A kinetic ensemble of the Alzheimer's Aβ peptide

Biomedical Applications of Gadolinium-Containing Biomaterials: Not Only MRI Contrast Agent

The potential applications of rare earth elements (REEs) in biomedical fields have been intensively investigated. Numerous studies have shown that doping biomaterials with REEs can enhance their properties. Gadolinium (Gd) is a biocompatible REE that holds promise in biomedical applications. This review examines the use of Gd-doped biomaterials in osteogenic, antimicrobial, anticancer applications, and in bioimaging and bioprobes, as reported in the literature until December 2024. The included studies demonstrate that Gd-containing biomaterials promote osteogenesis, enhance antimicrobial properties, and perform well in anticancer applications and bioimaging. Taken together, they point to the considerable potential of Gd-doped biomaterials and thus to avenues for future research.

Atomistic molecular dynamics simulations of intrinsically disordered proteins

Recent years have seen remarkable gains in the accuracy of atomistic molecular dynamics (MD) simulations of intrinsically disordered proteins (IDPs) and expansion in the types of calculated properties that can be directly compared with experimental measurements. These advances occurred due to the use of IDP-tested force fields and the porting of MD simulations to GPUs and other computational technologies. All-atom MD simulations are now explaining the sequence-dependent dynamics of IDPs; elucidating the mechanisms of their binding to other proteins, nucleic acids, and membranes; revealing the modes of drug action on them; and characterizing their phase separation. Artificial intelligence (AI) and machine learning (ML) are further expanding the reach of atomistic MD simulations.

AlphaFold prediction of structural ensembles of disordered proteins

Deep learning methods of predicting protein structures have reached an accuracy comparable to that of high-resolution experimental methods. It is thus possible to generate accurate models of the native states of hundreds of millions of proteins. An open question, however, concerns whether these advances can be translated to disordered proteins, which should be represented as structural ensembles because of their heterogeneous and dynamical nature. To address this problem, we introduce the AlphaFold-Metainference method to use AlphaFold-derived distances as structural restraints in molecular dynamics simulations to construct structural ensembles of ordered and disordered proteins. The results obtained using AlphaFold-Metainference illustrate the possibility of making predictions of the conformational properties of disordered proteins using deep learning methods trained on the large structural databases available for folded proteins.

Estimation of Ligand Binding Free Energy Using Multi-eGO

The computational study of ligand binding to a target protein provides mechanistic insight into the molecular determinants of this process and can improve the success rate of in silico drug design. All-atom molecular dynamics (MD) simulations can be used to evaluate the binding free energy, typically by thermodynamic integration, and to probe binding mechanisms, including the description of protein conformational dynamics. The advantages of MD come at a high computational cost, which limits its use. Such cost could be reduced by using coarse-grained models, but their use is generally associated with an undesirable loss of resolution and accuracy. To address the trade-off between speed and accuracy of MD simulations, we describe the use of the recently introduced multi-eGO atomic model for the estimation of binding free energies. We illustrate this approach in the case of the binding of benzene to lysozyme by both thermodynamic integration and metadynamics, showing multiple binding/unbinding pathways of benzene. We then provide equally accurate results for the binding free energy of dasatinib and PP1 to Src kinase by thermodynamic integration. Finally, we show how we can describe the binding of the small molecule 10074-G5 to Aβ42 by single molecule simulations and by explicit titration of the ligand as a function of concentration. These results demonstrate that multi-eGO has the potential to significantly reduce the cost of accurate binding free energy calculations and can be used to develop and benchmark in silico ligand binding techniques.

Helix-to-sheet transition of the Aβ42 peptide revealed using an enhanced sampling strategy and Markov state model

The self-assembly of Aβ peptides into toxic oligomers and fibrils is the primary cause of Alzheimer's disease. Moreover, the conformational transition from helix to sheet is considered a crucial step in the aggregation of Aβ peptides. However, the structural details of this process still remain unclear due to the heterogeneity and transient nature of the Aβ peptides. In this study, we developed an enhanced sampling strategy that combines artificial neural networks (ANN) with metadynamics to explore the conformational space of the Aβ42 peptides. The strategy consists of two parts: applying ANN to optimize CVs and conducting metadynamics based on the resulting CVs to sample conformations. The results showed that this strategy achieved better sampling performance in terms of the distribution of sampled conformations. The sampling efficiency is increased by 10-fold compared to our previous Hamiltonian Exchange Molecular Dynamics (MD) and by 1000-fold compared to ordinary MD. Based on the sampled conformations, we constructed a Markov state model to understand the detailed transition process. The intermediate states in this process are identified, and the connecting paths are analyzed. The conformational transitions in D23-K28 and M35-V40 are proven to be crucial for aggregation. These results are helpful in clarifying the mechanism and process of Aβ42 peptide aggregation. D23-K28 and M35-V40 can be identified as potential targets for screening and designing inhibitors of Aβ peptide aggregation.

Dynamic Mechanism for Subtype Selectivity of Endocannabinoids

Endocannabinoids are naturally occurring lipid-like molecules that bind to cannabinoid receptors (CB1 and CB2) and regulate many of human bodily functions via the endocannabinoid system. There is a tremendous interest in developing selective drugs that target the CB receptors. However, the biophysical mechanisms responsible for the subtype selectivity for endocannbinoids have not been established. Recent experimental structures of CB receptors show that endocannbinoids potentially bind via membrane using the lipid access channel in the transmembrane region of the receptors. Furthermore, the N-terminus of the receptor could move in and out of the binding pocket thereby modulating both the pocket volume and its residue composition. On the basis of these observations, we propose two hypothesis to explain the selectivity of the endocannabinoid, anandamide for CB1 receptor. First, the selectivity arises from distinct enthalpic ligand-protein interactions along the ligand binding pathway formed due to the movement of N-terminus and subsequent shifts in the binding pocket composition. Second, selectivity arises from the volumetric differences in the binding pocket allowing for differences in ligand conformational entropy. To quantitatively test these hypothesis, we perform extensive molecular dynamics simulations (∼0.9 milliseconds) along with Markov state modeling and deep learning-based VAMP-nets to provide an interpretable characterization of the anandamide binding process to cannabinoid receptors and explain its selectivity for CB1. Our findings reveal that the distinct N-terminus positions along lipid access channels between TM1 and TM7 lead to different binding mechanisms and interactions between anandamide and the binding pocket residues. To validate the critical stabilizing interactions along the binding pathway, relative free energy calculations of anandamide analogs are used. Moreover, the larger CB2 pocket volume increases the entropic effects of ligand binding by allowing higher ligand fluctuations but reduced stable interactions. Therefore, the opposing enthalpy and entropy effects between the receptors shape the endocannabinoid selectivity. Overall, the CB1 selectivity of anandamide is explained by the dominant enthalpy contributions due to ligand-protein interactions in stable binding poses. This study shed lights on potential selectivity mechanisms for endocannabinoids that would aid in the discovery of CB selective drugs.

Aggregation Rules of Short Peptides

The elucidation of aggregation rules for short peptides (e.g., tetrapeptides and pentapeptides) is crucial for the precise manipulation of aggregation. In this study, we derive comprehensive aggregation rules for tetrapeptides and pentapeptides across the entire sequence space based on the aggregation propensity values predicted by a transformer-based deep learning model. Our analysis focuses on three quantitative aspects. First, we investigate the type and positional effects of amino acids on aggregation, considering both the first- and second-order contributions. By identifying specific amino acids and amino acid pairs that promote or attenuate aggregation, we gain insights into the underlying aggregation mechanisms. Second, we explore the transferability of aggregation propensities between tetrapeptides and pentapeptides, aiming to explore the possibility of enhancing or mitigating aggregation by concatenating or removing specific amino acids at the termini. Finally, we evaluate the aggregation morphologies of over 20,000 tetrapeptides, regarding the morphology distribution and type and positional contributions of each amino acid. This work extends the existing aggregation rules from tripeptide sequences to millions of tetrapeptide and pentapeptide sequences, offering experimentalists an explicit roadmap for fine-tuning the aggregation behavior of short peptides for diverse applications, including hydrogels, emulsions, or pharmaceuticals.

RevGraphVAMP: A protein molecular simulation analysis model combining graph convolutional neural networks and physical constraints

Molecular dynamics simulation is a crucial research domain within the life sciences, focusing on comprehending the mechanisms of biomolecular interactions at atomic scales. Protein simulation, as a critical subfield, often utilizes MD for implementation, with trajectory data play a pivotal role in drug discovery. The advancement of high-performance computing and deep learning technology becomes popular and critical to predict protein properties from vast trajectory data, posing challenges regarding data features extraction from the complicated simulation data and dimensionality reduction. Simultaneously, it is essential to provide a meaningful explanation of the biological mechanism behind dimensionality. To tackle this challenge, we propose a new unsupervised model named RevGraphVAMP to intelligently analyze the simulation trajectory. This model is based on the variational approach for Markov processes (VAMP) and integrates graph convolutional neural networks and physical constraint optimization to enhance the learning performance. Additionally, we introduce attention mechanism to assess the importance of key interaction region, facilitating the interpretation of molecular mechanism. In comparison to other VAMPNets models, our model showcases competitive performance, improved accuracy in state transition prediction, as demonstrated through its application to two public datasets and the Shank3-Rap1 complex, which is associated with autism spectrum disorder. Moreover, it enhanced dimensionality reduction discrimination across different substates and provides interpretable results for protein structural characterization.

CoVAMPnet: Comparative Markov State Analysis for Studying Effects of Drug Candidates on Disordered Biomolecules

Computational study of the effect of drug candidates on intrinsically disordered biomolecules is challenging due to their vast and complex conformational space. Here, we developed a comparative Markov state analysis (CoVAMPnet) framework to quantify changes in the conformational distribution and dynamics of a disordered biomolecule in the presence and absence of small organic drug candidate molecules. First, molecular dynamics trajectories are generated using enhanced sampling, in the presence and absence of small molecule drug candidates, and ensembles of soft Markov state models (MSMs) are learned for each system using unsupervised machine learning. Second, these ensembles of learned MSMs are aligned across different systems based on a solution to an optimal transport problem. Third, the directional importance of inter-residue distances for the assignment to different conformational states is assessed by a discriminative analysis of aggregated neural network gradients. This final step provides interpretability and biophysical context to the learned MSMs. We applied this novel computational framework to assess the effects of ongoing phase 3 therapeutics tramiprosate (TMP) and its metabolite 3-sulfopropanoic acid (SPA) on the disordered Aβ42 peptide involved in Alzheimer's disease. Based on adaptive sampling molecular dynamics and CoVAMPnet analysis, we observed that both TMP and SPA preserved more structured conformations of Aβ42 by interacting nonspecifically with charged residues. SPA impacted Aβ42 more than TMP, protecting α-helices and suppressing the formation of aggregation-prone β-strands. Experimental biophysical analyses showed only mild effects of TMP/SPA on Aβ42 and activity enhancement by the endogenous metabolization of TMP into SPA. Our data suggest that TMP/SPA may also target biomolecules other than Aβ peptides. The CoVAMPnet method is broadly applicable to study the effects of drug candidates on the conformational behavior of intrinsically disordered biomolecules.

Kinetic Ensemble of Tau Protein through the Markov State Model and Deep Learning Analysis

The ordered assembly of Tau protein into filaments characterizes Alzheimer's and other neurodegenerative diseases, and thus, stabilization of Tau protein is a promising avenue for tauopathies therapy. To dissect the underlying aggregation mechanisms on Tau, we employ a set of molecular simulations and the Markov state model to determine the kinetics of ensemble of K18. K18 is the microtubule-binding domain of Tau protein and plays a vital role in the microtubule assembly, recycling processes, and amyloid fibril formation. Here, we efficiently explore the conformation of K18 with about 150 μs lifetimes in silico. Our results observe that all four repeat regions (R1-R4) are very dynamic, featuring frequent conformational conversion and lacking stable conformations, and the R2 region is more flexible than the R1, R3, and R4 regions. Additionally, it is worth noting that residues 300-310 in R2-R3 and residues 319-336 in R3 tend to form sheet structures, indicating that K18 has a broader functional role than individual repeat monomers. Finally, the simulations combined with Markov state models and deep learning reveal 5 key conformational states along the transition pathway and provide the information on the microsecond time scale interstate transition rates. Overall, this study offers significant insights into the molecular mechanism of Tau pathological aggregation and develops novel strategies for both securing tauopathies and advancing drug discovery.

Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model

A central challenge in the study of intrinsically disordered proteins is the characterization of the mechanisms by which they bind their physiological interaction partners. Here, we utilize a deep learning-based Markov state modeling approach to characterize the folding-upon-binding pathways observed in a long timescale molecular dynamics simulation of a disordered region of the measles virus nucleoprotein NTAIL reversibly binding the X domain of the measles virus phosphoprotein complex. We find that folding-upon-binding predominantly occurs via two distinct encounter complexes that are differentiated by the binding orientation, helical content, and conformational heterogeneity of NTAIL. We observe that folding-upon-binding predominantly proceeds through a multi-step induced fit mechanism with several intermediates and do not find evidence for the existence of canonical conformational selection pathways. We observe four kinetically separated native-like bound states that interconvert on timescales of eighty to five hundred nanoseconds. These bound states share a core set of native intermolecular contacts and stable NTAIL helices and are differentiated by a sequential formation of native and non-native contacts and additional helical turns. Our analyses provide an atomic resolution structural description of intermediate states in a folding-upon-binding pathway and elucidate the nature of the kinetic barriers between metastable states in a dynamic and heterogenous, or "fuzzy", protein complex.

Multi-eGO: Model Improvements toward the Study of Complex Self-Assembly Processes

Structure-based models have been instrumental in simulating protein folding and suggesting hypotheses about the mechanisms involved. Nowadays, at least for fast-folding proteins, folding can be simulated in explicit solvent using classical molecular dynamics. However, other self-assembly processes, such as protein aggregation, are still far from being accessible. Recently, we proposed that a hybrid multistate structure-based model, multi-eGO, could help to bridge the gap toward the simulation of out-of-equilibrium, concentration-dependent self-assembly processes. Here, we further improve the model and show how multi-eGO can effectively and accurately learn the conformational ensemble of the amyloid β42 intrinsically disordered peptide, reproduce the well-established folding mechanism of the B1 immunoglobulin-binding domain of streptococcal protein G, and reproduce the aggregation as a function of the concentration of the transthyretin 105-115 amyloidogenic peptide. We envision that by learning from the dynamics of a few minima, multi-eGO can become a platform for simulating processes inaccessible to other simulation techniques.

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.

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.

Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model

A central challenge in the study of intrinsically disordered proteins is the characterization of the mechanisms by which they bind their physiological interaction partners. Here, we utilize a deep learning based Markov state modeling approach to characterize the folding-upon-binding pathways observed in a long-time scale molecular dynamics simulation of a disordered region of the measles virus nucleoprotein NTAIL reversibly binding the X domain of the measles virus phosphoprotein complex. We find that folding-upon-binding predominantly occurs via two distinct encounter complexes that are differentiated by the binding orientation, helical content, and conformational heterogeneity of NTAIL. We do not, however, find evidence for the existence of canonical conformational selection or induced fit binding pathways. We observe four kinetically separated native-like bound states that interconvert on time scales of eighty to five hundred nanoseconds. These bound states share a core set of native intermolecular contacts and stable NTAIL helices and are differentiated by a sequential formation of native and non-native contacts and additional helical turns. Our analyses provide an atomic resolution structural description of intermediate states in a folding-upon-binding pathway and elucidate the nature of the kinetic barriers between metastable states in a dynamic and heterogenous, or "fuzzy", protein complex.

Transition Networks Unveil Disorder-to-Order Transformations in Aβ Caused by Glycosaminoglycans or Lipids

The aggregation of amyloid-β (Aβ) peptides, particularly of Aβ1-42, has been linked to the pathogenesis of Alzheimer's disease. In this study, we focus on the conformational change of Aβ1-42 in the presence of glycosaminoglycans (GAGs) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipids using molecular dynamics simulations. We analyze the conformational changes that occur in Aβ by extracting the key structural features that are then used to generate transition networks. Using the same three features per network highlights the transitions from intrinsically disordered states ubiquitous in Aβ1-42 in solution to more compact states arising from stable β-hairpin formation when Aβ1-42 is in the vicinity of a GAG molecule, and even more compact states characterized by a α-helix or β-sheet structures when Aβ1-42 interacts with a POPC lipid cluster. We show that the molecular mechanisms underlying these transitions from disorder to order are different for the Aβ1-42/GAG and Aβ1-42/POPC systems. While in the latter the hydrophobicity provided by the lipid tails facilitates the folding of Aβ1-42, in the case of GAG there are hardly any intermolecular Aβ1-42-GAG interactions. Instead, GAG removes sodium ions from the peptide, allowing stronger electrostatic interactions within the peptide that stabilize a β-hairpin. Our results contribute to the growing knowledge of the role of GAGs and lipids in the conformational preferences of the Aβ peptide, which in turn influences its aggregation into toxic oligomers and amyloid fibrils.

Stabilization of pre-existing neurotensin receptor conformational states by β-arrestin-1 and the biased allosteric modulator ML314

The neurotensin receptor 1 (NTS1) is a G protein-coupled receptor (GPCR) with promise as a drug target for the treatment of pain, schizophrenia, obesity, addiction, and various cancers. A detailed picture of the NTS1 structural landscape has been established by X-ray crystallography and cryo-EM and yet, the molecular determinants for why a receptor couples to G protein versus arrestin transducers remain poorly defined. We used 13CεH3-methionine NMR spectroscopy to show that binding of phosphatidylinositol-4,5-bisphosphate (PIP2) to the receptor's intracellular surface allosterically tunes the timescale of motions at the orthosteric pocket and conserved activation motifs - without dramatically altering the structural ensemble. β-arrestin-1 further remodels the receptor ensemble by reducing conformational exchange kinetics for a subset of resonances, whereas G protein coupling has little to no effect on exchange rates. A β-arrestin biased allosteric modulator transforms the NTS1:G protein complex into a concatenation of substates, without triggering transducer dissociation, suggesting that it may function by stabilizing signaling incompetent G protein conformations such as the non-canonical state. Together, our work demonstrates the importance of kinetic information to a complete picture of the GPCR activation landscape.

The quaternary question: Determining allostery in spastin through dynamics classification learning and bioinformatics

The nanomachine from the ATPases associated with various cellular activities superfamily, called spastin, severs microtubules during cellular processes. To characterize the functionally important allostery in spastin, we employed methods from evolutionary information, to graph-based networks, to machine learning applied to atomistic molecular dynamics simulations of spastin in its monomeric and the functional hexameric forms, in the presence or absence of ligands. Feature selection, using machine learning approaches, for transitions between spastin states recognizes all the regions that have been proposed as allosteric or functional in the literature. The analysis of the composition of the Markov State Model macrostates in the spastin monomer, and the analysis of the direction of change in the top machine learning features for the transitions, indicate that the monomer favors the binding of ATP, which primes the regions involved in the formation of the inter-protomer interfaces for binding to other protomer(s). Allosteric path analysis of graph networks, built based on the cross-correlations between residues in simulations, shows that perturbations to a hub specific for the pre-hydrolysis hexamer propagate throughout the structure by passing through two obligatory regions: the ATP binding pocket, and pore loop 3, which connects the substrate binding site to the ATP binding site. Our findings support a model where the changes in the terminal protomers due to the binding of ligands play an active role in the force generation in spastin. The secondary structures in spastin, which are found to be highly degenerative within the network paths, are also critical for feature transitions of the classification models, which can guide the design of allosteric effectors to enhance or block allosteric signaling.

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.

Chasing collective variables using temporal data-driven strategies

The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N'-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

An atlas of amyloid aggregation: the impact of substitutions, insertions, deletions and truncations on amyloid beta fibril nucleation

Multiplexed assays of variant effects (MAVEs) guide clinical variant interpretation and reveal disease mechanisms. To date, MAVEs have focussed on a single mutation type-amino acid (AA) substitutions-despite the diversity of coding variants that cause disease. Here we use Deep Indel Mutagenesis (DIM) to generate a comprehensive atlas of diverse variant effects for a disease protein, the amyloid beta (Aβ) peptide that aggregates in Alzheimer's disease (AD) and is mutated in familial AD (fAD). The atlas identifies known fAD mutations and reveals that many variants beyond substitutions accelerate Aβ aggregation and are likely to be pathogenic. Truncations, substitutions, insertions, single- and internal multi-AA deletions differ in their propensity to enhance or impair aggregation, but likely pathogenic variants from all classes are highly enriched in the polar N-terminal region of Aβ. This comparative atlas highlights the importance of including diverse mutation types in MAVEs and provides important mechanistic insights into amyloid nucleation.

Characterization of the Conformations of Amyloid Beta 42 in Solution That May Mediate Its Initial Hydrophobic Aggregation

Intrinsically disordered peptides, such as amyloid β42 (Aβ42), lack a well-defined structure in solution. Aβ42 can undergo abnormal aggregation and amyloidogenesis in the brain, forming fibrillar plaques, a hallmark of Alzheimer's disease. The insoluble fibrillar forms of Aβ42 exhibit well-defined, cross β-sheet structures at the molecular level and are less toxic than the soluble, intermediate disordered oligomeric forms. However, the mechanism of initial interaction of monomers and subsequent oligomerization is not well understood. The structural disorder of Aβ42 adds to the challenges of determining the structural properties of its monomers, making it difficult to understand the underlying molecular mechanism of pathogenic aggregation. Certain regions of Aβ42 are known to exhibit helical propensity in different physiological conditions. NMR spectroscopy has shown that the Aβ42 monomer at lower pH can adopt an α-helical conformation and as the pH is increased, the peptide switches to β-sheet conformation and aggregation occurs. CD spectroscopy studies of aggregation have shown the presence of an initial spike in the amount of α-helical content at the start of aggregation. Such an increase in α-helical content suggests a mechanism wherein the peptide can expose critical non-polar residues for interaction, leading to hydrophobic aggregation with other interacting peptides. We have used molecular dynamics simulations to characterize in detail the conformational landscape of monomeric Aβ42 in solution to identify molecular properties that may mediate the early stages of oligomerization. We hypothesized that conformations with α-helical structure have a higher probability of initiating aggregation because they increase the hydrophobicity of the peptide. Although random coil conformations were found to be the most dominant, as expected, α-helical conformations are thermodynamically accessible, more so than β-sheet conformations. Importantly, for the first time α-helical conformations are observed to increase the exposure of aromatic and hydrophobic residues to the aqueous solvent, favoring their hydrophobically driven interaction with other monomers to initiate aggregation. These findings constitute a first step toward characterizing the mechanism of formation of disordered, low-order oligomers of Aβ42.

Additive eigenvectors as optimal reaction coordinates, conditioned trajectories, and time-reversible description of stochastic processes

A fundamental way to analyze complex multidimensional stochastic dynamics is to describe it as diffusion on a free energy landscape—free energy as a function of reaction coordinates (RCs). For such a description to be quantitatively accurate, the RC should be chosen in an optimal way. The committor function is a primary example of an optimal RC for the description of equilibrium reaction dynamics between two states. Here, additive eigenvectors (addevs) are considered as optimal RCs to address the limitations of the committor. An addev master equation for a Markov chain is derived. A stationary solution of the equation describes a sub-ensemble of trajectories conditioned on having the same optimal RC for the forward and time-reversed dynamics in the sub-ensemble. A collection of such sub-ensembles of trajectories, called stochastic eigenmodes, can be used to describe/approximate the stochastic dynamics. A non-stationary solution describes the evolution of the probability distribution. However, in contrast to the standard master equation, it provides a time-reversible description of stochastic dynamics. It can be integrated forward and backward in time. The developed framework is illustrated on two model systems—unidirectional random walk and diffusion.

Multi-eGO: An in silico lens to look into protein aggregation kinetics at atomic resolution

Protein aggregation into amyloid fibrils is the archetype of aberrant biomolecular self-assembly processes, with more than 50 associated diseases that are mostly uncurable. Understanding aggregation mechanisms is thus of fundamental importance and goes in parallel with the structural characterization of the transient oligomers formed during the process. Oligomers have been proven elusive to high-resolution structural techniques, while the large sizes and long time scales, typical of aggregation processes, have limited the use of computational methods to date. To surmount these limitations, we here present multi-eGO, an atomistic, hybrid structure-based model which, leveraging the knowledge of monomers conformational dynamics and of fibril structures, efficiently captures the essential structural and kinetics aspects of protein aggregation. Multi-eGO molecular dynamics simulations can describe the aggregation kinetics of thousands of monomers. The concentration dependence of the simulated kinetics, as well as the structural features of the resulting fibrils, are in qualitative agreement with in vitro experiments carried out on an amyloidogenic peptide from Transthyretin, a protein responsible for one of the most common cardiac amyloidoses. Multi-eGO simulations allow the formation of primary nuclei in a sea of transient lower-order oligomers to be observed over time and at atomic resolution, following their growth and the subsequent secondary nucleation events, until the maturation of multiple fibrils is achieved. Multi-eGO, combined with the many experimental techniques deployed to study protein aggregation, can provide the structural basis needed to advance the design of molecules targeting amyloidogenic diseases.

A Small Molecule Stabilizes the Disordered Native State of the Alzheimer's Aβ Peptide

The stabilization of native states of proteins is a powerful drug discovery strategy. It is still unclear, however, whether this approach can be applied to intrinsically disordered proteins. Here, we report a small molecule that stabilizes the native state of the Aβ42 peptide, an intrinsically disordered protein fragment associated with Alzheimer's disease. We show that this stabilization takes place by a disordered binding mechanism, in which both the small molecule and the Aβ42 peptide remain disordered. This disordered binding mechanism involves enthalpically favorable local π-stacking interactions coupled with entropically advantageous global effects. These results indicate that small molecules can stabilize disordered proteins in their native states through transient non-specific interactions that provide enthalpic gain while simultaneously increasing the conformational entropy of the proteins.

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules

Finding a low dimensional representation of data from long-timescale trajectories of biomolecular processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of molecular representation results in a higher resolution and a more interpretable Markov model than the standard VAMPNet, enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

Molecular simulations of proteins: From simplified physical interactions to complex biological phenomena

Molecular dynamics simulation is the most popular computational technique for investigating the structural and dynamical behaviour of proteins, in search of the molecular basis of their function. Far from being a completely settled field of research, simulations are still evolving to best capture the essential features of the atomic interactions that govern a protein's inner motions. Modern force fields are becoming increasingly accurate in providing a physical description adequate to this purpose, and allow us to model complex biological systems under fairly realistic conditions. Furthermore, the use of accelerated sampling techniques is improving our access to the observation of progressively larger molecular structures, longer time scales, and more hidden functional events. In this review, the basic principles of molecular dynamics simulations and a number of key applications in the area of protein science are summarized, and some of the most important results are discussed. Examples include the study of the structure, dynamics and binding properties of 'difficult' targets, such as intrinsically disordered proteins and membrane receptors, and the investigation of challenging phenomena like hydration-driven processes and protein aggregation. The findings described provide an overall picture of the current state of this research field, and indicate new perspectives on the road ahead to the upcoming future of molecular simulations.

Early aggregation mechanism of Aβ16-22 revealed by Markov state models

Aβ_16-22 is believed to have critical role in early aggregation of full length amyloids that are associated with the Alzheimer's disease and can aggregate to form amyloid fibrils. However, the early aggregation mechanism is still unsolved. Here, multiple long-term molecular dynamics simulations combining with Markov state model were used to probe the early oligomerization mechanism of Aβ_16-22 peptides. The identified dimeric form adopted either globular random-coil or extended β-strand like conformations. The observed dimers of these variants shared many overall conformational characteristics but differed in several aspects at detailed level. In all cases, the most common type of secondary structure was intermolecular antiparallel β-sheets. The inter-state transitions were very frequent ranges from few to hundred nanoseconds. More strikingly, those states which contain fraction of β secondary structure and significant amount of extended coiled structures, therefore exposed to the solvent, were majorly participated in aggregation. The assembly of low-energy dimers, in which the peptides form antiparallel β sheets, occurred by multiple pathways with the formation of an obligatory intermediates. We proposed that these states might facilitate the Aβ_16-22 aggregation through a significant component of the conformational selection mechanism, because they might increase the aggregates population by promoting the inter-chain hydrophobic and the hydrogen bond contacts. The formation of early stage antiparallel β sheet structures is critical for oligomerization, and at the same time provided a flat geometry to seed the ordered β-strand packing of the fibrils. Our findings hint at reorganization of this part of the molecule as a potentially critical step in Aβ aggregation and will insight into early oligomerization for large β amyloids.

Interpretable artificial intelligence and exascale molecular dynamics simulations to reveal kinetics: Applications to Alzheimer's disease

The rapid increase in computing power, especially with the integration of graphics processing units, has dramatically increased the capabilities of molecular dynamics simulations. To date, these capabilities extend from running very long simulations (tens to hundreds of microseconds) to thousands of short simulations. However, the expansive data generated in these simulations must be made interpretable not only by the investigator who performs them but also by others as well. Here, we demonstrate how integrating learning techniques, such as artificial intelligence, machine learning, and neural networks, into analysis pipelines can reveal the kinetics of Alzheimer's disease (AD) protein aggregation. We review select AD targets, describe current simulation methods, and introduce learning concepts and their application in AD, highlighting limitations and potential solutions.

Progress in deep Markov state modeling: Coarse graining and experimental data restraints

Recent advances in deep learning frameworks have established valuable tools for analyzing the long-timescale behavior of complex systems, such as proteins. In particular, the inclusion of physical constraints, e.g., time-reversibility, was a crucial step to make the methods applicable to biophysical systems. Furthermore, we advance the method by incorporating experimental observables into the model estimation showing that biases in simulation data can be compensated for. We further develop a new neural network layer in order to build a hierarchical model allowing for different levels of details to be studied. Finally, we propose an attention mechanism, which highlights important residues for the classification into different states. We demonstrate the new methodology on an ultralong molecular dynamics simulation of the Villin headpiece miniprotein.

Molecular dynamics study of conformation transition from helix to sheet of Aβ42 peptide

Aβ42 peptides can form helix and sheet structure under different conditions. The conformational conversion is closely associated with Aβ peptides aggregation and their neurotoxicity. But the transition from helix to sheet is not be clearly understood. In this study we performed microsecond timescale MD simulations of Aβ42 peptide to investigate the conformation transition from α-helix to β-sheet. Markov state model (MSM) was built to facilitate identification of crucial intermediate states and possible transition pathway. Based on the analysis, we found that the region Y10-A21 in the middle of Aβ42 peptide plays an initial role in this transition. MSM model revealed that the collapse of helical structure in this region might trigger the formation of sheet structure. Moreover, we further simulated the aggregation of Aβ42 peptides with different conformations. We found that the Aβ42 peptides forming sheet structure have higher aggregation potential compared with peptides with helix structure. These results demonstrate that we can prevent the aggregation of Aβ42 peptides by stabilizing the helix structure in the region of Y10-A21. In addition, this study provides new insight into better understanding the conformational transition and aggregation of Aβ42 peptides.

Nonparametric Analysis of Nonequilibrium Simulations

We extend the nonparametric framework of reaction coordinate optimization to nonequilibrium ensembles of (short) trajectories. For example, we show how, starting from such an ensemble, one can obtain an equilibrium free-energy profile along the committor, which can be used to determine important properties of the dynamics exactly. A new adaptive sampling approach, the transition-state ensemble enrichment, is suggested, which samples the configuration space by "growing" committor segments toward each other starting from the boundary states. This framework is suggested as a general tool, alternative to the Markov state models, for a rigorous and accurate analysis of simulations of large biomolecular systems, as it has the following attractive properties. It is immune to the curse of dimensionality, does not require system-specific information, can approximate arbitrary reaction coordinates with high accuracy, and has sensitive and rigorous criteria to test optimality and convergence. The approaches are illustrated on a 50-dimensional model system and a realistic protein folding trajectory.

Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

Thermodynamics and kinetics of the amyloid-β peptide revealed by Markov state models based on MD data in agreement with experiment

The amlyoid-β peptide (Aβ) is closely linked to the development of Alzheimer's disease. Molecular dynamics (MD) simulations have become an indispensable tool for studying the behavior of this peptide at the atomistic level. General key aspects of MD simulations are the force field used for modeling the peptide and its environment, which is important for accurate modeling of the system of interest, and the length of the simulations, which determines whether or not equilibrium is reached. In this study we address these points by analyzing 30-μs MD simulations acquired for Aβ40 using seven different force fields. We assess the convergence of these simulations based on the convergence of various structural properties and of NMR and fluorescence spectroscopic observables. Moreover, we calculate Markov state models for the different MD simulations, which provide an unprecedented view of the thermodynamics and kinetics of the amyloid-β peptide. This further allows us to provide answers for pertinent questions, like: which force fields are suitable for modeling Aβ? (a99SB-UCB and a99SB-ILDN/TIP4P-D); what does Aβ peptide really look like? (mostly extended and disordered) and; how long does it take MD simulations of Aβ to attain equilibrium? (at least 20-30 μs). We believe the analyses presented in this study will provide a useful reference guide for important questions relating to the structure and dynamics of Aβ in particular, and by extension other similar disordered proteins.

The genetic landscape for amyloid beta fibril nucleation accurately discriminates familial Alzheimer's disease mutations

Plaques of the amyloid beta (Aß) peptide are a pathological hallmark of Alzheimer's disease (AD), the most common form of dementia. Mutations in Aß also cause familial forms of AD (fAD). Here, we use deep mutational scanning to quantify the effects of >14,000 mutations on the aggregation of Aß. The resulting genetic landscape reveals mechanistic insights into fibril nucleation, including the importance of charge and gatekeeper residues in the disordered region outside of the amyloid core in preventing nucleation. Strikingly, unlike computational predictors and previous measurements, the empirical nucleation scores accurately identify all known dominant fAD mutations in Aß, genetically validating that the mechanism of nucleation in a cell-based assay is likely to be very similar to the mechanism that causes the human disease. These results provide the first comprehensive atlas of how mutations alter the formation of any amyloid fibril and a resource for the interpretation of genetic variation in Aß.

Molecular simulations of IDPs: From ensemble generation to IDP interactions leading to disorder-to-order transitions

Intrinsically disordered proteins (IDPs) lack a well-defined three-dimensional structure but do exhibit some dynamical and structural ordering. The structural plasticity of IDPs indicates that entropy-driven motions are crucial for their function. Many IDPs undergo function-related disorder-to-order transitions upon by their interaction with specific binding partners. Approaches that are based on both experimental and theoretical tools enable the biophysical characterization of IDPs. Molecular simulations provide insights into IDP structural ensembles and disorder-to-order transition mechanisms. However, such studies depend strongly on the chosen force field parameters and simulation techniques. In this chapter, we provide an overview of IDP characteristics, review all-atom force fields recently developed for IDPs, and present molecular dynamics-based simulation methods that allow IDP ensemble generation as well as the characterization of disorder-to-order transitions. In particular, we introduce metadynamics, replica exchange molecular dynamics simulations, and also kinetic models resulting from Markov State modeling, and provide various examples for the successful application of these simulation methods to IDPs.