New advances in metadynamics

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.

pH-Dependent Assembly and Stability of Toll-Like Receptor 3/dsRNA Signaling Complex: Insights from Constant pH Molecular Dynamics and Metadynamics Simulations

The pH-dependent assembly of Toll-like receptors (TLRs), which triggers a threshold-like response, is a key principle in immune signaling. While crystallography has revealed the intricate structure of these assembly complexes, the mechanisms underlying their pH dependency remain unclear. Herein, constant pH simulations and metadynamics are employed to investigate the pH-dependent assembly and stability of the TLR3/dsRNA signaling complex. The findings demonstrate that system pH regulates complex assembly and stability by modulating the protonation and charge states of histidines. Histidines in TLR3 act as pH-dependent, positively charged binding sites that capture negatively charged dsRNA. Additionally, these histidines form a [H682⁺]-[E626⁻] dipole, facilitating the assembly of two TLR3 molecules into an antisymmetric dimer through dipole-dipole interactions. Surprisingly, TLR3 can shift the pKa values of key histidines from their model pKa of 6.5, increasing protonation likelihood and enhancing ligand binding. Notably, the aromatic residue Phe84, located within the dsRNA binding site [His39⁺-His60⁺-Phe84-His108⁺], alters the pKa of His60 through cation-π interactions with its protonated state. This study offers new insights into the molecular mechanisms underlying pH-dependent immune signaling via higher-order assemblies and suggests potential applications for histidine in self-assembling biomaterials.

Data Generation for Machine Learning Interatomic Potentials and Beyond

The field of data-driven chemistry is undergoing an evolution, driven by innovations in machine learning models for predicting molecular properties and behavior. Recent strides in ML-based interatomic potentials have paved the way for accurate modeling of diverse chemical and structural properties at the atomic level. The key determinant defining MLIP reliability remains the quality of the training data. A paramount challenge lies in constructing training sets that capture specific domains in the vast chemical and structural space. This Review navigates the intricate landscape of essential components and integrity of training data that ensure the extensibility and transferability of the resulting models. We delve into the details of active learning, discussing its various facets and implementations. We outline different types of uncertainty quantification applied to atomistic data acquisition and the correlations between estimated uncertainty and true error. The role of atomistic data samplers in generating diverse and informative structures is highlighted. Furthermore, we discuss data acquisition via modified and surrogate potential energy surfaces as an innovative approach to diversify training data. The Review also provides a list of publicly available data sets that cover essential domains of chemical space.

Cryptate binding energies towards high throughput chelator design: metadynamics ensembles with cluster-continuum solvation

A tiered forcefield/semiempirical/meta-GGA pipeline together with a thermodynamic scheme designed with error cancellation in mind was developed to calculate binding energies of [2.2.2] cryptate complexes of mono- and divalent cations. Stable complexes of Na, K, Rb, Ca, Zn and Pb were generated, revealing consistent cation-N lengths but highly variable cation-O lengths and an amine stacking mechanism potentially augmenting the cation size selectivity. Metadynamics, used for searching the high-dimensional potential energy surface, together with a cluster-continuum model for affordable - yet accurate - solvation modeling, enabled the discovery of more stable geometries than those previously reported. Similar solvation energy curve shapes for lone vs. coordinated ions enabled rapid solvation convergence via the cancellation of errors stemming from finite cluster sizes. An R2 of 0.850 vs. experimental aqueous binding energies was obtained, validating this scheme as the backbone of a high-throughput workflow for chelator design.

Parameter Optimization Method in Multidimensional Umbrella Sampling

Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.

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.

Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model

Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Interaction between Permeation Enhancers and Lipid Bilayers

Permeation enhancers (PEs) are a class of molecules that interact with the epithelial membrane and transiently increase its transcellular permeability. Although there have been few clinical trials of PE coformulated drugs, the mechanism of action of PEs remains elusive. In this paper, the interaction between two archetypes of PEs [salcaprozate sodium (SNAC) and sodium caprate (C10)] and membranes is investigated with extensive all-atom molecular dynamics simulations. The simulations show that (1) the association between the neutral PEs and membranes is favored in free energy, (2) the propensity of neutral PE aggregation is larger in aqueous solution than in lipid bilayers, (3) the equilibrium distribution of neutral PEs in membranes is fast, e.g., accessible with unbiased MD simulations, and (4) the micelle of neutral PEs formed in aqueous solution does not rupture the membranes (e.g., not forming pores or breaking up the membrane) under simulation conditions. All results combined, this study indicates that PEs insert into the membranes in an equilibrium or near equilibrium process. This study lays the foundation for future investigations of how PEs impact the free energy of permeation for small molecules.

Combining stochastic resetting with Metadynamics to speed-up molecular dynamics simulations

Metadynamics is a powerful method to accelerate molecular dynamics simulations, but its efficiency critically depends on the identification of collective variables that capture the slow modes of the process. Unfortunately, collective variables are usually not known a priori and finding them can be very challenging. We recently presented a collective variables-free approach to enhanced sampling using stochastic resetting. Here, we combine the two methods, showing that it can lead to greater acceleration than either of them separately. We also demonstrate that resetting Metadynamics simulations performed with suboptimal collective variables can lead to speedups comparable with those obtained with optimal collective variables. Therefore, applying stochastic resetting can be an alternative to the challenging task of improving suboptimal collective variables, at almost no additional computational cost. Finally, we propose a method to extract unbiased mean first-passage times from Metadynamics simulations with resetting, resulting in an improved tradeoff between speedup and accuracy. This work enables combining stochastic resetting with other enhanced sampling methods to accelerate a broad range of molecular simulations.

Catalytic Mechanism of Collagen Hydrolysis by Zinc(II)-Dependent Matrix Metalloproteinase-1

Human matrix metalloproteinase-1 (MMP-1) is a zinc(II)-dependent enzyme that catalyzes collagenolysis. Despite the availability of extensive experimental data, the mechanism of MMP-1-catalyzed collagenolysis remains poorly understood due to the lack of experimental structure of a catalytically productive enzyme-substrate complex of MMP-1. In this study, we apply molecular dynamics and combined quantum mechanics/molecular mechanics to reveal the reaction mechanism of MMP-1 based on a computationally modeled structure of the catalytically competent complex of MMP-1 that contains a large triple-helical peptide substrate. Our proposed mechanism involves the participation of an auxiliary (second) water molecule (wat2) in addition to the zinc(II)-coordinated water (wat1). The reaction initiates through a proton transfer to Glu219, followed by a nucleophilic attack by a zinc(II)-coordinated hydroxide anion nucleophile at the carbonyl carbon of the scissile bond, leading to the formation of a tetrahedral intermediate (IM2). The process continues with a hydrogen-bond rearrangement to facilitate proton transfer from wat2 to the amide nitrogen of the scissile bond and, finally, C-N bond cleavage. The calculations indicate that the rate-determining step is the water-mediated nucleophilic attack with an activation energy barrier of 22.3 kcal/mol. Furthermore, the calculations show that the hydrogen-bond rearrangement/proton-transfer step can proceed in a consecutive or concerted manner, depending on the conformation of the tetrahedral intermediate, with the consecutive mechanism being energetically preferable. Overall, the study reveals the crucial role of a second water molecule and the dynamics for effective MMP-1-catalyzed collagenolysis.

Methods for studying mammalian aquaporin biology

Aquaporins (AQPs), transmembrane water-conducting channels, have earned a great deal of scrutiny for their critical physiological roles in healthy and disease cell states, especially in the biomedical field. Numerous methods have been implemented to elucidate the involvement of AQP-mediated water transport and downstream signaling activation in eliciting whole cell, tissue, and organ functional responses. To modulate these responses, other methods have been employed to investigate AQP druggability. This review discusses standard in vitro, in vivo, and in silico methods for studying AQPs, especially for biomedical and mammalian cell biology applications. We also propose some new techniques and approaches for future AQP research to address current gaps in methodology.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Hydrogen-migration governed dynamic magnetic coupling characteristics in nitrogen-vacancy-hydrogen nanodiamonds

The nitrogen-vacancy center doped with hydrogen (NVH) is one of the most common defects in diamonds, and the doping of hydrogen is known to enable mobility among three equivalent C-radicals in the defect, which noticeably affects the spin coupling among the radicals. Here, we for the first time uncover the dynamic nature of magnetic coupling induced by H-migration in the NVH center of nanodiamonds, using spin-polarized density functional theory calculations and enhanced sampling metadynamics simulations. The mobility of doping H enables the interior NVH region to become a variable magnetic space (antiferromagnetic/AFM versus ferromagnetic/FM). That is, the dynamic H has three frequently reachable binding C sites where H enables the center to exhibit variable AFM coupling (high up to J = -1282 cm-1) and that in other H-reachable regions including N sites, it enables the center to exhibit FM coupling (high up to J = 598 cm-1). The magnetic switching (AFM ↔ FM) and strength fluctuation strongly depend on the H-position which can adjust the ratio of the C radical orbitals in their mixing orbitals for a special three-electron three-center covalent C⋯H⋯C H-bonding and radical orbital distributions. Clearly, this work provides insights into the dynamic switching of magnetic coupling in such multi-radical centers of defect nanodiamonds.

Using Diffusion Maps to Analyze Reaction Dynamics for a Hydrogen Combustion Benchmark Dataset

We use local diffusion maps to assess the quality of two types of collective variables (CVs) for a recently published hydrogen combustion benchmark dataset1 that contains ab initio molecular dynamics (MD) trajectories and normal modes along minimum energy paths. This approach was recently advocated in2 for assessing CVs and analyzing reactions modeled by classical MD simulations. We report the effectiveness of this approach to molecular systems modeled by quantum ab initio MD. In addition to assessing the quality of CVs, we also use global diffusion maps to perform committor analysis as proposed in.2 We show that the committor function obtained from the global diffusion map allows us to identify transition regions of interest in several hydrogen combustion reaction channels.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

Identifying and Overcoming the Sampling Challenges in Relative Binding Free Energy Calculations of a Model Protein:Protein Complex

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a graphics processing unit (GPU)-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches─alchemical replica exchange and alchemical replica exchange with solute tempering─for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and is available at https://github.com/choderalab/perses.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Identifying and overcoming the sampling challenges in relative binding free energy calculations of a model protein:protein complex

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a GPU-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches-alchemical replica exchange and alchemical replica exchange with solute tempering-for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally-determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and available at https://github.com/choderalab/perses .

Finding Excited-State Minimum Energy Crossing Points on a Budget: Non-Self-Consistent Tight-Binding Methods

The automated exploration and identification of minimum energy conical intersections (MECIs) is a valuable computational strategy for the study of photochemical processes. Due to the immense computational effort involved in calculating non-adiabatic derivative coupling vectors, simplifications have been introduced focusing instead on minimum energy crossing points (MECPs), where promising attempts were made with semiempirical quantum mechanical methods. A simplified treatment for describing crossing points between almost arbitrary diabatic states based on a non-self-consistent extended tight-binding method, GFN0-xTB, is presented. Involving only a single diagonalization of the Hamiltonian, the method can provide energies and gradients for multiple electronic states, which can be used in a derivative coupling-vector-free scheme to calculate MECPs. By comparison with high-lying MECIs of benchmark systems, it is demonstrated that the identified geometries are good starting points for further MECI refinement with ab initio methods.

Selectivity and Ranking of Tight-Binding JAK-STAT Inhibitors Using Markovian Milestoning with Voronoi Tessellations

Janus kinases (JAK), a group of proteins in the nonreceptor tyrosine kinase (NRTKs) family, play a crucial role in growth, survival, and angiogenesis. They are activated by cytokines through the Janus kinase-signal transducer and activator of a transcription (JAK-STAT) signaling pathway. JAK-STAT signaling pathways have significant roles in the regulation of cell division, apoptosis, and immunity. Identification of the V617F mutation in the Janus homology 2 (JH2) domain of JAK2 leading to myeloproliferative disorders has stimulated great interest in the drug discovery community to develop JAK2-specific inhibitors. However, such inhibitors should be selective toward JAK2 over other JAKs and display an extended residence time. Recently, novel JAK2/STAT5 axis inhibitors (N-(1H-pyrazol-3-yl)pyrimidin-2-amino derivatives) have displayed extended residence times (hours or longer) on target and adequate selectivity excluding JAK3. To facilitate a deeper understanding of the kinase-inhibitor interactions and advance the development of such inhibitors, we utilize a multiscale Markovian milestoning with Voronoi tessellations (MMVT) approach within the Simulation-Enabled Estimation of Kinetic Rates v.2 (SEEKR2) program to rank order these inhibitors based on their kinetic properties and further explain the selectivity of JAK2 inhibitors over JAK3. Our approach investigates the kinetic and thermodynamic properties of JAK-inhibitor complexes in a user-friendly, fast, efficient, and accurate manner compared to other brute force and hybrid-enhanced sampling approaches.

Fuzzy Drug Targets: Disordered Proteins in the Drug-Discovery Realm

Intrinsically disordered proteins (IDPs) and regions (IDRs) form a large part of the eukaryotic proteome. Contrary to the structure-function paradigm, the disordered proteins perform a myriad of functions in vivo. Consequently, they are involved in various disease pathways and are plausible drug targets. Unlike folded proteins, that have a defined structure and well carved out drug-binding pockets that can guide lead molecule selection, the disordered proteins require alternative drug-development methodologies that are based on an acceptable picture of their conformational ensemble. In this review, we discuss various experimental and computational techniques that contribute toward understanding IDP "structure" and describe representative pursuances toward IDP-targeting drug development. We also discuss ideas on developing rational drug design protocols targeting IDPs.

Uncertainty-driven dynamics for active learning of interatomic potentials

Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions.

Mechanism of the Early Catalytic Events in the Collagenolysis by Matrix Metalloproteinase-1

Metalloproteinase-1 (MMP-1) catalyzed collagen degradation is essential for a wide variety of normal physiological processes, while at the same time contributing to several diseases in humans. Therefore, a comprehensive understanding of this process is of great importance. Although crystallographic and spectroscopic studies provided fundamental information about the structure and function of MMP-1, the precise mechanism of collagen degradation especially considering the complex and flexible structure of the substrate, remains poorly understood. In addition, how the protein environment dynamically reorganizes at the atomic scale into a catalytically active state capable of collagen hydrolysis remains unknown. In this study, we applied experimentally-guided multiscale molecular modeling methods including classical molecular dynamics (MD), well-tempered (WT) classical metadynamics (MetD), combined quantum mechanics/molecular mechanics (QM/MM) MD and QM/MM MetD simulations to explore and characterize the early catalytic events of MMP-1 collagenolysis. Importantly the study provided a complete atomic and dynamic description of the transition from the open to the closed form of the MMP-1•THP complex. Notably, the formation of catalytically active Michaelis complex competent for collagen cleavage was characterized. The study identified the changes in the coordination state of the catalytic zinc(II) associated with the conformational transformation and the formation of catalytically productive ES complex. Our results confirm the essential role of the MMP-1 catalytic domain's α-helices (hA, hB and hC) and the linker region in the transition to the catalytically competent ES complex. Overall, the results provide unique mechanistic insight into the conformational transformations and associated changes in the coordination state of the catalytic zinc(II) that would be important for the design of effective MMP-1 inhibitors.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Open Binding Pose Metadynamics: An Effective Approach for the Ranking of Protein-Ligand Binding Poses

Predicting the correct pose of a ligand binding to a protein and its associated binding affinity is of great importance in computer-aided drug discovery. A number of approaches have been developed to these ends, ranging from the widely used fast molecular docking to the computationally expensive enhanced sampling molecular simulations. In this context, methods such as coarse-grained metadynamics and binding pose metadynamics (BPMD) use simulations with metadynamics biasing to probe the binding affinity without trying to fully converge the binding free energy landscape in order to decrease the computational cost. In BPMD, the metadynamics bias perturbs the ligand away from the initial pose. The resistance of the ligand to this bias is used to calculate a stability score. The method has been shown to be useful in reranking predicted binding poses from docking. Here, we present OpenBPMD, an open-source Python reimplementation and reinterpretation of BPMD. OpenBPMD is powered by the OpenMM simulation engine and uses a revised scoring function. The algorithm was validated by testing it on a wide range of targets and showing that it matches or exceeds the performance of the original BPMD. We also investigated the role of accurate water positioning on the performance of the algorithm and showed how the combination with a grand-canonical Monte Carlo algorithm improves the accuracy of the predictions.

Stochastic Resetting for Enhanced Sampling

We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on time scales that are unreachable in standard simulations. They are often characterized by broad transition time distributions, in which extremely slow events have a non-negligible probability. Stochastic resetting, i.e., restarting simulations at random times, was recently shown to significantly expedite processes that follow such distributions. Here, we employ resetting for enhanced sampling of molecular simulations for the first time. We show that it accelerates long time scale processes by up to an order of magnitude in examples ranging from simple models to a molecular system. Most importantly, we recover the mean transition time without resetting, which is typically too long to be sampled directly, from accelerated simulations at a single restart rate. Stochastic resetting can be used as a standalone method or combined with other sampling algorithms to further accelerate simulations.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.

Exploration of high dimensional free energy landscapes by a combination of temperature-accelerated sliced sampling and parallel biasing

Temperature-accelerated sliced sampling (TASS) is an enhanced sampling method for achieving accelerated and controlled exploration of high-dimensional free energy landscapes in molecular dynamics simulations. With the aid of umbrella bias potentials, the TASS method realizes a controlled exploration and divide-and-conquer strategy for computing high-dimensional free energy surfaces. In TASS, diffusion of the system in the collective variable (CV) space is enhanced with the help of metadynamics bias and elevated-temperature of the auxiliary degrees of freedom (DOF) that are coupled to the CVs. Usually, a low-dimensional metadynamics bias is applied in TASS. In order to further improve the performance of TASS, we propose here to use a highdimensional metadynamics bias, in the same form as in a parallel bias metadynamics scheme. Here, a modified reweighting scheme, in combination with artificial neural network is used for computing unbiased probability distribution of CVs and projections of high-dimensional free energy surfaces. We first validate the accuracy and efficiency of our method in computing the four-dimensional free energy landscape for alanine tripeptide in vacuo. Subsequently, we employ the approach to calculate the eight-dimensional free energy landscape of alanine pentapeptide in vacuo. Finally, the method is applied to a more realistic problem wherein we compute the broad four-dimensional free energy surface corresponding to the deacylation of a drug molecule which is covalently complexed with a β-lactamase enzyme. We demonstrate that using parallel bias in TASS improves the efficiency of exploration of high-dimensional free energy landscapes.

Tracing the Primordial Chemical Life of Glycine: A Review from Quantum Chemical Simulations

Glycine (Gly), NH2CH2COOH, is the simplest amino acid. Although it has not been directly detected in the interstellar gas-phase medium, it has been identified in comets and meteorites, and its synthesis in these environments has been simulated in terrestrial laboratory experiments. Likewise, condensation of Gly to form peptides in scenarios resembling those present in a primordial Earth has been demonstrated experimentally. Thus, Gly is a paradigmatic system for biomolecular building blocks to investigate how they can be synthesized in astrophysical environments, transported and delivered by fragments of asteroids (meteorites, once they land on Earth) and comets (interplanetary dust particles that land on Earth) to the primitive Earth, and there react to form biopolymers as a step towards the emergence of life. Quantum chemical investigations addressing these Gly-related events have been performed, providing fundamental atomic-scale information and quantitative energetic data. However, they are spread in the literature and difficult to harmonize in a consistent way due to different computational chemistry methodologies and model systems. This review aims to collect the work done so far to characterize, at a quantum mechanical level, the chemical life of Gly, i.e., from its synthesis in the interstellar medium up to its polymerization on Earth.

Free Energy Surfaces and Barriers for Vacancy Diffusion on Al(100), Al(110), Al(111) Reconstructed Surfaces

Metadynamics is a popular enhanced sampling method based on the recurrent application of a history-dependent adaptive bias potential that is a function of a selected number of appropriately chosen collective variables. In this work, using metadynamics simulations, we performed a computational study for the diffusion of vacancies on three different Al surfaces [reconstructed Al(100), Al(110), and Al(111) surfaces]. We explored the free energy landscape of diffusion and estimated the barriers associated with this process on each surface. It is found that the surfaces are unique regarding vacancy diffusion. More specically, the reconstructed Al(110) surface presents four metastable states on the free energy surface having sizable and connected passage-ways with an energy barrier of height 0.55 eV. On the other hand, the reconstructed Al(100)/Al(111) surfaces exhibit two/three metastable states, respectively, with an energy barrier of height 0.33 eV. The findings in this study can help to understand surface vacancy diffusion in technologically relevant Al surfaces.

Assessing the Intestinal Permeability of Small Molecule Drugs via Diffusion Motion on a Multidimensional Free Energy Surface

A protocol that accurately assesses the intestinal permeability of small molecule compounds plays an essential role in decreasing the cost and time in inventing a new drug. This manuscript presents a novel computational method to study the passive permeation of small molecule drugs based on the inhomogeneous solubility-diffusion model. The multidimensional free energy surface of the drug transiting through a lipid bilayer is computed with transition-tempered metadynamics that accurately captures the mechanisms of passive permeation. The permeability is computed by following the diffusion motion of the drug molecules along the minimal free energy path found on the multidimensional free energy surface. This computational method is assessed by studying the permeability of five small molecule drugs (ketoprofen, naproxen, metoprolol, propranolol, and salicylic acid). The results demonstrate a remarkable agreement between the computed permeabilities and those measured with the intestinal assay. The in silico method reported in this manuscript also reproduces the permeability measured from the intestinal assay (in vivo) better than the cell-based assays (e.g., PAMPA and Caco-2) do. In addition, the multidimensional free energy surface reveals the interplay between the structure of the small molecule and its permeability, shedding light on strategies of drug optimization.

Activation of Abl1 Kinase Explored Using Well-Tempered Metadynamics Simulations on an Essential Dynamics Sampled Path

Well-tempered metadynamics (wT-metaD) simulations using path collective variables (CVs) have been successfully applied in recent years to explore conformational transitions in protein kinases and other biomolecular systems. While this methodology has the advantage of describing the transitions with a limited number of predefined path CVs, it requires as an input a reference path connecting the initial and target states of the system. It is desirable to automate the path generation using approaches that do not rely on the choice of geometric CVs to describe the transition of interest. To this end, we developed an approach that couples essential dynamics sampling with wT-metaD simulations. We used this newly developed procedure to explore the activation mechanism of Abl1 kinase and compute the associated free energy barriers. Through these simulations, we identified a three-step mechanism for the activation that involved two metastable intermediates that possessed a partially open activation loop and differed primarily in the “in” or “out” conformation of the aspartate residue of the DFG motif. One of these states is similar to a conformation that was detected in previous spectroscopic studies of Abl1 kinase, albeit its mechanistic role in the activation was hitherto not well understood. The present study establishes its intermediary role in the activation and predicts a rate-determining free energy barrier of 13.8 kcal/mol that is in good agreement with previous experimental and computational estimates. Overall, our study demonstrates the usability of essential dynamics sampling as a path CV in wT-metaD to conveniently study conformational transitions and accurately calculate the associated barriers.

Chemistrees: Data-Driven Identification of Reaction Pathways via Machine Learning

We propose to analyze molecular dynamics (MD) output via a supervised machine learning (ML) algorithm, the decision tree. The approach aims to identify the predominant geometric features which correlate with trajectories that transition between two arbitrarily defined states. The data-driven algorithm aims to identify these features without the bias of human “chemical intuition”. We demonstrate the method by analyzing the proton exchange reactions in formic acid solvated in small water clusters. The simulations were performed with ab initio MD combined with a method to efficiently sample the rare event, path sampling. Our ML analysis identified relevant geometric variables involved in the proton transfer reaction and how they may change as the number of solvating water molecules changes.

Understanding the Effect of Solvent Environment on the Interaction of Hydronium Ion with Biomass Derived Species: A Molecular Dynamics and Metadynamics Investigation

The addition of aprotic solvents results in higher reactivities and selectivities in many key aqueous phase biomass reactions, including the acid-catalyzed conversion of fructose to 5-hydroxyl methyl furfural (HMF). The addition of certain co-solvents inhibits the formation of humins via preferential solvation of key functional groups and can alter reaction kinetics. An important factor in this context is the relative stability of the hydronium ion (the catalyst) in the vicinity of the biomass moiety as compared to that in bulk, as it could determine its efficacy in the protonation step. Hence, in the present work, molecular dynamics (MD) simulations of HMF (the model product) and fructose (the model reactant) in acidic water and water-DMSO mixtures are performed to analyze their interaction with the hydronium ions. We show that the presence of DMSO favors the interaction of the hydronium ion with fructose, whereas it has a detrimental effect on the interaction of hydronium ion with HMF. Well-tempered metadynamics (WT-MTD) simulations are performed to determine the relative stability of the hydronium ion in the immediate vicinity of fructose and HMF, as compared to that in the bulk solvent phase, as a function of solvent composition. We find that DMSO improves the stabilization of the hydronium ions in the first solvation shell of fructose compared to that in the bulk solvent. On the other hand, hydronium ions become less stable in the immediate vicinity of HMF, as the concentration of DMSO increases.

Free energy calculations of the functional selectivity of 5-HT2B G protein-coupled receptor

G Protein-Coupled Receptors (GPCRs) mediate intracellular signaling in response to extracellular ligand binding and are the target of one-third of approved drugs. Ligand binding modulates the GPCR molecular free energy landscape by preferentially stabilizing active or inactive conformations that dictate intracellular protein recruitment and downstream signaling. We perform enhanced sampling molecular dynamics simulations to recover the free energy surfaces of a thermostable mutant of the GPCR serotonin receptor 5-HT2B in the unliganded form and bound to a lysergic acid diethylamide (LSD) agonist and lisuride antagonist. LSD binding imparts a ∼110 kJ/mol driving force for conformational rearrangement into an active state. The lisuride-bound form is structurally similar to the apo form and only ∼24 kJ/mol more stable. This work quantifies ligand-induced conformational specificity and functional selectivity of 5-HT2B and presents a platform for high-throughput virtual screening of ligands and rational engineering of the ligand-bound molecular free energy landscape.

Protein Dynamics Enables Phosphorylation of Buried Residues in Cdk2/Cyclin-A-Bound p27

Proteins carry out a wide range of functions that are tightly regulated in space and time. Protein phosphorylation is the most common post-translation modification of proteins and plays a key role in the regulation of many biological processes. The finding that many phosphorylated residues are not solvent exposed in the unphosphorylated state opens several questions for understanding the mechanism that underlies phosphorylation and how phosphorylation may affect protein structures. First, because kinases need access to the phosphorylated residue, how do such buried residues become modified? Second, once phosphorylated, what are the structural effects of phosphorylation of buried residues, and do they lead to changed conformational dynamics? We have used the ternary complex between p27^Kip1 (p27), Cdk2, and cyclin A to study these questions using enhanced sampling molecular dynamics simulations. In line with previous NMR and single-molecule fluorescence experiments, we observe transient exposure of Tyr88 in p27, even in its unphosphorylated state. Once Tyr88 is phosphorylated, we observe a coupling to a second site, thus making Tyr74 more easily exposed and thereby the target for a second phosphorylation step. Our observations provide atomic details on how protein dynamics plays a role in modulating multisite phosphorylation in p27, thus supplementing previous experimental observations. More generally, we discuss how the observed phenomenon of transient exposure of buried residues may play a more general role in regulating protein function.

Refined metadynamics through canonical sampling using time-invariant bias potential: A study of polyalcohol dehydration in hot acidic solutions

We propose a canonical sampling method to refine metadynamics simulations a posteriori, where the hills obtained from metadynamics are used as a time-invariant bias potential. In this way, the statistical error in the computed reaction barriers is reduced by an efficient sampling of the collective variable space at the free energy level of interest. This simple approach could be useful particularly when two or more free energy barriers are to be compared among chemical reactions in different or competing conditions. The method was then applied to study the acid dependence of polyalcohol dehydration reactions in high-temperature aqueous solutions. It was found that the reaction proceeds consistently via an S_N 2 mechanism, whereby the free energy of protonation of the hydroxyl group created as an intermediate is affected significantly by the acidic species. Although demonstration is shown for a specific problem, the computational method suggested herein could be generally used for simulations of complex reactions in the condensed phase.

The transport pathway in the ABCG2 protein and its regulation revealed by molecular dynamics simulations

Atomic-level structural insight on the human ABCG2 membrane protein, a pharmacologically important transporter, has been recently revealed by several key papers. In spite of the wealth of structural data, the pathway of transmembrane movement for the large variety of structurally different ABCG2 substrates and the physiological lipid regulation of the transporter has not been elucidated. The complex molecular dynamics simulations presented here may provide a breakthrough in understanding the steps of the substrate transport process and its regulation by cholesterol. Our analysis revealed drug binding cavities other than the central binding site and delineated a putative dynamic transport pathway for substrates with variable structures. We found that membrane cholesterol accelerated drug transport by promoting the closure of cytoplasmic protein regions. Since ABCG2 is present in all major biological barriers and drug-metabolizing organs, influences the pharmacokinetics of numerous clinically applied drugs, and plays a key role in uric acid extrusion, this information may significantly promote a reliable prediction of clinically important substrate characteristics and drug-drug interactions.

Structure and Dynamics of a Thermostable Alcohol Dehydrogenase from the Antarctic Psychrophile Moraxella sp. TAE123

The structure of a recombinant (His-tagged at C-terminus) alcohol dehydrogenase (MoADH) from the cold-adapted bacterium Moraxella sp. TAE123 has been refined with X-ray diffraction data extending to 1.9 Å resolution. The enzyme assumes a homo-tetrameric structure. Each subunit comprises two distinct structural domains: the catalytic domain (residues 1-150 and 288-340/345) and the nucleotide-binding domain (residues 151-287). There are two Zn²⁺ ions in each protein subunit. Two additional zinc ions have been found in the crystal structure between symmetry-related subunits. The structure has been compared with those of homologous enzymes from Geobacillus stearothermophilus (GsADH), Escherichia coli (EcADH), and Thermus sp. ATN1 (ThADH) that thrive in environments of diverse temperatures. Unexpectedly, MoADH has been found active from 10 to at least 53 °C and unfolds at 89 °C according to circular dichroism spectropolarimetry data. MoADH with substrate ethanol exhibits a small value of activation enthalpy ΔH ^‡ of 30 kJ mol^-1. Molecular dynamics simulations for single subunits of the closely homologous enzymes MoADH and GsADH performed at 280, 310, and 340 K showed enhanced wide-ranging mobility of MoADH at high temperatures and generally lower but more distinct and localized mobility for GsADH. Principal component analysis of the fluctuations of both ADHs resulted in a prominent open-close transition of the structural domains mainly at 280 K for MoADH and 340 K for GsADH. In conclusion, MoADH is a very thermostable, cold-adapted enzyme and the small value of activation enthalpy allows the enzyme to function adequately at low temperatures.

Capturing the Flexibility of a Protein-Ligand Complex: Binding Free Energies from Different Enhanced Sampling Techniques

Enhanced sampling techniques are a promising approach to obtain reliable binding free-energy profiles for flexible protein-ligand complexes from molecular dynamics (MD) simulations. To put four popular enhanced sampling techniques to a biologically relevant and challenging test, we studied the partial dissociation of an antigenic peptide from the Major Histocompatibility Complex I (MHC I) HLA-B*35:01 to systematically investigate the performance of umbrella sampling (US), replica exchange with solute tempering 2 (REST2), bias exchange umbrella sampling (BEUS, or replica-exchange umbrella sampling), and well-tempered metadynamics (MTD). With regard to the speed of sampling and convergence, the peptide-MHC I complex (pMHC I) under study showcases intrinsic strengths and weaknesses of the four enhanced sampling techniques used. We found that BEUS can best handle the sampling challenges that arise from the coexistence of an enthalpically and an entropically stabilized free-energy minimum in the pMHC I under study. These findings might also be relevant for other flexible biomolecular systems with competing enthalpically and entropically stabilized minima.

Combining Machine Learning and Enhanced Sampling Techniques for Efficient and Accurate Calculation of Absolute Binding Free Energies

Calculating absolute binding free energies is challenging and important. In this paper, we test some recently developed metadynamics-based methods and develop a new combination with a Hamiltonian replica-exchange approach. The methods were tested on 18 chemically diverse ligands with a wide range of different binding affinities to a complex target; namely, human soluble epoxide hydrolase. The results suggest that metadynamics with a funnel-shaped restraint can be used to calculate, in a computationally affordable and relatively accurate way, the absolute binding free energy for small fragments. When used in combination with an optimal pathlike variable obtained using machine learning or with the Hamiltonian replica-exchange algorithm SWISH, this method can achieve reasonably accurate results for increasingly complex ligands, with a good balance of computational cost and speed. An additional benefit of using the combination of metadynamics and SWISH is that it also provides useful information about the role of water in the binding mechanism.

Alchemical free energy calculations via metadynamics: Application to the theophylline-RNA aptamer complex

We propose a computational workflow for robust and accurate prediction of both binding poses and their affinities at early stage in designing drug candidates. Small, rigid ligands with few intramolecular degrees of freedom, for example, fragment-like molecules, have multiple binding poses, even at a single binding site, and their affinities are often close to each other. We explore various structures of ligand binding to a target through metadynamics using a small number of collective variables, followed by reweighting to obtain the atomic coordinates. After identifying each binding pose by cluster analysis, we perform alchemical free energy calculations on each structure to obtain the overall value. We applied this protocol in computing free energy of binding for the theophylline-RNA aptamer complex. Of the six (meta)stable structures found, the most favorable binding structure is consistent with the structure obtained by NMR. The overall free energy of binding reproduces the experimental values very well.

Analytical Method Using a Scaled Hypersphere Search for High-Dimensional Metadynamics Simulations

Metadynamics (MTD) is one of the most effective methods for calculating the free energy surface and finding rare events. Nevertheless, numerous studies using MTD have been carried out using 3D or lower dimensional collective variables (CVs), as higher dimensional CVs require costly computational resources and the obtained results are too complex to understand the important events. The latter issue can be conveniently solved by utilizing the free energy reaction network (FERN), which is a graph structure consisting of edges of minimum free energy paths (MFEPs), nodes of equation (EQ) points, and transition state (TS) points. In the present article, a new method for exploring FERNs on high-dimensional CVs using MTD and the scaled hypersphere search (SHS) method is described. A test calculation based on the MTD-SHS simulation of met-enkephalin in explicit water with 7 CVs was conducted. As a result, 889 EQ points and 1805 TS points were found. The MTD-SHS approach can find MFEPs exhaustively; therefore, the FERNs can be estimated without any a priori knowledge of the EQ and TS points.