Reconciling Simulated Ensembles of Apomyoglobin with Experimental Hydrogen/Deuterium Exchange Data Using Bayesian Inference and Multiensemble Markov State Models

Integrative spatiotemporal modeling of biomolecular processes: application to the assembly of the Nuclear Pore Complex

Dynamic processes involving biomolecules are essential for the function of the cell. Here, we introduce an integrative method for computing models of these processes based on multiple heterogeneous sources of information, including time-resolved experimental data and physical models of dynamic processes. We first compute integrative structure models at fixed time points and then optimally select and connect these snapshots into a series of trajectories that optimize the likelihood of both the snapshots and transitions between them. The method is demonstrated by application to the assembly process of the human Nuclear Pore Complex in the context of the reforming nuclear envelope during mitotic cell division, based on live-cell correlated electron tomography, bulk fluorescence correlation spectroscopy-calibrated quantitative live imaging, and a structural model of the fully-assembled Nuclear Pore Complex. Modeling of the assembly process improves the model precision over static integrative structure modeling alone. The method is applicable to a wide range of time-dependent systems in cell biology, and is available to the broader scientific community through an implementation in the open source Integrative Modeling Platform software.

Exploring the Application of SiteMap and Site Finder for Focused Cryptic Pocket Identification

The characterization of cryptic pockets has been elusive, despite substantial efforts. Computational modeling approaches, such as molecular dynamics (MD) simulations, can provide atomic-level details of binding site motions and binding pathways. However, the time scale that MD can achieve at a reasonable cost often limits its application for cryptic pocket identification. Enhanced sampling techniques can improve the efficiency of MD simulations by focused sampling of important regions of the protein, but prior knowledge of the simulated system is required to define the appropriate coordinates. In the case of a novel, unknown cryptic pocket, such information is not available, limiting the application of enhanced sampling techniques for cryptic pocket identification. In this work, we explore the ability of SiteMap and Site Finder, widely used commercial packages for pocket identification, to detect focus points on the protein and further apply other advanced computational methods. The information gained from this analysis enables the use of computational modeling, including enhanced MD sampling techniques, to explore potential cryptic binding pockets suggested by SiteMap and Site Finder. Here, we examined SiteMap and Site Finder results on 136 known cryptic pockets from a combination of the PocketMiner dataset (a recently curated set of cryptic pockets), the Cryptosite Set (a classic set of cryptic pockets), and Natural killer group 2D (NKG2D, a protein target where a cryptic pocket is confirmed). Our findings demonstrate the application of existing, well-studied tools in efficiently mapping potential regions harboring cryptic pockets.

Tutorial on how to build non-Markovian dynamic models from molecular dynamics simulations for studying protein conformational changes

Protein conformational changes play crucial roles in their biological functions. In recent years, the Markov State Model (MSM) constructed from extensive Molecular Dynamics (MD) simulations has emerged as a powerful tool for modeling complex protein conformational changes. In MSMs, dynamics are modeled as a sequence of Markovian transitions among metastable conformational states at discrete time intervals (called lag time). A major challenge for MSMs is that the lag time must be long enough to allow transitions among states to become memoryless (or Markovian). However, this lag time is constrained by the length of individual MD simulations available to track these transitions. To address this challenge, we have recently developed Generalized Master Equation (GME)-based approaches, encoding non-Markovian dynamics using a time-dependent memory kernel. In this Tutorial, we introduce the theory behind two recently developed GME-based non-Markovian dynamic models: the quasi-Markov State Model (qMSM) and the Integrative Generalized Master Equation (IGME). We subsequently outline the procedures for constructing these models and provide a step-by-step tutorial on applying qMSM and IGME to study two peptide systems: alanine dipeptide and villin headpiece. This Tutorial is available at https://github.com/xuhuihuang/GME_tutorials. The protocols detailed in this Tutorial aim to be accessible for non-experts interested in studying the biomolecular dynamics using these non-Markovian dynamic models.

GaMD simulations as an alternative in the TFE-water mixture description

CONTEXT

2,2,2-Trifluoroethanol has been widely used to study the structure and dynamic properties of intrinsically disordered proteins. Experimentally, it is known that TFE-water mixtures stabilize secondary structures of IDPs, and therefore, it allows the studying of conformational ensembles of these proteins. In the last decades, molecular dynamic simulations have helped study the IDPs' conformational ensemble. Unfortunately, conventional MD requires very long simulation times to describe the properties of IDPs. Therefore, a variety of accelerated sampling techniques have been developed and employed. The TFE-water mixture arrangement description through MD has faced substantial difficulties since emulating the TFE nanocrowding at certain TFE:H[Formula: see text]O ratios (around 15-40% of TFE). In this work, we determine the most suitable conditions that reproduce experimentally reported properties of TFE-water mixtures. We compared the employment of conventional MD and GaMD simulations and various water parameters. Our results show that the combination of parameters that better reproduce the experimental information is the combination of the TIP4PD water model and GaMD simulations. Therefore, these conditions help accurately describe the structural ensemble of IDPs in TFE-water mixtures.

METHODS

Conventional MD and GaMD simulations were performed under AMBER 18 software. The TFE and water molecules were described using GAFF2 and a variety of water models, such as TIP3P, TIP4P2005, TIP4PD, and TIP5P, respectively. The systems were simulated a 100 ns at 298 K.

An Efficient Path Classification Algorithm Based on Variational Autoencoder to Identify Metastable Path Channels for Complex Conformational Changes

Conformational changes (i.e., dynamic transitions between pairs of conformational states) play important roles in many chemical and biological processes. Constructing the Markov state model (MSM) from extensive molecular dynamics (MD) simulations is an effective approach to dissect the mechanism of conformational changes. When combined with transition path theory (TPT), MSM can be applied to elucidate the ensemble of kinetic pathways connecting pairs of conformational states. However, the application of TPT to analyze complex conformational changes often results in a vast number of kinetic pathways with comparable fluxes. This obstacle is particularly pronounced in heterogeneous self-assembly and aggregation processes. The large number of kinetic pathways makes it challenging to comprehend the molecular mechanisms underlying conformational changes of interest. To address this challenge, we have developed a path classification algorithm named latent-space path clustering (LPC) that efficiently lumps parallel kinetic pathways into distinct metastable path channels, making them easier to comprehend. In our algorithm, MD conformations are first projected onto a low-dimensional space containing a small set of collective variables (CVs) by time-structure-based independent component analysis (tICA) with kinetic mapping. Then, MSM and TPT are constructed to obtain the ensemble of pathways, and a deep learning architecture named the variational autoencoder (VAE) is used to learn the spatial distributions of kinetic pathways in the continuous CV space. Based on the trained VAE model, the TPT-generated ensemble of kinetic pathways can be embedded into a latent space, where the classification becomes clear. We show that LPC can efficiently and accurately identify the metastable path channels in three systems: a 2D potential, the aggregation of two hydrophobic particles in water, and the folding of the Fip35 WW domain. Using the 2D potential, we further demonstrate that our LPC algorithm outperforms the previous path-lumping algorithms by making substantially fewer incorrect assignments of individual pathways to four path channels. We expect that LPC can be widely applied to identify the dominant kinetic pathways underlying complex conformational changes.

Gαs slow conformational transition upon GTP binding and a novel Gαs regulator

G proteins are major signaling partners for G protein-coupled receptors (GPCRs). Although stepwise structural changes during GPCR-G protein complex formation and guanosine diphosphate (GDP) release have been reported, no information is available with regard to guanosine triphosphate (GTP) binding. Here, we used a novel Bayesian integrative modeling framework that combines data from hydrogen-deuterium exchange mass spectrometry, tryptophan-induced fluorescence quenching, and metadynamics simulations to derive a kinetic model and atomic-level characterization of stepwise conformational changes incurred by the β2-adrenergic receptor (β2AR)-Gs complex after GDP release and GTP binding. Our data suggest rapid GTP binding and GTP-induced dissociation of Gαs from β2AR and Gβγ, as opposed to a slow closing of the Gαs α-helical domain (AHD). Yeast-two-hybrid screening using Gαs AHD as bait identified melanoma-associated antigen D2 (MAGE D2) as a novel AHD-binding protein, which was also shown to accelerate the GTP-induced closing of the Gαs AHD.

Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently

Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.

Integrating Hydrogen Deuterium Exchange-Mass Spectrometry with Molecular Simulations Enables Quantification of the Conformational Populations of the Sugar Transporter XylE

A yet unresolved challenge in structural biology is to quantify the conformational states of proteins underpinning function. This challenge is particularly acute for membrane proteins owing to the difficulties in stabilizing them for in vitro studies. To address this challenge, we present an integrative strategy that combines hydrogen deuterium exchange-mass spectrometry (HDX-MS) with ensemble modeling. We benchmark our strategy on wild-type and mutant conformers of XylE, a prototypical member of the ubiquitous Major Facilitator Superfamily (MFS) of transporters. Next, we apply our strategy to quantify conformational ensembles of XylE embedded in different lipid environments. Further application of our integrative strategy to substrate-bound and inhibitor-bound ensembles allowed us to unravel protein-ligand interactions contributing to the alternating access mechanism of secondary transport in atomistic detail. Overall, our study highlights the potential of integrative HDX-MS modeling to capture, accurately quantify, and subsequently visualize co-populated states of membrane proteins in association with mutations and diverse substrates and inhibitors.

Exploring the state- and allele-specific conformational landscapes of Ras: understanding their respective druggabilities

Recent advances in direct inhibition of Ras benefit from the protein's intrinsic dynamic nature that derives therapeutically vulnerable conformers bearing transiently formed cryptic pockets. Hotspot mutants of Ras are major tumor drivers and are hyperactivated in cells at variable levels, which may require allele-specific strategies for effective targeting. However, it remains unclear how the prevalent oncogenic mutations and activation states perturb the free energy landscape governing the protein dynamics and druggability. Here we characterized the nucleotide state- and allele-dependent alterations of Ras conformational dynamics using a combined NMR experimental and computational approach and constructed quantitative ensembles revealing the conservation of the cryptic SI/II-P and SII-P pockets in different states and alleles. Highly local but critical conformational reorganizations that undermine the SII-P accessibility to residue 12 have been identified as a common mechanism resulting in the low reactivities of Ras·GTP as well as Ras(G12D)·GDP with covalent SII-P inhibitors. Our results strongly support the conformational selection scenario for interactions between Ras and the previously reported binders and offer insights for the future development of state- and allele-specific, as well as pan-Ras, inhibitors.

Insights into Phosphorylation-Induced Protein Allostery and Conformational Dynamics of Glycogen Phosphorylase via Integrative Structural Mass Spectrometry and In Silico Modeling

Allosteric regulation plays a fundamental role in innumerable biological processes. Understanding its dynamic mechanism and impact at the molecular level is of great importance in disease diagnosis and drug discovery. Glycogen phosphorylase (GP) is a phosphoprotein responding to allosteric regulation and has significant biological importance to glycogen metabolism. Although the atomic structures of GP have been previously solved, the conformational dynamics of GP related to allostery regulation remain largely elusive due to its macromolecular size (∼196 kDa). Here, we integrated native top-down mass spectrometry (nTD-MS), hydrogen-deuterium exchange MS (HDX-MS), protection factor (PF) analysis, molecular dynamics (MD) simulations, and allostery signaling analysis to examine the structural basis and dynamics for the allosteric regulation of GP by phosphorylation. nTD-MS reveals differences in structural stability as well as oligomeric state between the unphosphorylated (GPb) and phosphorylated (GPa) forms. HDX-MS, PF analysis, and MD simulations further pinpoint the structural differences between GPb and GPa involving the binding interfaces (the N-terminal and tower-tower helices), catalytic site, and PLP-binding region. More importantly, it also allowed us to complete the missing link of the long-range communication process from the N-terminal tail to the catalytic site caused by phosphorylation. This integrative MS and in silico-based platform is highly complementary to biophysical approaches and yields valuable insights into protein structures and dynamic regulation.

Generating Ensembles of Dynamic Misfolding Proteins

The early stages of protein misfolding and aggregation involve disordered and partially folded protein conformers that contain a high degree of dynamic disorder. These dynamic species may undergo large-scale intra-molecular motions of intrinsically disordered protein (IDP) precursors, or flexible, low affinity inter-molecular binding in oligomeric assemblies. In both cases, generating atomic level visualization of the interconverting species that captures the conformations explored and their physico-chemical properties remains hugely challenging. How specific sub-ensembles of conformers that are on-pathway to aggregation into amyloid can be identified from their aggregation-resilient counterparts within these large heterogenous pools of rapidly moving molecules represents an additional level of complexity. Here, we describe current experimental and computational approaches designed to capture the dynamic nature of the early stages of protein misfolding and aggregation, and discuss potential challenges in describing these species because of the ensemble averaging of experimental restraints that arise from motions on the millisecond timescale. We give a perspective of how machine learning methods can be used to extract aggregation-relevant sub-ensembles and provide two examples of such an approach in which specific interactions of defined species within the dynamic ensembles of α-synuclein (αSyn) and β2-microgloblulin (β2m) can be captured and investigated.

Computational Modeling of Molecular Structures Guided by Hydrogen-Exchange Data

Data produced by hydrogen-exchange monitoring experiments have been used in structural studies of molecules for several decades. Despite uncertainties about the structural determinants of hydrogen exchange itself, such data have successfully helped guide the structural modeling of challenging molecular systems, such as membrane proteins or large macromolecular complexes. As hydrogen-exchange monitoring provides information on the dynamics of molecules in solution, it can complement other experimental techniques in so-called integrative modeling approaches. However, hydrogen-exchange data have often only been used to qualitatively assess molecular structures produced by computational modeling tools. In this paper, we look beyond qualitative approaches and survey the various paradigms under which hydrogen-exchange data have been used to quantitatively guide the computational modeling of molecular structures. Although numerous prediction models have been proposed to link molecular structure and hydrogen exchange, none of them has been widely accepted by the structural biology community. Here, we present as many hydrogen-exchange prediction models as we could find in the literature, with the aim of providing the first exhaustive list of its kind. From purely structure-based models to so-called fractional-population models or knowledge-based models, the field is quite vast. We aspire for this paper to become a resource for practitioners to gain a broader perspective on the field and guide research toward the definition of better prediction models. This will eventually improve synergies between hydrogen-exchange monitoring and molecular modeling.

HDX-MS and MD Simulations Provide Evidence for Stabilization of the IgG1-FcγRIa (CD64a) Immune Complex Through Intermolecular Glycoprotein Bonds

Previous reports present different models for the stabilization of the Fc-FcγRI immune complex. Although accord exists on the importance of L235 in IgG1 and some hydrophobic contacts for complex stabilization, discord exists regarding the existence of stabilizing glycoprotein contacts between glycans of IgG1 and a conserved FG-loop (¹⁷¹MGKHRY¹⁷⁶) of FcγRIa. Complexes formed from the FcγRIa receptor and IgG1s containing biantennary glycans with N-acetylglucosamine, galactose, and α2,6-N-acetylneuraminic terminations were measured by hydrogen-deuterium exchange mass spectrometry (HDX-MS), classified for dissimilarity with Welch's ANOVA and Games-Howell post hoc procedures, and modeled with molecular dynamics (MD) simulations. For each glycoform of the IgG1-FcγRIa complex peptic peptides of Fab, Fc and FcγRIa report distinct H/D exchange rates. MD simulations corroborate the differences in the peptide deuterium content through calculation of the percent of time that transient glycan-peptide bonds exist. These results indicate that stability of IgG1-FcγRIa complexes correlate with the presence of intermolecular glycoprotein interactions between the IgG1 glycans and the ¹⁷³KHR¹⁷⁵ motif within the FG-loop of FcγRIa. The results also indicate that intramolecular glycan-protein bonds stabilize the Fc region in isolated and complexed IgG1. Moreover, HDX-MS data evince that the Fab domain has glycan-protein binding contacts within the IgG1-FcγRI complex.

Protein structure prediction using residue-resolved protection factors from hydrogen-deuterium exchange NMR

Hydrogen-deuterium exchange (HDX) measured by nuclear magnetic resonance (NMR) provides structural information for proteins relating to solvent accessibility and flexibility. While this structural information is beneficial, the data cannot be used exclusively to elucidate structures. However, the structural information provided by the HDX-NMR data can be supplemented by computational methods. In previous work, we developed an algorithm in Rosetta to predict structures using qualitative HDX-NMR data (categories of exchange rate). Here we expand on the effort, and utilize quantitative protection factors (PFs) from HDX-NMR for structure prediction. From observed correlations between PFs and solvent accessibility/flexibility measures, we present a scoring function to quantify the agreement with HDX data. Using a benchmark set of 10 proteins, an average improvement of 5.13 Å in root-mean-square deviation (RMSD) is observed for cases of inaccurate Rosetta predictions. Ultimately, seven out of 10 predictions are accurate without including HDX data, and nine out of 10 are accurate when using our PF-based HDX score.

Metal Cation-Binding Mechanisms of Q-Proline Peptoid Macrocycles in Solution

The rational design of foldable and functionalizable peptidomimetic scaffolds requires the concerted application of both computational and experimental methods. Recently, a new class of designed peptoid macrocycle incorporating spiroligomer proline mimics (Q-prolines) has been found to preorganize when bound by monovalent metal cations. To determine the solution-state structure of these cation-bound macrocycles, we employ a Bayesian inference method (BICePs) to reconcile enhanced-sampling molecular simulations with sparse ROESY correlations from experimental NMR studies to predict and design conformational and binding properties of macrocycles as functional scaffolds for peptidomimetics. Conformations predicted to be most populated in solution were then simulated in the presence of explicit cations to yield trajectories with observed binding events, revealing a highly preorganized all-trans amide conformation, whose formation is likely limited by the slow rate of cis/trans isomerization. Interestingly, this conformation differs from a racemic crystal structure solved in the absence of cation. Free energies of cation binding computed from distance-dependent potentials of mean force suggest Na⁺ has a higher affinity to the macrocycle than K⁺, with both cations binding much more strongly in acetonitrile than water. The simulated affinities are able to correctly rank the extent to which different macrocycle sequences exhibit preorganization in the presence of different metal cations and solvents, suggesting our approach is suitable for solution-state computational design.

Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2

Understanding mechanisms of protein folding and binding is crucial to designing their molecular function. Molecular dynamics (MD) simulations and Markov state model (MSM) approaches provide a powerful way to understand complex conformational change that occurs over long time scales. Such dynamics are important for the design of therapeutic peptidomimetic ligands, whose affinity and binding mechanism are dictated by a combination of folding and binding. To examine the role of preorganization in peptide binding to protein targets, we performed massively parallel explicit-solvent MD simulations of cyclic β-hairpin ligands designed to mimic the p53 transactivation domain and competitively bind mouse double minute 2 homologue (MDM2). Disrupting the MDM2-p53 interaction is a therapeutic strategy to prevent degradation of the p53 tumor suppressor in cancer cells. MSM analysis of over 3 ms of aggregate trajectory data enabled us to build a detailed mechanistic model of coupled folding and binding of four cyclic peptides which we compare to experimental binding affinities and rates. The results show a striking relationship between the relative preorganization of each ligand in solution and its affinity for MDM2. Specifically, changes in peptide conformational populations predicted by the MSMs suggest that entropy loss upon binding is the main factor influencing affinity. The MSMs also enable detailed examination of non-native interactions which lead to misfolded states and comparison of structural ensembles with experimental NMR measurements. In contrast to an MSM study of p53 transactivation domain (TAD) binding to MDM2, MSMs of cyclic β-hairpin binding show a conformational selection mechanism. Finally, we make progress toward predicting accurate off rates of cyclic peptides using multiensemble Markov models (MEMMs) constructed from unbiased and biased simulated trajectories.

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.

Structural predictions of the functions of membrane proteins from HDX-MS

HDX-MS has emerged as a powerful tool to interrogate the structure and dynamics of proteins and their complexes. Recent advances in the methodology and instrumentation have enabled the application of HDX-MS to membrane proteins. Such targets are challenging to investigate with conventional strategies. Developing new tools are therefore pertinent for improving our fundamental knowledge of how membrane proteins function in the cell. Importantly, investigating this central class of biomolecules within their native lipid environment remains a challenge but also a key goal ahead. In this short review, we outline recent progresses in dissecting the conformational mechanisms of membrane proteins using HDX-MS. We further describe how the use of computational strategies can aid the interpretation of experimental data and enable visualisation of otherwise intractable membrane protein states. This unique integration of experiments with computations holds significant potential for future applications.

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.