Bayesian refinement of protein structures and ensembles against SAXS data using molecular dynamics

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.

SANS Spectra with PLUMED: Implementation and Application to Metainference

Using small-angle scattering with either X-ray or neutron sources has become common in the investigation of soft-matter systems. These experiments provide information about the coarse shape of the scattered objects, but obtaining more-detailed information can usually only be achieved with the aid of molecular simulations. In this Application Note, we report the implementation of an extension in PLUMED to compute the small-angle neutron scattering (SANS), which can be used for data processing as well for enhanced sampling, in particular with the metainference method to bias simulations and sample structures with a resulting spectrum in agreement with an experimental reference. Our implementation includes a resolution function that can be used to smear the SANS intensities according to beamline error sources and is compatible with both all-atom and coarse-grained simulations. Scripts to aid in the calculation of the scattering lengths when the system is coarse-grained and to aid in preparing the inputs are provided. We illustrate the use of the implementation with metainference by performing coarse-grained simulations of beta-octylglucoside and dodecylphosphocholine micelles in water. With different software and different Hamiltonians, we show that the metainference SANS bias can drive micelles to be split and to change shapes to achieve a better agreement with the experimental reference.

Bayesian methods in integrative structure modeling

There is a growing interest in characterizing the structure and dynamics of large biomolecular assemblies and their interactions within the cellular environment. A diverse array of experimental techniques allows us to study biomolecular systems on a variety of length and time scales. These techniques range from imaging with light, X-rays or electrons, to spectroscopic methods, cross-linking mass spectrometry and functional genomics approaches, and are complemented by AI-assisted protein structure prediction methods. A challenge is to integrate all of these data into a model of the system and its functional dynamics. This review focuses on Bayesian approaches to integrative structure modeling. We sketch the principles of Bayesian inference, highlight recent applications to integrative modeling and conclude with a discussion of current challenges and future perspectives.

Generation of unfolded outer membrane protein ensembles defined by hydrodynamic properties

Outer membrane proteins (OMPs) must exist as an unfolded ensemble while interacting with a chaperone network in the periplasm of Gram-negative bacteria. Here, we developed a method to model unfolded OMP (uOMP) conformational ensembles using the experimental properties of two well-studied OMPs. The overall sizes and shapes of the unfolded ensembles in the absence of a denaturant were experimentally defined by measuring the sedimentation coefficient as a function of urea concentration. We used these data to model a full range of unfolded conformations by parameterizing a targeted coarse-grained simulation protocol. The ensemble members were further refined by short molecular dynamics simulations to reflect proper torsion angles. The final conformational ensembles have polymer properties different from unfolded soluble and intrinsically disordered proteins and reveal inherent differences in the unfolded states that necessitate further investigation. Building these uOMP ensembles advances the understanding of OMP biogenesis and provides essential information for interpreting structures of uOMP-chaperone complexes.

Molecular dynamics simulations and X-ray scattering show the κ-carrageenan disorder-to-order transition to be the formation of double-helices

Recent molecular dynamics simulations, verified experimentally by solution-state x-ray scattering experiments, have found that κ-carrageenan chains contain helical secondary structure, akin to that found in the solid-state, even in aqueous solution. Furthermore, upon the addition of ions to single chains the simulations found no evidence that any conformational transitions take place. These findings challenge the long-held assumption that the so-called disorder-to-order transition in carrageenan systems involves a uni-molecular 'coil-to-helix transition'. Herein, the results of further molecular dynamics simulations undertaken using pairs of κ-carrageenan chains in 0.1 M NaI solutions are reported, and are validated experimentally using state-of-the-art solution-state WAXS experiments. From initially separated chains double-helices are shown to form, leading the authors to propose 'two single helices-to-stabilized double-helix' as a description of the molecular events taking place during the disorder-to-order transition.

Biophysical Approaches for the Characterization of Protein-Metabolite Interactions

With an estimate of hundred thousands of protein molecules per cell and the number of metabolites several orders of magnitude higher, protein-metabolite interactions are omnipresent. In vitro analyses are one of the main pillars on the way to establish a solid understanding of how these interactions contribute to maintaining cellular homeostasis. A repertoire of biophysical techniques is available by which protein-metabolite interactions can be quantitatively characterized in terms of affinity, specificity, and kinetics in a broad variety of solution environments. Several of those provide information on local or global conformational changes of the protein partner in response to ligand binding. This review chapter gives an overview of the state-of-the-art biophysical toolbox for the study of protein-metabolite interactions. It briefly introduces basic principles, highlights recent examples from the literature, and pinpoints promising future directions.

Structure and ensemble refinement against SAXS data: Combining MD simulations with Bayesian inference or with the maximum entropy principle

Small-angle X-ray scattering (SAXS) is a powerful method for tracking conformational transitions of proteins or soft-matter complexes in solution. However, the interpretation of the experimental data is challenged by the low spatial resolution and the low information content of the data, which lead to a high risk of overinterpreting the data. Here, we illustrate how SAXS data can be integrated into all-atom molecular dynamics (MD) simulation to derive atomic structures or heterogeneous ensembles that are compatible with the data. Besides providing atomistic insight, the MD simulation adds physicochemical information, as encoded in the MD force fields, which greatly reduces the risk of overinterpretation. We present an introduction into the theory of SAXS-driven MD simulations as implemented in GROMACS-SWAXS, a modified version of the GROMACS simulation software. We discuss SAXS-driven parallel-replica ensemble refinement with commitment to the maximum entropy principle as well as a Bayesian formulation of SAXS-driven structure refinement. Practical considerations for running and interpreting the simulations are presented. The methods are freely available via GitLab at https://gitlab.com/cbjh/gromacs-swaxs.

Extracting time series matching a small-angle X-ray scattering profile from trajectories of molecular dynamics simulations

Solving structural ensembles of flexible biomolecules is a challenging research area. Here, we propose a method to obtain possible structural ensembles of a biomolecule based on small-angle X-ray scattering (SAXS) and molecular dynamics simulations. Our idea is to clip a time series that matches a SAXS profile from a simulation trajectory. To examine its practicability, we applied our idea to a multi-domain protein ER-60 and successfully extracted time series longer than 1 micro second from trajectories of coarse-grained molecular dynamics simulations. In the extracted time series, the domain conformation was distributed continuously and smoothly in a conformational space. Preferred domain conformations were also observed. Diversity among scattering curves calculated from each ER-60 structure was interpreted to reflect an open-close motion of the protein. Although our approach did not provide a unique solution for the structural ensemble of the biomolecule, each extracted time series can be an element of the real behavior of ER-60. Considering its low computational cost, our approach will play a key role to identify biomolecular dynamics by integrating SAXS, simulations, and other experiments.

From Data to Knowledge: Systematic Review of Tools for Automatic Analysis of Molecular Dynamics Output

An increasing number of crystal structures available on one side, and the boost of computational power available for computer-aided drug design tasks on the other, have caused that the structure-based drug design tools are intensively used in the drug development pipelines. Docking and molecular dynamics simulations, key representatives of the structure-based approaches, provide detailed information about the potential interaction of a ligand with a target receptor. However, at the same time, they require a three-dimensional structure of a protein and a relatively high amount of computational resources. Nowadays, as both docking and molecular dynamics are much more extensively used, the amount of data output from these procedures is also growing. Therefore, there are also more and more approaches that facilitate the analysis and interpretation of the results of structure-based tools. In this review, we will comprehensively summarize approaches for handling molecular dynamics simulations output. It will cover both statistical and machine-learning-based tools, as well as various forms of depiction of molecular dynamics output.

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.

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.

Automatic Bayesian Weighting for SAXS Data

Small-angle X-ray scattering (SAXS) experiments are important in structural biology because they are solution methods, and do not require crystallization of protein complexes. Structure determination from SAXS data, however, poses some difficulties. Computation of a SAXS profile from a protein model is expensive in CPU time. Hence, rather than directly refining against the data, most computational methods generate a large number of conformers and then filter the structures based on how well they satisfy the SAXS data. To address this issue in an efficient manner, we propose here a Bayesian model for SAXS data and use it to directly drive a Monte Carlo simulation. We show that the automatic weighting of SAXS data is the key to finding optimal structures efficiently. Another key problem with obtaining structures from SAXS data is that proteins are often flexible and the data represents an average over a structural ensemble. To address this issue, we first characterize the stability of the best model with extensive molecular dynamics simulations. We analyse the resulting trajectories further to characterize a dynamic structural ensemble satisfying the SAXS data. The combination of methods is applied to a tandem of domains from the protein PTPN4, which are connected by an unstructured linker. We show that the SAXS data contain information that supports and extends other experimental findings. We also show that the conformation obtained by the Bayesian analysis is stable, but that a minor conformation is present. We propose a mechanism in which the linker may maintain PTPN4 in an inhibited enzymatic state.

Reconciling Simulations and Experiments With BICePs: A Review

Bayesian Inference of Conformational Populations (BICePs) is an algorithm developed to reconcile simulated ensembles with sparse experimental measurements. The Bayesian framework of BICePs enables population reweighting as a post-simulation processing step, with several advantages over existing methods, including the proper use of reference potentials, and the estimation of a Bayes factor-like quantity called the BICePs score for model selection. Here, we summarize the theory underlying this method in context with related algorithms, review the history of BICePs applications to date, and discuss current shortcomings along with future plans for improvement.

Including residual contact information into replica-exchange MD simulations significantly enriches native-like conformations

Proteins are complex biomolecules which perform critical tasks in living organisms. Knowledge of a protein's structure is essential for understanding its physiological function in detail. Despite the incredible progress in experimental techniques, protein structure determination is still expensive, time-consuming, and arduous. That is why computer simulations are often used to complement or interpret experimental data. Here, we explore how in silico protein structure determination based on replica-exchange molecular dynamics (REMD) can benefit from including contact information derived from theoretical and experimental sources, such as direct coupling analysis or NMR spectroscopy. To reflect the influence from erroneous and noisy data we probe how false-positive contacts influence the simulated ensemble. Specifically, we integrate varying numbers of randomly selected native and non-native contacts and explore how such a bias can guide simulations towards the native state. We investigate the number of contacts needed for a significant enrichment of native-like conformations and show the capabilities and limitations of this method. Adhering to a threshold of approximately 75% true-positive contacts within a simulation, we obtain an ensemble with native-like conformations of high quality. We find that contact-guided REMD is capable of delivering physically reasonable models of a protein's structure.

Comprehensive Structural and Thermodynamic Analysis of Prefibrillar WT α-Synuclein and Its G51D, E46K, and A53T Mutants by a Combination of Small-Angle X-ray Scattering and Variational Bayesian Weighting

The in solution synchrotron small-angle X-ray scattering SAXS technique has been used to investigate an intrinsically disordered protein (IDP) related to Parkinson's disease, the α-synuclein (α-syn), in prefibrillar diluted conditions. SAXS experiments have been performed as a function of temperature and concentration on the wild type (WT) and on the three pathogenic mutants G51D, E46K, and A53T. To identify the conformers that populate WT α-syn and the pathogenic mutants in prefibrillar conditions, scattering data have been analyzed by a new variational bayesian weighting method (VBWSAS) based on an ensemble of conformers, which includes unfolded monomers, trimers, and tetramers, both in helical-rich and strand-rich forms. The developed VBWSAS method uses a thermodynamic scheme to account for temperature and concentration effects and considers long-range protein-protein interactions in the framework of the random phase approximation. The global analysis of the whole set of data indicates that WT α-syn is mostly present as unfolded monomers and trimers (helical-rich trimers at low T and strand-rich trimers at high T), but not tetramers, as previously derived by several studies. On the contrary, different conformer combinations characterize mutants. In the α-syn G51D mutant, the most abundant aggregates at all the temperatures are strand-rich tetramers. Strand-rich tetramers are also the predominant forms in the A53T mutant, but their weight decreases with temperature. Only monomeric conformers, with a preference for the ones with the smallest sizes, are present in the E46K mutant. The derived conformational behavior then suggests a different availability of species prone to aggregate, depending on mutation, temperature, and concentration and accounting for the different neurotoxicity of α-syn variants. Indeed, this approach may be of pivotal importance to describe conformational and aggregational properties of other IDPs.

Machine learning deciphers structural features of RNA duplexes measured with solution X-ray scattering

Macromolecular structures can be determined from solution X-ray scattering. Small-angle X-ray scattering (SAXS) provides global structural information on length scales of 10s to 100s of Ångstroms, and many algorithms are available to convert SAXS data into low-resolution structural envelopes. Extension of measurements to wider scattering angles (WAXS or wide-angle X-ray scattering) can sharpen the resolution to below 10 Å, filling in structural details that can be critical for biological function. These WAXS profiles are especially challenging to interpret because of the significant contribution of solvent in addition to solute on these smaller length scales. Based on training with molecular dynamics generated models, the application of extreme gradient boosting (XGBoost) is discussed, which is a supervised machine learning (ML) approach to interpret features in solution scattering profiles. These ML methods are applied to predict key structural parameters of double-stranded ribonucleic acid (dsRNA) duplexes. Duplex conformations vary with salt and sequence and directly impact the foldability of functional RNA molecules. The strong structural periodicities in these duplexes yield scattering profiles with rich sets of features at intermediate-to-wide scattering angles. In the ML models, these profiles are treated as 1D images or features. These ML models identify specific scattering angles, or regions of scattering angles, which correspond with and successfully predict distinct structural parameters. Thus, this work demonstrates that ML strategies can integrate theoretical molecular models with experimental solution scattering data, providing a new framework for extracting highly relevant structural information from solution experiments on biological macromolecules.

Extended Experimental Inferential Structure Determination Method in Determining the Structural Ensembles of Disordered Protein States

Proteins with intrinsic or unfolded state disorder comprise a new frontier in structural biology, requiring the characterization of diverse and dynamic structural ensembles. We introduce a comprehensive Bayesian framework, the Extended Experimental Inferential Structure Determination (X-EISD) method, that calculates the maximum log-likelihood of a disordered protein ensemble. X-EISD accounts for the uncertainties of a range of experimental data and back-calculation models from structures, including NMR chemical shifts, J-couplings, Nuclear Overhauser Effects (NOEs), paramagnetic relaxation enhancements (PREs), residual dipolar couplings (RDCs), hydrodynamic radii (R h ), single molecule fluorescence Förster resonance energy transfer (smFRET) and small angle X-ray scattering (SAXS). We apply X-EISD to the joint optimization against experimental data for the unfolded drkN SH3 domain and find that combining a local data type, such as chemical shifts or J-couplings, paired with long-ranged restraints such as NOEs, PREs or smFRET, yields structural ensembles in good agreement with all other data types if combined with representative IDP conformers.

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.

Using NMR Chemical Shifts and Cryo-EM Density Restraints in Iterative Rosetta-MD Protein Structure Refinement

Cryo-EM has become one of the prime methods for protein structure elucidation, frequently yielding density maps with near-atomic or medium resolution. If protein structures cannot be deduced unambiguously from the density maps, computational structure refinement tools are needed to generate protein structural models. We have previously developed an iterative Rosetta-MDFF protocol that used cryo-EM densities to refine protein structures. Here we show that, in addition to cryo-EM densities, incorporation of other experimental restraints into the Rosetta-MDFF protocol further improved refined structures. We used NMR chemical shift (CS) data integrated with cryo-EM densities in our hybrid protocol in both the Rosetta step and the molecular dynamics (MD) simulations step. In 15 out of 18 cases for all MD rounds, the refinement results obtained when density maps and NMR chemical shift data were used in combination outperformed those of density map-only refinement. Notably, the improvement in refinement was highest when medium and low-resolution density maps were used. With our hybrid method, the RMSDs of final models obtained were always better than the RMSDs obtained by our previous protocol with just density refinement for both medium (6.9 Å) and low (9 Å) resolution maps. For all the six test proteins with medium resolution density maps (6.9 Å), the final refined structure RMSDs were lower for the hybrid method than for the cryo-EM only refinement. The final refined RMSDs were less than 1.5 Å when our hybrid protocol was used with 4 Å density maps. For four out of the six proteins the final RMSDs were even less than 1 Å. This study demonstrates that by using a combination of cryo-EM and NMR restraints, it is possible to refine structures to atomic resolution, outperforming single restraint refinement. This hybrid protocol will be a valuable tool when only low-resolution cryo-EM density data and NMR chemical shift data are available to refine structures.

Combining molecular dynamics simulations with small-angle X-ray and neutron scattering data to study multi-domain proteins in solution

Many proteins contain multiple folded domains separated by flexible linkers, and the ability to describe the structure and conformational heterogeneity of such flexible systems pushes the limits of structural biology. Using the three-domain protein TIA-1 as an example, we here combine coarse-grained molecular dynamics simulations with previously measured small-angle scattering data to study the conformation of TIA-1 in solution. We show that while the coarse-grained potential (Martini) in itself leads to too compact conformations, increasing the strength of protein-water interactions results in ensembles that are in very good agreement with experiments. We show how these ensembles can be refined further using a Bayesian/Maximum Entropy approach, and examine the robustness to errors in the energy function. In particular we find that as long as the initial simulation is relatively good, reweighting against experiments is very robust. We also study the relative information in X-ray and neutron scattering experiments and find that refining against the SAXS experiments leads to improvement in the SANS data. Our results suggest a general strategy for studying the conformation of multi-domain proteins in solution that combines coarse-grained simulations with small-angle X-ray scattering data that are generally most easy to obtain. These results may in turn be used to design further small-angle neutron scattering experiments that exploit contrast variation through 1H/2H isotope substitutions.

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.

Enhanced sampling and free energy calculations for protein simulations

Molecular dynamics simulation is a powerful computational technique to study biomolecular systems, which complements experiments by providing insights into the structural dynamics relevant to biological functions at atomic scale. It can also be used to calculate the free energy landscapes of the conformational transitions to better understand the functions of the biomolecules. However, the sampling of biomolecular configurations is limited by the free energy barriers that need to be overcome, leading to considerable gaps between the timescales reached by MD simulation and those governing biological processes. To address this issue, many enhanced sampling methodologies have been developed to increase the sampling efficiency of molecular dynamics simulations and free energy calculations. Usually, enhanced sampling algorithms can be classified into methods based on collective variables (CV-based) and approaches which do not require predefined CVs (CV-free). In this chapter, the theoretical basis of free energy estimation is briefly reviewed first, followed by the reviews of the most common CV-based and CV-free methods including the presentation of some examples and recent developments. Finally, the combination of different enhanced sampling methods is discussed.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.

Salt Dependence of A-Form RNA Duplexes: Structures and Implications

The biological functions of RNA range from gene regulation through catalysis and depend critically on its structure and flexibility. Conformational variations of flexible, non-base-paired components, including RNA hinges, bulges, or single-stranded tails, are well documented. Recent work has also identified variations in the structure of ubiquitous, base-paired duplexes found in almost all functional RNAs. Duplexes anchor the structures of folded RNAs, and their surface features are recognized by partner molecules. To date, no consistent picture has been obtained that describes the range of conformations assumed by RNA duplexes. Here, we apply wide angle, solution X-ray scattering (WAXS) to quantify these variations, by sampling length scales characteristic of helical geometries under different solution conditions. To identify the radius, helical rise, twist, and length of dsRNA helices, we exploit molecular dynamics generated structures, explicit solvent models, and ensemble optimization methods. Our results quantify the substantial and salt-dependent deviations of double-stranded (ds) RNA duplexes from the assumed canonical A-form conformation. Recent experiments underscore the need to properly describe the structures of RNA duplexes when interpreting the salt dependence of RNA conformations.

Evolving SAXS versatility: solution X-ray scattering for macromolecular architecture, functional landscapes, and integrative structural biology

Small-angle X-ray scattering (SAXS) has emerged as an enabling integrative technique for comprehensive analyses of macromolecular structures and interactions in solution. Over the past two decades, SAXS has become a mainstay of the structural biologist's toolbox, supplying multiplexed measurements of molecular shape and dynamics that unveil biological function. Here, we discuss evolving SAXS theory, methods, and applications that extend the field of small-angle scattering beyond simple shape characterization. SAXS, coupled with size-exclusion chromatography (SEC-SAXS) and time-resolved (TR-SAXS) methods, is now providing high-resolution insight into macromolecular flexibility and ensembles, delineating biophysical landscapes, and facilitating high-throughput library screening to assess macromolecular properties and to create opportunities for drug discovery. Looking forward, we consider SAXS in the integrative era of hybrid structural biology methods, its potential for illuminating cellular supramolecular and mesoscale structures, and its capacity to complement high-throughput bioinformatics sequencing data. As advances in the field continue, we look forward to proliferating uses of SAXS based upon its abilities to robustly produce mechanistic insights for biology and medicine.

The Structural and Functional Diversity of Intrinsically Disordered Regions in Transmembrane Proteins

The intrinsically disordered proteins and protein regions (IDPs/IDPRs) do not have unique structures, but are known to be functionally important and their conformational flexibility and structural plasticity have engendered a paradigmatic shift in the classical sequence-structure-function maxim. Fundamental understanding in this field has significantly evolved since the discovery of this class of proteins about 25 years ago. Though the IDPRs of transmembrane proteins (TMP-IDPRs) comply with the broad definition of typical IDPs and IDPRs found in water-soluble globular proteins, much less is explored and known about them. In this review, we assimilate the key emerging biophysical principles from the limited studies on TMP-IDPRs and provide several context-specific biological examples to highlight the ubiquitous nature of TMP-IDPRs and their functional importance in cellular functions. Besides providing a spectrum of insights from sequence to structural disorder and functions, we also review the challenges and methodological advances in studying the structure-function relationship of TMP-IDPRs. We also lay stress upon the importance of an integrative framework, where ensemble-averaged (and mostly low-resolution) data from multiple experiments can be faithfully integrated with modelling techniques such as advanced sampling, coarse-graining, and free energy minimization methods for a high-fidelity characterization of TMP-IDPRs. We close the review by providing futuristic perspective with suggestions on how we could use the ideas and methods from the exciting field of protein engineering in conjunction with integrative modelling framework to advance the IDPR field and harness the sequence-disorder-function paradigm towards functional design of proteins.

Generation of the configurational ensemble of an intrinsically disordered protein from unbiased molecular dynamics simulation

Intrinsically disordered proteins (IDPs) are abundant in eukaryotic proteomes, play a major role in cell signaling, and are associated with human diseases. To understand IDP function it is critical to determine their configurational ensemble, i.e., the collection of 3-dimensional structures they adopt, and this remains an immense challenge in structural biology. Attempts to determine this ensemble computationally have been hitherto hampered by the necessity of reweighting molecular dynamics (MD) results or biasing simulation in order to match ensemble-averaged experimental observables, operations that reduce the precision of the generated model because different structural ensembles may yield the same experimental observable. Here, by employing enhanced sampling MD we reproduce the experimental small-angle neutron and X-ray scattering profiles and the NMR chemical shifts of the disordered N terminal (SH4UD) of c-Src kinase without reweighting or constraining the simulations. The unbiased simulation results reveal a weakly funneled and rugged free energy landscape of SH4UD, which gives rise to a heterogeneous ensemble of structures that cannot be described by simple polymer theory. SH4UD adopts transient helices, which are found away from known phosphorylation sites and could play a key role in the stabilization of structural regions necessary for phosphorylation. Our findings indicate that adequately sampled molecular simulations can be performed to provide accurate physical models of flexible biosystems, thus rationalizing their biological function.

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala-Ala-Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala-Ala-Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.

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.

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.

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.

Analysis of small-angle scattering data using model fitting and Bayesian regularization

The structure of macromolecules can be studied by small-angle scattering (SAS), but as this is an ill-posed problem, prior knowledge about the sample must be included in the analysis. Regularization methods are used for this purpose, as already implemented in indirect Fourier transformation and bead-modeling-based analysis of SAS data, but not yet in the analysis of SAS data with analytical form factors. To fill this gap, a Bayesian regularization method was implemented, where the prior information was quantified as probability distributions for the model parameters and included via a functional S. The quantity Q = χ2 + αS was then minimized and the value of the regularization parameter α determined by probability maximization. The method was tested on small-angle X-ray scattering data from a sample of nanodiscs and a sample of micelles. The parameters refined with the Bayesian regularization method were closer to the prior values as compared with conventional χ2 minimization. Moreover, the errors on the refined parameters were generally smaller, owing to the inclusion of prior information. The Bayesian method stabilized the refined values of the fitted model upon addition of noise and can thus be used to retrieve information from data with low signal-to-noise ratio without risk of overfitting. Finally, the method provides a measure for the information content in data, N g, which represents the effective number of retrievable parameters, taking into account the imposed prior knowledge as well as the noise level in data.

Evaluating Anti-CD32b F(ab) Conformation Using Molecular Dynamics and Small-Angle X-Ray Scattering

Complementary strategies of small-angle x-ray scattering (SAXS) and crystallographic analysis are often used to determine atomistic three-dimensional models of macromolecules and their variability in solution. This combination of techniques is particularly valuable when applied to macromolecular complexes to detect changes within the individual binding partners. Here, we determine the x-ray crystallographic structure of a F(ab) fragment in complex with CD32b, the only inhibitory Fc-γ receptor in humans, and compare the structure of the F(ab) from the crystal complex to SAXS data for the F(ab) alone in solution. We investigate changes in F(ab) structure by predicting theoretical scattering profiles for atomistic structures extracted from molecular dynamics (MD) simulations of the F(ab) and assessing the agreement of these structures to our experimental SAXS data. Through principal component analysis, we are able to extract principal motions observed during the MD trajectory and evaluate the influence of these motions on the agreement of structures to the F(ab) SAXS data. Changes in the F(ab) elbow angle were found to be important to reach agreement with the experimental data; however, further discrepancies were apparent between our F(ab) structure from the crystal complex and SAXS data. By analyzing multiple MD structures observed in similar regions of the principal component analysis, we were able to pinpoint these discrepancies to a specific loop region in the F(ab) heavy chain. This method, therefore, not only allows determination of global changes but also allows identification of localized motions important for determining the agreement between atomistic structures and SAXS data. In this particular case, the findings allowed us to discount the hypothesis that structural changes were induced upon complex formation, a significant find informing the drug development process. The methodology described here is generally applicable to deconvolute global and local changes of macromolecular structures and is well suited to other systems.

Overview of refinement procedures within REFMAC5: utilizing data from different sources

Refinement is a process that involves bringing into agreement the structural model, available prior knowledge and experimental data. To achieve this, the refinement procedure optimizes a posterior conditional probability distribution of model parameters, including atomic coordinates, atomic displacement parameters (B factors), scale factors, parameters of the solvent model and twin fractions in the case of twinned crystals, given observed data such as observed amplitudes or intensities of structure factors. A library of chemical restraints is typically used to ensure consistency between the model and the prior knowledge of stereochemistry. If the observation-to-parameter ratio is small, for example when diffraction data only extend to low resolution, the Bayesian framework implemented in REFMAC5 uses external restraints to inject additional information extracted from structures of homologous proteins, prior knowledge about secondary-structure formation and even data obtained using different experimental methods, for example NMR. The refinement procedure also generates the `best' weighted electron-density maps, which are useful for further model (re)building. Here, the refinement of macromolecular structures using REFMAC5 and related tools distributed as part of the CCP4 suite is discussed.