Path Sampling Research Articles

Gating residues govern ligand unbinding kinetics from the buried cavity in HIF-2α PAS-B.

While transcription factors have been generally perceived as "undruggable," an exception is the HIF-2 hypoxia-inducible transcription factor, which contains an internal cavity that is sufficiently large to accommodate a range of small-molecules, including the therapeutically used inhibitor belzutifan. Given the relatively long ligand residence times of these small molecules and the lack of any experimentally observed pathway connecting the cavity to solvent, there has been great interest in understanding how these drug ligands exit the buried receptor cavity. Here, we focus on the relevant PAS-B domain of hypoxia-inducible factor 2α (HIF-2α) and examine how one such small molecule (THS-017) exits from the buried cavity within this domain on the seconds-timescale using atomistic simulations and ZZ-exchange NMR. To enable the simulations, we applied the weighted ensemble path sampling strategy, which generates continuous pathways for a rare-event process [e.g., ligand (un)binding] with rigorous kinetics in orders of magnitude less computing time compared to conventional simulations. Results reveal the formation of an encounter complex intermediate and two distinct classes of pathways for ligand exit. Based on these pathways, we identified two pairs of conformational gating residues in the receptor: one for the major class (N288 and S304) and another for the minor class (L272 and M309). ZZ-exchange NMR validated the kinetic importance of N288 for ligand unbinding. Our results provide an ideal simulation dataset for rational manipulation of ligand unbinding kinetics.

Elucidating Dynamical Behaviors in Kinetically Constrained Models via Energy-Activity Double-Biased Matrix Product State Analysis.

We investigate dynamical phase transitions in two representative kinetically constrained models: the 1D Fredrickson-Andersen and East Models. A recently developed energy-activity double-bias approach utilizing both s and g fields, conjugated with dynamical activity and trajectory energy, is combined with matrix product state (MPS) methods. It is demonstrated that MPS methods facilitate the numerical approximation of large-deviation statistics of dynamics by determining the eigenvalues of tilted dynamical generators under the influence of double-biasing fields. Specifically, by focusing on the g-field, a nearly "half-filled" state at moderate negative g values is identified, indicating the potential existence of an anomalous phase. Additionally, dynamical quantities under various s, g, and T conditions are obtained via tensor networks, showing good qualitative consistency with mean-field results and our previous extensive numerical simulation results obtained by the path sampling method. Our study introduces novel methodologies for examining decoupled dynamical behaviors that, although energetically active, remain dynamically inactive within the system. This approach offers a fresh perspective on the theoretical framework and computational strategies for studying dynamical phase transitions in kinetically constrained systems.

Rare-Event Sampling using a Reinforcement Learning-Based Weighted Ensemble Method.

Despite the power of path sampling strategies in enabling simulations of rare events, such strategies have not reached their full potential. A common challenge that remains is the identification of a progress coordinate that captures the slow relevant motions of a rare event. Here we have developed a weighted ensemble (WE) path sampling strategy that exploits reinforcement learning to automatically identify an effective progress coordinate among a set of potential coordinates during a simulation. We apply our WE strategy with reinforcement learning to three benchmark systems: (i) an egg carton-shaped toy potential, (ii) an S-shaped toy potential, and (iii) a dimer of the HIV-1 capsid protein (C-terminal domain). To enable rapid testing of the latter system at the atomic level, we employed discrete-state synthetic molecular dynamics trajectories using a generative, fine-grained Markov state model that was based on extensive conventional simulations. Our results demonstrate that using concepts from reinforcement learning with a weighted ensemble of trajectories automatically identifies relevant progress coordinates among multiple candidates at a given time during a simulation. Due to the rigorous weighting of trajectories, the simulations maintain rigorous kinetics.

Generating Protein Structures for Pathway Discovery Using Deep Learning.

Resolving the intricate details of biological phenomena at the molecular level is fundamentally limited by both length- and time scales that can be probed experimentally. Molecular dynamics (MD) simulations at various scales are powerful tools frequently employed to offer valuable biological insights beyond experimental resolution. However, while it is relatively simple to observe long-lived, stable configurations of, for example, proteins, at the required spatial resolution, simulating the more interesting rare transitions between such states often takes orders of magnitude longer than what is feasible even on the largest supercomputers available today. One common aspect of this challenge is pathway discovery, where the start and end states of a scientific phenomenon are known or can be approximated, but the mechanistic details in between are unknown. Here, we propose a representation-learning-based solution that uses interpolation and extrapolation in an abstract representation space to synthesize potential transition states, which are automatically validated using MD simulations. The new simulations of the synthesized transition states are subsequently incorporated into the representation learning, leading to an iterative framework for targeted path sampling. Our approach is demonstrated by recovering the transition of a RAS-RAF protein domain (CRD) from membrane-free to interacting with the membrane using coarse-grain MD simulations.

Microstructure and mechanical properties of 2195 Al-Li alloy via friction stir additive manufacturing with different stirring paths

Friction stir additive manufacturing (FSAM) is increasingly becoming a feasible method for aluminum alloy structure due to the unique forming characteristics. In this study, two different stirring paths were explored for 2195 Al-Li alloy and the microstructure evolution and mechanical properties were ‌investigated. An ultrafine grained microstructure was formed in the FSAMed zone with an average grain size ranging from 1 to 5μm. The microstructure in the FSAMed zone at the bottom exhibited a consistent direction trend and a significant increase in dislocation density. Different stirring paths had minimal impact on the phase distribution. Frictional heating led to the re-dissolution and re-precipitation of precipitates, resulting in T1, θ', and δ'/β' were distributed within the grains. The samples of intersecting stirring path showed similar mechanical properties in different directions, while the UTS of LD was 52.56 MPa higher than TD of the reciprocating path samples. The microhardness range for the intersecting stirring path ranged from 87.0 HV0.2 to 126.6 HV0.2, while the reciprocating stirring path exhibited a microhardness range of 83.8 HV0.2 to 132.4 HV0.2. In summary, this study provides valuable insights into designing processing paths for FSAM of 2195 Al-Li alloy.

The Evolution of the Acylation Mechanism in β-Lactamase and Rapid Protein Dynamics.

β-Lactamases are a class of well-studied enzymes that are known to have existed since billions of years ago, starting as a defense mechanism to stave off competitors and are now enzymes responsible for antibiotic resistance. Using ancestral sequence reconstruction, it is possible to study the crystal structure of a laboratory resurrected 2-3 billion year-old β-lactamase. Comparing the ancestral enzyme to its modern counterpart, a TEM-1 β-lactamase, the structural changes are minor, and it is probable that dynamic effects play an important role in the evolution of function. We used molecular dynamics simulations and employed transition path sampling methods to identify the presence of rate-enhancing dynamics at the femtosecond level in both systems, found that these fast motions are more efficiently coordinated in the modern enzyme, and examined how specific dynamics can pinpoint evolutionary effects that are essential for improving enzymatic catalysis.

Accelerating scientific discovery with generative knowledge extraction, graph-based representation, and multimodal intelligent graph reasoning

Abstract Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers focused on biological materials into a comprehensive ontological knowledge graph. Through an in-depth structural analysis of this graph, we have calculated node degrees, identified communities along with their connectivities, and evaluated clustering coefficients and betweenness centrality of pivotal nodes, uncovering fascinating knowledge architectures. We find that the graph has an inherently scale-free nature, shows a high level of connectedness, and can be used as a rich source for downstream graph reasoning by taking advantage of transitive and isomorphic properties to reveal insights into unprecedented interdisciplinary relationships that can be used to answer queries, identify gaps in knowledge, propose never-before-seen material designs, and predict material behaviors. Using a large language embedding model we compute deep node representations and use combinatorial node similarity ranking to develop a path sampling strategy that allows us to link dissimilar concepts that have previously not been related. One comparison revealed detailed structural parallels between biological materials and Beethoven's 9th Symphony, highlighting shared patterns of complexity through isomorphic mapping. In another example, the algorithm proposed an innovative hierarchical mycelium-based composite based on integrating path sampling with principles extracted from Kandinsky's `Composition VII' painting. The resulting material integrates an innovative set of concepts that include a balance of chaos and order, adjustable porosity, mechanical strength, and complex patterned chemical functionalization. We uncover other isomorphisms across science, technology and art, revealing a nuanced ontology of immanence that reveal a context-dependent heterarchical interplay of constituents. Because our method transcends established disciplinary boundaries through diverse data modalities (graphs, images, text, numerical data, etc.), graph-based generative AI achieves a far higher degree of novelty, explorative capacity, and technical detail, than conventional approaches and establishes a widely useful framework for innovation by revealing hidden connections.

PathMLP: Smooth path towards high-order homophily

Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance. Intriguingly, from the observation of heterophilous data, we notice that certain high-order information exhibits higher homophily, which motivates us to involve high-order information in node representation learning. However, common practices in GNNs to acquire high-order information mainly through increasing model depth and altering message-passing mechanisms, which, albeit effective to a certain extent, suffer from three shortcomings: (1) over-smoothing due to excessive model depth and propagation times; (2) high-order information is not fully utilized; (3) low computational efficiency. In this regard, we design a similarity-based path sampling strategy to capture smooth paths containing high-order homophily. Then we propose a lightweight model based on multi-layer perceptrons (MLP), named PathMLP, which can encode messages carried by paths via simple transformation and concatenation operations, and effectively learn node representations in heterophilous graphs through adaptive path aggregation. Extensive experiments demonstrate that our method outperforms baselines on 16 out of 20 datasets, underlining its effectiveness and superiority in alleviating the heterophily problem. In addition, our method is immune to over-smoothing and has high computational efficiency. The source code will be available in https://github.com/Graph4Sec-Team/PathMLP.

Energy landscapes for clusters of hexapeptides.

We present the results for energy landscapes of hexapeptides obtained using interfaces to the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) program. We have used basin-hopping global optimization and discrete path sampling to explore the landscapes of hexapeptide monomers, dimers, and oligomers containing 10, 100, and 200 monomers modeled using a residue-level coarse-grained potential, Mpipi, implemented in LAMMPS. We find that the dimers of peptides containing amino acid residues that are better at promoting phase separation, such as tyrosine and arginine, have melting peaks at higher temperature in their heat capacity compared to phenylalanine and lysine, respectively. This observation correlates with previous work on the same uncapped hexapeptide monomers modeled using atomistic potential. For oligomers, we compare the variation in monomer conformations with radial distance and observe trends for selected angles calculated for each monomer. The LAMMPS interfaces to the GMIN and OPTIM programs for landscape exploration offer new opportunities to investigate larger systems and provide access to the coarse-grained potentials implemented within LAMMPS.

Path ahead: Tackling the Challenge of Computationally Estimating Lithium Diffusion in Cathode Materials.

In the roadmap toward designing new and improved materials for Lithium ion batteries, the ability to estimate the diffusion coefficient of Li atoms in electrodes, and eventually solid-state electrolytes, is key. Nevertheless, as of today, accurate prediction through computational tools remains challenging. Its experimental measurement does not appear to be much easier. In this work, we devise a computational protocol for the determination of the Li-migration energy barrier and diffusion coefficient, focusing on a common cathode material such as LiNiO2, which represents a prototype of the widely adopted NMC (LiNi1-x-y Mn x Co y O2) class of materials. Different methodologies are exploited, combining ab initio metadynamics, path sampling, and density functional theory. Furthermore, we propose a novel, fast, and simple 1D approximation for the estimation of the effective frequency. The outlined computational protocol aims to be generally applicable to Lithium diffusion in other materials and components for batteries, including anodes and solid electrolytes.

Harvesting nucleating structures in nanoparticle crystallization: The example of gold, silver, and iron.

The thermodynamics and kinetics of nanoparticle crystallization, as opposed to bulk phases, may be influenced by surface and size effects. We investigate the importance of such factors in the crystallization process of gold, silver, and iron nanodroplets using numerical simulations in the form of molecular dynamics combined with path sampling. This modeling strategy is targeted at obtaining representative ensembles of structures located at the transition state of the crystallization process. A structural analysis of the transition state ensembles reveals that both the average size and location of the critical nucleation cluster are influenced by surface and nanoscale size effects. Furthermore, we also show that transition state structures in smaller nanodroplets exhibit a more ordered liquid phase, and differentiating between a well-ordered critical cluster and its surrounding disordered liquid phase becomes less evident. All in all, these findings demonstrate that crystallization mechanisms in nanoparticles go beyond the assumptions of classical nucleation theory.

Bridge Sampling for Connections via Multiple Scattering Events

AbstractExplicit sampling of and connecting to light sources is often essential for reducing variance in Monte Carlo rendering. In dense, forward‐scattering participating media, its benefit declines, as significant transport happens over longer multiple‐scattering paths around the straight connection to the light. Sampling these paths is challenging, as their contribution is shaped by the product of reciprocal squared distance terms and the phase functions. Previous work demonstrates that sampling several of these terms jointly is crucial. However, these methods are tied to low‐order scattering or struggle with highly‐peaked phase functions.We present a method for sampling a bridge: a subpath of arbitrary vertex count connecting two vertices. Its probability density is proportional to all phase functions at inner vertices and reciprocal squared distance terms. To achieve this, we importance sample the phase functions first, and subsequently all distances at once. For the latter, we sample an independent, preliminary distance for each edge of the bridge, and afterwards scale the bridge such that it matches the connection distance. The scale factor can be marginalized out analytically to obtain the probability density of the bridge. This approach leads to a simple algorithm and can construct bridges of any vertex count. For the case of one or two inserted vertices, we also show an alternative without scaling or marginalization.For practical path sampling, we present a method to sample the number of bridge vertices whose distribution depends on the connection distance, the phase function, and the collision coefficient. While our importance sampling treats media as homogeneous we demonstrate its effectiveness on heterogeneous media.

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In the field of autonomous mobile robots, sampling-based motion planning methods have demonstrated their efficiency in complex environments. Although the Rapidly-exploring Random Tree (RRT) algorithm and its variants have achieved significant success in known static environment, it is still challenging in achieving optimal motion planning in unknown dynamic environments. To address this issue, this paper proposes a novel motion planning algorithm Bi-HS-RRTX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\ ext {X}$$\\end{document}, which facilitates asymptotically optimal real-time planning in continuously changing unknown environments. The algorithm swiftly determines an initial feasible path by employing the bidirectional search. When dynamic obstacles render the planned path infeasible, the bidirectional search is reactivated promptly to reconstruct the search tree in a local area, thereby significantly reducing the search planning time. Additionally, this paper adopts a hybrid heuristic sampling strategy to optimize the planned path quality and search efficiency. The convergence of the proposed algorithm is accelerated by merging local biased sampling with nominal path and global heuristic sampling in hyper-ellipsoid region. To verify the effectiveness and efficiency of the proposed algorithm in unknown dynamic environments, numerous comparative experiments with existing algorithms were conducted. The experimental results indicate that the proposed planning algorithm has significant advantages in planned path length and planning time.

WEDAP: A Python Package for Streamlined Plotting of Molecular Simulation Data.

Given the growing interest in path sampling methods for extending the time scales of molecular dynamics (MD) simulations, there has been great interest in software tools that streamline the generation of plots for monitoring the progress of large-scale simulations. Here, we present the WEDAP Python package for simplifying the analysis of data generated from either conventional MD simulations or the weighted ensemble (WE) path sampling method, as implemented in the widely used WESTPA software package. WEDAP facilitates (i) the parsing of WE simulation data stored in highly compressed, hierarchical HDF5 files and (ii) incorporates trajectory weights from WE simulations into all generated plots. Our Python package consists of multiple user-friendly interfaces: a command-line interface, a graphical user interface, and a Python application programming interface. We demonstrate the plotting features of WEDAP through a series of examples using data from WE and conventional MD simulations that focus on the HIV-1 capsid protein's C-terminal domain dimer as a showcase system. The source code for WEDAP is freely available on GitHub at https://github.com/chonglab-pitt/wedap.

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.

Substrate Turnover Dynamics Guide Ketol-Acid Reductoisomerase Redesign for Increased Specific Activity.

The task of adapting enzymes for specific applications is often hampered by our incomplete ability to tune and tailor catalytic functions, particularly when seeking increased activity. Here, we develop and demonstrate a rational approach to address this challenge, applied to ketol-acid reductoisomerase (KARI), which has uses in industrial-scale isobutanol production. While traditional structure-based computational enzyme redesign strategies typically focus on the enzyme-bound ground state (GS) and transition state (TS), we postulated that additionally treating the underlying dynamics of complete turnover events that connect and pass through both states could further elucidate the structural properties affecting catalysis and help identify mutations that lead to increased catalytic activity. To examine the dynamics of substrate conversion with atomistic detail, we adapted and applied computational methods based on path sampling techniques to gather thousands of QM/MM simulations of attempted substrate turnover events by KARI: both productive (reactive) and unproductive (nonreactive) attempts. From these data, machine learning models were constructed and used to identify specific conformational features (interatomic distances, angles, and torsions) associated with successful, productive catalysis. Multistate protein redesign techniques were then used to select mutations that stabilized reactive-like structures over nonreactive-like ones while also meeting additional criteria consistent with enhanced specific activity. This procedure resulted in eight high-confidence enzyme mutants with a significant improvement in calculated specific activity relative to wild type (WT), with the fastest variant's increase in calculated k cat being (2 ± 1) × 104-fold. Collectively, these results suggest that introducing mutations designed to increase the population of reaction-promoting conformations of the enzyme-substrate complex before it reaches the barrier can provide an effective approach to engineering improved enzyme catalysts.

Energy landscapes for the quantum approximate optimization algorithm

Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary noisy intermediate-scale quantum (NISQ) era. The quantum approximate optimization algorithm (QAOA) is one such algorithm, used in solving the maximum cut (Max-Cut) problem for a given graph by successive implementation of L quantum circuit layers within a corresponding Trotterized ansatz. The challenge of exploring the cost function of VQAs arising from an exponential proliferation of local minima with increasing circuit depth has been well documented. However, fewer studies have investigated the impact of circuit depth on QAOA performance in finding the correct Max-Cut solution. Here we employ basin-hopping global optimization methods to navigate the energy landscapes for QAOA ansätze for various graphs, and analyze QAOA performance in finding the correct Max-Cut solution. The structure of the solution space is also investigated using discrete path sampling to build databases of local minima and the transition states that connect them, providing insightful visualizations using disconnectivity graphs. We find that the corresponding landscapes generally have a single funnel organization, which makes it relatively straightforward to locate low-lying minima with good Max-Cut solution probabilities. In some cases below the adiabatic limit the second lowest local minimum may even yield a higher solution probability than the global minimum. This important observation has motivated us to develop broader metrics in evaluating QAOA performance, based on collections of minima obtained from basin-hopping global optimization. Hence we establish expectation thresholds in elucidating useful solution probabilities from local minima, an approach that may provide significant gains in elucidating reasonable solution probabilities from local minima. Published by the American Physical Society 2024

Combining Transition Path Sampling with Data-Driven Collective Variables through a Reactivity-Biased Shooting Algorithm.

Rare event sampling is a central problem in modern computational chemistry research. Among the existing methods, transition path sampling (TPS) can generate unbiased representations of reaction processes. However, its efficiency depends on the ability to generate reactive trial paths, which in turn depends on the quality of the shooting algorithm used. We propose a new algorithm based on the shooting success rate, i.e., reactivity, measured as a function of a reduced set of collective variables (CVs). These variables are extracted with a machine learning approach directly from TPS simulations, using a multitask objective function. Iteratively, this workflow significantly improves the shooting efficiency without any prior knowledge of the process. In addition, the optimized CVs can be used with biased enhanced sampling methodologies to accurately reconstruct the free energy profiles. We tested the method on three different systems: a two-dimensional toy model, conformational transitions of alanine dipeptide, and hydrolysis of acetyl chloride in bulk water. In the latter, we integrated our workflow with an active learning scheme to learn a reactive machine learning-based potential, which allowed us to study the mechanism and free energy profile with an ab initio-like accuracy.

Competing Reaction Mechanisms of Peptide Bond Formation in Water Revealed by Deep Potential Molecular Dynamics and Path Sampling.

The formation of an amide bond is an essential step in the synthesis of materials and drugs, and in the assembly of amino acids to form peptides. The mechanism of this reaction has been studied extensively, in particular to understand how it can be catalyzed, but a representation capable of explaining all the experimental data is still lacking. Numerical simulation should provide the necessary molecular description, but the solvent involvement poses a number of challenges. Here, we combine the efficiency and accuracy of neural network potential-based reactive molecular dynamics with the extensive and unbiased exploration of reaction pathways provided by transition path sampling. Using microsecond-scale simulations at the density functional theory level, we show that this method reveals the presence of two competing distinct mechanisms for peptide bond formation between alanine esters in aqueous solution. We describe how both reaction pathways, via a general base catalysis mechanism and via direct cleavage of the tetrahedral intermediate respectively, change with pH. This result contrasts with the conventional mechanism involving a single pathway in which only the barrier heights are affected by pH. We show that this new proposal involving two competing mechanisms is consistent with the experimental data, and we discuss the implications for peptide bond formation under prebiotic conditions and in the ribosome. Our work shows that integrating deep potential molecular dynamics with path sampling provides a powerful approach for exploring complex chemical mechanisms.

Prediction of 3D RNA Structures from Sequence Using Energy Landscapes of RNA Dimers: Application to RNA Tetraloops.

Access to the three-dimensional structure of RNA enables an ability to gain a more profound understanding of its biological mechanisms, as well as the ability to design RNA-targeting drugs, which can take advantage of the unique chemical environment imposed by a folded RNA structure. Due to the dynamic and structurally complex properties of RNA, both experimental and traditional computational methods have difficulty in determining RNA's 3D structure. Herein, we introduce TAPERSS (Theoretical Analyses, Prediction, and Evaluation of RNA Structures from Sequence), a physics-based fragment assembly method for predicting 3D RNA structures from sequence. Using a fragment library created using discrete path sampling calculations of RNA dinucleoside monophosphates, TAPERSS can sample the physics-based energy landscapes of any RNA sequence with relatively low computational complexity. We have benchmarked TAPERSS on 21 RNA tetraloops, using a combinatorial algorithm as a proof-of-concept. We show that TAPERSS was successfully able to predict the apo-state structures of all 21 RNA hairpins, with 16 of those structures also having low predicted energies as well. We demonstrate that TAPERSS performs most accurately on GNRA-like tetraloops with mostly stacked loop-nucleotides, while having limited success with more dynamic UNCG and CUYG tetraloops, most likely due to the influence of the RNA force field used to create the fragment library. Moreover, we show that TAPERSS can successfully predict the majority of the experimental non-apo states, highlighting its potential in anticipating biologically significant yet unobserved states. This holds great promise for future applications in drug design and related studies. With discussed improvements and implementation of more efficient sampling algorithms, we believe TAPERSS may serve as a useful tool for a physics-based conformational sampling of large RNA structures.