MSMBuilder: Statistical Models for Biomolecular Dynamics

The αC-β4 loop controls the allosteric cooperativity between nucleotide and substrate in the catalytic subunit of protein kinase A

Allosteric cooperativity between ATP and substrates is a prominent characteristic of the cAMP-dependent catalytic subunit of protein kinase A (PKA-C). This long-range synergistic action is involved in substrate recognition and fidelity, and it may also regulate PKA's association with regulatory subunits and other binding partners. To date, a complete understanding of this intramolecular mechanism is still lacking. Here, we integrated NMR(Nuclear Magnetic Resonance)-restrained molecular dynamics simulations and a Markov State Model to characterize the free energy landscape and conformational transitions of PKA-C. We found that the apoenzyme populates a broad free energy basin featuring a conformational ensemble of the active state of PKA-C (ground state) and other basins with lower populations (excited states). The first excited state corresponds to a previously characterized inactive state of PKA-C with the αC helix swinging outward. The second excited state displays a disrupted hydrophobic packing around the regulatory (R) spine, with a flipped configuration of the F100 and F102 residues at the αC-β4 loop. We validated the second excited state by analyzing the F100A mutant of PKA-C, assessing its structural response to ATP and substrate binding. While PKA-CF100A preserves its catalytic efficiency with Kemptide, this mutation rearranges the αC-β4 loop conformation, interrupting the coupling of the two lobes and abolishing the allosteric binding cooperativity. The highly conserved αC-β4 loop emerges as a pivotal element to control the synergistic binding of nucleotide and substrate, explaining how mutations or insertions near or within this motif affect the function and drug sensitivity in homologous kinases.

Markov State Models Reveal How Folding Kinetics Influence Absorption Spectra of Foldamers

Self-assembly of platinum(II) complex foldamers is an essential approach to fabricate advanced luminescent materials. However, a comprehensive understanding of folding kinetics and their absorption spectra remains elusive. By constructing Markov state models (MSMs) from large-scale molecular dynamics simulations, we reveal that two largely similar dinuclear alknylplatinum(II) terpyridine foldamers, Pt-PEG and Pt-PE with slightly different bridges, exhibit distinctive folding kinetics. Particularly, Pt-PEG bears bridge-dominant, plane-dominant, and cooperative pathways, while Pt-PE only prefers the plane-dominant pathway. Such preference originates from their difference in intrabridge electrostatic interactions, leading to contrastive distributions of metastable states. We also found that the bridge-dominant pathway for Pt-PEG becomes more favorable when lowering the temperature. Interestingly, based on the comprehensive conformation ensembles from our MSMs, we reveal the conformation-dependent absorption spectra of Pt-PEG and Pt-PE. Our theoretical spectra not only align with experimental results but also reveal the contributions of diverse conformations to the overall absorption bands explicitly, facilitating the rational design of stimuli-responsive smart luminescent molecules.

Information Bottleneck Approach for Markov Model Construction

Markov state models (MSMs) have proven valuable in studying the dynamics of protein conformational changes via statistical analysis of molecular dynamics simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time necessitates defining states that circumvent significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process effectively coarse-grains time and space, integrating out rapid motions within metastable states. Thus, MSMs possess a multiresolution nature, where the granularity of states can be adjusted according to the time-resolution, offering flexibility in capturing system dynamics. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), a framework that unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of the VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multiresolution Markovian models. Through applications to well-validated mini-proteins, SPIB showcases unique advantages compared to competing methods. It autonomously and self-consistently adjusts the number of metastable states based on a specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. This contrasts with existing VAMP-based methods, which often emphasize slow dynamics at the expense of incorporating numerous sparsely populated states. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. With these benefits, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction.

Computational Analysis of Activation of Dimerized Epidermal Growth Factor Receptor Kinase Using the String Method and Markov State Model

Epidermal growth factor receptor (EGFR) activation is accompanied by dimerization. During the activation of the intracellular kinase domain, two EGFR kinases form an asymmetric dimer, and one side of the dimer (receiver) is activated. Using the string method and Markov state model (MSM), we performed a computational analysis of the structural changes in the activation of the EGFR dimer in this study. The string method reveals the minimum free-energy pathway (MFEP) from the inactive to active structure. The MSM was constructed from numerous trajectories of molecular dynamics simulations around the MFEP, which revealed the free-energy map of structural changes. In the activation of the receiver kinase, the unfolding of the activation loop (A-loop) is followed by the rearrangement of the C-helix, as observed in other kinases. However, unlike other kinases, the free-energy map of EGFR at the asymmetric dimer showed that the active state yielded the highest stability and revealed how interactions at the dimer interface induced receiver activation. As the H-helix of the activator approaches the C-helix of the receiver during activation, the A-loop unfolds. Subsequently, L782 of the receiver enters the pocket between the G- and H-helices of the activator, leading to a rearrangement of the hydrophobic residues around L782 of the receiver, which constitutes a structural rearrangement of the C-helix of the receiver from an outward to an inner position. The MSM analysis revealed long-time scale trajectories via kinetic Monte Carlo.

Early Aggregation Mechanism of SOD128-38 Based on Force Field Parameter of 5-Cyano-Tryptophan

The aggregation of superoxide dismutase 1 (SOD1) results in amyloid deposition and is involved in familial amyotrophic lateral sclerosis, a fatal motor neuron disease. There have been extensive studies of its aggregation mechanism. Noncanonical amino acid 5-cyano-tryptophan (5-CN-Trp), which has been incorporated into the amyloid segments of SOD1 as infrared probes to increase the structural sensitivity of IR spectroscopy, is found to accelerate the overall aggregation rate and potentially modulate the aggregation process. Despite these observations, the underlying mechanism remains elusive. Here, we optimized the force field parameters of 5-CN-Trp and then used molecular dynamics simulation along with the Markov state model on the SOD128-38 dimer to explore the kinetics of key intermediates in the presence and absence of 5-CN-Trp. Our findings indicate a significantly increased probability of protein aggregate formation in 5CN-Trp-modified ensembles compared to wildtype. Dimeric β-sheets of different natures were observed exclusively in the 5CN-Trp-modified peptides, contrasting with wildtype simulations. Free-energy calculations and detailed analyses of the dimer structure revealed augmented interstrand interactions attributed to 5-CN-Trp, which contributed more to peptide affinity than any other residues. These results explored the key events critical for the early nucleation of amyloid-prone proteins and also shed light on the practice of using noncanonical derivatives to study the aggregation mechanism.

Energetics of substrate transport in proton-dependent oligopeptide transporters

The PepT So transporter mediates the transport of peptides across biological membranes. Despite advancements in structural biology, including cryogenic electron microscopy structures resolving PepT So in different states, the molecular basis of peptide recognition and transport by PepT So is not fully elucidated. In this study, we employed molecular dynamics simulations, Markov State Models (MSMs), and Transition Path Theory (TPT) to investigate the transport mechanism of an alanine-alanine peptide (Ala-Ala) through the PepT So transporter. Our simulations revealed conformational changes and key intermediate states involved in peptide translocation. We observed that the presence of the Ala-Ala peptide substrate lowers the free energy barriers associated with transition to the inward-facing state. Furthermore, we elucidated the proton transport model and analyzed the pharmacophore features of intermediate states, providing insights for rational drug design. These findings highlight the significance of substrate binding in modulating the conformational dynamics of PepT So and identify critical residues that facilitate transport.

Functional protein dynamics in a crystal

Proteins are molecular machines and to understand how they work, we need to understand how they move. New pump-probe time-resolved X-ray diffraction methods open up ways to initiate and observe protein motions with atomistic detail in crystals on biologically relevant timescales. However, practical limitations of these experiments demands parallel development of effective molecular dynamics approaches to accelerate progress and extract meaning. Here, we establish robust and accurate methods for simulating dynamics in protein crystals, a nontrivial process requiring careful attention to equilibration, environmental composition, and choice of force fields. With more than seven milliseconds of sampling of a single chain, we identify critical factors controlling agreement between simulation and experiments and show that simulated motions recapitulate ligand-induced conformational changes. This work enables a virtuous cycle between simulation and experiments for visualizing and understanding the basic functional motions of proteins.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Understanding the Fast-Triggering Unfolding Dynamics of FK-11 upon Photoexcitation of Azobenzene

Photoswitchable molecules can control the activity and functions of biomolecules by triggering conformational changes. However, it is still challenging to fully understand such fast-triggering conformational evolution from nonequilibrium to equilibrium distribution at the molecular level. Herein, we successfully simulated the unfolding of the FK-11 peptide upon the photoinduced trans-to-cis isomerization of azobenzene based on the Markov state model. We found that the ensemble of FK-11 contains five conformational states, constituting two unfolding pathways. More intriguingly, we observed the microsecond-scale conformational propagation of the FK-11 peptide from the fully folded state to the equilibrium populations of the five states. The computed CD spectra match well with the experimental data, validating our simulation method. Overall, our study not only offers a protocol to study the photoisomerization-induced conformational changes of enzymes but also could orientate the rational design of a photoswitchable molecule to manipulate biological functions.

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

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

Functional Protein Dynamics in a Crystal

Proteins are molecular machines and to understand how they work, we need to understand how they move. New pump-probe time-resolved X-ray diffraction methods open up ways to initiate and observe protein motions with atomistic detail in crystals on biologically relevant timescales. However, practical limitations of these experiments demands parallel development of effective molecular dynamics approaches to accelerate progress and extract meaning. Here, we establish robust and accurate methods for simulating dynamics in protein crystals, a nontrivial process requiring careful attention to equilibration, environmental composition, and choice of force fields. With more than seven milliseconds of sampling of a single chain, we identify critical factors controlling agreement between simulation and experiments and show that simulated motions recapitulate ligand-induced conformational changes. This work enables a virtuous cycle between simulation and experiments for visualizing and understanding the basic functional motions of proteins.

Cooperative Membrane Binding of HIV-1 Matrix Proteins

The HIV-1 assembly process begins with a newly synthesized Gag polyprotein being targeted to the inner leaflet of the plasma membrane of the infected cells to form immature viral particles. Gag-membrane interactions are mediated through the myristoylated (Myr) N-terminal matrix (MA) domain of Gag, which eventually multimerize on the membrane to form trimers and higher order oligomers. The study of the structure and dynamics of peripheral membrane proteins like MA has been challenging for both experimental and computational studies due to the complex transient dynamics of protein-membrane interactions. Although the roles of anionic phospholipids (PIP2, PS) and the Myr group in the membrane targeting and stable membrane binding of MA are now well-established, the cooperative interactions between the MA monomers and MA-membrane remain elusive in the context of viral assembly and release. Our present study focuses on the membrane binding dynamics of a higher order oligomeric structure of MA protein (a dimer of trimers), which has not been explored before. Employing time-lagged independent component analysis (tICA) to our microsecond-long trajectories, we investigate conformational changes of the matrix protein induced by membrane binding. Interestingly, the Myr switch of an MA monomer correlates with the conformational switch of adjacent monomers in the same trimer. Together, our findings suggest complex protein dynamics during the formation of the immature HIV-1 lattice; while MA trimerization facilitates Myr insertion, MA trimer-trimer interactions in the immature lattice can hinder the same.

Analyzing Molecular Dynamics Trajectories Thermodynamically through Artificial Intelligence

Molecular dynamics simulations produce trajectories that correspond to vast amounts of structure when exploring biochemical processes. Extracting valuable information, e.g., important intermediate states and collective variables (CVs) that describe the major movement modes, from molecular trajectories to understand the underlying mechanisms of biological processes presents a significant challenge. To achieve this goal, we introduce a deep learning approach, coined DIKI (deep identification of key intermediates), to determine low-dimensional CVs distinguishing key intermediate conformations without a-priori assumptions. DIKI dynamically plans the distribution of latent space and groups together similar conformations within the same cluster. Moreover, by incorporating two user-defined parameters, namely, coarse focus knob and fine focus knob, to help identify conformations with low free energy and differentiate the subtle distinctions among these conformations, resolution-tunable clustering was achieved. Furthermore, the integration of DIKI with a path-finding algorithm contributes to the identification of crucial intermediates along the lowest free-energy pathway. We postulate that DIKI is a robust and flexible tool that can find widespread applications in the analysis of complex biochemical processes.

Revealing the conformational dynamics of UDP-GlcNAc recognition by O-GlcNAc transferase via Markov state model

The O-linked N-acetylglucosamine (O-GlcNAc) glycosylation is a critical post-translational modification and closely linked to various physiological and pathological conditions. The O-GlcNAc transferase (OGT) functions as the only glycosyltransferase of O-GlcNAc glycosylation by transferring GlcNAc from UDP-GlcNAc to serine or threonine residues on protein substrates. The interaction mode of UDP-GlcNAc against OGT has been preliminarily revealed by the crystal structures, yet an atomic-level comprehension for the conformational dynamics of the recognition process remains elusive. Here, we construct the Markov state model based on extensive all-atom molecular dynamics (MD) simulations with an aggregated simulation time of ∼9 μs, and reveal that the UDP-GlcNAc recognition process by OGT encompasses four key metastable states, occurring within an estimated timescale of ∼10 μs. During UDP-GlcNAc recognition process, we find the pyrophosphate moiety (P2O52-) initially anchors to the active pocket via salt bridge and hydrogen bonds, facilitating subsequent binding of the uridine and GlcNAc moieties. Furthermore, the functional roles of K842 involved in the salt bridge with P2O52- were evaluated through extra mutant MD simulations. Overall, our study provides valuable insights into the UDP-GlcNAc recognition mechanism by OGT, which could further aid in mechanistic studies of O-GlcNAc glycosylation and drug development targeting on OGT.

Markov State Model of Solvent Features Reveals Water Dynamics in Protein-Peptide Binding

In this work, we investigate the role of solvent in the binding reaction of the p53 transactivation domain (TAD) peptide to its receptor MDM2. Previously, our group generated 831 μs of explicit-solvent aggregate molecular simulation trajectory data for the MDM2-p53 peptide binding reaction using large-scale distributed computing and subsequently built a Markov State Model (MSM) of the binding reaction (Zhou et al. 2017). Here, we perform a tICA analysis and construct an MSM with similar hyperparameters while using only solvent-based structural features. We find a remarkably similar landscape but accelerated implied timescales for the slowest motions. The solvent shells contributing most to the first tICA eigenvector are those centered on Lys24 and Thr18 of the p53 TAD peptide in the range of 3-6 Å. Important solvent shells were visualized to reveal solvation and desolvation transitions along the peptide-protein binding trajectories. Our results provide a solvent-centric view of the hydrophobic effect in action for a realistic peptide-protein binding scenario.

Resolving binding pathways and solvation thermodynamics of plant hormone receptors

Plant hormones are small molecules that regulate plant growth, development, and responses to biotic and abiotic stresses. They are specifically recognized by the binding site of their receptors. In this work, we resolved the binding pathways for eight classes of phytohormones (auxin, jasmonate, gibberellin, strigolactone, brassinosteroid, cytokinin, salicylic acid, and abscisic acid) to their canonical receptors using extensive molecular dynamics simulations. Furthermore, we investigated the role of water displacement and reorganization at the binding site of the plant receptors through inhomogeneous solvation theory. Our findings predict that displacement of water molecules by phytohormones contributes to free energy of binding via entropy gain and is associated with significant free energy barriers for most systems analyzed. Also, our results indicate that displacement of unfavorable water molecules in the binding site can be exploited in rational agrochemical design. Overall, this study uncovers the mechanism of ligand binding and the role of water molecules in plant hormone perception, which creates new avenues for agrochemical design to target plant growth and development.

Unsupervised and supervised AI on molecular dynamics simulations reveals complex characteristics of HLA-A2-peptide immunogenicity

Immunologic recognition of peptide antigens bound to class I major histocompatibility complex (MHC) molecules is essential to both novel immunotherapeutic development and human health at large. Current methods for predicting antigen peptide immunogenicity rely primarily on simple sequence representations, which allow for some understanding of immunogenic features but provide inadequate consideration of the full scale of molecular mechanisms tied to peptide recognition. We here characterize contributions that unsupervised and supervised artificial intelligence (AI) methods can make toward understanding and predicting MHC(HLA-A2)-peptide complex immunogenicity when applied to large ensembles of molecular dynamics simulations. We first show that an unsupervised AI method allows us to identify subtle features that drive immunogenicity differences between a cancer neoantigen and its wild-type peptide counterpart. Next, we demonstrate that a supervised AI method for class I MHC(HLA-A2)-peptide complex classification significantly outperforms a sequence model on small datasets corrected for trivial sequence correlations. Furthermore, we show that both unsupervised and supervised approaches reveal determinants of immunogenicity based on time-dependent molecular fluctuations and anchor position dynamics outside the MHC binding groove. We discuss implications of these structural and dynamic immunogenicity correlates for the induction of T cell responses and therapeutic T cell receptor design.

Cooperative Membrane Binding of HIV-1 Matrix Proteins

The HIV-1 assembly process begins with a newly synthesized Gag polyprotein being targeted to the inner leaflet of the plasma membrane of the infected cells to form immature viral particles. Gag-membrane interactions are mediated through the myristoylated(Myr) N-terminal matrix (MA) domain of Gag which eventually multimerize on the membrane to form trimers and higher-order oligomers. The study of the structure and dynamics of peripheral membrane proteins like MA has been challenging for both experimental and computational studies due to the complex dynamics of protein-membrane interactions. Although the roles of anionic phospholipids (PIP2, PS) and the Myr group in the membrane targeting and stable membrane binding of MA are now well-established, the cooperative interactions between MA monomers and MA-membrane still remain elusive. Our present study focuses on the membrane binding dynamics of a higher-order oligomeric structure of MA protein (a dimer of trimers), which has not been explored before. Employing time-lagged independent component analysis (tICA) to our microsecond-long trajectories, we investigate conformational changes of the matrix protein induced by membrane binding. Interestingly, the Myr switch of a MA monomer correlates with the conformational switch of adjacent monomers in the same trimer. Together, our findings suggest that MA trimerization facilitates Myr insertion, but MA trimer-trimer interactions in the lattice of immature HIV-1 particles can hinder the same. Additionally, local lipid density patterns of different lipid species provide a signature of the initial stage of lipid-domain formation upon membrane binding of the protein complex.

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AIMD-Chig: Exploring the conformational space of a 166-atom protein Chignolin with ab initio molecular dynamics

Molecular dynamics (MD) simulations have revolutionized the modeling of biomolecular conformations and provided unprecedented insight into molecular interactions. Due to the prohibitive computational overheads of ab initio simulation for large biomolecules, dynamic modeling for proteins is generally constrained on force field with molecular mechanics, which suffers from low accuracy as well as ignores the electronic effects. Here, we report AIMD-Chig, an MD dataset including 2 million conformations of 166-atom protein Chignolin sampled at the density functional theory (DFT) level with 7,763,146 CPU hours. 10,000 conformations were initialized covering the whole conformational space of Chignolin, including folded, unfolded, and metastable states. Ab initio simulations were driven by M06-2X/6-31 G* with a Berendsen thermostat at 340 K. We reported coordinates, energies, and forces for each conformation. AIMD-Chig brings the DFT level conformational space exploration from small organic molecules to real-world proteins. It can serve as the benchmark for developing machine learning potentials for proteins and facilitate the exploration of protein dynamics with ab initio accuracy.

Open-Source Machine Learning in Computational Chemistry

The field of computational chemistry has seen a significant increase in the integration of machine learning concepts and algorithms. In this Perspective, we surveyed 179 open-source software projects, with corresponding peer-reviewed papers published within the last 5 years, to better understand the topics within the field being investigated by machine learning approaches. For each project, we provide a short description, the link to the code, the accompanying license type, and whether the training data and resulting models are made publicly available. Based on those deposited in GitHub repositories, the most popular employed Python libraries are identified. We hope that this survey will serve as a resource to learn about machine learning or specific architectures thereof by identifying accessible codes with accompanying papers on a topic basis. To this end, we also include computational chemistry open-source software for generating training data and fundamental Python libraries for machine learning. Based on our observations and considering the three pillars of collaborative machine learning work, open data, open source (code), and open models, we provide some suggestions to the community.

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

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

Molecular recognition of two endogenous hormones by the human parathyroid hormone receptor-1

Parathyroid hormone (PTH) and PTH-related peptide (PTHrP) are two endogenous hormones recognized by PTH receptor-1 (PTH1R), a member of class B G protein- coupled receptors (GPCRs). Both PTH and PTHrP analogs including teriparatide and abaloparatide are approved drugs for osteoporosis, but they exhibit distinct pharmacology. Here we report two cryo-EM structures of human PTH1R bound to PTH and PTHrP in the G protein-bound state at resolutions of 2.62 Å and 3.25 Å, respectively. Detailed analysis of these structures uncovers both common and unique features for the agonism of PTH and PTHrP. Molecular dynamics (MD) simulation together with site-directed mutagenesis studies reveal the molecular basis of endogenous hormones recognition specificity and selectivity to PTH1R. These results provide a rational template for the clinical use of PTH and PTHrP analogs as an anabolic therapy for osteoporosis and other disorders.

Markov State Models and Perturbation-Based Approaches Reveal Distinct Dynamic Signatures and Hidden Allosteric Pockets in the Emerging SARS-Cov-2 Spike Omicron Variants Complexes with the Host Receptor: The Interplay of Dynamics and Convergent Evolution Modulates Allostery and Functional Mechanisms

The new generation of SARS-CoV-2 Omicron variants displayed a significant growth advantage and the increased viral fitness by acquiring convergent mutations, suggesting that the immune pressure can promote convergent evolution leading to the sudden acceleration of SARS-CoV-2 evolution. In the current study, we combined structural modeling, extensive microsecond MD simulations and Markov state models to characterize conformational landscapes and identify specific dynamic signatures of the SARS-CoV-2 spike complexes with the host receptor ACE2 for the recently emerged highly transmissible XBB.1, XBB.1.5, BQ.1, and BQ.1.1 Omicron variants. Microsecond simulations and Markovian modeling provided a detailed characterization of the conformational landscapes and revealed the increased thermodynamic stabilization of the XBB.1.5 subvariant which is contrasted to more dynamic BQ.1 and BQ.1.1 subvariants. Despite considerable structural similarities, Omicron mutations can induce unique dynamic signatures and specific distributions of conformational states. The results suggested that variant-specific changes of conformational mobility in the functional interfacial loops of the spike receptor binding domain can be fine-tuned through cross-talk between convergent mutations thereby providing an evolutionary path for modulation of immune escape. By combining atomistic simulations and Markovian modeling analysis with perturbation-based approaches, we determined important complementary roles of convergent mutation sites as effectors and receivers of allosteric signaling involved in modulating conformational plasticity at the binding interface and regulating allosteric responses. This study also characterized the dynamics-induced evolution of allosteric pockets in the Omicron complexes that revealed hidden allosteric pockets and suggested that convergent mutation sites could control evolution and distribution of allosteric pockets through modulation of conformational plasticity in the flexible adaptable regions. Through integrative computational approaches, this investigation provides a systematic analysis and comparison of the effects of Omicron subvariants on conformational dynamics and allosteric signaling in the complexes with the ACE2 receptor.

For Table of Contents Use Only

Novel Allosteric Effectors Targeting Human Transcription Factor TEAD

The Hippo pathway is an evolutionary conserved signaling network involved in several cellular regulatory processes. Dephosphorylation and overexpression of Yes-associated proteins (YAPs) in the Hippo-off state are common in several types of solid tumors. YAP overexpression results in its nuclear translocation and interaction with transcriptional enhanced associate domain 1-4 (TEAD1-4) transcription factors. Covalent and non-covalent inhibitors have been developed to target several interaction sites between TEAD and YAP. The most targeted and effective site for these developed inhibitors is the palmitate-binding pocket in the TEAD1-4 proteins. Screening of a DNA-encoded library against the TEAD central pocket was performed experimentally to identify six new allosteric inhibitors. Inspired by the structure of the TED-347 inhibitor, chemical modification was performed on the original inhibitors by replacing secondary methyl amide with a chloromethyl ketone moiety. Various computational tools, including molecular dynamics, free energy perturbation, and Markov state model analysis, were employed to study the effect of ligand binding on the protein conformational space. Four of the six modified ligands were associated with enhanced allosteric communication between the TEAD4 and YAP1 domains indicated by the relative free energy perturbation to original molecules. Phe229, Thr332, Ile374, and Ile395 residues were revealed to be essential for the effective binding of the inhibitors.

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations

The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.

DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling

Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.

Phosphorylation Regulation Mechanism of β2 Integrin for the Binding of Filamin Revealed by Markov State Model

Leukocyte adhesion deficiency-1 (LAD-1) disorder is a severe immunodeficiency syndrome caused by deficiency or mutation of β2 integrin. The phosphorylation on threonine 758 of β2 integrin acts as a molecular switch inhibiting the binding of filamin. However, the switch mechanism of site-specific phosphorylation at the atom level is still poorly understood. To resolve the regulation mechanism, all-atom molecular dynamics simulation and Markov state model were used to study the dynamic regulation pathway of phosphorylation. Wild type system possessed lower binding free energy and fewer number of states than the phosphorylated system. Both systems underwent local disorder-to-order conformation conversion when achieving steady states. To reach steady states, wild type adopted less number of transition paths/shortest path according to the transition path theory than the phosphorylated system. The underlying phosphorylated regulation pathway was from P1 to P0 and then P4 state, and the main driving force should be hydrogen bond and hydrophobic interaction disturbing the secondary structure of phosphorylated states. These studies will shed light on the pathogenesis of LAD-1 disease and lay a foundation for drug development.

Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

Dynamic conformational states of apo, ATP and cabozantinib bound TAM kinases to differentiate active-inactive kinetic models

The dynamically active and inactive conformations of kinases play a crucial role in the activation of intracellular downstream signaling pathways. The all-atom molecular dynamics (MD) simulations at microsecond (µs) timescale and longer provide robust insights into the structural details of conformational alterations in kinases that contribute to their cellular metabolic activities and signaling pathways. Tyro3, Axl and Mer (TAM) receptor tyrosine kinases (RTKs) are overexpressed in several types of human cancers. Cabozantinib, a small molecule inhibitor constrains the activity of TAM kinases at nanomolar concentrations. The apo, complexes of ATP (active state) and cabozantinib (active and inactive states) with TAM RTKs were studied by 1 µs MD simulations followed by trajectory analyses. The dynamic mechanistic pathways intrinsic to the kinase activity and protein conformational landscape in the cabozantinib bound TAM kinases are revealed due to the alterations in the P-loop, α-helix and activation loop that result in breaking the regulatory (R) and catalytic (C) spines, while the active states of ATP bound TAM kinases are retained. The co-existence of dynamical states when bound to cabozantinib was observed and the long-lived kinetic transition states of distinct active and inactive structural models were deciphered from MD simulation trajectories that have not been revealed so far.Communicated by Ramaswamy H. Sarma.

Probing conformational landscapes and mechanisms of allosteric communication in the functional states of the ABL kinase domain using multiscale simulations and network-based mutational profiling of allosteric residue potentials

In the current study, multiscale simulation approaches and dynamic network methods are employed to examine the dynamic and energetic details of conformational landscapes and allosteric interactions in the ABL kinase domain that determine the kinase functions. Using a plethora of synergistic computational approaches, we elucidate how conformational transitions between the active and inactive ABL states can employ allosteric regulatory switches to modulate intramolecular communication networks between the ATP site, the substrate binding region, and the allosteric binding pocket. A perturbation-based network approach that implements mutational profiling of allosteric residue propensities and communications in the ABL states is proposed. Consistent with biophysical experiments, the results reveal functionally significant shifts of the allosteric interaction networks in which preferential communication paths between the ATP binding site and substrate regions in the active ABL state become suppressed in the closed inactive ABL form, which in turn features favorable allosteric coupling between the ATP site and the allosteric binding pocket. By integrating the results of atomistic simulations with dimensionality reduction methods and Markov state models, we analyze the mechanistic role of macrostates and characterize kinetic transitions between the ABL conformational states. Using network-based mutational scanning of allosteric residue propensities, this study provides a comprehensive computational analysis of long-range communications in the ABL kinase domain and identifies conserved regulatory hotspots that modulate kinase activity and allosteric crosstalk between the allosteric pocket, ATP binding site, and substrate binding regions.

DeepCV: A Deep Learning Framework for Blind Search of Collective Variables in Expanded Configurational Space

We present Deep learning for Collective Variables (DeepCV), a computer code that provides an efficient and customizable implementation of the deep autoencoder neural network (DAENN) algorithm that has been developed in our group for computing collective variables (CVs) and can be used with enhanced sampling methods to reconstruct free energy surfaces of chemical reactions. DeepCV can be used to conveniently calculate molecular features, train models, generate CVs, validate rare events from sampling, and analyze a trajectory for chemical reactions of interest. We use DeepCV in an example study of the conformational transition of cyclohexene, where metadynamics simulations are performed using DAENN-generated CVs. The results show that the adopted CVs give free energies in line with those obtained by previously developed CVs and experimental results. DeepCV is open-source software written in Python/C++ object-oriented languages, based on the TensorFlow framework and distributed free of charge for noncommercial purposes, which can be incorporated into general molecular dynamics software. DeepCV also comes with several additional tools, i.e., an application program interface (API), documentation, and tutorials.

Stochastic Lag Time Parameterization for Markov State Models of Protein Dynamics

Markov state models (MSMs) play a key role in studying protein conformational dynamics. A sliding count window with a fixed lag time is widely used to sample sub-trajectories for transition counting and MSM construction. However, sub-trajectories sampled with a fixed lag time may not perform well under different selections of lag time, which requires strong prior practice and leads to less robust estimation. To alleviate it, we propose a novel stochastic method from a Poisson process to generate perturbative lag time for sub-trajectory sampling and utilize it to construct a Markov chain. Comprehensive evaluations on the double-well system, WW domain, BPTI, and RBD-ACE2 complex of SARS-CoV-2 reveal that our algorithm significantly increases the robustness and power of a constructed MSM without disturbing the Markovian properties. Furthermore, the superiority of our algorithm is amplified for slow dynamic modes in complex biological processes.

Deep learning to decompose macromolecules into independent Markovian domains

The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data.

Markov state modelling reveals heterogeneous drug-inhibition mechanism of Calmodulin

Calmodulin (CaM) is a calcium sensor which binds and regulates a wide range of target-proteins. This implicitly enables the concentration of calcium to influence many downstream physiological responses, including muscle contraction, learning and depression. The antipsychotic drug trifluoperazine (TFP) is a known CaM inhibitor. By binding to various sites, TFP prevents CaM from associating to target-proteins. However, the molecular and state-dependent mechanisms behind CaM inhibition by drugs such as TFP are largely unknown. Here, we build a Markov state model (MSM) from adaptively sampled molecular dynamics simulations and reveal the structural and dynamical features behind the inhibitory mechanism of TFP-binding to the C-terminal domain of CaM. We specifically identify three major TFP binding-modes from the MSM macrostates, and distinguish their effect on CaM conformation by using a systematic analysis protocol based on biophysical descriptors and tools from machine learning. The results show that depending on the binding orientation, TFP effectively stabilizes features of the calcium-unbound CaM, either affecting the CaM hydrophobic binding pocket, the calcium binding sites or the secondary structure content in the bound domain. The conclusions drawn from this work may in the future serve to formulate a complete model of pharmacological modulation of CaM, which furthers our understanding of how these drugs affect signaling pathways as well as associated diseases.

Calmodulin (CaM) is a calcium-sensing protein which makes other proteins dependent on the surrounding calcium concentration by binding to these proteins. Such protein-protein interactions with CaM are vital for calcium to control many physiological pathways within the cell. The antipsychotic drug trifluoperazine (TFP) inhibits CaM’s ability to bind and regulate other proteins. Here, we use molecular dynamics simulations together with Markov state modeling and machine learning to understand the structural and dynamical features by which TFP bound to the one domain of CaM prevents association to other proteins. We find that TFP encourages CaM to adopt a conformation that is like the one stabilized in absence of calcium: depending on the binding orientation of TFP, the drug indeed either affects the CaM hydrophobic binding pocket, the calcium binding sites or the secondary structure content in the domain. Understanding TFP binding is a first step towards designing better drugs targeting CaM.

A rationale for the unlike potency of avibactam and ETX2514 against OXA-24 β-lactamase

Diazabicyclooctanone inhibitors such as ETX2514 and avibactam have shown enhanced inhibitory performance to fight the antibiotic resistance developed by pathogens. However, avibactam is ineffective against Acinetobacter baumannii infections, unlike ETX2514. The molecular basis for this difference has not been tackled from a molecular approach, precluding the knowledge of relevant information. In this article, the mechanisms involved in the inhibition of OXA-24 by ETX2514 and avibactam are studied theoretically by hybrid QM/MM calculations. The results show that both inhibitors share the same inhibition mechanisms, comprising acylation a deacylation stages. The involved mechanisms include the same number of steps, transition states and intermediates; although they differ in the involved activation barriers. This difference accounts for the dissimilar inhibitory ability of both inhibitors. The molecular reason for this is the endocyclic double bond in the piperidine ring of ETX2514 increasing the ring strain and chemical reactivity on the N6 and C7 atoms, besides the methyl substituent, which enhance the hydrophobic character of the ring. Furthermore, Lys218 and the carboxylated Lys84 of ETX2514, play a crucial role in the mechanism by coordinating their protonation states in an on/off (protonated/deprotonated) manner, favoring the proton transference between the residues and the inhibitor.

The allosteric mechanism leading to an open-groove lipid conductive state of the TMEM16F scramblase

TMEM16F is a Ca²⁺-activated phospholipid scramblase in the TMEM16 family of membrane proteins. Unlike other TMEM16s exhibiting a membrane-exposed hydrophilic groove that serves as a translocation pathway for lipids, the experimentally determined structures of TMEM16F shows the groove in a closed conformation even under conditions of maximal scramblase activity. It is currently unknown if/how TMEM16F groove can open for lipid scrambling. Here we describe the analysis of ~400 µs all-atom molecular dynamics (MD) simulations of the TMEM16F revealing an allosteric mechanism leading to an open-groove, lipid scrambling competent state of the protein. The groove opens into a continuous hydrophilic conduit that is highly similar in structure to that seen in other activated scramblases. The allosteric pathway connects this opening to an observed destabilization of the Ca²⁺ ion bound at the distal site near the dimer interface, to the dynamics of specific protein regions that produces the open-groove state to scramble phospholipids.

Molecular dynamics simulations reveal the allosteric mechanism leading to an open, lipid scrambling competent state of a mammalian TMEM16F.

Protein Function Analysis through Machine Learning

Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein–ligand binding, including allosteric effects, protein–protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics.

Markov State Models and Molecular Dynamics Simulations Reveal the Conformational Transition of the Intrinsically Disordered Hypervariable Region of K-Ras4B to the Ordered Conformation

K-Ras4B, the most frequently mutated Ras isoform in human tumors, plays a vital part in cell growth, differentiation, and survival. Its tail, the C-terminal hypervariable region (HVR), is involved in anchoring K-Ras4B at the cellular plasma membrane and in isoform-specific protein-protein interactions and signaling. In the inactive guanosine diphosphate-bound state, the intrinsically disordered HVR interacts with the catalytic domain at the effector-binding region, rendering K-Ras4B in its autoinhibited state. Activation releases the HVR from the catalytic domain, with its ensemble favoring an ordered α-helical structure. The large-scale conformational transition of the HVR from the intrinsically disordered to the ordered conformation remains poorly understood. Here, we deploy a computational scheme that integrates a transition path-generation algorithm, extensive molecular dynamics simulation, and Markov state model analysis to investigate the conformational landscape of the HVR transition pathway. Our findings reveal a stepwise pathway for the HVR transition and uncover several key conformational substates along the transition pathway. Importantly, key interactions between the HVR and the catalytic domain are unraveled, highlighting the pathogenesis of K-Ras4B mild mutations in several congenital developmental anomaly syndromes. Together, these findings provide a deeper understanding of the HVR transition mechanism and the regulation of K-Ras4B activity at an atomic level.

Investigating the Bioactive Conformation of Angiotensin II Using Markov State Modeling Revisited with Web-Scale Clustering

Molecular dynamics simulation is a powerful technique for studying the structure and dynamics of biomolecules in atomic-level detail by sampling their various conformations in real time. Because of the long timescales that need to be sampled to study biomolecular processes and the big and complex nature of the corresponding data, relevant analyses of important biophysical phenomena are challenging. Clustering and Markov state models (MSMs) are efficient computational techniques that can be used to extract dominant conformational states and to connect those with kinetic information. In this work, we perform Molecular Dynamics simulations to investigate the free energy landscape of Angiotensin II (AngII) in order to unravel its bioactive conformations using different clustering techniques and Markov state modeling. AngII is an octapeptide hormone, which binds to the AT1 transmembrane receptor, and plays a vital role in the regulation of blood pressure, conservation of total blood volume, and salt homeostasis. To mimic the water-membrane interface as AngII approaches the AT1 receptor and to compare our findings with available experimental results, the simulations were performed in water as well as in water-ethanol mixtures. Our results show that in the water-ethanol environment, AngII adopts more compact U-shaped (folded) conformations than in water, which resembles its structure when bound to the AT1 receptor. For clustering of the conformations, we validate the efficiency of an inverted-quantized k-means algorithm, as a fast approximate clustering technique for web-scale data (millions of points into thousands or millions of clusters) compared to k-means, on data from trajectories of molecular dynamics simulations with reasonable trade-offs between time and accuracy. Finally, we extract MSMs using various clustering techniques for the generation of microstates and macrostates and for the selection of the macrostate representatives.

Fewer Dimensions, More Structures for Improved Discrete Models of Dynamics of Free versus Antigen-Bound Antibody

Over the past decade, Markov State Models (MSM) have emerged as powerful methodologies to build discrete models of dynamics over structures obtained from Molecular Dynamics trajectories. The identification of macrostates for the MSM is a central decision that impacts the quality of the MSM but depends on both the selected representation of a structure and the clustering algorithm utilized over the featurized structures. Motivated by a large molecular system in its free and bound state, this paper investigates two directions of research, further reducing the representation dimensionality in a non-parametric, data-driven manner and including more structures in the computation. Rigorous evaluation of the quality of obtained MSMs via various statistical tests in a comparative setting firmly shows that fewer dimensions and more structures result in a better MSM. Many interesting findings emerge from the best MSM, advancing our understanding of the relationship between antibody dynamics and antibody–antigen recognition.

Sampling constrained stochastic trajectories using Brownian bridges

We present a new method to sample conditioned trajectories of a system evolving under Langevin dynamics, based on Brownian bridges. <p>The trajectories are conditioned to end at a certain point (or in a certain region) in space.</p> <p>The bridge equations can be recast exactly in the form of a non linear stochastic integro-differential equation.</p> <p>This equation can be very well approximated when the trajectories are closely bundled together in space, i.e. at low temperature, or for transition paths. The approximate equation can be solved iteratively, using a fixed point method.</p> <p>We discuss how to choose the initial trajectories and show some examples of the performance of this method on some simple problems.</p> <p>The method allows to generate conditioned trajectories with a high accuracy.

Identifying a Feasible Transition Pathway between Two Conformational States for a Protein

Proteins usually need to transit between different conformational states to fulfill their biological functions. In the mechanistic study of such transition processes by molecular dynamics simulations, identification of the minimum free energy path (MFEP) can substantially reduce the sampling space, thus enabling rigorous thermodynamic evaluation of the process. Conventionally, the MFEP is derived by iterative local optimization from an initial path, which is typically generated by simple brute force techniques like the targeted molecular dynamics (tMD). Therefore, the quality of the initial path determines the successfulness of MFEP estimation. In this work, we propose a method to improve derivation of the initial path. Through iterative relaxation-biasing simulations in a bidirectional manner, this method can construct a feasible transition pathway connecting two known states for a protein. Evaluation on small, fast-folding proteins against long equilibrium trajectories supports the good sampling efficiency of our method. When applied to larger proteins including the catalytic domain of human c-Src kinase as well as the converter domain of myosin VI, the paths generated by our method deviate significantly from those computed with the generic tMD approach. More importantly, free energy profiles and intermediate states obtained from our paths exhibit remarkable improvements over those from tMD paths with respect to both physical rationality and consistency with a priori knowledge.

Principal Component Analysis and Related Methods for Investigating the Dynamics of Biological Macromolecules

Principal component analysis (PCA) is used to reduce the dimensionalities of high-dimensional datasets in a variety of research areas. For example, biological macromolecules, such as proteins, exhibit many degrees of freedom, allowing them to adopt intricate structures and exhibit complex functions by undergoing large conformational changes. Therefore, molecular simulations of and experiments on proteins generate a large number of structure variations in high-dimensional space. PCA and many PCA-related methods have been developed to extract key features from such structural data, and these approaches have been widely applied for over 30 years to elucidate macromolecular dynamics. This review mainly focuses on the methodological aspects of PCA and related methods and their applications for investigating protein dynamics.

DNA Deformation Exerted by Regulatory DNA-Binding Motifs in Human Alkyladenine DNA Glycosylase Promotes Base Flipping

Human alkyladenine DNA glycosylase (AAG) is a key enzyme that corrects a broad range of alkylated and deaminated nucleobases to maintain genomic integrity. When encountering the lesions, AAG adopts a base-flipping strategy to extrude the target base from the DNA duplex to its active site, thereby cleaving the glycosidic bond. Despite its functional importance, the detailed mechanism of such base extrusion and how AAG distinguishes the lesions from an excess of normal bases both remain elusive. Here, through the Markov state model constructed on extensive all-atom molecular dynamics simulations, we find that the alkylated nucleobase (N3-methyladenine, 3MeA) everts through the DNA major groove. Two key AAG motifs, the intercalation and E131-N146 motifs, play active roles in bending/pressing the DNA backbone and widening the DNA minor groove during 3MeA eversion. In particular, the intercalated residue Y162 is involved in buckling the target site at the early stage of 3MeA eversion. Our traveling-salesman based automated path searching algorithm further revealed that a non-target normal adenine tends to be trapped in an exo site near the active site, which however barely exists for a target base 3MeA. Collectively, these results suggest that the Markov state model combined with traveling-salesman based automated path searching acts as a promising approach for studying complex conformational changes of biomolecules and dissecting the elaborate mechanism of target recognition by this unique enzyme.

Large-scale flow in a cubic Rayleigh-Bénard cell: long-term turbulence statistics and Markovianity of macrostate transitions

We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 10⁶. The numerical studies are conducted for single flow trajectories up to 10⁵ convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Structural insights into the SARS-CoV-2 Omicron RBD-ACE2 interaction

Since SARS-CoV-2 Omicron variant (B.1.1.529) was reported in November 2021, it has quickly spread to many countries and outcompeted the globally dominant Delta variant in several countries. The Omicron variant contains the largest number of mutations to date, with 32 mutations located at spike (S) glycoprotein, which raised great concern for its enhanced viral fitness and immune escape[1–4]. In this study, we reported the crystal structure of the receptor binding domain (RBD) of Omicron variant S glycoprotein bound to human ACE2 at a resolution of 2.6 Å. Structural comparison, molecular dynamics simulation and binding free energy calculation collectively identified four key mutations (S477N, G496S, Q498R and N501Y) for the enhanced binding of ACE2 by the Omicron RBD compared to the WT RBD. Representative states of the WT and Omicron RBD-ACE2 systems were identified by Markov State Model, which provides a dynamic explanation for the enhanced binding of Omicron RBD. The effects of the mutations in the RBD for antibody recognition were analyzed, especially for the S371L/S373P/S375F substitutions significantly changing the local conformation of the residing loop to deactivate several class IV neutralizing antibodies.

Cholesterol occupies the lipid translocation pathway to block phospholipid scrambling by a G protein-coupled receptor

Class A (rhodopsin-like) G protein-coupled receptors (GPCRs) are constitutive phospholipid scramblases as evinced after their reconstitution into liposomes. Yet phospholipid scrambling is not detectable in the resting plasma membrane of mammalian cells that is replete with GPCRs. We considered whether cholesterol, a prominent component of the plasma membrane, limits the ability of GPCRs to scramble lipids. Our previous Markov State Model (MSM) analysis of molecular dynamics simulations of membrane-embedded opsin indicated that phospholipid headgroups traverse a dynamically revealed hydrophilic groove between transmembrane helices (TM) 6 and 7 while their tails remain in the bilayer. Here, we present comparative MSM analyses of 150-μs simulations of opsin in cholesterol-free and cholesterol-rich membranes. Our analyses reveal that cholesterol inhibits phospholipid scrambling by occupying the TM6/7 interface and stabilizing the closed groove conformation while itself undergoing flip-flop. This mechanism may explain the inability of GPCRs to scramble lipids at the plasma membrane.

Dynamics of peptide loading into major histocompatibility complex class I molecules chaperoned by TAPBPR

Major histocompatibility complex class I (MHC-I) molecules display antigenic peptides on the cell surface for T cell receptor scanning, thereby activating the immune response. Peptide loading into MHC-I molecules is thus a critical step during the antigen presentation process. Chaperone TAP-binding protein related (TAPBPR) plays a critical role in promoting high-affinity peptide loading into MHC-I, by discriminating against the low-affinity ones. However, the complete peptide loading dynamics into TAPBPR-bound MHC-I is still elusive. Here, we constructed kinetic network models based on hundreds of short-time MD simulations with an aggregated simulation time of ∼21.7 μs, and revealed, at atomic level, four key intermediate states of one antigenic peptide derived from melanoma-associated MART-1/Melan-A protein during its loading process into TAPBPR-bound MHC-I. We find that the TAPBPR binding at the MHC-I pocket-F can substantially reshape the distant pocket-B via allosteric regulations, which in turn promotes the following peptide N-terminal loading. Intriguingly, the partially loaded peptide could profoundly weaken the TAPBPR-MHC stability, promoting the dissociation of the TAPBPR scoop-loop (SL) region from the pocket-F to a more solvent-exposed conformation. Structural inspections further indicate that the peptide loading could remotely affect the SL binding site through both allosteric perturbations and direct contacts. In addition, another structural motif of TAPBPR, the jack hairpin region, was also found to participate in mediating the peptide editing. Our study sheds light on the detailed molecular mechanisms underlying the peptide loading process into TAPBPR-bound MHC-I and pinpoints the key structural factors responsible for dictating the peptide-loading dynamics.

Allosteric control of ACE2 peptidase domain dynamics

The Angiotensin Converting Enzyme 2 (ACE2) assists the regulation of blood pressure and is the main target of the coronaviruses responsible for SARS and COVID19. The catalytic function of ACE2 relies on the opening and closing motion of its peptidase domain (PD). In this study, we investigated the possibility of allosterically controlling the ACE2 PD functional dynamics. After confirming that ACE2 PD binding site opening-closing motion is dominant in characterizing its conformational landscape, we observed that few mutations in the viral receptor binding domain fragments were able to impart different effects on the binding site opening of ACE2 PD. This showed that binding to the solvent exposed area of ACE2 PD can effectively alter the conformational profile of the protein, and thus likely its catalytic function. Using a targeted machine learning model and relative entropy-based statistical analysis, we proposed the mechanism for the allosteric perturbation that regulates the ACE2 PD binding site dynamics at atomistic level. The key residues and the source of the allosteric regulation of ACE PD dynamics are also presented.