Reaction Coordinates for Conformational Transitions Using Linear Discriminant Analysis on Positions

Accelerating Molecular Dynamics through Informed Resetting

We present a procedure for enhanced sampling of molecular dynamics simulations through informed stochastic resetting. Many phenomena, such as protein folding and crystal nucleation, occur over time scales inaccessible in standard simulations. We recently showed that stochastic resetting can accelerate molecular simulations that exhibit broad transition time distributions. However, standard stochastic resetting does not exploit any information about the reaction progress. For a model system and chignolin in explicit water, we demonstrate that an informed resetting protocol leads to greater accelerations than standard stochastic resetting in molecular dynamics and Metadynamics simulations. This is achieved by resetting only when a certain condition is met, e.g., when the distance from the target along the reaction coordinate is larger than some threshold. We use these accelerated simulations to infer important kinetic observables such as the unbiased mean first-passage time and direct transit time. For the latter, Metadynamics with informed resetting leads to speedups of 2-3 orders of magnitude over unbiased simulations with relative errors of only ∼35-70%. Our work significantly extends the applicability of stochastic resetting for enhanced sampling of molecular simulations.

A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a Mode evolution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.

Analysis of mapping atomic models to coarse-grained resolution

Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.

Molecular simulation approaches to probing the effects of mechanical forces in the actin cytoskeleton

In this article we give our perspective on the successes and promise of various molecular and coarse-grained simulation approaches to probing the effect of mechanical forces in the actin cytoskeleton.

Good Rates From Bad Coordinates: The Exponential Average Time-dependent Rate Approach

Our ability to calculate rate constants of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barrier heights. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables (CVs). This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the "CV biasing efficiency" γ. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect CV, where γ = 1. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different CVs to bias, but which is sufficiently simple that we are able to compute the unbiased rate directly. For this system, we demonstrate that predictions from our new Exponential Average Time-Dependent Rate (EATR) estimator converge to the true rate constant more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the γ parameter can serve as a good metric for assessing the quality of the biasing coordinate. We demonstrate that these results hold when applying the methods to an atomistic protein folding example. Finally, we demonstrate that our approach works when combining multiple less-than-optimal bias coordinates, and adapt our method to the related "OPES flooding" approach. Overall, our time-dependent rate approach offers a powerful framework for predicting rate constants from biased simulations.

Motif-VI loop acts as a nucleotide valve in the West Nile Virus NS3 Helicase

The Orthoflavivirus NS3 helicase (NS3h) is crucial in virus replication, representing a potential drug target for pathogenesis. NS3h utilizes nucleotide triphosphate (ATP) for hydrolysis energy to translocate on single-stranded nucleic acids, which is an important step in the unwinding of double-stranded nucleic acids. Intermediate states along the ATP hydrolysis cycle and conformational changes between these states, represent important yet difficult-to-identify targets for potential inhibitors. Extensive molecular dynamics simulations of West Nile virus NS3h+ssRNA in the apo, ATP, ADP+Pi and ADP bound states were used to model the conformational ensembles along this cycle. Energetic and structural clustering analyses depict a clear trend of differential enthalpic affinity of NS3h with ADP, demonstrating a probable mechanism of hydrolysis turnover regulated by the motif-VI loop (MVIL). Based on these results, MVIL mutants (D471L, D471N and D471E) were found to have a substantial reduction in ATPase activity and RNA replication compared to the wild-type. Simulations of the mutants in the apo state indicate a shift in MVIL populations favoring either a closed or open 'valve' conformation, affecting ATP entry or stabilization, respectively. Combining our molecular modeling with experimental evidence highlights a conformation-dependent role for MVIL as a 'valve' for the ATP-pocket, presenting a promising target for antiviral development.

Machine Learning Deciphered Molecular Mechanistics with Accurate Kinetic and Thermodynamic Prediction

Time-lagged independent component analysis (tICA) and the Markov state model (MSM) have been extensively employed for extracting conformational dynamics and kinetic community networks from unbiased trajectory ensembles. However, these techniques may not be the optimal choice for elucidating transition mechanisms within low-dimensional representations, especially for intricate biosystems. Unraveling the association mechanism in such complex systems always necessitates permutations of several essential independent components or collective variables, a process that is inherently obscure and may require empirical knowledge for selection. To address these challenges, we have implemented an integrated unsupervised dimension reduction model: uniform manifold approximation and projection (UMAP) with hierarchy density-based spatial clustering of applications with noise (HDBSCAN). This approach effectively generates low-dimensional configurational embeddings. The hierarchical application of this architecture, in conjunction with MSM, reveals global kinetic connectivity while identifying local conformational states. Consequently, our methodology establishes a multiscale mechanistic elucidation framework. Leveraging the benefits of the uniform sample distribution and a denoising approach, our model demonstrates robustness in preserving global and local data structures compared to traditional dimension reduction methods in the field of MD analysis area. The interpretability of hyperparameter selection and compatibility with downstream tasks are cross-validated across various simulation data sets, utilizing both computational evaluation metrics and experimental kinetic observables. Furthermore, the predicted Mcl1-BH3 association kinetics (0.76 s-1) is in close agreement with surface plasmon resonance experiments (0.12 s-1), affirming the plausibility of the identified pathway composed of representative conformations. We anticipate that the devised workflow will serve as a foundational framework for studying recognition patterns in complex biological systems. Its contributions extend to the exploration of protein functional dynamics and rational drug design, offering a potent avenue for advancing research in these domains.

Enhanced Sampling with Machine Learning

Molecular dynamics (MD) enables the study of physical systems with excellent spatiotemporal resolution but suffers from severe timescale limitations. To address this, enhanced sampling methods have been developed to improve the exploration of configurational space. However, implementing these methods is challenging and requires domain expertise. In recent years, integration of machine learning (ML) techniques into different domains has shown promise, prompting their adoption in enhanced sampling as well. Although ML is often employed in various fields primarily due to its data-driven nature, its integration with enhanced sampling is more natural with many common underlying synergies. This review explores the merging of ML and enhanced MD by presenting different shared viewpoints. It offers a comprehensive overview of this rapidly evolving field, which can be difficult to stay updated on. We highlight successful strategies such as dimensionality reduction, reinforcement learning, and flow-based methods. Finally, we discuss open problems at the exciting ML-enhanced MD interface.

Quantifying Unbiased Conformational Ensembles from Biased Simulations Using ShapeGMM

Quantifying the conformational ensembles of biomolecules is fundamental to describing mechanisms of processes such as protein folding, interconversion between folded states, ligand binding, and allosteric regulation. Accurate quantification of these ensembles remains a challenge for conventional molecular simulations of all but the simplest molecules due to insufficient sampling. Enhanced sampling approaches, such as metadynamics, were designed to overcome this challenge; however, the nonuniform frame weights that result from many of these approaches present an additional challenge to ensemble quantification techniques such as Markov State Modeling or structural clustering. Here, we present rigorous inclusion of nonuniform frame weights into a structural clustering method entitled shapeGMM. The result of frame-weighted shapeGMM is a high dimensional probability density and generative model for the unbiased system from which we can compute important thermodynamic properties such as relative free energies and configurational entropy. The accuracy of this approach is demonstrated by the quantitative agreement between GMMs computed by Hamiltonian reweighting and direct simulation of a coarse-grained helix model system. Furthermore, the relative free energy computed from a shapeGMM probability density of alanine dipeptide reweighted from a metadynamics simulation quantitatively reproduces the underlying free energy in the basins. Finally, the method identifies hidden structures along the actin globular to filamentous-like structural transition from a metadynamics simulation on a linear discriminant analysis coordinate trained on GMM states, illustrating how structural clustering of biased data can lead to biophysical insight. Combined, these results demonstrate that frame-weighted shapeGMM is a powerful approach to quantifying biomolecular ensembles from biased simulations.

Short-Time Infrequent Metadynamics for Improved Kinetics Inference

Infrequent Metadynamics is a popular method to obtain the rates of long time-scale processes from accelerated simulations. The inference procedure is based on rescaling the first-passage times of the Metadynamics trajectories using a bias-dependent acceleration factor. While useful in many cases, it is limited to Poisson kinetics, and a reliable estimation of the unbiased rate requires slow bias deposition and prior knowledge of efficient collective variables. Here, we propose an improved inference scheme, which is based on two key observations: (1) the time-independent rate of Poisson processes can be estimated using short trajectories only. (2) Short trajectories experience minimal bias, and their rescaled first-passage times follow the unbiased distribution even for relatively high deposition rates and suboptimal collective variables. Therefore, by basing the inference procedure on short time scales, we obtain an improved trade-off between speedup and accuracy at no additional computational cost, especially when employing suboptimal collective variables. We demonstrate the improved inference scheme for a model system and two molecular systems.

Improved Prediction of Molecular Response to Pulling by Combining Force Tempering with Replica Exchange Methods

Small mechanical forces play important functional roles in many crucial cellular processes, including in the dynamic behavior of the cytoskeleton and in the regulation of osmotic pressure through membrane-bound proteins. Molecular simulations offer the promise of being able to design the behavior of proteins that sense and respond to these forces. However, it is difficult to predict and identify the effect of the relevant piconewton (pN) scale forces due to their small magnitude. Previously, we introduced the Infinite Switch Simulated Tempering in Force (FISST) method, which allows one to estimate the effect of a range of applied forces from a single molecular dynamics simulation, and also demonstrated that FISST additionally accelerates sampling of a molecule's conformational landscape. For some problems, we find that this acceleration is not sufficient to capture all relevant conformational fluctuations, and hence, here we demonstrate that FISST can be combined with either temperature replica exchange or solute tempering approaches to produce a hybrid method that enables more robust prediction of the effect of small forces on molecular systems.

Role of ATP Hydrolysis and Product Release in the Translocation Mechanism of SARS-CoV-2 NSP13

In response to the emergence of COVID-19, caused by SARS-CoV-2, there has been a growing interest in understanding the functional mechanisms of the viral proteins to aid in the development of new therapeutics. Nonstructural protein 13 (nsp13) helicase is an attractive target for antivirals because it is essential for viral replication and has a low mutation rate, yet the structural mechanisms by which this enzyme binds and hydrolyzes ATP to cause unidirectional RNA translocation remain elusive. Using Gaussian accelerated molecular dynamics (GaMD), we generated comprehensive conformational ensembles of all substrate states along the ATP-dependent cycle. Shape-GMM clustering of the protein yields four protein conformations that describe an opening and closing of both the ATP pocket and the RNA cleft that is achieved through a combination of conformational selection and induction along the ATP hydrolysis cycle. Furthermore, three protein-RNA conformations are observed that implicate motifs Ia, IV, and V as playing a pivotal role in an ATP-dependent inchworm translocation mechanism. Finally, based on a linear discriminant analysis of protein conformations, we identify L405 as a pivotal residue for the opening and closing mechanism and propose a L405D mutation as a way to disrupt translocation. This research enhances our understanding of nsp13's role in viral replication and could contribute to the development of antiviral strategies.

Motif-VI Loop Acts as a Nucleotide Valve in the West Nile Virus NS3 Helicase

The flavivirus NS3 helicase (NS3h), a highly conserved protein, plays a pivotal role in virus replication and thus represents a potential drug target for flavivirus pathogenesis. NS3h utilizes nucleotide triphosphate, such as ATP, for hydrolysis energy (ATPase) to translocate on single-stranded nucleic acids, which is an important step in the unwinding of double-stranded nucleic acids. The intermediate states along the ATP binding and hydrolysis cycle, as well as the conformational changes between these states, represent important yet difficult-to-identify targets for potential inhibitors. We use extensive molecular dynamics simulations of apo, ATP, ADP+Pi, and ADP bound to WNV NS3h+ssRNA to model the conformational ensembles along this cycle. Energetic and structural clustering analyses on these trajectories depict a clear trend of differential enthalpic affinity of NS3h with ADP, demonstrating a probable mechanism of hydrolysis turnover regulated by the motif-VI loop (MVIL). These findings were experimentally corroborated using viral replicons encoding three mutations at the D471 position. Replication assays using these mutants demonstrated a substantial reduction in viral replication compared to the wild-type. Molecular simulations of the D471 mutants in the apo state indicate a shift in MVIL populations favoring either a closed or open 'valve' conformation, affecting ATP entry or stabilization, respectively. Combining our molecular modeling with experimental evidence highlights a conformation-dependent role for MVIL as a 'valve' for the ATP-pocket, presenting a promising target for antiviral development.

The Role of ATP Hydrolysis and Product Release in the Translocation Mechanism of SARS-CoV-2 NSP13

In response to the emergence of COVID-19, caused by SARS-CoV-2, there has been a growing interest in understanding the functional mechanisms of the viral proteins to aid in the development of new therapeutics. Non-structural protein 13 (Nsp13) helicase is an attractive target for antivirals because it is essential for viral replication and has a low mutation rate; yet, the structural mechanisms by which this enzyme binds and hydrolyzes ATP to cause unidirectional RNA translocation remain elusive. Using Gaussian accelerated molecular dynamics (GaMD), we generated a comprehensive conformational ensemble of all substrate states along the ATP-dependent cycle. ShapeGMM clustering of the protein yields four protein conformations that describe an opening and closing of both the ATP pocket and RNA cleft. This opening and closing is achieved through a combination of conformational selection and induction along the ATP cycle. Furthermore, three protein-RNA conformations are observed that implicate motifs Ia, IV, and V as playing a pivotal role in an ATP-dependent inchworm translocation mechanism. Finally, based on a linear discriminant analysis of protein conformations, we identify L405 as a pivotal residue for the opening and closing mechanism and propose a L405D mutation as a way of testing our proposed mechanism. This research enhances our understanding of nsp13's role in viral replication and could contribute to the development of antiviral strategies.