can be used to predict the impact of structural fluctuations on solution scattering data. In cases where the observed and calculated intensities correspond, we can conclude that the X-ray scattering provides direct experimental validation of the structural and MD results. In cases where calculated and observed intensities are at odds, the inconsistencies can be used to determine the origins of these discrepancies. They may be because of overestimates or underestimates of structural fluctuations in MD simulations, under-sampling of the structural ensemble in the simulations, errors in the structural model, or a mismatch between the experimental conditions and the parameters used in carrying out the MD simulation.

On the Calculation of SAXS Profiles of Folded and Intrinsically Disordered Proteins from Computer Simulations

Solution techniques such as small-angle X-ray scattering (SAXS) play a central role in structural studies of intrinsically disordered proteins (IDPs); yet, due to low resolution, it is generally necessary to combine SAXS with additional experimental sources of data and to use molecular simulations. Computational methods for the calculation of theoretical SAXS intensity profiles can be separated into two groups, depending on whether the solvent is modeled implicitly as continuous electron density or considered explicitly. The former offers reduced computational cost but requires the definition of a number of free parameters to account for, for example, the excess density of the solvation layer. Overfitting can thus be an issue, particularly when the structural ensemble is unknown. Here, we investigate and show how small variations of the contrast of the hydration shell, δρ, severely affect the outcome, analysis and interpretation of computed SAXS profiles for folded and disordered proteins. For both the folded and disordered proteins studied here, using a default δρ may, in some cases, result in the calculation of non-representative SAXS profiles, leading to an overestimation of their size and a misinterpretation of their structural nature. The solvation layer of the different IDP simulations also impacts their size estimates differently, depending on the protein force field used. The same is not true for the folded protein simulations, suggesting differences in the solvation of the two classes of proteins, and indicating that different force fields optimized for IDPs may cause expansion of the polypeptide chain through different physical mechanisms.

Quantifying the influence of the ion cloud on SAXS profiles of charged proteins

MD simulations and Poisson–Boltzmann calculations predict ion cloud effects on SAXS experiments.

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.

Structures of Dynamic Protein Complexes: Hybrid Techniques to Study MAP Kinase Complexes and the ESCRT System

The integration of complementary molecular methods (including X-ray crystallography, NMR spectroscopy, small angle X-ray/neutron scattering, and computational techniques) is frequently required to obtain a comprehensive understanding of dynamic macromolecular complexes. In particular, these techniques are critical for studying intrinsically disordered protein regions (IDRs) or intrinsically disordered proteins (IDPs) that are part of large protein:protein complexes. Here, we explain how to prepare IDP samples suitable for study using NMR spectroscopy, and describe a novel SAXS modeling method (ensemble refinement of SAXS; EROS) that integrates the results from complementary methods, including crystal structures and NMR chemical shift perturbations, among others, to accurately model SAXS data and describe ensemble structures of dynamic macromolecular complexes.

Effects of Catalytic Action and Ligand Binding on Conformational Ensembles of Adenylate Kinase

Crystal structures of adenylate kinase (AdK) from Escherichia coli capture two states: an "open" conformation (apo) obtained in the absence of ligands and a "closed" conformation in which ligands are bound. Other AdK crystal structures suggest intermediate conformations that may lie on the transition pathway between these two states. To characterize the transition from open to closed states in solution, X-ray solution scattering data were collected from AdK in the apo form and with progressively increasing concentrations of five different ligands. Scattering data from apo AdK are consistent with scattering predicted from the crystal structure of AdK in the open conformation. In contrast, data from AdK samples saturated with Ap5A do not agree with that calculated from AdK in the closed conformation. Using cluster analysis of available structures, we selected representative structures in five conformational states: open, partially open, intermediate, partially closed, and closed. We used these structures to estimate the relative abundances of these states for each experimental condition. X-ray solution scattering data obtained from AdK with AMP are dominated by scattering from AdK in the open conformation. For AdK in the presence of high concentrations of ATP and ADP, the conformational ensemble shifts to a mixture of partially open and closed states. Even when AdK is saturated with Ap5A, a significant proportion of AdK remains in a partially open conformation. These results are consistent with an induced-fit model in which the transition of AdK from an open state to a closed state is initiated by ATP binding.

Combining NMR and small angle X-ray scattering for the study of biomolecular structure and dynamics

Small-angle X-ray scattering (SAXS) and Nuclear Magnetic Resonance (NMR) are established methods to analyze the structure and structural transitions of biological macromolecules in solution. Both methods are directly applicable to near-native macromolecular solutions and allow one to study structural responses to physical and chemical changes or ligand additions. Whereas SAXS is applied to elucidate overall structure, interactions and flexibility over a wide range of particle sizes, NMR yields atomic resolution detail for moderately sized macromolecules. NMR is arguably the most powerful technique for the experimental analysis of dynamics. The joint application of these two highly complementary techniques provides an extremely useful approach that facilitates comprehensive characterization of biomacromolecular solutions.

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SAXS and NMR are effective and highly complementary techniques in structural biology.

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Constraints from SAXS can be readily incorporated in NMR structure calculations.

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High resolution NMR models of domains can serve as building blocks for SAXS-based rigid body modeling.

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Flexible systems can be well described using ensemble approaches combining SAXS and NMR.

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Dynamics studies can be enhanced by combining SAXS and NMR.

Pepsi-SAXS: an adaptive method for rapid and accurate computation of small-angle X-ray scattering profiles

A new method called Pepsi-SAXS is presented that calculates small-angle X-ray scattering profiles from atomistic models. The method is based on the multipole expansion scheme and is significantly faster compared with other tested methods. In particular, using the Nyquist-Shannon-Kotelnikov sampling theorem, the multipole expansion order is adapted to the size of the model and the resolution of the experimental data. It is argued that by using the adaptive expansion order, this method has the same quadratic dependence on the number of atoms in the model as the Debye-based approach, but with a much smaller prefactor in the computational complexity. The method has been systematically validated on a large set of over 50 models collected from the BioIsis and SASBDB databases. Using a laptop, it was demonstrated that Pepsi-SAXS is about seven, 29 and 36 times faster compared with CRYSOL, FoXS and the three-dimensional Zernike method in SAStbx, respectively, when tested on data from the BioIsis database, and is about five, 21 and 25 times faster compared with CRYSOL, FoXS and SAStbx, respectively, when tested on data from SASBDB. On average, Pepsi-SAXS demonstrates comparable accuracy in terms of χ² to CRYSOL and FoXS when tested on BioIsis and SASBDB profiles. Together with a small allowed variation of adjustable parameters, this demonstrates the effectiveness of the method. Pepsi-SAXS is available at http://team.inria.fr/nano-d/software/pepsi-saxs.

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.

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.

Atomistic modelling of scattering data in the Collaborative Computational Project for Small Angle Scattering (CCP-SAS)

The capabilities of current computer simulations provide a unique opportunity to model small-angle scattering (SAS) data at the atomistic level, and to include other structural constraints ranging from molecular and atomistic energetics to crystallography, electron microscopy and NMR. This extends the capabilities of solution scattering and provides deeper insights into the physics and chemistry of the systems studied. Realizing this potential, however, requires integrating the experimental data with a new generation of modelling software. To achieve this, the CCP-SAS collaboration (http://www.ccpsas.org/) is developing open-source, high-throughput and user-friendly software for the atomistic and coarse-grained molecular modelling of scattering data. Robust state-of-the-art molecular simulation engines and molecular dynamics and Monte Carlo force fields provide constraints to the solution structure inferred from the small-angle scattering data, which incorporates the known physical chemistry of the system. The implementation of this software suite involves a tiered approach in which GenApp provides the deployment infrastructure for running applications on both standard and high-performance computing hardware, and SASSIE provides a workflow framework into which modules can be plugged to prepare structures, carry out simulations, calculate theoretical scattering data and compare results with experimental data. GenApp produces the accessible web-based front end termed SASSIE-web, and GenApp and SASSIE also make community SAS codes available. Applications are illustrated by case studies: (i) inter-domain flexibility in two- to six-domain proteins as exemplified by HIV-1 Gag, MASP and ubiquitin; (ii) the hinge conformation in human IgG2 and IgA1 antibodies; (iii) the complex formed between a hexameric protein Hfq and mRNA; and (iv) synthetic 'bottlebrush' polymers.

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.

Deciphering solution scattering data with experimentally guided molecular dynamics simulations

Time-resolved X-ray solution scattering is an increasingly popular method to measure conformational changes in proteins. Extracting structural information from the resulting difference X-ray scattering data is a daunting task. We present a method in which the limited but precious information encoded in such scattering curves is combined with the chemical knowledge of molecular force fields. The molecule of interest is then refined toward experimental data using molecular dynamics simulation. Therefore, the energy landscape is biased toward conformations that agree with experimental data. We describe and verify the method, and we provide an implementation in GROMACS.

SAXS/SANS on Supercharged Proteins Reveals Residue-Specific Modifications of the Hydration Shell

Water molecules in the immediate vicinity of biomacromolecules, including proteins, constitute a hydration layer characterized by physicochemical properties different from those of bulk water and play a vital role in the activity and stability of these structures, as well as in intermolecular interactions. Previous studies using solution scattering, crystallography, and molecular dynamics simulations have provided valuable information about the properties of these hydration shells, including modifications in density and ionic concentration. Small-angle scattering of x-rays (SAXS) and neutrons (SANS) are particularly useful and complementary techniques to study biomacromolecular hydration shells due to their sensitivity to electronic and nuclear scattering-length density fluctuations, respectively. Although several sophisticated SAXS/SANS programs have been developed recently, the impact of physicochemical surface properties on the hydration layer remains controversial, and systematic experimental data from individual biomacromolecular systems are scarce. Here, we address the impact of physicochemical surface properties on the hydration shell by a systematic SAXS/SANS study using three mutants of a single protein, green fluorescent protein (GFP), with highly variable net charge (+36, -6, and -29). The combined analysis of our data shows that the hydration shell is locally denser in the vicinity of acidic surface residues, whereas basic and hydrophilic/hydrophobic residues only mildly modify its density. Moreover, the data demonstrate that the density modifications result from the combined effect of residue-specific recruitment of ions from the bulk in combination with water structural rearrangements in their vicinity. Finally, we find that the specific surface-charge distributions of the different GFP mutants modulate the conformational space of flexible parts of the protein.

Fast antibody fragment motion: flexible linkers act as entropic spring

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.

Validating solution ensembles from molecular dynamics simulation by wide-angle X-ray scattering data

Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q≈15nm(-1). Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by < 1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.

Emerging applications of small angle solution scattering in structural biology

Small angle solution X-ray and neutron scattering recently resurfaced as powerful tools to address an array of biological problems including folding, intrinsic disorder, conformational transitions, macromolecular crowding, and self or hetero-assembling of biomacromolecules. In addition, small angle solution scattering complements crystallography, nuclear magnetic resonance spectroscopy, and other structural methods to aid in the structure determinations of multidomain or multicomponent proteins or nucleoprotein assemblies. Neutron scattering with hydrogen/deuterium contrast variation, or X-ray scattering with sucrose contrast variation to a certain extent, is a convenient tool for characterizing the organizations of two-component systems such as a nucleoprotein or a lipid-protein assembly. Time-resolved small and wide-angle solution scattering to study biological processes in real time, and the use of localized heavy-atom labeling and anomalous solution scattering for applications as FRET-like molecular rulers, are amongst promising newer developments. Despite the challenges in data analysis and interpretation, these X-ray/neutron solution scattering based approaches hold great promise for understanding a wide variety of complex processes prevalent in the biological milieu.

Review of the fundamental theories behind small angle X-ray scattering, molecular dynamics simulations, and relevant integrated application

In this paper, the fundamental concepts and equations necessary for performing small angle X-ray scattering (SAXS) experiments, molecular dynamics (MD) simulations, and MD-SAXS analyses were reviewed. Furthermore, several key biological and non-biological applications for SAXS, MD, and MD-SAXS are presented in this review; however, this article does not cover all possible applications. SAXS is an experimental technique used for the analysis of a wide variety of biological and non-biological structures. SAXS utilizes spherical averaging to produce one- or two-dimensional intensity profiles, from which structural data may be extracted. MD simulation is a computer simulation technique that is used to model complex biological and non-biological systems at the atomic level. MD simulations apply classical Newtonian mechanics' equations of motion to perform force calculations and to predict the theoretical physical properties of the system. This review presents several applications that highlight the ability of both SAXS and MD to study protein folding and function in addition to non-biological applications, such as the study of mechanical, electrical, and structural properties of non-biological nanoparticles. Lastly, the potential benefits of combining SAXS and MD simulations for the study of both biological and non-biological systems are demonstrated through the presentation of several examples that combine the two techniques.

Uniqueness of models from small-angle scattering data: the impact of a hydration shell and complementary NMR restraints

Small-angle scattering (SAS) has witnessed a breathtaking renaissance and expansion over the past 15 years regarding the determination of biomacromolecular structures in solution. While important issues such as sample quality, good experimental practice and guidelines for data analysis, interpretation, presentation, publication and deposition are increasingly being recognized, crucial topics such as the uniqueness, precision and accuracy of the structural models obtained by SAS are still only poorly understood and addressed. The present article provides an overview of recent developments in these fields with a focus on the influence of complementary NMR restraints and of a hydration shell on the uniqueness of biomacromolecular models. As a first topic, the impact of incorporating NMR orientational restraints in addition to SAS distance restraints is discussed using a quantitative visual representation that illustrates how the possible conformational space of a two-body system is reduced as a function of the available data. As a second topic, the impact of a hydration shell on modelling parameters of a two-body system is illustrated, in particular on its inter-body distance. Finally, practical recommendations are provided to take both effects into account and promising future perspectives of SAS approaches are discussed.

Slow internal protein dynamics in solution

Large-scale domain dynamics in proteins are found when flexible linkers or hinges connect domains. The related conformational changes are often related to the function of the protein,for example by arranging the active center after substrate binding or allowing transport and release of products. The adaptation of a specific active structure is referred to as ‘induced fit’ and is challenged by models such as ‘conformational sampling’. Newer models about protein unction include some flexibility within the protein structure or even internal dynamics of the protein. As larger domains contribute to the configurational changes, the timescale of the involved motions is slowed down. The role of slow domain dynamics is being increasingly recognized as essential to understanding the function of proteins. Neutron spin echospectroscopy (NSE) is a technique that is able to access the related timescales from 0.1 up to several hundred nanoseconds and simultaneously covers the length scale relevant for protein domain movements of several nanometers distance between domains. Here we focus on these large-scale domain fluctuations and show how the structure and dynamics of proteins can be assessed by small-angle neutron scattering and NSE.

Methods for SAXS-based structure determination of biomolecular complexes

Measurements from small-angle X-ray scattering (SAXS) are highly informative to determine the structures of bimolecular complexes in solution. Here, current and recent SAXS-driven developments are described, with an emphasis on computational modeling. In particular, accurate methods to computing one theoretical scattering profile from a given structure model are discussed, with a key focus on structure factor coarse-graining and hydration contribution. Methods for reconstructing topological structures from an experimental SAXS profile are currently under active development. We report on several modeling tools designed for conformation generation that make use of either atomic-level or coarse-grained representations. Furthermore, since large, flexible biomolecules can adopt multiple well-defined conformations, a traditional single-conformation SAXS analysis is inappropriate, so we also discuss recent methods that utilize the concept of ensemble optimization, weighing in on the SAXS contributions of a heterogeneous mixture of conformations. These tools will ultimately posit the usefulness of SAXS data beyond a simple space-filling approach by providing a reliable structure characterization of biomolecular complexes under physiological conditions.

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.