Metadynamics with Discriminants: A Tool for Understanding Chemistry

Automated collective variable discovery for MFSD2A transporter from molecular dynamics simulations

Biomolecules often exhibit complex free energy landscapes in which long-lived metastable states are separated by large energy barriers. Overcoming these barriers to robustly sample transitions between the metastable states with classical molecular dynamics (MD) simulations presents a challenge. To circumvent this issue, collective variable (CV)-based enhanced sampling MD approaches are often employed. Traditional CV selection relies on intuition and prior knowledge of the system. This approach introduces bias, which can lead to incomplete mechanistic insights. Thus, automated CV detection is desired to gain a deeper understanding of the system/process. Analysis of MD data with various machine-learning algorithms, such as principal component analysis (PCA), support vector machine, and linear discriminant analysis (LDA) based approaches have been implemented for automated CV detection. However, their performance has not been systematically evaluated on structurally and mechanistically complex biological systems. Here, we applied these methods to MD simulations of the MFSD2A (Major Facilitator Superfamily Domain 2A) lysolipid transporter in multiple functionally relevant metastable states with the goal of identifying optimal CVs that would structurally discriminate these states. Specific emphasis was on the automated detection and interpretive power of LDA-based CVs. We found that LDA methods, which included a novel gradient descent-based multiclass harmonic variant, termed GDHLDA, we developed here, outperform PCA in class separation, exhibiting remarkable consistency in extracting CVs critical for distinguishing metastable states. Furthermore, the identified CVs included features previously associated with conformational transitions in MFSD2A. Specifically, conformational shifts in transmembrane helix 7 and in residue Y294 on this helix emerged as critical features discriminating the metastable states in MFSD2A. This highlights the effectiveness of LDA-based approaches in automatically extracting from MD trajectories CVs of functional relevance that can be used to drive biased MD simulations to efficiently sample conformational transitions in the molecular system.

Generating High-Precision Force Fields for Molecular Dynamics Simulations to Study Chemical Reaction Mechanisms Using Molecular Configuration Transformer

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that used enhanced sampling in molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limited the use of high-precision potential energy functions for simulations. To address this issue, we presented a scheme for training high-precision force fields for molecular modeling using a previously developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allowed for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We applied this approach to study a Claisen rearrangement reaction and a carbonyl insertion reaction catalyzed by manganese.

One Descriptor to Fold Them All: Harnessing Intuition and Machine Learning to Identify Transferable Lasso Peptide Reaction Coordinates

Identifying optimal reaction coordinates for complex conformational changes and protein folding remains an outstanding challenge. This study combines collective variable (CV) discovery based on chemical intuition and machine learning with enhanced sampling to converge the folding free energy landscape of lasso peptides, a unique class of natural products with knot-like tertiary structures. This knotted scaffold imparts remarkable stability, making lasso peptides resistant to proteolytic degradation, thermal denaturation, and extreme pH conditions. Although their direct synthesis would enable therapeutic design, it has not yet been possible due to the improbable occurrence of spontaneous lasso folding. Thus, simulations characterizing the folding propensity are needed to identify strategies for increasing access to the lasso architecture by stabilizing the pre-lasso ensemble before isopeptide bond formation. Herein, harmonic linear discriminant analysis (HLDA) is combined with metadynamics-enhanced sampling to discover CVs capable of distinguishing the pre-lasso fold and converging the folding propensity. Intuitive CVs are compared to iterative rounds of HLDA to identify CVs that not only accomplish these goals for one lasso peptide but also seem to be transferable to others, establishing a protocol for the identification of folding reaction coordinates for lasso peptides.

Finite temperature string by K-means clustering sampling with order parameters as collective variables for molecular crystals: application to polymorphic transformation between β-CL-20 and ε-CL-20

Polymorphic transformation of molecular crystals is a fundamental phase transition process, and it is important practically in the chemical, material, biopharmaceutical, and energy storage industries. However, understanding of the transformation mechanism at the molecular level is poor due to the extreme simulating challenges in enhanced sampling and formulating order parameters (OPs) as the collective variables that can distinguish polymorphs with quite similar and complicated structures so as to describe the reaction coordinate. In this work, two kinds of OPs for CL-20 were constructed by the bond distances, bond orientations and relative orientations. A K-means clustering algorithm based on the Euclidean distance and sample weight was used to smooth the initial finite temperature string (FTS), and the minimum free energy path connecting β-CL-20 and ε-CL-20 was sketched by the string method in collective variables, and the free energy profile along the path and the nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations. In comparison with the average-based sampling, the K-means clustering algorithm provided an improved convergence rate of FTS. The simulation of transformation was independent of OP types but was affected greatly by finite-size effects. A surface-mediated local nucleation mechanism was confirmed and the configuration located at the shoulder of potential of mean force, rather than overall maximum, was confirmed to be the critical nucleus formed by the cooperative effect of the intermolecular interactions. This work provides an effective way to explore the polymorphic transformation of caged molecular crystals at the molecular level.

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.

Application of Machine Learning Algorithms to Metadynamics for the Elucidation of the Binding Modes and Free Energy Landscape of Drug/Target Interactions: a Case Study

In the context of drug discovery, computational methods were able to accelerate the challenging process of designing and optimizing a new drug candidate. Amongst the possible atomistic simulation approaches, metadynamics (metaD) has proven very powerful. However, the choice of collective variables (CVs) is not trivial for complex systems. To automate the process of CVs identification, two different machine learning algorithms were applied in this study, namely DeepLDA and Autoencoder, to the metaD simulation of a well-researched drug/target complex, consisting in a pharmacologically relevant non-canonical DNA secondary structure (G-quadruplex) and a metallodrug acting as its stabilizer, as well as solvent molecules.

Anisotropic Collective Variables with Machine Learning Potential for Ab Initio Crystallization of Complex Ceramics

Enhanced sampling molecular dynamics (MD) simulations have been extensively used in the phase transition study of simple crystalline materials, such as aluminum, silica, and ice. However, MD simulation of the crystallization process for complex crystalline materials still faces a formidable challenge due to their multicomponent induced multiphase problem. Here, we realize the ab initio accuracy MD crystallization simulations of complex ceramics by using anisotropic collective variables (CVs) and machine learning (ML) potential. The anisotropic X-ray diffraction intensity CVs provide precise identification of complex crystal structures with detailed crystallography information, while the ML potential makes it feasible to further perform enhanced sampling simulations with ab initio accuracy. We verify the universality and accuracy of this method through complex ceramics with three kinds of representative structures, i.e., Ti3SiC2 for the MAX structure, zircon for the mineral structure, and lead zirconate titanate for the perovskite structure. It demonstrates exceptional efficiency and ab initio quality in achieving crystallization and generating free energy surfaces of all these ceramics, facilitating the analysis and design of complex crystalline materials.

Reaction Coordinates for Conformational Transitions Using Linear Discriminant Analysis on Positions

In this work, we demonstrate that Linear Discriminant Analysis (LDA) applied to atomic positions in two different states of a biomolecule produces a good reaction coordinate between those two states. Atomic coordinates of a macromolecule are a direct representation of a macromolecular configuration, and yet, they are not used in enhanced sampling studies due to a lack of rotational and translational invariance. We resolve this issue using the technique of our prior work, whereby a molecular configuration is considered a member of an equivalence class in size-and-shape space, which is the set of all configurations that can be translated and rotated to a single point within a reference multivariate Gaussian distribution characterizing a single molecular state. The reaction coordinates produced by LDA applied to positions are shown to be good reaction coordinates both in terms of characterizing the transition between two states of a system within a long molecular dynamics (MD) simulation and also ones that allow us to readily produce free energy estimates along that reaction coordinate using enhanced sampling MD techniques.

Systematic modification of functionality in disordered elastic networks through free energy surface tailoring

A combined machine learning-physics-based approach is explored for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning model trained on data gathered from a single system. Through the constructed collective variables, it becomes possible to identify critical molecular interactions in the considered system, the modulation of which enables a systematic tailoring of the system's free energy landscape. To explore the efficacy of the proposed approach, we use it to engineer allosteric regulation and uniaxial strain fluctuations in a complex disordered elastic network. Its successful application in these two cases provides insights regarding how functionality is governed in systems characterized by extensive connectivity and points to its potential for design of complex molecular systems.

Collective Variables for Conformational Polymorphism in Molecular Crystals

Controlling polymorphism in molecular crystals is crucial in the pharmaceutical, dye, and pesticide industries. However, its theoretical description is extremely challenging, due to the associated long time scales (>1 μs). We present an efficient procedure for identifying collective variables that promote transitions between conformational polymorphs in molecular dynamics simulations. It involves applying a simple dimensionality reduction algorithm to data from short (∼ps) simulations of the isolated conformers that correspond to each polymorph. We demonstrate the utility of our method in the challenging case of the important energetic material, CL-20, which has three anhydrous conformational polymorphs at ambient pressure. Using these collective variables in Metadynamics simulations, we observe transitions between all solid polymorphs in the biased trajectories. We reconstruct the free energy surface and identify previously unknown defect and intermediate forms in the transition from one known polymorph to another. Our method provides insights into complex conformational polymorphic transitions of flexible molecular crystals.

Collective Variables for Crystallization Simulations-from Early Developments to Recent Advances

Crystallization is an important physicochemical process which has relevance in material science, biology, and the environment. Decades of experimental and theoretical efforts have been made to understand this fundamental symmetry-breaking transition. While experiments provide equilibrium structures and shapes of crystals, they are limited to unraveling how molecules aggregate to form crystal nuclei that subsequently transform into bulk crystals. Computer simulations, mainly molecular dynamics (MD), can provide such microscopic details during the early stage of a crystallization event. Crystallization is a rare event that takes place in time scales much longer than a typical equilibrium MD simulation can sample. This inadequate sampling of the MD method can be easily circumvented by the use of enhanced sampling (ES) simulations. In most of the ES methods, the fluctuations of a system's slow degrees of freedom, called collective variables (CVs), are enhanced by applying a bias potential. This transforms the system from one state to the other within a short time scale. The most crucial part of such CV-based ES methods is to find suitable CVs, which often needs intuition and several trial-and-error optimization steps. Over the years, a plethora of CVs has been developed and applied in the study of crystallization. In this review, we provide a brief overview of CVs that have been developed and used in ES simulations to study crystallization from melt or solution. These CVs can be categorized mainly into four types: (i) spherical particle-based, (ii) molecular template-based, (iii) physical property-based, and (iv) CVs obtained from dimensionality reduction techniques. We present the context-based evolution of CVs, discuss the current challenges, and propose future directions to further develop effective CVs for the study of crystallization of complex systems.

Solubility of Organic Salts in Solvent-Antisolvent Mixtures: A Combined Experimental and Molecular Dynamics Simulations Approach

We combine molecular dynamics simulations with experiments to estimate solubilities of an organic salt in complex growth environments. We predict the solubility by simulations of the growth and dissolution of ions at the crystal surface kink sites at different solution concentrations. Thereby, the solubility is identified as the solution's salt concentration, where the energy of the ion pair dissolved in solution equals the energy of the ion pair crystallized at the kink sites. The simulation methodology is demonstrated for the case of anhydrous sodium acetate crystallized from various solvent-antisolvent mixtures. To validate the predicted solubilities, we have measured the solubilities of sodium acetate in-house, using an experimental setup and measurement protocol that guarantees moisture-free conditions, which is key for a hygroscopic compound like sodium acetate. We observe excellent agreement between the experimental and the computationally evaluated solubilities for sodium acetate in different solvent-antisolvent mixtures. Given the agreement and the rich data the simulations produce, we can use them to complement experimental tasks, which in turn will reduce time and capital in the design of complicated industrial crystallization processes of organic salts.

Enhanced Sampling Simulation Reveals How Solvent Influences Chirogenesis of the Intra-Molecular Diels-Alder Reaction

The timescale involved in chemical reactions is quite often beyond that of normal molecular dynamics simulations. Here, we combine metadynamics with selective integrated tempering sampling to simulate an intra-molecular Diels-Alder reaction in explicit solvents. Based on a one-dimensional collective variable obtained from harmonic linear discriminant analysis, four chiral isomers of products were observed in the simulation. Analyses of reactive trajectories showed that this reaction follows a concerted mechanism in all four solvents. In addition, the hydrogen bond between the reactant and water solvent plays an important role in the water-accelerated reaction mechanism. The dynamics of chirality formation varies significantly with solvents. The chirality of products forms significantly before the transition state, especially in ionic liquid.

Collective Variables for Free Energy Surface Tailoring: Understanding and Modifying Functionality in Systems Dominated by Rare Events

We introduce a method for elucidating and modifying the functionality of systems dominated by rare events that relies on the semiautomated tuning of their underlying free energy surface. The proposed approach seeks to construct collective variables (CVs) that encode the essential information regarding the rare events of the system of interest. The appropriate CVs are identified using harmonic linear discriminant analysis (HLDA), a machine-learning-based method that is trained solely on data collected from short ordinary simulations in the relevant metastable states of the system. Utilizing the interpretable form of the resulting CVs, the critical interaction potentials that determine the system's rare transitions are identified and purposely modified to tailor the free energy surface in a manner that alters functionality as desired. The applicability of the method is illustrated in the context of three different systems, thereby demonstrating that thermodynamic and kinetic properties can be tractably modified with little to no prior knowledge or intuition.

Efficient Reaction Space Exploration with ChemTraYzer-TAD

The development of a reaction model is often a time-consuming process, especially if unknown reactions have to be found and quantified. To alleviate the reaction modeling process, automated procedures for reaction space exploration are highly desired. We present ChemTraYzer-TAD, a new reactive molecular dynamics acceleration technique aimed at efficient reaction space exploration. The new method is based on the basin confinement strategy known from the temperature-accelerated dynamics (TAD) acceleration method. Our method features integrated ChemTraYzer bond-order processing steps for the automatic and on-the-fly determination of the positions of virtual walls in configuration space that confine the system in a potential energy basin. We use the example of 1,3-dioxolane-4-hydroperoxide-2-yl radical oxidation to show that ChemTraYzer-TAD finds more than 100 different parallel reactions for the given set of reactants in less than 2 ns of simulation time. Among the many observed reactions, ChemTraYzer-TAD finds the expected typical low-temperature reactions despite the use of extremely high simulation temperatures up to 5000 K. Our method also finds a new concerted β-scission plus O₂ addition with a lower reaction barrier than the literature-known and so-far dominant β-scission.

Nonlinear Reaction Coordinate of an Enzyme Catalyzed Proton Transfer Reaction

We present an in-depth study on the theoretical calculation of an optimum reaction coordinate as a linear or nonlinear combination of important collective variables (CVs) sampled from an ensemble of reactive transition paths for an intramolecular proton transfer reaction catalyzed by the enzyme human carbonic anhydrase (HCA) II. The linear models are optimized by likelihood maximization for a given number of CVs. The nonlinear models are based on an artificial neural network with the same number of CVs and optimized by minimizing the root-mean-square error in comparison to a training set of committor estimators generated for the given transition. The nonlinear reaction coordinate thus obtained yields the free energy of activation and rate constant as 9.46 kcal mol^-1 and 1.25 × 10⁶ s^-1, respectively. These estimates are found to be in quantitative agreement with the known experimental results. We have also used an extended autoencoder model to show that a similar analysis can be carried out using a single CV only. The resultant free energies and kinetics of the reaction slightly overestimate the experimental data. The implications of these results are discussed using a detailed microkinetic scheme of the proton transfer reaction catalyzed by HCA II.

CARNOT: a Fragment-Based Direct Molecular Dynamics and Virtual-Reality Simulation Package for Reactive Systems

Traditionally, the study of reaction mechanisms of complex reaction systems such as combustion has been performed on an individual basis by optimizations of transition structure and minimum energy path or by reaction dynamics trajectory calculations for one elementary reaction at a time. It is effective, but time-consuming, whereas important and unexpected processes could have been missed. In this article, we present a direct molecular dynamics (DMD) approach and a virtual-reality simulation program, CARNOT, in which plausible chemical reactions are simulated simultaneously at finite temperature and pressure conditions. A key concept of the present ab initio molecular dynamics method is to partition a large, chemically reactive system into molecular fragments that can be adjusted on the fly of a DMD simulation. The theory represents an extension of the explicit polarization method to reactive events, called ReX-Pol. We propose a highest-and-lowest adapted-spin approximation to define the local spins of individual fragments, rather than treating the entire system by a delocalized wave function. Consequently, the present ab initio DMD can be applied to reactive systems consisting of an arbitrarily varying number of closed and open-shell fragments such as free radicals, zwitterions, and separate ions found in combustion and other reactions. A graph-data structure algorithm was incorporated in CARNOT for the analysis of reaction networks, suitable for reaction mechanism reduction. Employing the PW91 density functional theory and the 6-31+G(d) basis set, the capabilities of the CARNOT program were illustrated by a combustion reaction, consisting of 28 650 atoms, and by reaction network analysis that revealed a range of mechanistic and dynamical events. The method may be useful for applications to other types of complex reactions.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis

Enhanced sampling ab initio simulations enable to study chemical phenomena in catalytic systems including thermal effects & anharmonicity, & collective dynamics describing enthalpic & entropic contributions, which can significantly impact on reaction free energy landscapes.

Reweighted Jarzynski Sampling: Acceleration of Rare Events and Free Energy Calculation with a Bias Potential Learned from Nonequilibrium Work

We introduce a simple enhanced sampling approach for the calculation of free energy differences and barriers along a one-dimensional reaction coordinate. First, a small number of short nonequilibrium simulations are carried out along the reaction coordinate, and the Jarzynski equality is used to learn an approximate free energy surface from the nonequilibrium work distribution. This free energy estimate is represented in a compact form as an artificial neural network and used as an external bias potential to accelerate rare events in a subsequent molecular dynamics simulation. The final free energy estimate is then obtained by reweighting the equilibrium probability distribution of the reaction coordinate sampled under the influence of the external bias. We apply our reweighted Jarzynski sampling recipe to four processes of varying scales and complexities─spanning chemical reaction in the gas phase, pair association in solution, and droplet nucleation in supersaturated vapor. In all cases, we find reweighted Jarzynski sampling to be a very efficient strategy, resulting in rapid convergence of the free energy to high precision.

Deep learning the slow modes for rare events sampling

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an appropriate set of collective variables. These are meant to describe the system's modes that most slowly approach equilibrium under the action of the sampling algorithm. Once identified, the equilibration of these modes is accelerated by the enhanced sampling method of choice. An attractive way of determining the collective variables is to relate them to the eigenfunctions and eigenvalues of the transfer operator. Unfortunately, this requires knowing the long-term dynamics of the system beforehand, which is generally not available. However, we have recently shown that it is indeed possible to determine efficient collective variables starting from biased simulations. In this paper, we bring the power of machine learning and the efficiency of the recently developed on the fly probability-enhanced sampling method to bear on this approach. The result is a powerful and robust algorithm that, given an initial enhanced sampling simulation performed with trial collective variables or generalized ensembles, extracts transfer operator eigenfunctions using a neural network ansatz and then accelerates them to promote sampling of rare events. To illustrate the generality of this approach, we apply it to several systems, ranging from the conformational transition of a small molecule to the folding of a miniprotein and the study of materials crystallization.

Closer Look at Inverse Electron Demand Diels–Alder and Nucleophilic Addition Reactions on s-Tetrazines Using Enhanced Sampling Methods

Inverse electron demand [4+2] Diels–Alder (iEDDA) reactions as well as unprecedented nucleophilic (azaphilic) additions of R-substituted silyl-enol ethers (where R is Phenyl, Methyl, and Hydrogen) to 1,2,4,5-tetrazine (s-tetrazine) catalyzed by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3 have recently been discovered (Simon et al. in Org Lett 23(7):2426–2430, 2021), where static calculations were employed for calculation of activation energies. In order to have a more realistic dynamic description of these reactions in explicit solution at ambient conditions, in this work we use a semiempirical tight-binding method combined with enhanced sampling techniques to calculate free energy surfaces (FESs) of the iEDDA and azaphilic addition reactions. Relevant products of not only s-tetrazine but also its derivatives such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3-mediated s-tetrazine adducts are investigated. We reconstruct the FESs of the iEDDA and azaphilic addition reactions using metadynamics and blue moon ensemble, and compare the ability of different collective variables (CVs) including bond distances, Social PeRmutation INvarianT (SPRINT) coordinates, and path-CV to describe the reaction pathway. We find that when a bulky Phenyl is used as a substituent at the dienophile the azaphilic addition is preferred over the iEDDA reaction. In addition, we also investigate the effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3 in the diene and steric hindrance in the dienophile on the competition between the iEDDA and azaphilic addition reactions, providing chemical insight for reaction design.

From Enhanced Sampling to Reaction Profiles

The determination of efficient collective variables is crucial to the success of many enhanced sampling methods. As inspired by previous discrimination approaches, we first collect a set of data from the different metastable basins. The data are then projected with the help of a neural network into a low-dimensional manifold in which data from different basins are well-discriminated. This is here guaranteed by imposing that the projected data follows a preassigned distribution. The collective variables thus obtained lead to an efficient sampling and often allow reducing the number of collective variables in a multibasin scenario. We first check the validity of the method in two-state systems. We then move to multistep chemical processes. In the latter case, at variance with previous approaches, one single collective variable suffices, leading not only to computational efficiency but also to a very clear representation of the reaction free-energy profile.

Data-Driven Molecular Dynamics: A Multifaceted Challenge

The big data concept is currently revolutionizing several fields of science including drug discovery and development. While opening up new perspectives for better drug design and related strategies, big data analysis strongly challenges our current ability to manage and exploit an extraordinarily large and possibly diverse amount of information. The recent renewal of machine learning (ML)-based algorithms is key in providing the proper framework for addressing this issue. In this respect, the impact on the exploitation of molecular dynamics (MD) simulations, which have recently reached mainstream status in computational drug discovery, can be remarkable. Here, we review the recent progress in the use of ML methods coupled to biomolecular simulations with potentially relevant implications for drug design. Specifically, we show how different ML-based strategies can be applied to the outcome of MD simulations for gaining knowledge and enhancing sampling. Finally, we discuss how intrinsic limitations of MD in accurately modeling biomolecular systems can be alleviated by including information coming from experimental data.

Gaussian Mixture-Based Enhanced Sampling for Statics and Dynamics

We introduce an enhanced sampling method that is based on constructing a model probability density from which a bias potential is derived. The model relies on the fact that in a physical system most of the configurations visited can be grouped into isolated metastable islands. With each island we associate a distribution that is fitted to a Gaussian mixture. The different distributions are linearly combined together with coefficients that are computed self-consistently. This leads to an integrated procedure for discovering new metastable states, exploring reaction pathways, computing free energy differences, and estimating reaction rates.

Integrating NMR and simulations reveals motions in the UUCG tetraloop

We provide an atomic-level description of the structure and dynamics of the UUCG RNA stem-loop by combining molecular dynamics simulations with experimental data. The integration of simulations with exact nuclear Overhauser enhancements data allowed us to characterize two distinct states of this molecule. The most stable conformation corresponds to the consensus three-dimensional structure. The second state is characterized by the absence of the peculiar non-Watson-Crick interactions in the loop region. By using machine learning techniques we identify a set of experimental measurements that are most sensitive to the presence of non-native states. We find that although our MD ensemble, as well as the consensus UUCG tetraloop structures, are in good agreement with experiments, there are remaining discrepancies. Together, our results show that (i) the MD simulation overstabilize a non-native loop conformation, (ii) eNOE data support its presence with a population of ≈10% and (iii) the structural interpretation of experimental data for dynamic RNAs is highly complex, even for a simple model system such as the UUCG tetraloop.

Data-Driven Collective Variables for Enhanced Sampling

Designing an appropriate set of collective variables is crucial to the success of several enhanced sampling methods. Here we focus on how to obtain such variables from information limited to the metastable states. We characterize these states by a large set of descriptors and employ neural networks to compress this information in a lower-dimensional space, using Fisher's linear discriminant as an objective function to maximize the discriminative power of the network. We test this method on alanine dipeptide, using the nonlinearly separable data set composed by atomic distances. We then study an intermolecular aldol reaction characterized by a concerted mechanism. The resulting variables are able to promote sampling by drawing nonlinear paths in the physical space connecting the fluctuations between metastable basins. Lastly, we interpret the behavior of the neural network by studying its relation to the physical variables. Through the identification of its most relevant features, we are able to gain chemical insight into the process.

Graphene Oxyhydride Catalysts in View of Spin Radical Chemistry

This article discusses carbocatalysis that are provided with amorphous carbons. The discussion is conducted from the standpoint of the spin chemistry of graphene molecules, in the framework of which the amorphous carbocatalysts are a conglomerate of graphene-oxynitrothiohydride stable radicals presenting the basic structure units (BSUs) of the species. The chemical activity of the BSUs atoms is reliably determined computationally, which allows mapping the distribution of active sites in these molecular catalysts. The presented maps reliably show the BSUs radicalization provided with carbon atoms only, the nonterminated edge part of which presents a set of active sites. Spin mapping of carbocatalysts active sites is suggested as the first step towards the spin carbocatalysis of the species.

A metadynamics perspective on the reduction mechanism of the Pt(IV) asplatin prodrug

Enhanced sampling molecular dynamics has been used to model the reduction mechanism of the antitumoral Asplatin Pt(IV) complex, c,c,t-[PtCl2(NH3)2(OH)(aspirin)] in the presence of l-ascorbic acid as reducing agent. In order to overcome the timescale problem, characteristic of many chemical reactions, we enhanced the sampling of the free energy landscape using Metadynamics. To achieve such a goal, the selection of adequate collective variables is crucial for the application of the method. Recently, a new method called Multi-Class Harmonic Linear Discriminant Analysis (MC-HLDA) has been proposed as a tool for constructing collective variables (CVs) for complex chemical processes. The method reduces the dimensionality of the variable space by generating appropriate linear combinations of several relevant chemical descriptors. The aim of this work is to assess the ability and performance of this method in describing the fundamental features of complex chemical reactions such as the Asplatin reduction mechanism in a compact, simple, and physically transparent manner. © 2019 Wiley Periodicals, Inc.

Enhanced sampling in molecular dynamics

Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.

Accurate Quantum Chemical Free Energies at Affordable Cost

Free energy sampling methods allow studying the full dynamics of activated processes. Unfortunately, the affordable accuracy of the potential describing the energy and forces of the system is usually rather low. Here we introduce a new method that by combining metadynamics and free energy perturbation allows calculating accurate quantum chemical free energies for chemical reactions. To prove the effectiveness of this new approach we study the S_N2 reaction of CH₃F + Cl^- → CH₃Cl + F^- in vacuo and solvated by water. Comparisons are made with harmonic transition-state theory to show how this method could provide accurate equilibrium and rate constants for complex systems.

Improving collective variables: The case of crystallization

Several enhanced sampling methods, such as umbrella sampling or metadynamics, rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient collective variables. One is based on linear discriminant analysis; the other is based on a variational approach to conformational dynamics and uses time-lagged independent component analysis. In this paper, we compare the performance of these two approaches in the study of the homogeneous crystallization of two simple metals. We focus on Na and Al and search for the most efficient collective variables that can be expressed as a linear combination of X-ray diffraction peak intensities. We find that the performances of the two methods are very similar. Wherever the different metastable states are well-separated, the method based on linear discriminant analysis, based on its harmonic version, is to be preferred because simpler to implement and less computationally demanding. The variational approach, however, has the potential to discover the existence of different metastable states.

The reaction mechanism of the azide–alkyne Huisgen cycloaddition

By means of computational methods to sample reaction free energies, this paper provides novel insights into the Huisgen cycloaddition mechanism.