Metadynamic metainference: Enhanced sampling of the metainference ensemble using metadynamics

Conformational Plasticity in dsRNA-Binding Domains Drives Functional Divergence in RNA Recognition

The functional specificity of proteins is often attributed to their sequence and structural homology while frequently neglecting the underlying conformational dynamics occurring at different time scales that can profoundly impact biological consequences. Using 15N-CEST NMR and RDC-corrected metainference molecular dynamics simulations, here, we reveal differential substrate recognition mechanisms in two dsRNA-binding domain (dsRBD) paralogs, DRB2D1 and DRB3D1. Despite their nearly identical solution structures and conserved dsRNA interaction interfaces, DRB3D1 demonstrates structural plasticity that enables it to recognize conformationally flexible dsRNA, a feature notably absent in the more rigid DRB2D1. We present the pivotal role of intrinsic structural dynamics in driving functional divergence and provide insights into the mechanisms that govern specificity in dsRBD:dsRNA interactions. Importantly, our combined experimental and computational approach captures a cluster of intermediate conformations, complementing conventional methods to resolve the dominant ground state and sparsely populated excited states.

A conformational fingerprint for amyloidogenic light chains

Both immunoglobulin light-chain (LC) amyloidosis (AL) and multiple myeloma (MM) share the overproduction of a clonal LC. However, while LCs in MM remain soluble in circulation, AL LCs misfold into toxic-soluble species and amyloid fibrils that accumulate in organs, leading to distinct clinical manifestations. The significant sequence variability of LCs has hindered the understanding of the mechanisms driving LC aggregation. Nevertheless, emerging biochemical properties, including dimer stability, conformational dynamics, and proteolysis susceptibility, distinguish AL LCs from those in MM under native conditions. This study aimed to identify a2 conformational fingerprint distinguishing AL from MM LCs. Using small-angle X-ray scattering (SAXS) under native conditions, we analyzed four AL and two MM LCs. We observed that AL LCs exhibited a slightly larger radius of gyration and greater deviations from X-ray crystallography-determined or predicted structures, reflecting enhanced conformational dynamics. SAXS data, integrated with molecular dynamics simulations, revealed a conformational ensemble where LCs adopt multiple states, with variable and constant domains either bent or straight. AL LCs displayed a distinct, low-populated, straight conformation (termed H state), which maximized solvent accessibility at the interface between constant and variable domains. Hydrogen-deuterium exchange mass spectrometry experimentally validated this H state. These findings reconcile diverse experimental observations and provide a precise structural target for future drug design efforts.

Atomic-level mechanisms of abnormal activation in NRAS oncogenes from two-dimensional free energy landscapes

The NRAS-mutant subset of melanoma is one of the most aggressive and lethal types associated with poor overall survival. Unfortunately, a low understanding of the NRAS-mutant dynamic behavior has led to the lack of clinically approved therapeutic agents able to directly target NRAS oncogenes. In this work, accurate local structures of NRAS and its mutants have been fully explored through the corresponding free energy surfaces obtained by microsecond scale well-tempered metadynamics simulations. Free energy calculations are crucial to reveal the precise mechanisms of Q61 mutations at the atomic level. Considering specific atom-atom distances d and angles ϕ as appropriate reaction coordinates we have obtained free energy surfaces revealing local and global minima together with their main transition states, unveiling the mechanisms of abnormal NRAS activation from the atomic-level and quantitatively analyzing the corresponding stable states. This will help in advancing our understanding of the basic mechanisms of NRAS mutations, offering new opportunities for the design of potential inhibitors.

SOP-MULTI: A Self-Organized Polymer-Based Coarse-Grained Model for Multidomain and Intrinsically Disordered Proteins with Conformation Ensemble Consistent with Experimental Scattering Data

Multidomain proteins with long flexible linkers and full-length intrinsically disordered proteins (IDPs) are best defined as an ensemble of conformations rather than a single structure. Determining high-resolution ensemble structures of such proteins poses various challenges by using tools from experimental structural biophysics. Integrative approaches combining available low-resolution ensemble-averaged experimental data and in silico biomolecular reconstructions are now often used for the purpose. However, extensive Boltzmann weighted conformation sampling for large proteins, especially for ones where both the folded and disordered domains exist in the same polypeptide chain, remains a challenge. In this work, we present a 2-site per amino-acid resolution SOP-MULTI force field for simulating coarse-grained models of multidomain proteins. SOP-MULTI combines two well-established self-organized polymer models─: (i) SOP-SC models for folded systems and (ii) SOP-IDP for IDPs. For the SOP-MULTI, we introduce cross-interaction terms between the beads belonging to the folded and disordered regions to generate conformation ensembles for full-length multidomain proteins such as hnRNP A1, TDP-43, G3BP1, hGHR-ECD, TIA1, HIV-1 Gag, polyubiquitin, and FUS. When back-mapped to all-atom resolution, SOP-MULTI trajectories faithfully recapitulate the scattering data over the range of the reciprocal space. We also show that individual folded domains preserve native contacts with respect to solved folded structures, and root-mean-square fluctuations of residues in folded domains match those obtained from all-atom molecular dynamics simulation trajectories of the same folded systems. SOP-MULTI force field is made available as a LAMMPS-compatible user package along with setup codes for generating the required files for any full-length protein with folded and disordered regions.

Determining accurate conformational ensembles of intrinsically disordered proteins at atomic resolution

Determining accurate atomic resolution conformational ensembles of intrinsically disordered proteins (IDPs) is extremely challenging. Molecular dynamics (MD) simulations provide atomistic conformational ensembles of IDPs, but their accuracy is highly dependent on the quality of physical models, or force fields, used. Here, we demonstrate how to determine accurate atomic resolution conformational ensembles of IDPs by integrating all-atom MD simulations with experimental data from nuclear magnetic resonance (NMR) spectroscopy and small-angle x-ray scattering (SAXS) with a simple, robust and fully automated maximum entropy reweighting procedure. We demonstrate that when this approach is applied with sufficient experimental data, IDP ensembles derived from different MD force fields converge to highly similar conformational distributions. The maximum entropy reweighting procedure presented here facilitates the integration of MD simulations with extensive experimental datasets and enables the calculation of accurate, force-field independent atomic resolution conformational ensembles of IDPs.

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.

Investigating the Aryl Hydrocarbon Receptor Agonist/Antagonist Conformational Switch Using Well-Tempered Metadynamics Simulations

The aryl hydrocarbon receptor (AhR) is a ligand-dependent transcription factor that mediates biological signals to control various complicated cellular functions. It plays a crucial role in environmental sensing and xenobiotic metabolism. Dysregulation of AhR is associated with health concerns, including cancer and immune system disorders. Upon binding to AhR ligands, AhR, along with heat shock protein 90 and other partner proteins undergoes a transformation in the nucleus, heterodimerizes with the aryl hydrocarbon receptor nuclear translocator (ARNT), and mediates numerous biological functions by inducing the transcription of various AhR-responsive genes. In this manuscript, the 3-dimensional structure of the entire human AhR is obtained using an artificial intelligence tool, and molecular dynamics (MD) simulations are performed to study different structural conformations. These conformations provide insights into the protein's function and movement in response to ligand binding. Understanding the dynamic behavior of AhR will contribute to the development of targeted therapies for associated health conditions. Therefore, we employ well-tempered metadynamics (WTE-metaD) simulations to explore the conformational landscape of AhR and obtain a better understanding of its functional behavior. Our computational results are in excellent agreement with previous experimental findings, revealing the closed and open states of helix α1 in the basic helix-loop-helix (bHLH domain) in the cytoplasm at the atomic level. We also predict the inactive form of AhR and identify Arginine 42 as a key residue that regulates switching between closed and open conformations in existing AhR modulators.

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.

Thermodynamic Basis for the Stabilization of Helical Peptoids by Chiral Sidechains

Peptoids are a class of highly customizable biomimetic foldamers that retain properties from both proteins and polymers. It has been shown that peptoids can adopt peptide-like secondary structures through the careful selection of sidechain chemistries, but the underlying conformational landscapes that drive these assemblies at the molecular level remain poorly understood. Given the high flexibility of the peptoid backbone, it is essential that methods applied to study peptoid secondary structure formation possess the requisite sensitivity to discriminate between structurally similar yet energetically distinct microstates. In this work, a generalizable simulation scheme is used to robustly sample the complex folding landscape of various 12mer polypeptoids, resulting in a predictive model that links sidechain chemistry with preferential assembly into one of 12 accessible backbone motifs. Using a variant of the metadynamics sampling method, four peptoid dodecamers are simulated in water: sarcosine, N-(1-phenylmethyl)glycine (Npm), (S)-N-(1-phenylethyl)glycine (Nspe), and (R)-N-(1-phenylethyl)glycine (Nrpe)─to determine the underlying entropic and energetic impacts of hydrophobic and chiral peptoid sidechains on secondary structure formation. Our results indicate that the driving forces to assemble Nrpe and Nspe sequences into polyproline type-I helices in water are found to be enthalpically driven, with small benefits from an entropic gain for isomerization and steric strain due to the presence of the chiral center. The minor entropic gains from bulky chiral sidechains in Nrpe- and Nspe-containing peptoids can be explained through increased configurational entropy in the cis state. However, overall assembly into a helix is found to be overall entropically unfavorable. These results highlight the importance of considering the many various competing interactions in the rational design of peptoid secondary structure building blocks.

Origins of Conformational Heterogeneity in Peptoid Helices Formed by Chiral N-1-Phenylethyl Sidechains

N-substituted glycines (polypeptoids) containing chiral hydrophobic sidechains are known to fold into biomimetic alpha helices. These helix formers often produce conformationally heterogeneous structures and are difficult to characterize at a sub-nanometer resolution. Previously, peptoid N-1-phenylethyl (R)-enantiomer sidechains (Nspe) were inferred from various experiments to form right-handed helices and (S)-enantiomers (Nrpe), left-handed helices. Prior computational work for N(s/r)pe oligomers has struggled to reproduce this trend. Herein, quantum mechanics calculations and molecular dynamics simulations are used to understand the origins of this discrepancy. Results from DFT and molecular mechanics calculations on a variety of Nspe and Nrpe oligomers as a function of chain length are in agreement, showing that Nspe and Nrpe prefer left- and right-handed helices, respectively. Additional metadynamics simulations are used to study Nrpe and Nspe oligomers folding in water. These results show that the free-energy driving forces for assembly into a helical backbone configuration are very small (within ∼k_BT). Lastly, we compare DFT calculations for other experimentally characterized peptoid sidechains, N(r/s)sb, N(r/s)tbe, and N(r/s)npe. In this analysis, we show that peptoid sidechains determined to be more robust experimentally (tbe and npe) have helical preferences opposite the trend seen in less robust assemblies formed by N(r/s)pe and N(r/s)sb chemistries. The more robust tbe and nnpe favor the (S)-enantiomer to right-handed and the (R)-enantiomers to left-handed helices.

BICePs v2.0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations

Bayesian Inference of Conformational Populations (BICePs) version 2.0 (v2.0) is a free, open-source Python package that reweights theoretical predictions of conformational state populations using sparse and/or noisy experimental measurements. In this article, we describe the implementation and usage of the latest version of BICePs (v2.0), a powerful, user-friendly and extensible package which makes several improvements upon the previous version. The algorithm now supports many experimental NMR observables (NOE distances, chemical shifts, J-coupling constants, and hydrogen-deuterium exchange protection factors), and enables convenient data preparation and processing. BICePs v2.0 can perform automatic analysis of the sampled posterior, including visualization, and evaluation of statistical significance and sampling convergence. We provide specific coding examples for these topics, and present a detailed example illustrating how to use BICePs v2.0 to reweight a theoretical ensemble using experimental measurements.

Structural ensembles of disordered proteins from hierarchical chain growth and simulation

Disordered proteins and nucleic acids play key roles in cellular function and disease. Here, we review recent advances in the computational exploration of the conformational dynamics of flexible biomolecules. While atomistic molecular dynamics (MD) simulation has seen a lot of improvement in recent years, large-scale computing resources and careful validation are required to simulate full-length disordered biopolymers in solution. As a computationally efficient alternative, hierarchical chain growth (HCG) combines pre-sampled chain fragments in a statistically reproducible manner into ensembles of full-length atomically detailed biomolecular structures. Experimental data can be integrated during and after chain assembly. Applications to the neurodegeneration-linked proteins α-synuclein, tau, and TDP-43, including as condensate, illustrate the use of HCG. We conclude by highlighting the emerging connections to AI-based structural modeling including AlphaFold2.

Predicting the conformational variability of oncogenic GTP-bound G12D mutated KRas-4B proteins at zwitterionic model cell membranes

KRas proteins are the largest family of mutated Ras isoforms, participating in a wide variety of cancers. Due to their importance, large effort is being carried out on drug development by small-molecule inhibitors. However, understanding protein conformational variability remains a challenge in drug discovery. In the case of the Ras family, their multiple conformational states can affect the binding of potential drug inhibitors. To overcome this challenge, we propose a computational framework based on combined all-atom Molecular Dynamics and Metadynamics simulations in order to accurately access conformational variants of the target protein. We tested the methodology using a G12D mutated GTP bound oncogenic KRas-4B protein located at the interface of a DOPC/DOPS/cholesterol model anionic cell membrane. Two main orientations of KRas-4B at the anionic membrane have been determined. The corresponding torsional angles are taken as reliable reaction coordinates so that free-energy landscapes are obtained by well-tempered metadynamics simulations, revealing local and global minima of the free-energy hypersurface and unveiling reactive paths of the system between the two preferential orientations. We have observed that GTP-binding to KRas-4B has huge influence on the stabilisation of the protein and it can potentially help to open Switch I/II druggable pockets, lowering energy barriers between stable states and resulting in cumulative conformers of KRas-4B. This may highlight new opportunities for targeting the unique meta-stable states through the design of new efficient drugs.

When Order Meets Disorder: Modeling and Function of the Protein Interface in Fuzzy Complexes

The degree of proteins structural organization ranges from highly structured, compact folding to intrinsic disorder, where each degree of self-organization corresponds to specific functions: well-organized structural motifs in enzymes offer a proper environment for precisely positioned functional groups to participate in catalytic reactions; at the other end of the self-organization spectrum, intrinsically disordered proteins act as binding hubs via the formation of multiple, transient and often non-specific interactions. This review focusses on cases where structurally organized proteins or domains associate with highly disordered protein chains, leading to the formation of interfaces with varying degrees of fuzziness. We present a review of the computational methods developed to provide us with information on such fuzzy interfaces, and how they integrate experimental information. The discussion focusses on two specific cases, microtubules and homologous recombination nucleoprotein filaments, where a network of intrinsically disordered tails exerts regulatory function in recruiting partner macromolecules, proteins or DNA and tuning the atomic level association. Notably, we show how computational approaches such as molecular dynamics simulations can bring new knowledge to help bridging the gap between experimental analysis, that mostly concerns ensemble properties, and the behavior of individual disordered protein chains that contribute to regulation functions.

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.

An Integrative Approach to Determine 3D Protein Structures Using Sparse Paramagnetic NMR Data and Physical Modeling

Paramagnetic nuclear magnetic resonance (NMR) methods have emerged as powerful tools for structure determination of large, sparsely protonated proteins. However traditional applications face several challenges, including a need for large datasets to offset the sparsity of restraints, the difficulty in accounting for the conformational heterogeneity of the spin-label, and noisy experimental data. Here we propose an integrative approach to structure determination combining sparse paramagnetic NMR with physical modelling to infer approximate protein structural ensembles. We use calmodulin in complex with the smooth muscle myosin light chain kinase peptide as a model system. Despite acquiring data from samples labeled only at the backbone amide positions, we are able to produce an ensemble with an average RMSD of ∼2.8 Å from a reference X-ray crystal structure. Our approach requires only backbone chemical shifts and measurements of the paramagnetic relaxation enhancement and residual dipolar couplings that can be obtained from sparsely labeled samples.

Forcefield evaluation and accelerated molecular dynamics simulation of Zn(II) binding to N-terminus of amyloid-β

We report conventional and accelerated molecular dynamics simulation of Zn(II) bound to the N-terminus of amyloid-β. By comparison against NMR data for the experimentally determined binding mode, we find that certain combinations of forcefield and solvent model perform acceptably in describing the size, shape and secondary structure, and that there is no appreciable difference between implicit and explicit solvent models. We therefore used the combination of ff14SB forcefield and GBSA solvent model to compare the result of different binding modes of Zn(II) to the same peptide, using accelerated MD to enhance sampling and comparing the free peptide simulated in the same way. We show that Zn(II) imparts significant rigidity to the peptide, disrupts the secondary structure and pattern of salt bridges seen in the free peptide, and induces closer contact between residues. Free energy surfaces in 1 or 2 dimensions further highlight the effect of metal coordination on peptide's spatial extent. We also provide evidence that accelerated MD provides improved sampling over conventional MD by visiting as many or more configurations in much shorter simulation times.

How to Determine Accurate Conformational Ensembles by Metadynamics Metainference: A Chignolin Study Case

The reliability and usefulness of molecular dynamics simulations of equilibrium processes rests on their statistical precision and their capability to generate conformational ensembles in agreement with available experimental knowledge. Metadynamics Metainference (M&M), coupling molecular dynamics with the enhanced sampling ability of Metadynamics and with the ability to integrate experimental information of Metainference, can in principle achieve both goals. Here we show that three different Metadynamics setups provide converged estimate of the populations of the three-states populated by a model peptide. Errors are estimated correctly by block averaging, but higher precision is obtained by performing independent replicates. One effect of Metadynamics is that of dramatically decreasing the number of effective frames resulting from the simulations and this is relevant for M&M where the number of replicas should be large enough to capture the conformational heterogeneity behind the experimental data. Our simulations allow also us to propose that monitoring the relative error associated with conformational averaging can help to determine the minimum number of replicas to be simulated in the context of M&M simulations. Altogether our data provides useful indication on how to generate sound conformational ensemble in agreement with experimental data.

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.

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.

A kinetic ensemble of the Alzheimer's Aβ peptide

The conformational and thermodynamic properties of disordered proteins are commonly described in terms of structural ensembles and free energy landscapes. To provide information on the transition rates between the different states populated by these proteins, it would be desirable to generalize this description to kinetic ensembles. Approaches based on the theory of stochastic processes can be particularly suitable for this purpose. Here, we develop a Markov state model and apply it to determine a kinetic ensemble of Aβ42, a disordered peptide associated with Alzheimer's disease. Through the Google Compute Engine, we generated 315-µs all-atom molecular dynamics trajectories. Using a probabilistic-based definition of conformational states in a neural network approach, we found that Aβ42 is characterized by inter-state transitions on the microsecond timescale, exhibiting only fully unfolded or short-lived, partially folded states. Our results illustrate how kinetic ensembles provide effective information about the structure, thermodynamics and kinetics of disordered proteins.

Small-molecule sequestration of amyloid-β as a drug discovery strategy for Alzheimer's disease

Disordered proteins are challenging therapeutic targets, and no drug is currently in clinical use that modifies the properties of their monomeric states. Here, we identify a small molecule (10074-G5) capable of binding and sequestering the intrinsically disordered amyloid-β (Aβ) peptide in its monomeric, soluble state. Our analysis reveals that this compound interacts with Aβ and inhibits both the primary and secondary nucleation pathways in its aggregation process. We characterize this interaction using biophysical experiments and integrative structural ensemble determination methods. We observe that this molecule increases the conformational entropy of monomeric Aβ while decreasing its hydrophobic surface area. We also show that it rescues a Caenorhabditis elegans model of Aβ-associated toxicity, consistent with the mechanism of action identified from the in silico and in vitro studies. These results illustrate the strategy of stabilizing the monomeric states of disordered proteins with small molecules to alter their behavior for therapeutic purposes.

The dynamics of linear polyubiquitin

Polyubiquitin chains are flexible multidomain proteins, whose conformational dynamics enable them to regulate multiple biological pathways. Their dynamic is determined by the linkage between ubiquitins and by the number of ubiquitin units. Characterizing polyubiquitin behavior as a function of their length is hampered because of increasing system size and conformational variability. Here, we introduce a new approach to efficiently integrating small-angle x-ray scattering with simulations allowing us to accurately characterize the dynamics of linear di-, tri-, and tetraubiquitin in the free state as well as of diubiquitin in complex with NEMO, a central regulator in the NF-κB pathway. Our results show that the behavior of the diubiquitin subunits is independent of the presence of additional ubiquitin modules and that the dynamics of polyubiquitins with different lengths follow a simple model. Together with experimental data from multiple biophysical techniques, we then rationalize the 2:1 NEMO:polyubiquitin binding.

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.

Conformational Stability and Dynamics in Crystals Recapitulate Protein Behavior in Solution

A growing body of evidences has established that in many cases proteins may preserve most of their function and flexibility in a crystalline environment, and several techniques are today capable to characterize molecular properties of proteins in tightly packed lattices. Intriguingly, in the case of amyloidogenic precursors, the presence of transiently populated states (hidden to conventional crystallographic studies) can be correlated to the pathological fate of the native fold; the low fold stability of the native state is a hallmark of aggregation propensity. It remains unclear, however, to which extent biophysical properties of proteins such as the presence of transient conformations or protein stability characterized in crystallo reflect the protein behavior that is more commonly studied in solution. Here, we address this question by investigating some biophysical properties of a prototypical amyloidogenic system, β2-microglobulin in solution and in microcrystalline state. By combining NMR chemical shifts with molecular dynamics simulations, we confirmed that conformational dynamics of β2-microglobulin native state in the crystal lattice is in keeping with what observed in solution. A comparative study of protein stability in solution and in crystallo is then carried out, monitoring the change in protein secondary structure at increasing temperature by Fourier transform infrared spectroscopy. The increased structural order of the crystalline state contributes to provide better resolved spectral components compared to those collected in solution and crucially, the crystalline samples display thermal stabilities in good agreement with the trend observed in solution. Overall, this work shows that protein stability and occurrence of pathological hidden states in crystals parallel their solution counterpart, confirming the interest of crystals as a platform for the biophysical characterization of processes such as unfolding and aggregation.

Structural Insight into IAPP-Derived Amyloid Inhibitors and Their Mechanism of Action

Designed peptides derived from the islet amyloid polypeptide (IAPP) cross-amyloid interaction surface with Aβ (termed interaction surface mimics or ISMs) have been shown to be highly potent inhibitors of Aβ amyloid self-assembly. However, the molecular mechanism of their function is not well understood. Using solution-state and solid-state NMR spectroscopy in combination with ensemble-averaged dynamics simulations and other biophysical methods including TEM, fluorescence spectroscopy and microscopy, and DLS, we characterize ISM structural preferences and interactions. We find that the ISM peptide R3-GI is highly dynamic, can adopt a β-like structure, and oligomerizes into colloid-like assemblies in a process that is reminiscent of liquid-liquid phase separation (LLPS). Our results suggest that such assemblies yield multivalent surfaces for interactions with Aβ40. Sequestration of substrates into these colloid-like structures provides a mechanistic basis for ISM function and the design of novel potent anti-amyloid molecules.

A Practical Guide to the Simultaneous Determination of Protein Structure and Dynamics Using Metainference

Accurate protein structural ensembles can be determined with metainference, a Bayesian inference method that integrates experimental information with prior knowledge of the system and deals with all sources of uncertainty and errors as well as with system heterogeneity. Furthermore, metainference can be implemented using the metadynamics approach, which enables the computational study of complex biological systems requiring extensive conformational sampling. In this chapter, we provide a step-by-step guide to perform and analyse metadynamic metainference simulations using the ISDB module of the open-source PLUMED library, as well as a series of practical tips to avoid common mistakes. Specifically, we will guide the reader in the process of learning how to model the structural ensemble of a small disordered peptide by combining state-of-the-art molecular mechanics force fields with nuclear magnetic resonance data, including chemical shifts, scalar couplings and residual dipolar couplings.

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.

Comparing the Hinge-Type Mobility of Natural and Designed Intermolecular Bi-disulfide Domains

A pair of intermolecular disulfide bonds connecting two protein domains restricts their relative mobility in a systematic way. The bi-disulfide hinge cannot rotate like a single intermolecular disulfide bond yet is less restrained than three or more intermolecular disulfides which restrict the relative motion to a minimum. The intermediate mobility of bi-disulfide linked domains is characterized by their dominating opening and closing modes comparable to the mechanics of a door hinge on the macroscopic scale. Here we compare the central hinge region of Immunoglobulin G1 (IgG1) which is highly conserved among different species, with a recently designed hinge-type motif CHWECRGCRLVC from our lab, that was successfully used for the dimerization of the IgG1/κ-ab CL4 monocolonal antibody (mab). The minimal length of these synthetic hinges comprises only 12 amino acids, rendering them ideal models for computational studies. Well-tempered metadynamics was performed to adequately describe the available conformational space defined by the different hinges. In spite of the differences in amino acid composition and ring sizes, there are characteristic similarities of designed and natural hinges like the dependent mobility of the individual strands of each hinge domain.

New technologies to analyse protein function: an intrinsic disorder perspective

Functions of intrinsically disordered proteins do not require structure. Such structure-independent functionality has melted away the classic rigid "lock and key" representation of structure-function relationships in proteins, opening a new page in protein science, where molten keys operate on melted locks and where conformational flexibility and intrinsic disorder, structural plasticity and extreme malleability, multifunctionality and binding promiscuity represent a new-fangled reality. Analysis and understanding of this new reality require novel tools, and some of the techniques elaborated for the examination of intrinsically disordered protein functions are outlined in this review.

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.

Biochemical and biophysical comparison of human and mouse beta-2 microglobulin reveals the molecular determinants of low amyloid propensity

The molecular bases of amyloid aggregation propensity are still poorly understood, especially for proteins that display a stable folded native structure. A prototypic example is human beta-2 microglobulin (β2m), which, when accumulated in patients, gives rise to dialysis-related amyloidosis. Interestingly, although the physiologic concentration of β2m in mice is five times higher than that found in human patients, no amyloid deposits are observed in mice. Moreover, murine β2m (mβ2m) not only displays a lower amyloid propensity both in vivo and in vitro but also inhibits the aggregation of human β2m in vitro. Here, we compared human and mβ2m for their aggregation propensity, ability to form soluble oligomers, stability, three-dimensional structure and dynamics. Our results indicate that mβ2m low-aggregation propensity is due to two concomitant aspects: the low-aggregation propensity of its primary sequence combined with the absence of high-energy amyloid-competent conformations under native conditions. The identification of the specific properties determining the low-aggregation propensity of mouse β2m will help delineate the molecular risk factors which cause a folded protein to aggregate.

Metadynamics to Enhance Sampling in Biomolecular Simulations

Molecular dynamics is a powerful simulation method to provide detailed atomic-scale insight into a range of biological processes including protein folding, biochemical reactions, ligand binding, and many others. Over the last several decades, enhanced sampling methods have been developed to address the large separation in time scales between a molecular dynamics simulation (usually microseconds or shorter) and the time scales of biological processes (often orders of magnitude longer). This chapter specifically focuses on the metadynamics family of methods, which achieves enhanced sampling through the introduction of a history-dependent bias potential that is based on one or more slow degrees of freedom, called collective variables. We introduce the method and its recent variants related to biomolecular studies and then discuss frontier areas of the method. A large part of this chapter is devoted to helping new users of the method understand how to choose metadynamics parameters properly and apply the method to their system of interest.

Hybrid Refinement of Heterogeneous Conformational Ensembles Using Spectroscopic Data

Multistructured biomolecular systems play crucial roles in a wide variety of cellular processes but have resisted traditional methods of structure determination, which often resolve only a few low-energy states. High-resolution structure determination using experimental methods that yield distributional data remains extremely difficult, especially when the underlying conformational ensembles are quite heterogeneous. We have therefore developed a method to integrate sparse, multimultimodal spectroscopic data to obtain high-resolution estimates of conformational ensembles. We have tested our method by incorporating double electron-electron resonance data on the soluble N-ethylmaleimide-sensitive factor attachment receptor (SNARE) protein syntaxin-1a into biased molecular dynamics simulations. We find that our method substantially outperforms existing state-of-the-art methods in capturing syntaxin's open-closed conformational equilibrium and further yields new conformational states that are consistent with experimental data and may help in understanding syntaxin's function. Our improved methods for refining heterogeneous conformational ensembles from spectroscopic data will greatly accelerate the structural understanding of such systems.

Efficient Ensemble Refinement by Reweighting

Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J-couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

Solid-State NMR and MD Study of the Structure of the Statherin Mutant SNa15 on Mineral Surfaces

Elucidation of the structure and interactions of proteins at native mineral interfaces is key to understanding how biological systems regulate the formation of hard tissue structures. In addition, understanding how these same proteins interact with non-native mineral surfaces has important implications for the design of medical and dental implants, chromatographic supports, diagnostic tools, and a host of other applications. Here, we combine solid-state NMR spectroscopy, isotherm measurements, and molecular dynamics simulations to study how SNa15, a peptide derived from the hydroxyapatite (HAP) recognition domain of the biomineralization protein statherin, interacts with HAP, silica (SiO2), and titania (TiO2) mineral surfaces. Adsorption isotherms are used to characterize the binding affinity of SNa15 to HAP, SiO2, and TiO2. We also apply 1D 13C CP MAS, 1D 15N CP MAS, and 2D 13C-13C DARR experiments to SNa15 samples with uniformly 13C- and 15N-enriched residues to determine backbone and side-chain chemical shifts. Different computational tools, namely TALOS-N and molecular dynamics simulations, are used to deduce secondary structure from backbone and side-chain chemical shift data. Our results show that SNa15 adopts an α-helical conformation when adsorbed to HAP and TiO2, but the helix largely unravels upon adsorption to SiO2. Interactions with HAP are mediated in general by acidic and some basic amino acids, although the specific amino acids involved in direct surface interaction vary with surface. The integrated experimental and computational approach used in this study is able to provide high-resolution insights into adsorption of proteins on interfaces.

Analyzing Biomolecular Ensembles

Several techniques are available to generate conformational ensembles of proteins and other biomolecules either experimentally or computationally. These methods produce a large amount of data that need to be analyzed to identify structure-dynamics-function relationship. In this chapter, we will cover different tools to unveil the information hidden in conformational ensemble data and to guide toward the rationalization of the data. We included routinely used approaches such as dimensionality reduction, as well as new methods inspired by high-order statistics and graph theory.

Nature of the Pre-Chemistry Ensemble in Mitogen-Activated Protein Kinases

In spite of the availability of a significant amount of structural detail on docking interactions involving mitogen-activated protein kinases (MAPKs) and their substrates, the mechanism by which the disordered phospho-acceptor on the substrate transiently interacts with the kinase catalytic elements and is phosphorylated, often with high efficiency, remains poorly understood. Here, this dynamic interaction is analyzed in the context of available biophysical and biochemical data for ERK2, an archetypal MAPK. A hypothesis about the nature of the ternary complex involving a MAPK, its substrate, and ATP immediately prior to the chemical step (the pre-chemistry complex) is proposed. It is postulated that the solution ensemble (the pre-chemistry ensemble) representing the pre-chemistry complex comprises several conformations that are linked by dynamics on multiple timescales. These individual conformations possess different intrinsic abilities to proceed through the chemical step. The overall rate of chemistry is therefore related to the microscopic nature of the pre-chemistry ensemble, its constituent conformational microstates, and their intrinsic abilities to yield a phosphorylated product. While characterizing these microstates within the pre-chemistry ensemble in atomic or near-atomic detail is an extremely challenging proposition, recent developments in hybrid methodologies that employ computational approaches driven by experimental data appear to provide the most promising path forward toward achieving this goal.

The Antibody Light-Chain Linker Regulates Domain Orientation and Amyloidogenicity

The antibody light chain (LC) consists of two domains and is essential for antigen binding in mature immunoglobulins. The two domains are connected by a highly conserved linker that comprises the structurally important Arg108 residue. In antibody light chain (AL) amyloidosis, a severe protein amyloid disease, the LC and its N-terminal variable domain (V_L) convert to fibrils deposited in the tissues causing organ failure. Understanding the factors shaping the architecture of the LC is important for basic science, biotechnology and for deciphering the principles that lead to fibril formation. In this study, we examined the structure and properties of LC variants with a mutated or extended linker. We show that under destabilizing conditions, the linker modulates the amyloidogenicity of the LC. The fibril formation propensity of LC linker variants and their susceptibility to proteolysis directly correlate implying an interplay between the two LC domains. Using NMR and residual dipolar coupling-based simulations, we found that the linker residue Arg108 is a key factor regulating the relative orientation of the V_L and C_L domains, keeping them in a bent and dense, but still flexible conformation. Thus, inter-domain contacts and the relative orientation of V_L and C_L to each other are of major importance for maintaining the structural integrity of the full-length LC.

Molecular dynamics ensemble refinement of the heterogeneous native state of NCBD using chemical shifts and NOEs

Many proteins display complex dynamical properties that are often intimately linked to their biological functions. As the native state of a protein is best described as an ensemble of conformations, it is important to be able to generate models of native state ensembles with high accuracy. Due to limitations in sampling efficiency and force field accuracy it is, however, challenging to obtain accurate ensembles of protein conformations by the use of molecular simulations alone. Here we show that dynamic ensemble refinement, which combines an accurate atomistic force field with commonly available nuclear magnetic resonance (NMR) chemical shifts and NOEs, can provide a detailed and accurate description of the conformational ensemble of the native state of a highly dynamic protein. As both NOEs and chemical shifts are averaged on timescales up to milliseconds, the resulting ensembles reflect the structural heterogeneity that goes beyond that probed, e.g., by NMR relaxation order parameters. We selected the small protein domain NCBD as object of our study since this protein, which has been characterized experimentally in substantial detail, displays a rich and complex dynamical behaviour. In particular, the protein has been described as having a molten-globule like structure, but with a relatively rigid core. Our approach allowed us to describe the conformational dynamics of NCBD in solution, and to probe the structural heterogeneity resulting from both short- and long-timescale dynamics by the calculation of order parameters on different time scales. These results illustrate the usefulness of our approach since they show that NCBD is rather rigid on the nanosecond timescale, but interconverts within a broader ensemble on longer timescales, thus enabling the derivation of a coherent set of conclusions from various NMR experiments on this protein, which could otherwise appear in contradiction with each other.

Reversible inhibition of the ClpP protease via an N-terminal conformational switch

Protein homeostasis is critically important for cell viability. Key to this process is the refolding of misfolded or aggregated proteins by molecular chaperones or, alternatively, their degradation by proteases. In most prokaryotes and in chloroplasts and mitochondria, protein degradation is performed by the caseinolytic protease ClpP, a tetradecamer barrel-like proteolytic complex. Dysregulating ClpP function has shown promise in fighting antibiotic resistance and as a potential therapy for acute myeloid leukemia. Here we use methyl-transverse relaxation-optimized spectroscopy (TROSY)-based NMR, cryo-EM, biochemical assays, and molecular dynamics simulations to characterize the structural dynamics of ClpP from Staphylococcus aureus (SaClpP) in wild-type and mutant forms in an effort to discover conformational hotspots that regulate its function. Wild-type SaClpP was found exclusively in the active extended form, with the N-terminal domains of its component protomers in predominantly β-hairpin conformations that are less well-defined than other regions of the protein. A hydrophobic site was identified that, upon mutation, leads to unfolding of the N-terminal domains, loss of SaClpP activity, and formation of a previously unobserved split-ring conformation with a pair of 20-Å-wide pores in the side of the complex. The extended form of the structure and partial activity can be restored via binding of ADEP small-molecule activators. The observed structural plasticity of the N-terminal gates is shown to be a conserved feature through studies of Escherichia coli and Neisseria meningitidis ClpP, suggesting a potential avenue for the development of molecules to allosterically modulate the function of ClpP.

Metadynamic metainference: Convergence towards force field independent structural ensembles of a disordered peptide

Metadynamic metainference has been recently introduced as a theoretical framework to determine structural ensembles by combining and weighting their noise multiple sources of experimental data with molecular mechanics force fields and metadynamics simulations. Here we build upon these initial developments to further extend and streamline the computational approach. We also show that metadynamic metainference can actually determine a structural ensemble for a disordered peptide that is essentially independent from the employed force field. We further show that it is possible to use a very computationally efficient implicit solvent force field in the place of very expensive state-of-the-art explicit solvent ones without a significant loss in accuracy.

An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations

Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data, and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such a principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow us to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed.

Combining enhanced sampling with experiment-directed simulation of the GYG peptide

Experiment-directed simulation (EDS) is a technique to minimally bias molecular dynamics simulations to match experimentally observed results. The method improves accuracy but does not address the sampling problem of molecular dynamics simulations of large systems. This work combines EDS with both the parallel-tempering or parallel-tempering well-tempered ensemble replica-exchange methods to enhance sampling. These methods are demonstrated on the GYG tripeptide in explicit water. The collective variables biased by EDS are chemical shifts, where the set-points are determined by NMR experiments. The results show that it is possible to enhance sampling with either parallel-tempering and parallel-tempering well-tempered ensemble in the EDS method. This combination of methods provides a novel approach for both accurately and exhaustively simulating biological systems.