Estimation and uncertainty of reversible Markov models

Kinetic Network in Milestoning: Clustering, Reduction, and Transition Path Analysis

We present a reduction of the Milestoning (ReM) algorithm to analyze the high-dimensional Milestoning kinetic network. The algorithm reduces the Milestoning network to low dimensions but preserves essential kinetic information, such as local residence time, exit time, and mean first passage time between any two states. This is achieved in three steps. First, nodes (milestones) in the high-dimensional Milestoning network are grouped into clusters based on the metastability identified by an auxiliary continuous-time Markov chain. Our clustering method is applicable not only to time-reversible networks but also to nonreversible networks generated from practical simulations with statistical fluctuations. Second, a reduced network is established via network transformation, containing only the core sets of clusters as nodes. Finally, transition pathways are analyzed in the reduced network based on the transition path theory. The algorithm is illustrated using a toy model and a solvated alanine dipeptide in two and four dihedral angles.

Identification of a Cryptic Pocket in Methionine Aminopeptidase-II Using Adaptive Bandit Molecular Dynamics Simulations and Markov State Models

Methionine aminopeptidase-II (MetAP-II) is a metalloprotease, primarily responsible for the cotranslational removal of the N-terminal initiator methionine from the nascent polypeptide chain during protein synthesis. MetAP-II has been implicated in angiogenesis and endothelial cell proliferation and is therefore considered a validated target for cancer therapeutics. However, there is no effective drug available against MetAP-II. In this study, we employ Adaptive Bandit molecular dynamics simulations to investigate the structural dynamics of the apo and ligand-bound MetAP-II. Our results focus on the dynamic behavior of the disordered loop that is not resolved in most of the crystal structures. Further analysis of the conformational flexibility of the disordered loop reveals a hidden cryptic pocket that is predicted to be potentially druggable. The network analysis indicates that the disordered loop region has a direct signaling route to the active site. These findings highlight a new way to target MetAP-II by designing inhibitors for the allosteric site within this disordered loop region.

β-sheets mediate the conformational change and allosteric signal transmission between the AsLOV2 termini

Avena sativa phototropin 1 light-oxygen-voltage 2 domain (AsLOV2) is a model protein of Per-Arnt-Sim (PAS) superfamily, characterized by conformational changes in response to external environmental stimuli. This conformational change begins with the unfolding of the N-terminal A'α helix in the dark state followed by the unfolding of the C-terminal Jα helix. The light state is characterized by the unfolded termini and the subsequent modifications in hydrogen bond patterns. In this photoreceptor, β-sheets are identified as crucial components for mediating allosteric signal transmission between the two termini. Through combined experimental and computational investigations, the Hβ and Iβ strands are recognized as the most critical and influential β-sheets in AsLOV2's allosteric mechanism. To elucidate the role of these β-sheets, we introduced 13 distinct mutations (F490L, N492A, L493A, F494L, H495L, L496F, Q497A, R500A, F509L, Q513A, L514A, D515V, and T517V) and conducted comprehensive molecular dynamics simulations. In-depth hydrogen bond analyses emphasized the role of two hydrogen bonds, Asn482-Leu453 and Gln479-Val520, in the observed distinct behaviors of L493A, L496F, Q497A, and D515V mutants. This illustrates the role of β-sheets in the transmission of the allosteric signal upon the photoactivation of the light state.

Bayesian Mechanistic Inference, Statistical Mechanics, and a New Era for Monte Carlo

On the one hand, much of computational chemistry is concerned with "bottom-up" calculations which elucidate observable behavior starting from exact or approximated physical laws, a paradigm exemplified by typical quantum mechanical calculations and molecular dynamics simulations. On the other hand, "top down" computations aiming to formulate mathematical models consistent with observed data, e.g., parametrizing force fields, binding or kinetic models, have been of interest for decades but recently have grown in sophistication with the use of Bayesian inference (BI). Standard BI provides an estimation of parameter values, uncertainties, and correlations among parameters. Used for "model selection," BI can also distinguish between model structures such as the presence or absence of individual states and transitions. Fortunately for physical scientists, BI can be formulated within a statistical mechanics framework, and indeed, BI has led to a resurgence of interest in Monte Carlo (MC) algorithms, many of which have been directly adapted from or inspired by physical strategies. Certain MC algorithms─notably procedures using an "infinite temperature" reference state─can be successful in a 5-20 parameter BI context which would be unworkable in molecular spaces of 103 coordinates and more. This Review provides a pedagogical introduction to BI and reviews key aspects of BI through a physical lens, setting the computations in terms of energy landscapes and free energy calculations and describing promising sampling algorithms. Statistical mechanics and basic probability theory also provide a reference for understanding intrinsic limitations of Bayesian inference with regard to model selection and the choice of priors.

PaCS-Toolkit: Optimized Software Utilities for Parallel Cascade Selection Molecular Dynamics (PaCS-MD) Simulations and Subsequent Analyses

Parallel cascade selection molecular dynamics (PaCS-MD) is an enhanced conformational sampling method conducted as a "repetition of time leaps in parallel worlds", comprising cycles of multiple molecular dynamics (MD) simulations performed in parallel and selection of the initial structures of MDs for the next cycle. We developed PaCS-Toolkit, an optimized software utility enabling the use of different MD software and trajectory analysis tools to facilitate the execution of the PaCS-MD simulation and analyze the obtained trajectories, including the preparation for the subsequent construction of the Markov state model. PaCS-Toolkit is coded with Python, is compatible with various computing environments, and allows for easy customization by editing the configuration file and specifying the MD software and analysis tools to be used. We present the software design of PaCS-Toolkit and demonstrate applications of PaCS-MD variations: original targeted PaCS-MD to peptide folding; rmsdPaCS-MD to protein domain motion; and dissociation PaCS-MD to ligand dissociation from adenosine A2A receptor.

Diffusive dynamics of a model protein chain in solution

A Markov state model is a powerful tool that can be used to track the evolution of populations of configurations in an atomistic representation of a protein. For a coarse-grained linear chain model with discontinuous interactions, the transition rates among states that appear in the Markov model when the monomer dynamics is diffusive can be determined by computing the relative entropy of states and their mean first passage times, quantities that are unchanged by the specification of the energies of the relevant states. In this paper, we verify the folding dynamics described by a diffusive linear chain model of the crambin protein in three distinct solvent systems, each differing in complexity: a hard-sphere solvent, a solvent undergoing multi-particle collision dynamics, and an implicit solvent model. The predicted transition rates among configurations agree quantitatively with those observed in explicit molecular dynamics simulations for all three solvent models. These results suggest that the local monomer-monomer interactions provide sufficient friction for the monomer dynamics to be diffusive on timescales relevant to changes in conformation. Factors such as structural ordering and dynamic hydrodynamic effects appear to have minimal influence on transition rates within the studied solvent densities.

Markov State Models: To Optimize or Not to Optimize

Markov state models (MSM) are a popular statistical method for analyzing the conformational dynamics of proteins including protein folding. With all statistical and machine learning (ML) models, choices must be made about the modeling pipeline that cannot be directly learned from the data. These choices, or hyperparameters, are often evaluated by expert judgment or, in the case of MSMs, by maximizing variational scores such as the VAMP-2 score. Modern ML and statistical pipelines often use automatic hyperparameter selection techniques ranging from the simple, choosing the best score from a random selection of hyperparameters, to the complex, optimization via, e.g., Bayesian optimization. In this work, we ask whether it is possible to automatically select MSM models this way by estimating and analyzing over 16,000,000 observations from over 280,000 estimated MSMs. We find that differences in hyperparameters can change the physical interpretation of the optimization objective, making automatic selection difficult. In addition, we find that enforcing conditions of equilibrium in the VAMP scores can result in inconsistent model selection. However, other parameters that specify the VAMP-2 score (lag time and number of relaxation processes scored) have only a negligible influence on model selection. We suggest that model observables and variational scores should be only a guide to model selection and that a full investigation of the MSM properties should be undertaken when selecting hyperparameters.

Designing Reaction Coordinate for Ion-Induced Pore-Assisted Mechanism of Halide Ions Permeation through Lipid Bilayer by Umbrella Sampling

Ion permeation mechanism through lipid membranes helps to understand cellular processes. We propose new reaction coordinates that allow ions to permeate according to their water affinity and interaction with the hydrophilic layer. Simulations were done for three different halides (F-, Cl-, and I-) in two different lipid bilayers, 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dinervonoyl-sn-glycero-3-phosphocholine (DNPC). It is found that the involvement of the water molecules decreases the free energy barrier. The ions were found to follow different pathways for permeation. Formation of proper pores required a collaboration effort of the hydration shell water molecules and the hydrophilic lipid layer, which was favored in the case of Cl- ions. The optimum charge density and good water affinity of Cl- with respect to F- and I- ions helped to form the pore. The effect was prominently seen in the case of DNPC membrane because of its higher hydrophobic thickness. The umbrella sampling results were compared with other methods such as the Markov state model (MSM) and well-tempered metadynamics (WT-metaD).

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

Comparative Analysis of Conformational Dynamics and Systematic Characterization of Cryptic Pockets in the SARS-CoV-2 Omicron BA.2, BA.2.75 and XBB.1 Spike Complexes with the ACE2 Host Receptor: Confluence of Binding and Structural Plasticity in Mediating Networks of Conserved Allosteric Sites

In the current study, we explore coarse-grained simulations and atomistic molecular dynamics together with binding energetics scanning and cryptic pocket detection in a comparative examination of conformational landscapes and systematic characterization of allosteric binding sites in the SARS-CoV-2 Omicron BA.2, BA.2.75 and XBB.1 spike full-length trimer complexes with the host receptor ACE2. Microsecond simulations, Markov state models and mutational scanning of binding energies of the SARS-CoV-2 BA.2 and BA.2.75 receptor binding domain complexes revealed the increased thermodynamic stabilization of the BA.2.75 variant and significant dynamic differences between these Omicron variants. Molecular simulations of the SARS-CoV-2 Omicron spike full-length trimer complexes with the ACE2 receptor complemented atomistic studies and enabled an in-depth analysis of mutational and binding effects on conformational dynamic and functional adaptability of the Omicron variants. Despite considerable structural similarities, Omicron variants BA.2, BA.2.75 and XBB.1 can induce unique conformational dynamic signatures and specific distributions of the conformational states. Using conformational ensembles of the SARS-CoV-2 Omicron spike trimer complexes with ACE2, we conducted a comprehensive cryptic pocket screening to examine the role of Omicron mutations and ACE2 binding on the distribution and functional mechanisms of the emerging allosteric binding sites. This analysis captured all experimentally known allosteric sites and discovered networks of inter-connected and functionally relevant allosteric sites that are governed by variant-sensitive conformational adaptability of the SARS-CoV-2 spike structures. The results detailed how ACE2 binding and Omicron mutations in the BA.2, BA.2.75 and XBB.1 spike complexes modulate the distribution of conserved and druggable allosteric pockets harboring functionally important regions. The results are significant for understanding the functional roles of druggable cryptic pockets that can be used for allostery-mediated therapeutic intervention targeting conformational states of the Omicron variants.

Functionalized Fullerene Potentially Inhibits SARS-CoV-2 Infection by Modulating Spike Protein Conformational Changes

The disease of SARS-CoV-2 has caused considerable morbidity and mortality globally. Spike proteins on the surface of SARS-CoV-2 allow it to bind with human cells, leading to infection. Fullerenes and their derivatives are promising SARS-CoV-2 inhibitors and drug-delivery vehicles. In this study, Gaussian accelerated molecular dynamics simulations and the Markov state model were employed to delve into the inhibitory mechanism of Fullerene-linear-polyglycerol-b-amine sulfate (F-LGPS) on spike proteins. During the study, it was discovered that fullerene derivatives can operate at the interface of the receptor-binding domain (RBD) and the N-terminal domain (NTD), keeping structural domains in a downward conformation. It was also observed that F-LGPS demonstrated superior inhibitory effects on the XBB variant in comparison to the wild-type variant. This study yielded invaluable insights for the potential development of efficient therapeutics targeting the spike protein of SARS-CoV-2.

Examining Functional Linkages Between Conformational Dynamics, Protein Stability and Evolution of Cryptic Binding Pockets in the SARS-CoV-2 Omicron Spike Complexes with the ACE2 Host Receptor: Recombinant Omicron Variants Mediate Variability of Conserved Allosteric Sites and Binding Epitopes

In the current study, we explore coarse-grained simulations and atomistic molecular dynamics together with binding energetics scanning and cryptic pocket detection in a comparative examination of conformational landscapes and systematic characterization of allosteric binding sites in the SARS-CoV-2 Omicron BA.2, BA.2.75 and XBB.1 spike full-length trimer complexes with the host receptor ACE2. Microsecond simulations, Markov state models and mutational scanning of binding energies of the SARS-CoV-2 BA.2 and BA.2.75 receptor binding domain complexes revealed the increased thermodynamic stabilization of the BA.2.75 variant and significant dynamic differences between these Omicron variants. Molecular simulations of the SARS-CoV-2 Omicron spike full length trimer complexes with the ACE2 receptor complemented atomistic studies and enabled an in-depth analysis of mutational and binding effects on conformational dynamic and functional adaptability of the Omicron variants. Despite considerable structural similarities, Omicron variants BA.2, BA.2.75 and XBB.1 can induce unique conformational dynamic signatures and specific distributions of the conformational states. Using conformational ensembles of the SARS-CoV-2 Omicron spike trimer complexes with ACE2, we conducted a comprehensive cryptic pocket screening to examine the role of Omicron mutations and ACE2 binding on the distribution and functional mechanisms of the emerging allosteric binding sites. This analysis captured all experimentally known allosteric sites and discovered networks of inter-connected and functionally relevant allosteric sites that are governed by variant-sensitive conformational adaptability of the SARS-CoV-2 spike structures. The results detailed how ACE2 binding and Omicron mutations in the BA.2, BA.2.75 and XBB.1 spike complexes modulate the distribution of conserved and druggable allosteric pockets harboring functionally important regions. The results of are significant for understanding functional roles of druggable cryptic pockets that can be used for allostery-mediated therapeutic intervention targeting conformational states of the Omicron variants.

Markov State Models and Perturbation-Based Approaches Reveal Distinct Dynamic Signatures and Hidden Allosteric Pockets in the Emerging SARS-Cov-2 Spike Omicron Variant 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 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, microsecond molecular dynamics 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 functional conformational states and revealed the increased thermodynamic stabilization of the XBB.1.5 subvariant, which can be 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 the conformational states. The results suggested that variant-specific changes of the conformational mobility in the functional interfacial loops of the receptor-binding domain in the SARS-CoV-2 spike protein can be fine-tuned through crosstalk between convergent mutations which could provide 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 modulation of conformational plasticity and regulation of allosteric communications. This study also 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.

Uncertainties in Markov State Models of Small Proteins

Markov state models are widely used to describe and analyze protein dynamics based on molecular dynamics simulations, specifically to extract functionally relevant characteristic time scales and motions. Particularly for larger biomolecules such as proteins, however, insufficient sampling is a notorious concern and often the source of large uncertainties that are difficult to quantify. Furthermore, there are several other sources of uncertainty, such as choice of the number of Markov states and lag time, choice and parameters of dimension reduction preprocessing step, and uncertainty due to the limited number of observed transitions; the latter is often estimated via a Bayesian approach. Here, we quantified and ranked all of these uncertainties for four small globular test proteins. We found that the largest uncertainty is due to insufficient sampling and initially increases with the total trajectory length T up to a critical tipping point, after which it decreases as 1 / T , thus providing guidelines for how much sampling is required for given accuracy. We also found that single long trajectories yielded better sampling accuracy than many shorter trajectories starting from the same structure. In comparison, the remaining sources of the above uncertainties are generally smaller by a factor of about 5, rendering them less of a concern but certainly not negligible. Importantly, the Bayes uncertainty, commonly used as the only uncertainty estimate, captures only a relatively small part of the true uncertainty, which is thus often drastically underestimated.

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.

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.

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Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data.

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.

Deciphering the QR Code of the CRISPR-Cas9 System: Synergy between Gln768 (Q) and Arg976 (R)

Markov state models (MSMs) and machine learning (ML) algorithms can extrapolate the long-time-scale behavior of large biomolecules from molecular dynamics (MD) trajectories. In this study, an MD-MSM-ML scheme has been applied to probe the large endonuclease (Cas9) in the bacterial adaptive immunity CRISPR-Cas9 system. CRISPR has become a programmable and state-of-the-art powerful genome editing tool that has already revolutionized life sciences. CRISPR-Cas9 is programmed to process specific DNA sequences in the genome. However, human/biomedical applications are compromised by off-target DNA damage. Characterization of Cas9 at the structural and biophysical levels is a prerequisite for the development of efficient and high-fidelity Cas9 variants. The Cas9 wild type and two variants (R63A-R66A-R70A, R69A-R71A-R74A-R78A) are studied herein. The configurational space of Cas9 is provided with a focus on the conformations of the side chains of two residues (Gln768 and Arg976). A model for the synergy between those two residues is proposed. The results are discussed within the context of experimental literature. The results and methodology can be exploited for the study of large biomolecules in general and for the engineering of more efficient and safer Cas9 variants for applications.

Breathing and tilting: mesoscale simulations illuminate influenza glycoprotein vulnerabilities

Influenza virus has resurfaced recently from inactivity during the early stages of the COVID-19 pandemic, raising serious concerns about the nature and magnitude of future epidemics. The main antigenic targets of influenza virus are two surface glycoproteins, hemagglutinin (HA) and neuraminidase (NA). Whereas the structural and dynamical properties of both glycoproteins have been studied previously, the understanding of their plasticity in the whole-virion context is fragmented. Here, we investigate the dynamics of influenza glycoproteins in a crowded protein environment through mesoscale all-atom molecular dynamics simulations of two evolutionary-linked glycosylated influenza A whole-virion models. Our simulations reveal and kinetically characterize three main molecular motions of influenza glycoproteins: NA head tilting, HA ectodomain tilting, and HA head breathing. The flexibility of HA and NA highlights antigenically relevant conformational states, as well as facilitates the characterization of a novel monoclonal antibody, derived from human convalescent plasma, that binds to the underside of the NA head. Our work provides previously unappreciated views on the dynamics of HA and NA, advancing the understanding of their interplay and suggesting possible strategies for the design of future vaccines and antivirals against influenza.

Oncogenic Mutations in the DNA-Binding Domain of FOXO1 that Disrupt Folding: Quantitative Insights from Experiments and Molecular Simulations

FOXO1, a member of the family of winged-helix motif Forkhead box (FOX) transcription factors, is the most abundantly expressed FOXO member in mature B cells. Sequencing of diffuse large B-cell lymphoma (DLBCL) tumors and cell lines identified specific mutations in the forkhead domain linked to loss of function. Differential scanning calorimetry and thermal shift assays were used to characterize how eight of these mutations affect the stability of the FOX domain. Mutations L183P and L183R were found to be particularly destabilizing. Electrophoresis mobility shift assays show these same mutations also disrupt FOXO1 binding to their canonical DNA sequences, suggesting that the loss of function is due to destabilization of the folded structure. Computational modeling of the effect of mutations on FOXO1 folding was performed using alchemical free energy perturbation (FEP), and a Markov model of the entire folding reaction was constructed from massively parallel molecular simulations, which predicts folding pathways involving the late folding of helix α3. Although FEP can qualitatively predict the destabilization from L183 mutations, we find that a simple hydrophobic transfer model, combined with estimates of unfolded-state solvent-accessible surface areas from molecular simulations, is able to more accurately predict changes in folding free energies due to mutations. These results suggest that the atomic detail provided by simulations is important for the accurate prediction of mutational effects on folding stability. Corresponding disease-associated mutations in other FOX family members support further experimental and computational studies of the folding mechanism of FOX domains.

A litmus test for classifying recognition mechanisms of transiently binding proteins

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin’s paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks.

The authors provide a litmus test for the recognition mechanism of transiently binding proteins based on nuclear magnetic resonance and find a conformational selection binding mechanism through concentration-dependent kinetics of ubiquitin and SH3.

Investigating the entropic nature of membrane-mediated interactions driving the aggregation of peripheral proteins

Peripheral membrane-associated proteins are known to accumulate on the surface of biomembranes as a result of membrane-mediated interactions. For a pair of rotationally-symmetric curvature-inducing proteins, membrane mechanics at the low-temperature limit predicts pure repulsion. On the other hand, temperature-dependent entropic forces arise between pairs of stiff-binding proteins suppressing membrane fluctuations. These Casimir-like interactions have thus been suggested as candidates for attractive forces leading to aggregation. With dense assemblies of peripheral proteins on the membrane, both these abstractions encounter short-range and multi-body complications. Here, we make use of a particle-based membrane model augmented with flexible peripheral proteins to quantify purely membrane-mediated interactions and investigate their underlying nature. We introduce a continuous reaction coordinate corresponding to the progression of protein aggregation. We obtain free energy and entropy landscapes for different surface concentrations along this reaction coordinate. In parallel, we investigate time-dependent estimates of membrane entropy corresponding to membrane undulations and coarse-grained director field and how they change dynamically with protein aggregation. Congruent outcomes of the two approaches point to the conclusion that for low surface concentrations, interactions with an entropic nature may drive the aggregation. But at high concentrations, enthalpic contributions due to concerted membrane deformation by protein clusters are dominant.

Deeptime: a Python library for machine learning dynamical models from time series data

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/.

Discovery of Novel GR Ligands toward Druggable GR Antagonist Conformations Identified by MD Simulations and Markov State Model Analysis

Binding of different ligands to glucocorticoid receptor (GR) may induce different conformational changes and even trigger completely opposite biological functions. To understand the allosteric communication within the GR ligand binding domain, the folding pathway of helix 12 (H12) induced by the binding of the agonist dexamethasone (DEX), antagonist RU486, and modulator AZD9567 are explored by molecular dynamics simulations and Markov state model analysis. The ligands can regulate the volume of the activation function-2 through the residues Phe737 and Gln738. Without ligand or with agonist binding, H12 swings from inward to outward to visit different folding positions. However, the binding of RU486 or AZD9567 perturbs the structural state, and the passive antagonist state appears more stable. Structure-based virtual screening and in vitro bioassays are used to discover novel GR ligands that bias the conformation equilibria toward the passive antagonist state. HP-19 exhibits the best anti-inflammatory activity (IC50 = 0.041 ± 0.011 µm) in nuclear factor-kappa B signaling pathway, which is comparable to that of DEX. HP-19 also does not induce adverse effect-related transactivation functions of GR. The novel ligands discovered here may serve as promising starting points for the development of GR modulators.

Nearly reducible finite Markov chains: Theory and algorithms

Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.

Crystallization in Microgravity and the Atomic-Resolution Structure of Uridine Phosphorylase from Vibrio cholerae

Abstract

Uridine phosphorylases are known as key targets for the development of new anticancer and antiparasitic agents. Crystals of uridine phosphorylase from the pathogenic bacterium Vibrio cholerae were grown in microgravity by the capillary counter-diffusion method on board of the International Space Station. The three-dimensional structure of this enzyme was determined at atomic (1.04 Å) resolution (RCSB PDB ID: 6Z9Z). Alternative conformations of long fragments (β-strands and adjacent loops) of the protein molecule were found for the first time in the three-dimensional structure of uridine phosphorylase in the absence of specific bound ligands. Apparently, these alternative conformations are related to the enzyme function. Conformational analysis with Markov state models demonstrated that conformational rearrangements can occur in the ligand-free state of the enzyme.

Dissecting Multiple Pathways in the Relaxation Dynamics of Helix <==> Coil Transitions with Optimum Dimensionality Reduction

Fast kinetic experiments with dramatically improved time resolution have contributed significantly to understanding the fundamental processes in protein folding pathways involving the formation of a-helices and b-hairpin, contact formation, and overall collapse of the peptide chain. Interpretation of experimental results through application of a simple statistical mechanical model was key to this understanding. Atomistic description of all events observed in the experimental findings was challenging. Recent advancements in theory, more sophisticated algorithms, and a true long-term trajectory made way for an atomically detailed description of kinetics, examining folding pathways, validating experimental results, and reporting new findings for a wide range of molecular processes in biophysical chemistry. This review describes how optimum dimensionality reduction theory can construct a simplified coarse-grained model with low dimensionality involving a kinetic matrix that captures novel insights into folding pathways. A set of metastable states derived from molecular dynamics analysis generate an optimally reduced dimensionality rate matrix following transition pathway analysis. Analysis of the actual long-term simulation trajectory extracts a relaxation time directly comparable to the experimental results and confirms the validity of the combined approach. The application of the theory is discussed and illustrated using several examples of helix <==> coil transition pathways. This paper focuses primarily on a combined approach of time-resolved experiments and long-term molecular dynamics simulation from our ongoing work.

Enhanced sampling protocol to elucidate fusion peptide opening of SARS-CoV-2 spike protein

Large-scale conformational transitions in the spike protein S2 domain are required during host-cell infection of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Although conventional molecular dynamics simulations have been extensively used to study therapeutic targets of SARS-CoV-2, it is still challenging to gain molecular insight into the key conformational changes because of the size of the spike protein and the long timescale required to capture these transitions. In this work, we have developed an efficient simulation protocol that leverages many short simulations, a dynamic selection algorithm, and Markov state models to interrogate the structural changes of the S2 domain. We discovered that the conformational flexibility of the dynamic region upstream of the fusion peptide in S2 is coupled to the proteolytic cleavage state of the spike protein. These results suggest that opening of the fusion peptide likely occurs on a submicrosecond timescale after cleavage at the S2' site. Building on the structural and dynamical information gained to date about S2 domain dynamics, we provide proof of principle that a small molecule bound to a seam neighboring the fusion peptide can slow the opening of the fusion peptide, leading to a new inhibition strategy for experiments to confirm. In aggregate, these results will aid the development of drug cocktails to inhibit infections caused by SARS-CoV-2 and other coronaviruses.

What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models

Markov state models (MSMs) have been widely applied to study the kinetics and pathways of protein conformational dynamics based on statistical analysis of molecular dynamics (MD) simulations. These MSMs coarse-grain both configuration space and time in ways that limit what kinds of observables they can reproduce with high fidelity over different spatial and temporal resolutions. Despite their popularity, there is still limited understanding of which biophysical observables can be computed from these MSMs in a robust and unbiased manner, and which suffer from the space-time coarse-graining intrinsic in the MSM model. Most theoretical arguments and practical validity tests for MSMs rely on long-time equilibrium kinetics, such as the slowest relaxation time scales and experimentally observable time-correlation functions. Here, we perform an extensive assessment of the ability of well-validated protein folding MSMs to accurately reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis. We also assess a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs. We conclude with some practical guidance on the use of MSMs to study various problems in conformational dynamics of biomolecules. In brief, MSMs can accurately reproduce correlation functions slower than the lag time, but path-based observables can only be reliably reproduced if the lifetimes of states exceed the lag time, which is a much stricter requirement. Even in the presence of short-lived states, we find that haMSMs reproduce path-based observables more reliably.

How do antiporters exchange substrates across the cell membrane? An atomic-level description of the complete exchange cycle in NarK

Major facilitator superfamily (MFS) proteins operate via three different mechanisms: uniport, symport, and antiport. Despite extensive investigations, the molecular understanding of antiporters is less advanced than that of other transporters due to the complex coupling between two substrates and the lack of distinct structures. We employ extensive all-atom molecular dynamics simulations to dissect the complete substrate exchange cycle of the bacterial NO₃^-/NO₂^- antiporter, NarK. We show that paired basic residues in the binding site prevent the closure of unbound protein and ensure the exchange of two substrates. Conformational transition occurs only in the presence of substrate, which weakens the electrostatic repulsion and stabilizes the transporter. Furthermore, we propose a state-dependent substrate exchange model, in which the relative spacing between the paired basic residues determines whether NO₃^- and NO₂^- bind simultaneously or sequentially. Overall, this work presents a general working model for the antiport mechanism within the MFS.

Comparison between slow anisotropic LE4PD fluctuations and the principal component analysis modes of ubiquitin

The biological function and folding mechanisms of proteins are often guided by large-scale slow motions, which involve crossing high energy barriers. In a simulation trajectory, these slow fluctuations are commonly identified using a principal component analysis (PCA). Despite the popularity of this method, a complete analysis of its predictions based on the physics of protein motion has been so far limited. This study formally connects the PCA to a Langevin model of protein dynamics and analyzes the contributions of energy barriers and hydrodynamic interactions to the slow PCA modes of motion. To do so, we introduce an anisotropic extension of the Langevin equation for protein dynamics, called the LE4PD-XYZ, which formally connects to the PCA "essential dynamics." The LE4PD-XYZ is an accurate coarse-grained diffusive method to model protein motion, which describes anisotropic fluctuations in the alpha carbons of the protein. The LE4PD accounts for hydrodynamic effects and mode-dependent free-energy barriers. This study compares large-scale anisotropic fluctuations identified by the LE4PD-XYZ to the mode-dependent PCA predictions, starting from a microsecond-long alpha carbon molecular dynamics atomistic trajectory of the protein ubiquitin. We observe that the inclusion of free-energy barriers and hydrodynamic interactions has important effects on the identification and timescales of ubiquitin's slow modes.

A kinetic ensemble of the Alzheimer's Aβ peptide

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

Multiple Pathways in NaCl Homogeneous Crystal Nucleation

NaCl crystal nucleation from metastable solutions has long been considered to occur according to a single-step mechanism where the growth in the size and crystalline order of the emerging nuclei...

Understanding the Structure and Apo Dynamics of the Functionally Active JIP1 Fragment

Recent experiments indicate that the C-Jun amino-terminal kinase-interacting protein 1 (JIP1) binds to and activates the c-Jun N-terminal kinase (JNK) protein. JNK is an integral part of cell apoptosis, and misregulation of this process is a causative factor in diseases such as Alzheimer's disease (AD), obesity, and cancer. It has also been shown that JIP1 may increase the phosphorylation of tau by facilitating the interaction between the tau protein and JNK, which could also be a causative factor in AD. Very little is known about the structure and dynamics of JIP1; however, the amino acid composition of the first 350 residues suggests that it contains an intrinsically disordered region. Molecular dynamics (MD) simulations using AMBER 14 were used to study the structure and dynamics of a functionally active JIP1 10mer fragment to better understand the solution behavior of the fragment. Two microseconds of unbiased MD was performed on the JIP1 10mer fragment in 10 different seeds for a total of 20 μs of simulation time, and from this, seven structurally stable conformations of the 10mer fragment were identified via classical clustering. The 10mer ensemble was also used to build a Markov state model (MSM) that identified four metastable states that encompassed six of the seven conformational families identified by classical dimensional reduction. Based on this MSM, conformational interconversions between the four states occur via two dominant pathways with probability fluxes of 55 and 44% for each individual pathway. Transitions between the initial and final states occur with mean first passage times of 31 (forward) and 16 (reverse) μs.

Optimal dimensionality reduction of Markov chains using graph transformation

Markov chains can accurately model the state-to-state dynamics of a wide range of complex systems, but the underlying transition matrix is ill-conditioned when the dynamics feature a separation of timescales. Graph transformation (GT) provides a numerically stable method to compute exact mean first passage times (MFPTs) between states, which are the usual dynamical observables in continuous-time Markov chains (CTMCs). Here, we generalize the GT algorithm to discrete-time Markov chains (DTMCs), which are commonly estimated from simulation data, for example, in the Markov state model approach. We then consider the dimensionality reduction of CTMCs and DTMCs, which aids model interpretation and facilitates more expensive computations, including sampling of pathways. We perform a detailed numerical analysis of existing methods to compute the optimal reduced CTMC, given a partitioning of the network into metastable communities (macrostates) of nodes (microstates). We show that approaches based on linear algebra encounter numerical problems that arise from the requisite metastability. We propose an alternative approach using GT to compute the matrix of intermicrostate MFPTs in the original Markov chain, from which a matrix of weighted intermacrostate MFPTs can be obtained. We also propose an approximation to the weighted-MFPT matrix in the strongly metastable limit. Inversion of the weighted-MFPT matrix, which is better conditioned than the matrices that must be inverted in alternative dimensionality reduction schemes, then yields the optimal reduced Markov chain. The superior numerical stability of the GT approach therefore enables us to realize optimal Markovian coarse-graining of systems with rare event dynamics.

High-resolution structures of multiple 5-HT3AR-setron complexes reveal a novel mechanism of competitive inhibition

Serotonin receptors (5-HT3AR) play a crucial role in regulating gut movement, and are the principal target of setrons, a class of high-affinity competitive antagonists, used in the management of nausea and vomiting associated with radiation and chemotherapies. Structural insights into setron-binding poses and their inhibitory mechanisms are just beginning to emerge. Here, we present high-resolution cryo-EM structures of full-length 5-HT3AR in complex with palonosetron, ondansetron, and alosetron. Molecular dynamic simulations of these structures embedded in a fully-hydrated lipid environment assessed the stability of ligand-binding poses and drug-target interactions over time. Together with simulation results of apo- and serotonin-bound 5-HT3AR, the study reveals a distinct interaction fingerprint between the various setrons and binding-pocket residues that may underlie their diverse affinities. In addition, varying degrees of conformational change in the setron-5-HT3AR structures, throughout the channel and particularly along the channel activation pathway, suggests a novel mechanism of competitive inhibition.

Atomic-Level Characterization of the Methadone-Stabilized Active Conformation of µ-Opioid Receptor

Methadone is a synthetic opioid agonist with notoriously unique properties, such as lower abuse liability and induced relief of withdrawal symptoms and drug cravings, despite acting on the same opioid receptors triggered by classic opioids-in particular the µ-opioid receptor (MOR). Its distinct pharmacologic properties, which have recently been attributed to the preferential activation of β-arrestin over G proteins, make methadone a standard-of-care maintenance medication for opioid addiction. Although a recent biophysical study suggests that methadone stabilizes different MOR active conformations from those stabilized by classic opioid drugs or G protein-biased agonists, how this drug modulates the conformational equilibrium of MOR and what specific active conformation of the receptor it stabilizes are unknown. Here, we report the results of submillisecond adaptive sampling molecular dynamics simulations of a predicted methadone-bound MOR complex and compare them with analogous data obtained for the classic opioid morphine and the G protein-biased ligand TRV130. The model, which is supported by existing experimental data, is analyzed using Markov state models and transfer entropy analysis to provide testable hypotheses of methadone-specific conformational dynamics and activation kinetics of MOR. SIGNIFICANCE STATEMENT: Opioid addiction has reached epidemic proportions in both industrialized and developing countries. Although methadone maintenance treatment represents an effective therapeutic approach for opioid addiction, it is not as widely used as needed. In this study, we contribute an atomic-level understanding of how methadone exerts its unique function in pursuit of more accessible treatments for opioid addiction. In particular, we present details of a methadone-specific active conformation of the µ-opioid receptor that has thus far eluded experimental structural characterization.

Markov State Model of Lassa Virus Nucleoprotein Reveals Large Structural Changes during the Trimer to Monomer Transition

Lassa virus contains a nucleoprotein (NP) that encapsulates the viral genomic RNA forming the ribonucleoprotein (RNP). The NP forms trimers that do not bind RNA, but a structure of only the NP N-terminal domain was co-crystallized with RNA bound. These structures suggested a model in which the NP forms a trimer to keep the RNA gate closed, but then is triggered to undergo a change to a form competent for RNA binding. Here, we investigate the scenario in which the trimer is disrupted to observe whether monomeric NP undergoes significant conformational changes. From multi-microsecond molecular dynamics simulations and an adaptive sampling scheme to sample the conformational space, a Markov state model (MSM) is constructed. The MSM reveals an energetically favorable conformational change, with the most significant changes occurring at the domain interface. These results support a model in which significant structural reorganization of the NP is required for RNP formation.

Coupling of Conformational Switches in Calcium Sensor Unraveled with Local Markov Models and Transfer Entropy

Proteins often have multiple switching domains that are coupled to each other and to the binding of ligands in order to realize signaling functions. Here we investigate the C2A domain of Synaptotagmin-1 (Syt-1), a calcium sensor in the neurotransmitter release machinery and a model system for the large family of C2 membrane binding domains. We combine extensive molecular dynamics (MD) simulations with Markov modeling in order to model conformational switching domains, their states, and their dependence on bound calcium ions. Then, we use transfer entropy to characterize how the switching domains are coupled via directed or allosteric mechanisms and give rise to the calcium sensing function of the protein. Our proposed switching mechanism contributes to the understanding of the neurotransmitter release machinery. Furthermore, the methodological approach we develop serves as a template to analyze conformational switching domains and the broad study of their coupling in macromolecular machines.

Dynamical matrix propagator scheme for large-scale proton dynamics simulations

We derive a matrix formalism for the simulation of long range proton dynamics for extended systems and timescales. On the basis of an ab initio molecular dynamics simulation, we construct a Markov chain, which allows us to store the entire proton dynamics in an M × M transition matrix (where M is the number of oxygen atoms). In this article, we start from common topology features of the hydrogen bond network of good proton conductors and utilize them as constituent constraints of our dynamic model. We present a thorough mathematical derivation of our approach and verify its uniqueness and correct asymptotic behavior. We propagate the proton distribution by means of transition matrices, which contain kinetic data from both ultra-short (sub-ps) and intermediate (ps) timescales. This concept allows us to keep the most relevant features from the microscopic level while effectively reaching larger time and length scales. We demonstrate the applicability of the transition matrices for the description of proton conduction trends in proton exchange membrane materials.

Identification of Druggable Kinase Target Conformations Using Markov Model Metastable States Analysis of apo-Abl

Kinases are important targets for drug development. However, accounting for the impact of possible structural rearrangements on the binding of kinase inhibitors is complicated by the extensive flexibility of their catalytic domain. The dynamic N-lobe contains four particular mobile structural elements: the Asp-Phe-Gly (DFG) motif, the phosphate (P) positioning loop, the activation (A) loop, and the αC helix. In our previous study [Meng et al. J. Chem. Theory Comput. 2018 14, 2721-2732], we combined various simulation techniques with Markov state modeling (MSM) to explore the free energy landscape of Abl kinase beyond conformations that are known from X-ray crystallography. Here we examine the resulting Markov model in greater detail by analyzing its metastable states. A characterization of the states in terms of their DFG state, P-loop, and αC conformations is presented and compared to existing classification schemes. Several metastable states are found to be structurally close to known crystal structures of different kinases in complex with a variety of inhibitors. These results suggest that the set of conformations accessible to tyrosine kinases may be shared within the entire family and that the conformational dynamics of one kinase in the absence of any ligand can provide meaningful information about possible target conformations for inhibitors of any member of the kinase family.

Dynamical Behavior of β-Lactamases and Penicillin- Binding Proteins in Different Functional States and Its Potential Role in Evolution

β-Lactamases are enzymes produced by bacteria to hydrolyze β-lactam-based antibiotics, and pose serious threat to public health through related antibiotic resistance. Class A β-lactamases are structurally and functionally related to penicillin-binding proteins (PBPs). Despite the extensive studies of the structures, catalytic mechanisms and dynamics of both β-lactamases and PBPs, the potentially different dynamical behaviors of these proteins in different functional states still remain elusive in general. In this study, four evolutionarily related proteins, including TEM-1 and TOHO-1 as class A β-lactamases, PBP-A and DD-transpeptidase as two PBPs, are subjected to molecular dynamics simulations and various analyses to characterize their dynamical behaviors in different functional states. Penicillin G and its ring opening product serve as common ligands for these four proteins of interest. The dynamic analyses of overall structures, the active sites with penicillin G, and three catalytically important residues commonly shared by all four proteins reveal unexpected cross similarities between Class A β-lactamases and PBPs. These findings shed light on both the hidden relations among dynamical behaviors of these proteins and the functional and evolutionary relations among class A β-lactamases and PBPs.

Kinetics analysis of ubiquitin local fluctuations with Markov state modeling of the LE4PD normal modes

Local fluctuations are important for protein binding and molecular recognition because they provide conformational states that can be trapped through a selection mechanism of binding. Thus, an accurate characterization of local fluctuations may be important for modeling the kinetic mechanism that leads to the biological activity of a protein. In this paper, we study the fluctuation dynamics of the regulatory protein ubiquitin and propose a novel theoretical approach to model its fluctuations. A coarse-grained, diffusive, mode-dependent description of fluctuations is accomplished using the Langevin Equation for Protein Dynamics (LE4PD). This equation decomposes the dynamics of a protein, simulated by molecular dynamics, into dynamical pathways that explore mode-dependent free energy surfaces. We calculate the time scales of the slow, high-amplitude fluctuations by modeling the kinetics of barrier crossing in the two-dimensional free energy surfaces using Markov state modeling. We find that the LE4PD predicts slow fluctuations in three important binding regions in ubiquitin: the C-terminal tail, the Lys11 loop, and the 50 s loop. These results suggest that the LE4PD can provide useful information on the role of fluctuations in the process of molecular recognition regulating the biological activity of ubiquitin.