SAXS-Restrained Ensemble Simulations of Intrinsically Disordered Proteins with Commitment to the Principle of Maximum Entropy

Using NMR diffusion data to validate MD models of disordered proteins: Test case of N-terminal tail of histone H4

MD simulations can provide uniquely detailed models of intrinsically disordered proteins (IDPs). However, these models need careful experimental validation. The coefficient of translational diffusion Dtr, measurable by pulsed field gradient NMR, offers a potentially useful piece of experimental information related to the compactness of the IDP's conformational ensemble. Here, we investigate, both experimentally and via the MD modeling, the translational diffusion of a 25-residue N-terminal fragment from histone H4 (N-H4). We found that the predicted values of Dtr, as obtained from mean-square displacement of the peptide in the MD simulations, are largely determined by the viscosity of the MD water (which has been reinvestigated as a part of our study). Beyond that, our analysis of the diffusion data indicates that MD simulations of N-H4 in the TIP4P-Ew water give rise to an overly compact conformational ensemble for this peptide. In contrast, TIP4P-D and OPC simulations produce the ensembles that are consistent with the experimental Dtr result. These observations are supported by the analyses of the 15N spin relaxation rates. We also tested a number of empirical methods to predict Dtr based on IDP's coordinates extracted from the MD snapshots. In particular, we show that the popular approach involving the program HYDROPRO can produce misleading results. This happens because HYDROPRO is not intended to predict the diffusion properties of highly flexible biopolymers such as IDPs. Likewise, recent empirical schemes that exploit the relationship between the small-angle x-ray scattering-informed conformational ensembles of IDPs and the respective experimental Dtr values also prove to be problematic. In this sense, the first-principle calculations of Dtr from the MD simulations, such as demonstrated in this work, should provide a useful benchmark for future efforts in this area.

Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules

The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.

Insight into structural biophysics from solution X-ray scattering

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement.

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.

Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy

In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.

Experiment-guided molecular simulations define a heterogeneous structural ensemble for the PTPN11 tandem SH2 domains

SHP2 plays an important role in regulating cellular processes, and its pathogenic mutations cause developmental disorders and are linked to cancer. SHP2 is a multidomain protein, comprising two SH2 domains arranged in tandem, a catalytic PTP domain, and a disordered C-terminal tail. SHP2 is activated upon binding two linked phosphopeptides to its SH2 domains, and the peptide orientation and spacing between binding sites are critical for enzymatic activation. For decades, the tandem SH2 has been extensively studied to identify the relative orientation of the two SH2 domains that most effectively binds effectors. So far, neither crystallography nor experiments in solution have provided conclusive results. Using experiment-guided molecular simulations, we determine the heterogeneous structural ensemble of the tandem SH2 in solution in agreement with experimental data from small-angle X-ray scattering and NMR residual dipolar couplings. In the solution ensemble, N-SH2 adopts different orientations and positions relative to C-SH2. We suggest that the intrinsic structural plasticity of the tandem SH2 allows SHP2 to respond to external stimuli and is essential for its functional activity.

Interaction of the tau fibrils with the neuronal membrane

Tau proteins are recently gaining a lot of interest due to their active role in causing a range of tauopathies. Molecular mechanisms underlying the tau interaction with the neuronal membrane are hitherto unknown and difficult to characterize using experimental methods. Using the cryo-EM structure of the tau-fibrils we have used atomistic molecular dynamics simulation to model the tau fibril and neuronal membrane interaction using explicit solvation. The dynamics and structural characteristics of the tau fibril with the neuronal membrane are compared to the tau fibril in the aqueous phase to corroborate the effect of the neuronal membrane in the tau structure. Tau fibrils have been modelled using CHARMM-36m force field and the six component neuronal membrane composition is taken from the earlier simulation results. The timescale conceivable in our molecular dynamics simulations is of the order of microseconds which captures the onset of the interaction of the tau fibrils with the neuronal membrane. This interaction is found to impact the tau pathogenesis that finally causes neuronal toxicity. Our study initiates the understanding of tau conformational ensemble in the presence of neuronal membrane and sheds the light on the significant tau-membrane interactions.

Modeling of flexible membrane-bound biomolecular complexes for solution small-angle scattering

Recent advances in protein expression protocols, sample handling, and experimental set up of small-angle scattering experiments have allowed users of the technique to structurally investigate biomolecules of growing complexity and structural disorder. Notable examples include intrinsically disordered proteins, multi-domain proteins and membrane proteins in suitable carrier systems. Here, we outline a modeling scheme for calculating the scattering profiles from such complex samples. This kind of modeling is necessary for structural information to be refined from the corresponding data. The scheme bases itself on a hybrid of classical form factor based modeling and the well-known spherical harmonics-based formulation of small-angle scattering amplitudes. Our framework can account for flexible domains alongside other structurally elaborate components of the molecular system in question. We demonstrate the utility of this modeling scheme through a recent example of a structural model of the growth hormone receptor membrane protein in a phospholipid bilayer nanodisc which is refined against experimental SAXS data. Additionally we investigate how the scattering profiles from the complex would appear under different scattering contrasts. For each contrast situation we discuss what structural information is contained and the related consequences for modeling of the data.

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

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

From dilute to concentrated solutions of intrinsically disordered proteins: Interpretation and analysis of collected data

Intrinsically disordered proteins (IDPs) have a broad energy landscape and consequently sample many different conformations in solution. The innate flexibility of IDPs is exploited in their biological function, and in many instances allows a single IDP to regulate a range of processes in vivo. Due to their highly flexible nature, characterizing the structural properties of IDPs is not straightforward. Often solution-based methods such as Nuclear Magnetic Resonance (NMR), Förster Resonance Energy Transfer (FRET), and Small-Angle X-ray Scattering (SAXS) are used. SAXS is indeed a powerful technique to study the structural and conformational properties of IDPs in solution, and from the obtained SAXS spectra, information about the average size, shape, and extent of oligomerization can be determined. In this chapter, we will introduce model-free methods that can be used to interpret SAXS data and introduce methods that can be used to interpret SAXS data beyond analytical models, for example, by using atomistic and different levels of coarse-grained models in combination with molecular dynamics (MD) and Monte Carlo simulations.

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.

Recent advances in structural characterization of biomacromolecules in foods via small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) is a method for examining the solution structure, oligomeric state, conformational changes, and flexibility of biomacromolecules at a scale ranging from a few Angstroms to hundreds of nanometers. Wide time scales ranging from real time (milliseconds) to minutes can be also covered by SAXS. With many advantages, SAXS has been extensively used, it is widely used in the structural characterization of biomacromolecules in food science and technology. However, the application of SAXS in charactering the structure of food biomacromolecules has not been reviewed so far. In the current review, the principle, theoretical calculations and modeling programs are summarized, technical advances in the experimental setups and corresponding applications of in situ capabilities: combination of chromatography, time-resolved, temperature, pressure, flow-through are elaborated. Recent applications of SAXS for monitoring structural properties of biomacromolecules in food including protein, carbohydrate and lipid are also highlighted, and limitations and prospects for developing SAXS based on facility upgraded and artificial intelligence to study the structural properties of biomacromolecules are finally discussed. Future research should focus on extending machine time, simplifying SAXS data treatment, optimizing modeling methods in order to achieve an integrated structural biology based on SAXS as a practical tool for investigating the structure-function relationship of biomacromolecules in food industry.

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

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

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.

Intrinsically disordered proteins: Ensembles at the limits of Anfinsen's dogma

Intrinsically disordered proteins (IDPs) are proteins that lack rigid 3D structure. Hence, they are often misconceived to present a challenge to Anfinsen's dogma. However, IDPs exist as ensembles that sample a quasi-continuum of rapidly interconverting conformations and, as such, may represent proteins at the extreme limit of the Anfinsen postulate. IDPs play important biological roles and are key components of the cellular protein interaction network (PIN). Many IDPs can interconvert between disordered and ordered states as they bind to appropriate partners. Conformational dynamics of IDPs contribute to conformational noise in the cell. Thus, the dysregulation of IDPs contributes to increased noise and "promiscuous" interactions. This leads to PIN rewiring to output an appropriate response underscoring the critical role of IDPs in cellular decision making. Nonetheless, IDPs are not easily tractable experimentally. Furthermore, in the absence of a reference conformation, discerning the energy landscape representation of the weakly funneled IDPs in terms of reaction coordinates is challenging. To understand conformational dynamics in real time and decipher how IDPs recognize multiple binding partners with high specificity, several sophisticated knowledge-based and physics-based in silico sampling techniques have been developed. Here, using specific examples, we highlight recent advances in energy landscape visualization and molecular dynamics simulations to discern conformational dynamics and discuss how the conformational preferences of IDPs modulate their function, especially in phenotypic switching. Finally, we discuss recent progress in identifying small molecules targeting IDPs underscoring the potential therapeutic value of IDPs. Understanding structure and function of IDPs can not only provide new insight on cellular decision making but may also help to refine and extend Anfinsen's structure/function paradigm.

Visualizing RNA Structures by SAXS-Driven MD Simulations

The biological role of biomolecules is intimately linked to their structural dynamics. Experimental or computational techniques alone are often insufficient to determine accurate structural ensembles in atomic detail. We use all-atom molecular dynamics (MD) simulations and couple it to small-angle X-ray scattering (SAXS) experiments to resolve the structural dynamics of RNA molecules. To accomplish this task, we utilize a set of re-weighting and biasing techniques tailored for RNA molecules. To showcase our approach, we study two RNA molecules: a riboswitch that shows structural variations upon ligand binding, and a two-way junction RNA that displays structural heterogeneity and sensitivity to salt conditions. Integration of MD simulations and experiments allows the accurate construction of conformational ensembles of RNA molecules. We observe a dynamic change of the SAM-I riboswitch conformations depending on its binding partners. The binding of SAM and Mg²⁺ cations stabilizes the compact state. The absence of Mg²⁺ or SAM leads to the loss of tertiary contacts, resulting in a dramatic expansion of the riboswitch conformations. The sensitivity of RNA structures to the ionic strength demonstrates itself in the helix junction helix (HJH). The HJH shows non-monotonic compaction as the ionic strength increases. The physics-based picture derived from the experimentally guided MD simulations allows biophysical characterization of RNA molecules. All in all, SAXS-guided MD simulations offer great prospects for studying RNA structural dynamics.

Recent Developments in Data-Assisted Modeling of Flexible Proteins

Many proteins can fold into well-defined conformations. However, intrinsically-disordered proteins (IDPs) do not possess a defined structure. Moreover, folded multi-domain proteins often digress into alternative conformations. Collectively, the conformational dynamics enables these proteins to fulfill specific functions. Thus, most experimental observables are averaged over the conformations that constitute an ensemble. In this article, we review the recent developments in the concept and methods for the determination of the dynamic structures of flexible peptides and proteins. In particular, we describe ways to extract information from nuclear magnetic resonance small-angle X-ray scattering (SAXS), and chemical cross-linking coupled with mass spectroscopy (XL-MS) measurements. All these techniques can be used to obtain ensemble-averaged restraints or to re-weight the simulated conformational ensembles.

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales─picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure-function relationships require atomistic knowledge of the populated states in the ensemble. In this Perspective, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

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.

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

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

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

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.

Refinement of α-Synuclein Ensembles Against SAXS Data: Comparison of Force Fields and Methods

The inherent flexibility of intrinsically disordered proteins (IDPs) makes it difficult to interpret experimental data using structural models. On the other hand, molecular dynamics simulations of IDPs often suffer from force-field inaccuracies, and long simulation times or enhanced sampling methods are needed to obtain converged ensembles. Here, we apply metainference and Bayesian/Maximum Entropy reweighting approaches to integrate prior knowledge of the system with experimental data, while also dealing with various sources of errors and the inherent conformational heterogeneity of IDPs. We have measured new SAXS data on the protein α-synuclein, and integrate this with simulations performed using different force fields. We find that if the force field gives rise to ensembles that are much more compact than what is implied by the SAXS data it is difficult to recover a reasonable ensemble. On the other hand, we show that when the simulated ensemble is reasonable, we can obtain an ensemble that is consistent with the SAXS data, but also with NMR diffusion and paramagnetic relaxation enhancement data.

Unfolding bovine α-lactalbumin with T-jump: Characterizing disordered intermediates via time-resolved x-ray solution scattering and molecular dynamics simulations

The protein folding process often proceeds through partially folded transient states. Therefore, a structural understanding of these disordered states is crucial for developing mechanistic models of the folding process. Characterization of unfolded states remains challenging due to their disordered nature, and incorporating multiple methods is necessary. Combining the time-resolved x-ray solution scattering (TRXSS) signal with molecular dynamics (MD), we are able to characterize transient partially folded states of bovine α-lactalbumin, a model system widely used for investigation of molten globule states, during its unfolding triggered by a temperature jump. We track the unfolding process between 20 µs and 70 ms and demonstrate that it passes through three distinct kinetic states. The scattering signals associated with these transient species are then analyzed with TRXSS constrained MD simulations to produce protein structures that are compatible with the input signals. Without utilizing any experimentally extracted kinetic information, the constrained MD simulation successfully drove the protein to an intermediate molten globule state; signals for two later disordered states are refined to terminal unfolded states. From our examination of the structural characteristics of these disordered states, we discuss the implications disordered states have on the folding process, especially on the folding pathway. Finally, we discuss the potential applications and limitations of this method.

Full structural ensembles of intrinsically disordered proteins from unbiased molecular dynamics simulations

Molecular dynamics (MD) simulation is widely used to complement ensemble-averaged experiments of intrinsically disordered proteins (IDPs). However, MD often suffers from limitations of inaccuracy. Here, we show that enhancing the sampling using Hamiltonian replica-exchange MD (HREMD) led to unbiased and accurate ensembles, reproducing small-angle scattering and NMR chemical shift experiments, for three IDPs of varying sequence properties using two recently optimized force fields, indicating the general applicability of HREMD for IDPs. We further demonstrate that, unlike HREMD, standard MD can reproduce experimental NMR chemical shifts, but not small-angle scattering data, suggesting chemical shifts are insufficient for testing the validity of IDP ensembles. Surprisingly, we reveal that despite differences in their sequence, the inter-chain statistics of all three IDPs are similar for short contour lengths (< 10 residues). The results suggest that the major hurdle of generating an accurate unbiased ensemble for IDPs has now been largely overcome.

Conformational Preferences of an Intrinsically Disordered Protein Domain: A Case Study for Modern Force Fields

Molecular simulations of intrinsically disordered proteins (IDPs) are challenging because they require sampling a very large number of relevant conformations, corresponding to a multitude of shallow minima in a flat free energy landscape. However, in the presence of a binding partner, the free energy landscape of an IDP can be dominated by few deep minima. This characteristic imposes high demands on the accuracy of the force field used to describe the molecular interactions. Here, as a model system for an IDP that is unstructured in solution but folds upon binding to a structured interaction partner, the transactivation domain of c-Myb was studied both in the unbound (free) form and when bound to the KIX domain. Six modern biomolecular force fields were systematically tested and compared in terms of their ability to describe the structural ensemble of the IDP. The protein force field/water model combinations included in this study are AMBER ff99SB-disp with its corresponding water model that was derived from TIP4P-D, CHARMM36m with TIP3P, ff15ipq with SPC/E_b, ff99SB*-ILDNP with TIP3P and TIP4P-D, and FB15 with TIP3P-FB water. Comparing the results from REST2-enhanced sampling simulations with experimental CD spectra and secondary chemical shifts reveals that the ff99SB-disp force field can realistically capture the broad and mildly helical structural ensemble of free c-Myb. The structural ensembles yielded by CHARMM36m, ff99SB*-ILDNP together with TIP4P-D water, and FB15 are also mildly helical; however, each of these force fields can be assigned a specific subset of c-Myb residues for which the simulations could not reproduce the experimental secondary chemical shifts. In addition, microsecond-timescale MD simulations of the KIX/c-Myb complex show that most force fields used preserve a stable helix fold of c-Myb in the complex. Still, all force fields predict a KIX/c-Myb complex interface that differs slightly from the structures provided by NMR because several NOE-derived distances between KIX and c-Myb were exceeded in the simulations. Taken together, the ff99SB-disp force field in the first place but also CHARMM36m, ff99SB*-ILDNP together with TIP4P-D water, and FB15 can be suitable choices for future simulation studies of the coupled folding and binding mechanism of the KIX/c-Myb complex and potentially also other IDPs.

Hybrid methods for combined experimental and computational determination of protein structure

Knowledge of protein structure is paramount to the understanding of biological function, developing new therapeutics, and making detailed mechanistic hypotheses. Therefore, methods to accurately elucidate three-dimensional structures of proteins are in high demand. While there are a few experimental techniques that can routinely provide high-resolution structures, such as x-ray crystallography, nuclear magnetic resonance (NMR), and cryo-EM, which have been developed to determine the structures of proteins, these techniques each have shortcomings and thus cannot be used in all cases. However, additionally, a large number of experimental techniques that provide some structural information, but not enough to assign atomic positions with high certainty have been developed. These methods offer sparse experimental data, which can also be noisy and inaccurate in some instances. In cases where it is not possible to determine the structure of a protein experimentally, computational structure prediction methods can be used as an alternative. Although computational methods can be performed without any experimental data in a large number of studies, inclusion of sparse experimental data into these prediction methods has yielded significant improvement. In this Perspective, we cover many of the successes of integrative modeling, computational modeling with experimental data, specifically for protein folding, protein-protein docking, and molecular dynamics simulations. We describe methods that incorporate sparse data from cryo-EM, NMR, mass spectrometry, electron paramagnetic resonance, small-angle x-ray scattering, Förster resonance energy transfer, and genetic sequence covariation. Finally, we highlight some of the major challenges in the field as well as possible future directions.

Data-Driven Molecular Dynamics: A Multifaceted Challenge

The big data concept is currently revolutionizing several fields of science including drug discovery and development. While opening up new perspectives for better drug design and related strategies, big data analysis strongly challenges our current ability to manage and exploit an extraordinarily large and possibly diverse amount of information. The recent renewal of machine learning (ML)-based algorithms is key in providing the proper framework for addressing this issue. In this respect, the impact on the exploitation of molecular dynamics (MD) simulations, which have recently reached mainstream status in computational drug discovery, can be remarkable. Here, we review the recent progress in the use of ML methods coupled to biomolecular simulations with potentially relevant implications for drug design. Specifically, we show how different ML-based strategies can be applied to the outcome of MD simulations for gaining knowledge and enhancing sampling. Finally, we discuss how intrinsic limitations of MD in accurately modeling biomolecular systems can be alleviated by including information coming from experimental data.

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.

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.

Interpretation of HDX Data by Maximum-Entropy Reweighting of Simulated Structural Ensembles

Hydrogen-deuterium exchange combined with mass spectrometry (HDX-MS) is a widely applied biophysical technique that probes the structure and dynamics of biomolecules without the need for site-directed modifications or bio-orthogonal labels. The mechanistic interpretation of HDX data, however, is often qualitative and subjective, owing to a lack of quantitative methods to rigorously translate observed deuteration levels into atomistic structural information. To help address this problem, we have developed a methodology to generate structural ensembles that faithfully reproduce HDX-MS measurements. In this approach, an ensemble of protein conformations is first generated, typically using molecular dynamics simulations. A maximum-entropy bias is then applied post hoc to the resulting ensemble such that averaged peptide-deuteration levels, as predicted by an empirical model, agree with target values within a given level of uncertainty. We evaluate this approach, referred to as HDX ensemble reweighting (HDXer), for artificial target data reflecting the two major conformational states of a binding protein. We demonstrate that the information provided by HDX-MS experiments and by the model of exchange are sufficient to recover correctly weighted structural ensembles from simulations, even when the relevant conformations are rarely observed. Degrading the information content of the target data—e.g., by reducing sequence coverage, by averaging exchange levels over longer peptide segments, or by incorporating different sources of uncertainty—reduces the structural accuracy of the reweighted ensemble but still allows for useful insights into the distinctive structural features reflected by the target data. Finally, we describe a quantitative metric to rank candidate structural ensembles according to their correspondence with target data and illustrate the use of HDXer to describe changes in the conformational ensemble of the membrane protein LeuT. In summary, HDXer is designed to facilitate objective structural interpretations of HDX-MS data and to inform experimental approaches and further developments of theoretical exchange models.

Small-Angle X-ray Scattering Curves of Detergent Micelles: Effects of Asymmetry, Shape Fluctuations, Disorder, and Atomic Details

Small-angle X-ray scattering (SAXS) is a widely used experimental technique, providing structural and dynamic insight into soft-matter complexes and biomolecules under near-native conditions. However, interpreting the one-dimensional scattering profiles in terms of three-dimensional structures and ensembles remains challenging, partly because it is poorly understood how structural information is encoded along the measured scattering angle. We combined all-atom SAXS-restrained ensemble simulations, simplified continuum models, and SAXS experiments of a n-dodecyl-β-d-maltoside (DDM) micelle to decipher the effects of model asymmetry, shape fluctuations, atomic disorder, and atomic details on SAXS curves. Upon interpreting the small-angle regime, we find remarkable agreement between (i) a two-component triaxial ellipsoid model fitted against the data and (ii) a SAXS-refined all-atom ensemble. However, continuum models fail at wider angles, even if they account for shape fluctuations, disorder, and asymmetry of the micelle. We conclude that modeling atomic details is mandatory for explaining SAXS curves at wider angles.

Computing, Analyzing, and Comparing the Radius of Gyration and Hydrodynamic Radius in Conformational Ensembles of Intrinsically Disordered Proteins

The level of compaction of an intrinsically disordered protein may affect both its physical and biological properties, and can be probed via different types of biophysical experiments. Small-angle X-ray scattering (SAXS) probe the radius of gyration (R_g) whereas pulsed-field-gradient nuclear magnetic resonance (NMR) diffusion, fluorescence correlation spectroscopy, and dynamic light scattering experiments can be used to determine the hydrodynamic radius (R_h). Here we show how to calculate R_g and R_h from a computationally generated conformational ensemble of an intrinsically disordered protein. We further describe how to use a Bayesian/Maximum Entropy procedure to integrate data from SAXS and NMR diffusion experiments, so as to derive conformational ensembles in agreement with those experiments.