Markov models of molecular kinetics: Generation and validation

Investigating the effects of cysteine-118 oxidation on G12D KRas structure and dynamics: insights from MD simulations

Mutations of Ras proteins are believed to be among the most prominent causes of cancer. There is increasing evidence that the activity of Ras may be controlled by the redox state of cysteine residues located within the NKCD motif. This redox signaling is critical to both physiological and pathological processes and occurs when C118 is oxidized in a reversible manner. In this study, we used atomistic molecular dynamics simulations and Markov state models to investigate the structural and conformational effects of C118 oxidation on the oncogenic mutant KRas(G12D). While both mutants share common features and exhibit some distinct conformational states and fluctuations, we have found that the oxidized variant KRas(G12D/C118SOH) is more dynamic than the unoxidized counterpart, particularly in the switch II region. Additionally, C118 oxidation is found to alter the structure of the nucleotide-binding site and the switch regions as well as perturb the conformational equilibrium between Ras active and inactive states. These conformational preferences may alter the affinity to different effectors, resulting in selective downstream activation. Our results are anticipated to help future drug development efforts aimed at KRAS-related anticancer treatment.Communicated by Ramaswamy H. Sarma.

Interactions between Inhibitors and 5-Lipoxygenase: Insights from Gaussian Accelerated Molecular Dynamics and Markov State Models

Inflammation is a protective stress response triggered by external stimuli, with 5-lipoxygenase (5LOX) playing a pivotal role as a potent mediator of the leukotriene (Lts) inflammatory pathway. Nordihydroguaiaretic acid (NDGA) functions as a natural orthosteric inhibitor of 5LOX, while 3-acetyl-11-keto-β-boswellic acid (AKBA) acts as a natural allosteric inhibitor targeting 5LOX. However, the precise mechanisms of inhibition have remained unclear. In this study, Gaussian accelerated molecular dynamics (GaMD) simulation was employed to elucidate the inhibitory mechanisms of NDGA and AKBA on 5LOX. It was found that the orthosteric inhibitor NDGA was tightly bound in the protein's active pocket, occupying the active site and inhibiting the catalytic activity of the 5LOX enzyme through competitive inhibition. The binding of the allosteric inhibitor AKBA induced significant changes at the distal active site, leading to a conformational shift of residues 168-173 from a loop to an α-helix and significant negative correlated motions between residues 285-290 and 375-400, reducing the distance between these segments. In the simulation, the volume of the active cavity in the stable conformation of the protein was reduced, hindering the substrate's entry into the active cavity and, thereby, inhibiting protein activity through allosteric effects. Ultimately, Markov state models (MSM) were used to identify and classify the metastable states of proteins, revealing the transition times between different conformational states. In summary, this study provides theoretical insights into the inhibition mechanisms of 5LOX by AKBA and NDGA, offering new perspectives for the development of novel inhibitors specifically targeting 5LOX, with potential implications for anti-inflammatory drug development.

Unveiling Allosteric Regulation and Binding Mechanism of BRD9 through Molecular Dynamics Simulations and Markov Modeling

Bromodomain-containing protein 9 (BRD9) is a key player in chromatin remodeling and gene expression regulation, and it is closely associated with the development of various diseases, including cancers. Recent studies have indicated that inhibition of BRD9 may have potential value in the treatment of certain cancers. Molecular dynamics (MD) simulations, Markov modeling and principal component analysis were performed to investigate the binding mechanisms of allosteric inhibitor POJ and orthosteric inhibitor 82I to BRD9 and its allosteric regulation. Our results indicate that binding of these two types of inhibitors induces significant structural changes in the protein, particularly in the formation and dissolution of α-helical regions. Markov flux analysis reveals notable changes occurring in the α-helicity near the ZA loop during the inhibitor binding process. Calculations of binding free energies reveal that the cooperation of orthosteric and allosteric inhibitors affects binding ability of inhibitors to BRD9 and modifies the active sites of orthosteric and allosteric positions. This research is expected to provide new insights into the inhibitory mechanism of 82I and POJ on BRD9 and offers a theoretical foundation for development of cancer treatment strategies targeting BRD9.

Incorporating Prior Knowledge in the Seeds of Adaptive Sampling Molecular Dynamics Simulations of Ligand Transport in Enzymes with Buried Active Sites

Because most proteins have buried active sites, protein tunnels or channels play a crucial role in the transport of small molecules into buried cavities for enzymatic catalysis. Tunnels can critically modulate the biological process of protein-ligand recognition. Various molecular dynamics methods have been developed for exploring and exploiting the protein-ligand conformational space to extract high-resolution details of the binding processes, a recent example being energetically unbiased high-throughput adaptive sampling simulations. The current study systematically contrasted the role of integrating prior knowledge while generating useful initial protein-ligand configurations, called seeds, for these simulations. Using a nontrivial system of a haloalkane dehalogenase mutant with multiple transport tunnels leading to a deeply buried active site, simulations were employed to derive kinetic models describing the process of association and dissociation of the substrate molecule. The most knowledge-based seed generation enabled high-throughput simulations that could more consistently capture the entire transport process, explore the complex network of transport tunnels, and predict equilibrium dissociation constants, koff/kon, on the same order of magnitude as experimental measurements. Overall, the infusion of more knowledge into the initial seeds of adaptive sampling simulations could render analyses of transport mechanisms in enzymes more consistent even for very complex biomolecular systems, thereby promoting drug development efforts and the rational design of enzymes with buried active sites.

Capturing the Effects of Single Atom Substitutions on the Inhibition Efficiency of Glycogen Synthase Kinase-3β Inhibitors via Markov State Modeling and Experiments

Small modifications in the chemical structure of ligands are known to dramatically change their ability to inhibit the activity of a protein. Unraveling the mechanisms that govern these dramatic changes requires scrutinizing the dynamics of protein-ligand binding and unbinding at the atomic level. As an exemplary case, we have studied Glycogen Synthase Kinase-3β (GSK-3β), a multifunctional kinase that has been implicated in a host of pathological processes. As such, there is a keen interest in identifying ligands that inhibit GSK-3β activity. One family of compounds that are highly selective and potent inhibitors of GSK-3β is exemplified by a molecule termed COB-187. COB-187 consists of a five-member heterocyclic ring with a thione at C2, a pyridine substituted methyl at N3, and a hydroxyl and phenyl at C4. We have studied the inhibition of GSK-3β by COB-187-related ligands that differ in a single heavy atom from each other (either in the location of nitrogen in their pyridine ring, or with the pyridine ring replaced by a phenyl ring), or in the length of the alkyl group joining the pyridine and the N3. The inhibition experiments show a large range of half-maximal inhibitory concentration (IC50) values from 10 nM to 10 μM, implying that these ligands exhibit vastly different propensities to inhibit GSK-3β. To explain these differences, we perform Markov State Modeling (MSM) using fully atomistic simulations. Our MSM results are in excellent agreement with the experiments in that they accurately capture differences in the binding propensities of the ligands. The simulations show that the binding propensities are related to the ligands' ability to attain a compact conformation where their two aromatic rings are spatially close. We rationalize this result by sampling numerous binding and unbinding events via funnel metadynamics simulations, which show that indeed while approaching the bound state, the ligands prefer to be in their compact conformation. We find that the presence of nitrogen in the aromatic ring increases the probability of attaining the compact conformation. Protein-ligand binding is understood to be dictated by the energetics of interactions and entropic factors, like the release of bound water from the binding pockets. This work shows that changes in the conformational distribution of ligands due to atom-level modifications in the structure play an important role in protein-ligand binding.

Unravelling Guest Dynamics in Crystalline Molecular Organics Using 2H Solid-State NMR and Molecular Dynamics Simulation

2H solid-state NMR and atomistic molecular dynamics (MD) simulations are used to understand the disorder of guest solvent molecules in two cocrystal solvates of the pharmaceutical furosemide. Traditional approaches to interpreting the NMR data fail to provide a coherent model of molecular behavior and indeed give misleading kinetic data. In contrast, the direct prediction of the NMR properties from MD simulation trajectories allows the NMR data to be correctly interpreted in terms of combined jump-type and libration-type motions. Time-independent component analysis of the MD trajectories provides additional insights, particularly for motions that are invisible to NMR. This allows a coherent picture of the dynamics of molecules restricted in molecular-sized cavities to be determined.

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.

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.

Impact of Nonnative Interactions on the Binding Kinetics of Intrinsically Disordered p53 with MDM2: Insights from All-Atom Simulation and Markov State Model Analysis

Intrinsically disordered proteins (IDPs) lack a well-defined tertiary structure but are essential players in various biological processes. Their ability to undergo a disorder-to-order transition upon binding to their partners, known as the folding-upon-binding process, is crucial for their function. One classical example is the intrinsically disordered transactivation domain (TAD) of the tumor suppressor protein p53, which quickly forms a structured α-helix after binding to its partner MDM2, with clinical significance for cancer treatment. However, the contribution of nonnative interactions between the IDP and its partner to the rapid binding kinetics, as well as their interplay with native interactions, is not well understood at the atomic level. Here, we used molecular dynamics simulation and Markov state model (MSM) analysis to study the folding-upon-binding mechanism between p53-TAD and MDM2. Our results suggest that the system progresses from the nascent encounter complex to the well-structured encounter complex and finally reaches the native complex, following an induced-fit mechanism. We found that nonnative hydrophobic and hydrogen bond interactions, combined with native interactions, effectively stabilize the nascent and well-structured encounter complexes. Among the nonnative interactions, Leu25p53-Leu54MDM2 and Leu25p53-Phe55MDM2 are particularly noteworthy, as their interaction strength is close to the optimum. Evidently, strengthening or weakening these interactions could both adversely affect the binding kinetics. Overall, our findings suggest that nonnative interactions are evolutionarily optimized to accelerate the binding kinetics of IDPs in conjunction with native interactions.

Using Gaussian accelerated molecular dynamics combined with Markov state models to explore the mechanism of action of new oral inhibitors on Complex I

In this study, our focus was on investigating H-1,2,3-triazole derivative HP661 as a novel and highly efficient oral OXPHOS inhibitor, with its molecular-level inhibitory mechanism not yet fully understood. We selected the ND1, NDUFS2, and NDUFS7 subunits of Mitochondrial Complex I as the receptor proteins and established three systems for comparative analysis: protein-IACS-010759, protein-lead compound 10, and protein-HP661. Through extensive analysis involving 500 ns Gaussian molecular dynamics simulations, we gained insights into these systems. Additionally, we constructed a Markov State Models to examine changes in secondary structures during the motion processes. The research findings suggest that the inhibitor HP661 enhances the extensibility and hydrophilicity of the receptor protein. Furthermore, HP661 induces the unwinding of the α-helical structure in the region of residues 726-730. Notably, key roles were identified for Met37, Phe53, and Pro212 in the binding of various inhibitors. In conclusion, we delved into the potential molecular mechanisms of triazole derivative HP661 in inhibiting Complex I. These research outcomes provide crucial information for a deeper understanding of the mechanisms underlying OXPHOS inhibition, offering valuable theoretical support for drug development and disease treatment design.

Implementation of Girsanov Reweighting in OpenMM and Deeptime

Classical molecular dynamics (MD) simulations provide invaluable insights into complex molecular systems but face limitations in capturing phenomena occurring on time scales beyond their reach. To bridge this gap, various enhanced sampling techniques have been developed, which are complemented by reweighting techniques to recover the unbiased dynamics. Girsanov reweighting is a reweighting technique that reweights simulation paths, generated by a stochastic MD integrator, without evoking an effective model of the dynamics. Instead, it calculates the relative path probability density at the time resolution of the MD integrator. Efficient implementation of Girsanov reweighting requires that the reweighting factors are calculated on-the-fly during the simulations and thus needs to be implemented within the MD integrator. Here, we present a comprehensive guide for implementing Girsanov reweighting into MD simulations. We demonstrate the implementation in the MD simulation package OpenMM by extending the library openmmtools. Additionally, we implemented a reweighted Markov state model estimator within the time series analysis package Deeptime.

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.

Interplay between phosphorylation and oligomerization tunes the conformational ensemble of SWEET transporters

SWEET sugar transporters are desirable biotechnological targets for improving plant growth. One engineering strategy includes modulating how SWEET transporters are regulated. Phosphorylation and oligomerization have been shown to positively regulate SWEET function, leading to increased sugar transport activity. However, constitutive phosphorylation may not be beneficial to plant health under basal conditions. Structural and mechanistic understanding of the interplay between phosphorylation and oligomerization in functional regulation of SWEETs remains limited. Using extensive molecular dynamics simulations coupled with Markov state models, we demonstrate the thermodynamic and kinetic effects of SWEET phosphorylation and oligomerization using OsSWEET2b as a model. We report that the beneficial effects of these SWEET regulatory mechanisms bias outward-facing states and improved extracellular gating, which complement published experimental findings. Our results offer molecular insights to SWEET regulation and may guide engineering strategies throughout the SWEET transport family.

Dynamical Reweighting for Biased Rare Event Simulations

Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.

Mechanistic insights into G-protein activation via phosphorylation mediated non-canonical pathway

Activation of heterotrimeric G-proteins (Gαβγ) downstream to receptor tyrosine kinases (RTKs) is a well-established crosstalk between the signaling pathways mediated by G-protein coupled receptors (GPCRs) and RTKs. While GPCR serves as a guanine exchange factor (GEF) in the canonical activation of Gα that facilitates the exchange of GDP for GTP, the mechanism through which RTK phosphorylations induce Gα activation remains unclear. Recent experimental studies revealed that the epidermal growth factor receptor (EGFR), a well-known RTK, phosphorylates the helical domain tyrosine residues Y154 and Y155 and accelerates the GDP release from the Gαi3, a subtype of Gα-protein. Using well-tempered metadynamics and extensive unbiased molecular dynamics simulations, we captured the GDP release event and identified the intermediates between bound and unbound states through Markov state models. In addition to weakened salt bridges at the domain interface, phosphorylations induced the unfolding of helix αF, which contributed to increased flexibility near the hinge region, facilitating a greater distance between domains in the phosphorylated Gαi3. Although the larger domain separation in the phosphorylated system provided an unobstructed path for the nucleotide, the accelerated release of GDP was attributed to increased fluctuations in several conserved regions like P-loop, switch 1, and switch 2. Overall, this study provides atomistic insights into the activation of G-proteins induced by RTK phosphorylations and identifies the specific structural motifs involved in the process. The knowledge gained from the study could establish a foundation for targeting non-canonical signaling pathways and developing therapeutic strategies against the ailments associated with dysregulated G-protein signaling.

Conformational Dynamics in Corynebacterium glutamicum Diaminopimelate Epimerase: Insights from Ligand Parameterization, Atomistic Simulation, and Markov State Modeling

The microbial enzyme diaminopimelate epimerase (DapF), a vital enzyme in the lysine biosynthetic pathway, catalyzes the conversion of L, L-diaminopimelate (L, L-DAP) to D, L-diaminopimelate (D, L-DAP) using a catalytic cysteine dyad with one cysteine in thiol state and another in thiolate. Under oxidizing conditions, the catalytic cysteines of apo DapF form a disulfide bond that alters the structure and function of DapF. Given its potential as a target for antimicrobial resistance treatments, understanding DapF's functional dynamics is imperative. In the present work, we employ microsecond-scale all-atom molecular dynamics simulations of product-bound DapF and apo-DapF under oxidized and reduced conditions. We employ a polarized charge model for the ligand and the active site residues, which was necessary to preserve the electrostatic environment in the active site and retain the ligand in the active site. The product-bound DapF and apo-DapF in oxidized and reduced conditions exhibit a closed, semi-open, and open conformation, respectively, as identified using the internal coordinates of the dimeric enzyme and the principal component analysis. The conformational switch is guided by the dynamic catalytic (DC) loop, loop II, and loop III movements in the active site. The time scale of the close-to-open conformational transition is estimated to be 0.8 μs through Markov state modeling (MSM) and transition path theory (TPT). The present study explains the role of various active site residues and loops in ligand binding and protein dynamics in the DapF enzyme under different redox conditions. Such information will be helpful in future inhibitor design studies targeting the DapF enzyme.

Quantitative Prediction of Dissociation Rates of PYK2 Ligands Using Umbrella Sampling and Milestoning

We used umbrella sampling and the milestoning simulation method to study the dissociation of multiple ligands from protein kinase PYK2. The activation barriers obtained from the potential of mean force of the umbrella sampling simulations correlated well with the experimental dissociation rates. Using the zero-temperature string method, we obtained optimized paths along the free-energy surfaces for milestoning simulations of three ligands with a similar structure. The milestoning simulations gave an absolute dissociation rate within 2 orders of magnitude of the experimental value for two ligands but at least 3 orders of magnitude too high for the third. Despite the similarity in their structures, the ligands took different pathways to exit from the binding site of PYK2, making contact with different sets of residues. In addition, the protein experienced different conformational changes for dissociation of the three ligands.

From Latent Dynamics to Meaningful Representations

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned representation through prior probability distributions. However, such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted toward leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density─a prior driven by statistical mechanics. We show that this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie data set. We show that our algorithm can uniquely identify orthogonal, isometric, and meaningful latent representations.

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.

Reconnaissance of Allostery via the Restoration of Native p53 DNA-Binding Domain Dynamics in Y220C Mutant p53 Tumor Suppressor Protein

Allosteric regulation of protein dynamics infers a long-range deliberate propagation of information via micro- and macroscale interactions. The Y220C structural mutant is one of the most frequent cancerous p53 mutants. The mutation is distally located from the DNA-binding site of the p53 DNA-binding domain yet causes changes in DNA recognition. This system presents a unique opportunity to examine the allosteric control of mutated proteins under a drug design paradigm. We focus on the key case study of p53 Y220C mutation restoration by a series of new compounds suggested to have Y220C reactivation properties in comparison to our previous findings on the restorative potential of PK11000, a compound studied extensively for reactivation in vitro and in vivo. Previously, we implemented all-atom molecular dynamics (MD) simulations and our lab's techniques of MD-Sectors and MD-Markov state models on the wild type, the Y220C mutant, and Y220C with PK11000 to characterize the effector's restorative properties in terms of conformational dynamics and hydrogen bonding. In this study, we turn to probing the effects made by docking the battery of a new but less well-tested set of aminobenzothiazole derivative compounds reported by Baud et al., which show promise of Y220C rescue. We find that while complete and precise reconstitution of p53 WT molecular dynamics may not be observed as was the case with PK11000, dispersed local reconstitution of loop dynamics provides evidence of rescuing effects by aminobenzothiazole derivative N,2-dihydroxy-3,5-diiodo-4-(1H-pyrrol-1-yl)benzamide, Effector 22, like what we observed for PK11000. Generalizable insights into the mutation and allosteric reactivation of p53 by various effectors by reconstitution of WT dynamics observed in statistical conformational ensemble analysis and network inference are discussed, considering the development of allosteric drug design rooted in first principles.

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.

Characterization of binding kinetics and intracellular signaling of new psychoactive substances targeting cannabinoid receptor using transition-based reweighting method

New psychoactive substances (NPS) targeting cannabinoid receptor 1 pose a significant threat to society as recreational abusive drugs that have pronounced physiological side effects. These greater adverse effects compared to classical cannabinoids have been linked to the higher downstream β-arrestin signaling. Thus, understanding the mechanism of differential signaling will reveal important structure-activity relationship essential for identifying and potentially regulating NPS molecules. In this study, we simulate the slow (un)binding process of NPS MDMB-Fubinaca and classical cannabinoid HU-210 from CB1 using multi-ensemble simulation to decipher the effects of ligand binding dynamics on downstream signaling. The transition-based reweighing method is used for the estimation of transition rates and underlying thermodynamics of (un)binding processes of ligands with nanomolar affinities. Our analyses reveal major interaction differences with transmembrane TM7 between NPS and classical cannabinoids. A variational autoencoder-based approach, neural relational inference (NRI), is applied to assess the allosteric effects on intracellular regions attributable to variations in binding pocket interactions. NRI analysis indicate a heightened level of allosteric control of NPxxY motif for NPS-bound receptors, which contributes to the higher probability of formation of a crucial triad interaction (Y7.53-Y5.58-T3.46) necessary for stronger β-arrestin signaling. Hence, in this work, MD simulation, data-driven statistical methods, and deep learning point out the structural basis for the heightened physiological side effects associated with NPS, contributing to efforts aimed at mitigating their public health impact.

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

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

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.

Analyzing Multimodal Probability Measures with Autoencoders

Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two-dimensional systems and on alanine dipeptide.

Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

A Koopman operator-based prediction algorithm and its application to COVID-19 pandemic and influenza cases

Future state prediction for nonlinear dynamical systems is a challenging task. Classical prediction theory is based on a, typically long, sequence of prior observations and is rooted in assumptions on statistical stationarity of the underlying stochastic process. These algorithms have trouble predicting chaotic dynamics, "Black Swans" (events which have never previously been seen in the observed data), or systems where the underlying driving process fundamentally changes. In this paper we develop (1) a global and local prediction algorithm that can handle these types of systems, (2) a method of switching between local and global prediction, and (3) a retouching method that tracks what predictions would have been if the underlying dynamics had not changed and uses these predictions when the underlying process reverts back to the original dynamics. The methodology is rooted in Koopman operator theory from dynamical systems. An advantage is that it is model-free, purely data-driven and adapts organically to changes in the system. While we showcase the algorithms on predicting the number of infected cases for COVID-19 and influenza cases, we emphasize that this is a general prediction methodology that has applications far outside of epidemiology.

Learning Markovian dynamics with spectral maps

The long-time behavior of many complex molecular systems can often be described by Markovian dynamics in a slow subspace spanned by a few reaction coordinates referred to as collective variables (CVs). However, determining CVs poses a fundamental challenge in chemical physics. Depending on intuition or trial and error to construct CVs can lead to non-Markovian dynamics with long memory effects, hindering analysis. To address this problem, we continue to develop a recently introduced deep-learning technique called spectral map [J. Rydzewski, J. Phys. Chem. Lett. 14, 5216-5220 (2023)]. Spectral map learns slow CVs by maximizing a spectral gap of a Markov transition matrix describing anisotropic diffusion. Here, to represent heterogeneous and multiscale free-energy landscapes with spectral map, we implement an adaptive algorithm to estimate transition probabilities. Through a Markov state model analysis, we validate that spectral map learns slow CVs related to the dominant relaxation timescales and discerns between long-lived metastable states.

Main role of fractal-like nature of conformational space in subdiffusion in proteins

Protein dynamics involves a myriad of mechanical movements happening at different time and space scales, which make it highly complex. One of the less understood features of protein dynamics is subdiffusivity, defined as sublinear dependence between displacement and time. Here, we use all-atoms molecular dynamics (MD) simulations to directly interrogate an already well-established theory and demonstrate that subdiffusivity arises from the fractal nature of the network of metastable conformations over which the dynamics, thought of as a diffusion process, takes place.

Toward physics-based precision medicine: Exploiting protein dynamics to design new therapeutics and interpret variants

The goal of precision medicine is to utilize our knowledge of the molecular causes of disease to better diagnose and treat patients. However, there is a substantial mismatch between the small number of food and drug administration (FDA)-approved drugs and annotated coding variants compared to the needs of precision medicine. This review introduces the concept of physics-based precision medicine, a scalable framework that promises to improve our understanding of sequence-function relationships and accelerate drug discovery. We show that accounting for the ensemble of structures a protein adopts in solution with computer simulations overcomes many of the limitations imposed by assuming a single protein structure. We highlight studies of protein dynamics and recent methods for the analysis of structural ensembles. These studies demonstrate that differences in conformational distributions predict functional differences within protein families and between variants. Thanks to new computational tools that are providing unprecedented access to protein structural ensembles, this insight may enable accurate predictions of variant pathogenicity for entire libraries of variants. We further show that explicitly accounting for protein ensembles, with methods like alchemical free energy calculations or docking to Markov state models, can uncover novel lead compounds. To conclude, we demonstrate that cryptic pockets, or cavities absent in experimental structures, provide an avenue to target proteins that are currently considered undruggable. Taken together, our review provides a roadmap for the field of protein science to accelerate precision medicine.

Learning stochastic dynamics and predicting emergent behavior using transformers

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior under conditions not observed during training. We consider a lattice model of active matter undergoing continuous-time Monte Carlo dynamics, simulated at a density at which its steady state comprises small, dispersed clusters. We train a neural network called a transformer on a single trajectory of the model. The transformer, which we show has the capacity to represent dynamical rules that are numerous and nonlocal, learns that the dynamics of this model consists of a small number of processes. Forward-propagated trajectories of the trained transformer, at densities not encountered during training, exhibit motility-induced phase separation and so predict the existence of a nonequilibrium phase transition. Transformers have the flexibility to learn dynamical rules from observation without explicit enumeration of rates or coarse-graining of configuration space, and so the procedure used here can be applied to a wide range of physical systems, including those with large and complex dynamical generators.

Molecular Insights into the Inhibitory Role of α-Crystallin against γD-Crystallin Aggregation

Cataracts, a major cause of global blindness, contribute significantly to the overall prevalence of blindness. The opacification of the lens, resulting in cataract formation, primarily occurs due to the aggregation of crystallin proteins within the eye lens. Despite the high concentration of these crystallins, they remarkably maintain the lens transparency and refractive index. α-Crystallins (α-crys), acting as chaperones, play a crucial role in preventing crystallin aggregation, although the exact molecular mechanism remains uncertain. In this study, we employed a combination of molecular docking, all-atom molecular dynamics simulations, and advanced free energy calculations to investigate the interaction between γD-crystallin (γD-crys), a major structural protein of the eye lens, and α-crystallin proteins. Our findings demonstrate that α-crys exhibits an enhanced affinity for the NTD2 and CTD4 regions of γD-crys. The NTD2 and CTD4 regions form the interface between the N-terminal domain (NTD) and the C-terminal domain (CTD) of the γD-crys protein. By binding to the interface region between the NTD and CTD of the protein, α-crys effectively inhibits the formation of domain-swapped aggregates and mitigates protein aggregation. Analysis of the Markov state models using molecular dynamics trajectories confirms that minimum free energy conformations correspond to the binding of the α-crystallin domain (ACD) of α-crys to NTD2 and CTD4 that form the interdomain interface.

Unraveling the Interplay of Extracellular Domain Conformational Changes and Parathyroid Hormone Type 1 Receptor Activation in Class B1 G Protein-Coupled Receptors: Integrating Enhanced Sampling Molecular Dynamics Simulations and Markov State Models

Parathyroid hormone (PTH) type 1 receptor (PTH1R), as a typical class B1 G protein-coupled receptor (GPCR), is responsible for regulating bone turnover and maintaining calcium homeostasis, and its dysregulation has been implicated in the development of several diseases. The extracellular domain (ECD) of PTH1R is crucial for the recognition and binding of ligands, and the receptor may exhibit an autoinhibited state with the closure of the ECD in the absence of ligands. However, the correlation between ECD conformations and PTH1R activation remains unclear. Thus, this study combines enhanced sampling molecular dynamics (MD) simulations and Markov state models (MSMs) to reveal the possible relevance between the ECD conformations and the activation of PTH1R. First, 22 intermediate structures are generated from the autoinhibited state to the active state and conducted for 10 independent 200 ns simulations each. Then, the MSM is constructed based on the cumulative 44 μs simulations with six identified microstates. Finally, the potential interplay between ECD conformational changes and PTH1R activation as well as cryptic allosteric pockets in the intermediate states during receptor activation is revealed. Overall, our findings reveal that the activation of PTH1R has a specific correlation with ECD conformational changes and provide essential insights for GPCR biology and developing novel allosteric modulators targeting cryptic sites.

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.

PopShift: A Thermodynamically Sound Approach to Estimate Binding Free Energies by Accounting for Ligand-Induced Population Shifts from a Ligand-Free Markov State Model

Obtaining accurate binding free energies from in silico screens has been a long-standing goal for the computational chemistry community. However, accuracy and computational cost are at odds with one another, limiting the utility of methods that perform this type of calculation. Many methods achieve massive scale by explicitly or implicitly assuming that the target protein adopts a single structure, or undergoes limited fluctuations around that structure, to minimize computational cost. Others simulate each protein-ligand complex of interest, accepting lower throughput in exchange for better predictions of binding affinities. Here, we present the PopShift framework for accounting for the ensemble of structures a protein adopts and their relative probabilities. Protein degrees of freedom are enumerated once, and then arbitrarily many molecules can be screened against this ensemble. Specifically, we use Markov state models (MSMs) as a compressed representation of a protein's thermodynamic ensemble. We start with a ligand-free MSM and then calculate how addition of a ligand shifts the populations of each protein conformational state based on the strength of the interaction between that protein conformation and the ligand. In this work we use docking to estimate the affinity between a given protein structure and ligand, but any estimator of binding affinities could be used in the PopShift framework. We test PopShift on the classic benchmark pocket T4 Lysozyme L99A. We find that PopShift is more accurate than common strategies, such as docking to a single structure and traditional ensemble docking─producing results that compare favorably with alchemical binding free energy calculations in terms of RMSE but not correlation─and may have a more favorable computational cost profile in some applications. In addition to predicting binding free energies and ligand poses, PopShift also provides insight into how the probability of different protein structures is shifted upon addition of various concentrations of ligand, providing a platform for predicting affinities and allosteric effects of ligand binding. Therefore, we expect PopShift will be valuable for hit finding and for providing insight into phenomena like allostery.

Quantifying Disorder in a Protein by Mapping its Locally Correlated Structure and Kinetics

Proteins under physiological conditions are inherently mobile and sample a vast array of structures. Consequently, the need arises, on the one hand, at a local level to determine the independent moving parts and their associated conformations and kinetics, and on the other hand, at a global level, to quantify the disorder in the full protein molecule. We present an approach that provides these quantities in the form of local kinetic network models, which are constructed by analyzing the molecular dynamics (MD) trajectories of the protein molecule. Entropies of independent parts of the molecule are quantified. The method outlined here, using the Trp-cage miniprotein prototype, offers a new tool to understand the dynamic structural changes that ultimately govern the functioning of a protein. The method is particularly suited to problems where there are subtle changes in the structure or dynamics at local levels, for example, due to ligand binding.

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

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

Computational Workflow for Refining AlphaFold Models in Drug Design Using Kinetic and Thermodynamic Binding Calculations: A Case Study for the Unresolved Inactive Human Adenosine A3 Receptor

A structure-based drug design pipeline that considers both thermodynamic and kinetic binding data of ligands against a receptor will enable the computational design of improved drug molecules. For unresolved GPCR-ligand complexes, a workflow that can apply both thermodynamic and kinetic binding data in combination with alpha-fold (AF)-derived or other homology models and experimentally resolved binding modes of relevant ligands in GPCR-homologs needs to be tested. Here, as test case, we studied a congeneric set of ligands that bind to a structurally unresolved G protein-coupled receptor (GPCR), the inactive human adenosine A3 receptor (hA3R). We tested three available homology models from which two have been generated from experimental structures of hA1R or hA2AR and one model was a multistate alphafold 2 (AF2)-derived model. We applied alchemical calculations with thermodynamic integration coupled with molecular dynamics (TI/MD) simulations to calculate the experimental relative binding free energies and residence time (τ)-random accelerated MD (τ-RAMD) simulations to calculate the relative residence times (RTs) for antagonists. While the TI/MD calculations produced, for the three homology models, good Pearson correlation coefficients, correspondingly, r = 0.74, 0.62, and 0.67 and mean unsigned error (mue) values of 0.94, 1.31, and 0.81 kcal mol-1, the τ-RAMD method showed r = 0.92 and 0.52 for the first two models but failed to produce accurate results for the multistate AF2-derived model. With subsequent optimization of the AF2-derived model by reorientation of the side chain of R1735.34 located in the extracellular loop 2 (EL2) that blocked ligand's unbinding, the computational model showed r = 0.84 for kinetic data and improved performance for thermodynamic data (r = 0.81, mue = 0.56 kcal mol-1). Overall, after refining the multistate AF2 model with physics-based tools, we were able to show a strong correlation between predicted and experimental ligand relative residence times and affinities, achieving a level of accuracy comparable to an experimental structure. The computational workflow used can be applied to other receptors, helping to rank candidate drugs in a congeneric series and enabling the prioritization of leads with stronger binding affinities and longer residence times.

Reaction coordinate flows for model reduction of molecular kinetics

In this work, we introduce a flow based machine learning approach called reaction coordinate (RC) flow for the discovery of low-dimensional kinetic models of molecular systems. The RC flow utilizes a normalizing flow to design the coordinate transformation and a Brownian dynamics model to approximate the kinetics of RC, where all model parameters can be estimated in a data-driven manner. In contrast to existing model reduction methods for molecular kinetics, RC flow offers a trainable and tractable model of reduced kinetics in continuous time and space due to the invertibility of the normalizing flow. Furthermore, the Brownian dynamics-based reduced kinetic model investigated in this work yields a readily discernible representation of metastable states within the phase space of the molecular system. Numerical experiments demonstrate how effectively the proposed method discovers interpretable and accurate low-dimensional representations of given full-state kinetics from simulations.

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.

Analysis and interpretation of first passage time distributions featuring rare events

In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.

Unraveling the allosteric inhibition mechanism of PARP-1 CAT and the D766/770A mutation effects via Gaussian accelerated molecular dynamics and Markov state model

PARP-1 (Poly (ADP-ribose) polymerase 1) is a nuclear enzyme and plays a key role in many cellular functions, such as DNA repair, modulation of chromatin structure, and recombination. Developing the PARP-1 inhibitors has emerged as an effective therapeutic strategy for a growing list of cancers. The catalytic structural domain (CAT) of PARP-1 upon binding the inhibitor allosterically regulates the conformational changes of helix domain (HD), affecting its identification with the damaged DNA. The typical type I (EB47) and III (veliparib) inhibitors were able to lengthening or shortening the retention time of this enzyme on DNA damage and thus regulating the cytotoxicity. Nonetheless, the basis underlying allosteric inhibition is unclear, which limits the development of novel PARP-1 inhibitors. Here, to investigate the distinct allosteric changes of EB47 and veliparib against PARP-1 CAT, each complex was simulated via classical and Gaussian accelerated molecular dynamics (cMD and GaMD). To study the reverse allosteric basis and mutation effects, the complexes PARP-1 with UKTT15 and PARP-1 D766/770A mutant with EB47 were also simulated. Importantly, the markov state models were built to identify the transition pathways of crucial substates of allosteric communication and the induction basis of PARP-1 reverse allostery. The conformational change differences of PARP-1 CAT regulated by allosteric inhibitors were concerned with to their interaction at the active site. Energy calculations suggested the energy advantage of EB47 in inhibiting the wild-type PARP-1, compared with D766/770A PARP-1. Secondary structure results showed the change of two key loops (αB-αD and αE-αF) in different systems. This work reported the basis of PARP-1 allostery from both thermodynamic and kinetic views, providing the guidance for the discovery and design of more innovative PARP-1 allosteric inhibitors.

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.

On committor functions in milestoning

As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions.

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).

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.

Navigating the Expansive Landscapes of Soft Materials: A User Guide for High-Throughput Workflows

Synthetic polymers are highly customizable with tailored structures and functionality, yet this versatility generates challenges in the design of advanced materials due to the size and complexity of the design space. Thus, exploration and optimization of polymer properties using combinatorial libraries has become increasingly common, which requires careful selection of synthetic strategies, characterization techniques, and rapid processing workflows to obtain fundamental principles from these large data sets. Herein, we provide guidelines for strategic design of macromolecule libraries and workflows to efficiently navigate these high-dimensional design spaces. We describe synthetic methods for multiple library sizes and structures as well as characterization methods to rapidly generate data sets, including tools that can be adapted from biological workflows. We further highlight relevant insights from statistics and machine learning to aid in data featurization, representation, and analysis. This Perspective acts as a "user guide" for researchers interested in leveraging high-throughput screening toward the design of multifunctional polymers and predictive modeling of structure-property relationships in soft materials.

Staphylococcus aureus functional amyloids catalyze degradation of β-lactam antibiotics

Antibiotic resistance of bacteria is considered one of the most alarming developments in modern medicine. While varied pathways for bacteria acquiring antibiotic resistance have been identified, there still are open questions concerning the mechanisms underlying resistance. Here, we show that alpha phenol-soluble modulins (PSMαs), functional bacterial amyloids secreted by Staphylococcus aureus, catalyze hydrolysis of β-lactams, a prominent class of antibiotic compounds. Specifically, we show that PSMα2 and, particularly, PSMα3 catalyze hydrolysis of the amide-like bond of the four membered β-lactam ring of nitrocefin, an antibiotic β-lactam surrogate. Examination of the catalytic activities of several PSMα3 variants allowed mapping of the active sites on the amyloid fibrils' surface, specifically underscoring the key roles of the cross-α fibril organization, and the combined electrostatic and nucleophilic functions of the lysine arrays. Molecular dynamics simulations further illuminate the structural features of β-lactam association upon the fibril surface. Complementary experimental data underscore the generality of the functional amyloid-mediated catalytic phenomenon, demonstrating hydrolysis of clinically employed β-lactams by PSMα3 fibrils, and illustrating antibiotic degradation in actual S. aureus biofilms and live bacteria environments. Overall, this study unveils functional amyloids as catalytic agents inducing degradation of β-lactam antibiotics, underlying possible antibiotic resistance mechanisms associated with bacterial biofilms.

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.