Intramolecular and Water Mediated Tautomerism of Solvated Glycine

Understanding tautomerism and characterizing solvent effects on the dynamic processes pose significant challenges. Using enhanced-sampling molecular dynamics based on state-of-the-art deep learning potentials, we investigated the tautomeric equilibria of glycine in water. We observed that the tautomerism between neutral and zwitterionic glycine can occur through both intramolecular and intermolecular proton transfers. The latter proceeds involving a contact anionic-glycine-hydronium ion pair or separate cationic-glycine-hydroxide ion pair. These pathways with comparable barriers contribute almost equally to the reaction flux.

Effective data-driven collective variables for free energy calculations from metadynamics of paths

A variety of enhanced sampling (ES) methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets-ideally incorporating information about physical pathways and transition states-which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of ES simulations in trajectory space via the metadynamics of paths algorithm. The approach is expected to provide a general and efficient way to generate efficient ML-based CVs for the fast prediction of free energy landscapes in ES simulations. We demonstrate our approach with two numerical examples, a 2D model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice.

Data-driven classification of ligand unbinding pathways

Studying the pathways of ligand-receptor binding is essential to understand the mechanism of target recognition by small molecules. The binding free energy and kinetics of protein-ligand complexes can be computed using molecular dynamics (MD) simulations, often in quantitative agreement with experiments. However, only a qualitative picture of the ligand binding/unbinding paths can be obtained through a conventional analysis of the MD trajectories. Besides, the higher degree of manual effort involved in analyzing pathways limits its applicability in large-scale drug discovery. Here, we address this limitation by introducing an automated approach for analyzing molecular transition paths with a particular focus on protein-ligand dissociation. Our method is based on the dynamic time-warping algorithm, originally designed for speech recognition. We accurately classified molecular trajectories using a very generic descriptor set of contacts or distances. Our approach outperforms manual classification by distinguishing between parallel dissociation channels, within the pathways identified by visual inspection. Most notably, we could compute exit-path-specific ligand-dissociation kinetics. The unbinding timescale along the fastest path agrees with the experimental residence time, providing a physical interpretation to our entirely data-driven protocol. In combination with appropriate enhanced sampling algorithms, this technique can be used for the initial exploration of ligand-dissociation pathways as well as for calculating path-specific thermodynamic and kinetic properties.

Structure and polymerization of liquid sulfur across the λ-transition

The anomalous λ-transition of liquid sulfur, which is supposed to be related to the transformation of eight-membered sulfur rings into long polymeric chains, has attracted considerable attention. However, a detailed description of the underlying dynamical polymerization process is still missing. Here, we study the structures and the mechanism of the polymerization processes of liquid sulfur across the λ-transition as well as its reverse process of formation of the rings. We do so by performing ab initio-quality molecular dynamics simulations thanks to a combination of machine learning potentials and state-of-the-art enhanced sampling techniques. With our approach, we obtain structural results that are in good agreement with the experiments and we report precious dynamical insights into the mechanisms involved in the process.

Cation Chloride Cotransporter NKCC1 Operates through a Rocking-Bundle Mechanism

The sodium, potassium, and chloride cotransporter 1 (NKCC1) plays a key role in tightly regulating ion shuttling across cell membranes. Lately, its aberrant expression and function have been linked to numerous neurological disorders and cancers, making it a novel and highly promising pharmacological target for therapeutic interventions. A better understanding of how NKCC1 dynamically operates would therefore have broad implications for ongoing efforts toward its exploitation as a therapeutic target through its modulation. Based on recent structural data on NKCC1, we reveal conformational motions that are key to its function. Using extensive deep-learning-guided atomistic simulations of NKCC1 models embedded into the membrane, we captured complex dynamical transitions between alternate open conformations of the inner and outer vestibules of the cotransporter and demonstrated that NKCC1 has water-permeable states. We found that these previously undefined conformational transitions occur via a rocking-bundle mechanism characterized by the cooperative angular motion of transmembrane helices (TM) 4 and 9, with the contribution of the extracellular tip of TM 10. We found these motions to be critical in modulating ion transportation and in regulating NKCC1's water transporting capabilities. Specifically, we identified interhelical dynamical contacts between TM 10 and TM 6, which we functionally validated through mutagenesis experiments of 4 new targeted NKCC1 mutants. We conclude showing that those 4 residues are highly conserved in most Na+-dependent cation chloride cotransporters (CCCs), which highlights their critical mechanistic implications, opening the way to new strategies for NKCC1's function modulation and thus to potential drug action on selected CCCs.

The role of dynamics in heterogeneous catalysis: Surface diffusivity and N2 decomposition on Fe(111)

Dynamics has long been recognized to play an important role in heterogeneous catalytic processes. However, until recently, it has been impossible to study their dynamical behavior at industry-relevant temperatures. Using a combination of machine learning potentials and advanced simulation techniques, we investigate the cleavage of the N[Formula: see text] triple bond on the Fe(111) surface. We find that at low temperatures our results agree with the well-established picture. However, if we increase the temperature to reach operando conditions, the surface undergoes a global dynamical change and the step structure of the Fe(111) surface is destabilized. The catalytic sites, traditionally associated with this surface, appear and disappear continuously. Our simulations illuminate the danger of extrapolating low-temperature results to operando conditions and indicate that the catalytic activity can only be inferred from calculations that take dynamics fully into account. More than that, they show that it is the transition to this highly fluctuating interfacial environment that drives the catalytic process.

Free energies at QM accuracy from force fields via multimap targeted estimation

Accurate predictions of ligand binding affinities would greatly accelerate the first stages of drug discovery campaigns. However, using highly accurate interatomic potentials based on quantum mechanics (QM) in free energy methods has been so far largely unfeasible due to their prohibitive computational cost. Here, we present an efficient method to compute QM free energies from simulations using cheap reference potentials, such as force fields (FFs). This task has traditionally been out of reach due to the slow convergence of computing the correction from the FF to the QM potential. To overcome this bottleneck, we generalize targeted free energy methods to employ multiple maps-implemented with normalizing flow neural networks (NNs)-that maximize the overlap between the distributions. Critically, the method requires neither a separate expensive training phase for the NNs nor samples from the QM potential. We further propose a one-epoch learning policy to efficiently avoid overfitting, and we combine our approach with enhanced sampling strategies to overcome the pervasive problem of poor convergence due to slow degrees of freedom. On the drug-like molecules in the HiPen dataset, the method accelerates the calculation of the free energy difference of switching from an FF to a DFTB3 potential by three orders of magnitude compared to standard free energy perturbation and by a factor of eight compared to previously published nonequilibrium calculations. Our results suggest that our method, in combination with efficient QM/MM calculations, may be used in lead optimization campaigns in drug discovery and to study protein-ligand molecular recognition processes.

Kinetics from Metadynamics: Principles, Applications, and Outlook

Metadynamics is a popular enhanced sampling algorithm for computing the free energy landscape of rare events by using molecular dynamics simulation. Ten years ago, Tiwary and Parrinello introduced the infrequent metadynamics approach for calculating the kinetics of transitions across free energy barriers. Since then, metadynamics-based methods for obtaining rate constants have attracted significant attention in computational molecular science. Such methods have been applied to study a wide range of problems, including protein-ligand binding, protein folding, conformational transitions, chemical reactions, catalysis, and nucleation. Here, we review the principles of elucidating kinetics from metadynamics-like approaches, subsequent methodological developments in this area, and successful applications on chemical, biological, and material systems. We also highlight the challenges of reconstructing accurate kinetics from enhanced sampling simulations and the scope of future developments.

A unified framework for machine learning collective variables for enhanced sampling simulations: mlcolvar

Identifying a reduced set of collective variables is critical for understanding atomistic simulations and accelerating them through enhanced sampling techniques. Recently, several methods have been proposed to learn these variables directly from atomistic data. Depending on the type of data available, the learning process can be framed as dimensionality reduction, classification of metastable states, or identification of slow modes. Here, we present mlcolvar, a Python library that simplifies the construction of these variables and their use in the context of enhanced sampling through a contributed interface to the PLUMED software. The library is organized modularly to facilitate the extension and cross-contamination of these methodologies. In this spirit, we developed a general multi-task learning framework in which multiple objective functions and data from different simulations can be combined to improve the collective variables. The library's versatility is demonstrated through simple examples that are prototypical of realistic scenarios.

Deep learning collective variables from transition path ensemble

The study of the rare transitions that take place between long lived metastable states is a major challenge in molecular dynamics simulations. Many of the methods suggested to address this problem rely on the identification of the slow modes of the system, which are referred to as collective variables. Recently, machine learning methods have been used to learn the collective variables as functions of a large number of physical descriptors. Among many such methods, Deep Targeted Discriminant Analysis has proven to be useful. This collective variable is built from data harvested from short unbiased simulations in the metastable basins. Here, we enrich the set of data on which the Deep Targeted Discriminant Analysis collective variable is built by adding data from the transition path ensemble. These are collected from a number of reactive trajectories obtained using the On-the-fly Probability Enhanced Sampling flooding method. The collective variables thus trained lead to more accurate sampling and faster convergence. The performance of these new collective variables is tested on a number of representative examples.

Enhanced Sampling Aided Design of Molecular Photoswitches

Advances in the evolving field of atomistic simulations promise important insights for the design and fundamental understanding of novel molecular photoswitches. Here, we use state-of-the-art enhanced simulation techniques to unravel the complex, multistep chemistry of donor-acceptor Stenhouse adducts (DASAs). Our reaction discovery workflow consists of enhanced sampling for efficient chemical space exploration, refinement of newly observed pathways with more accurate ab initio electronic structure calculations, and structural modifications to introduce design principles within future generations of DASAs. We showcase our discovery workflow by not only recovering the full photoswitching mechanism of DASA but also predicting a plethora of new plausible thermal pathways and suggesting a way for their experimental validation. Furthermore, we illustrate the tunability of these newly discovered reactions, leading to a potential avenue for controlling DASA dynamics through multiple external stimuli. Overall, these insights could offer alternative routes to increase the efficiency and control of DASA's photoswitching mechanism, providing new elements to design more complex light-responsive materials.

Rare Event Kinetics from Adaptive Bias Enhanced Sampling

We introduce a novel enhanced sampling approach named on-the-fly probability enhanced sampling (OPES) flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the OPES approach [Invernizzi and Parrinello, J. Phys. Chem. Lett. 2020, 11, 7, 2731-2736], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double-well potential, conformational transition in the alanine dipeptide in the gas phase, and the folding and unfolding of the chignolin polypeptide in an aqueous environment. From extensive tests, we show that the calculation of accurate kinetics not only requires the transition state to be bias-free, but the amount of bias deposited should also not exceed the effective barrier height measured along the chosen collective variables. In this vein, the possibility of computing rates from biasing suboptimal order parameters has also been explored. Furthermore, we describe the choice of optimum parameter combinations for obtaining accurate results from limited computational effort.

Characterizing Metastable States with the Help of Machine Learning

Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature are becoming increasingly challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, chignolin and bovine pancreatic trypsin inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.

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.

Exploration vs Convergence Speed in Adaptive-Bias Enhanced Sampling

In adaptive-bias enhanced sampling methods, a bias potential is added to the system to drive transitions between metastable states. The bias potential is a function of a few collective variables and is gradually modified according to the underlying free energy surface. We show that when the collective variables are suboptimal, there is an exploration–convergence tradeoff, and one must choose between a quickly converging bias that will lead to fewer transitions or a slower to converge bias that can explore the phase space more efficiently but might require a much longer time to produce an accurate free energy estimate. The recently proposed on-the-fly probability enhanced sampling (OPES) method focuses on fast convergence, but there are cases where fast exploration is preferred instead. For this reason, we introduce a new variant of the OPES method that focuses on quickly escaping metastable states at the expense of convergence speed. We illustrate the benefits of this approach in prototypical systems and show that it outperforms the popular metadynamics method.

Computing Rates and Understanding Unbinding Mechanisms in Host-Guest Systems

The long time scale associated with ligand residence times renders their computation challenging. Therefore, the influence of factors like solvation and steric hindrance on residence times is not fully understood. Here, we demonstrate in a set of model host-guest systems that the recently developed Gaussian mixture based enhanced sampling allows residence times to be computed and enables an understanding of their unbinding mechanism. We observe that guest unbinding often proceeds via a series of intermediate states that can be labeled by the number of water molecules present in the binding cavity. In several cases the residence time is correlated to the water trapping times in the cavity.

Discover, Sample, and Refine: Exploring Chemistry with Enhanced Sampling Techniques

Over the last few decades, enhanced sampling methods have been continuously improved. Here, we exploit this progress and propose a modular workflow for blind reaction discovery and determination of reaction paths. In a three-step strategy, at first we use a collective variable derived from spectral graph theory in conjunction with the explore variant of the on-the-fly probability enhanced sampling method to drive reaction discovery runs. Once different chemical products are determined, we construct an ad-hoc neural network-based collective variable to improve sampling, and finally we refine the results using the free energy perturbation theory and a more accurate Hamiltonian. We apply this strategy to both intramolecular and intermolecular reactions. Our workflow requires minimal user input and extends the power of ab initio molecular dynamics to explore and characterize the reaction space.

Prediction of a Supersolid Phase in High-Pressure Deuterium

Supersolid is a mysterious and puzzling state of matter whose possible existence has stirred a vigorous debate among physicists for over 60 years. Its elusive nature stems from the coexistence of two seemingly contradicting properties, long-range order and superfluidity. We report computational evidence of a supersolid phase of deuterium under high pressure (p>800  GPa) and low temperature (T<1.0  K). In our simulations, that are based on bosonic path integral molecular dynamics, we observe a highly concerted exchange of atoms while the system preserves its crystalline order. The exchange processes are favored by the soft core interactions between deuterium atoms that form a densely packed metallic solid. At the zero temperature limit, Bose-Einstein condensation is observed as the permutation probability of N deuterium atoms approaches 1/N with a finite superfluid fraction. Our study provides concrete evidence for the existence of a supersolid phase in high-pressure deuterium and could provide insights on the future investigation of supersolid phases in real materials.

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.

Targeted Free Energy Perturbation Revisited: Accurate Free Energies from Mapped Reference Potentials

We present an approach that extends the theory of targeted free energy perturbation (TFEP) to calculate free energy differences and free energy surfaces at an accurate quantum mechanical level of theory from a cheaper reference potential. The convergence is accelerated by a mapping function that increases the overlap between the target and the reference distributions. Building on recent work, we show that this map can be learned with a normalizing flow neural network, without requiring simulations with the expensive target potential but only a small number of single-point calculations, and, crucially, avoiding the systematic error that was found previously. We validate the method by numerically evaluating the free energy difference in a system with a double-well potential and by describing the free energy landscape of a simple chemical reaction in the gas phase.

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.

Water-Triggered, Irreversible Conformational Change of SARS-CoV-2 Main Protease on Passing from the Solid State to Aqueous Solution

The main protease from SARS-CoV-2 is a homodimer. Yet, a recent 0.1-ms-long molecular dynamics simulation performed by D. E. Shaw's research group shows that it readily undergoes a symmetry-breaking event on passing from the solid state to aqueous solution. As a result, the subunits present distinct conformations of the binding pocket. By analyzing this long simulation, we uncover a previously unrecognized role of water molecules in triggering the transition. Interestingly, each subunit presents a different collection of long-lived water molecules. Enhanced sampling simulations performed here, along with machine learning approaches, further establish that the transition to the asymmetric state is essentially irreversible.

A modified nudged elastic band algorithm with adaptive spring lengths

We present a modified version of the nudged elastic band (NEB) algorithm to find minimum energy paths connecting two known configurations. We show that replacing the harmonic band-energy term with a discretized version of the Onsager-Machlup action leads to a NEB algorithm with adaptive spring lengths that automatically increase the resolution of the minimum energy path around the saddle point of the potential energy surface. The method has the same computational cost per optimization step of the standard NEB algorithm and does not introduce additional parameters. We present applications to the isomerization of alanine dipeptide, the elimination of hydrogen from ethane, and the healing of a 5-77-5 defect in graphene.

Liquid-Liquid Critical Point in Phosphorus

The study of liquid-liquid phase transitions has attracted considerable attention. One interesting example of this phenomenon is phosphorus, for which the existence of a first-order phase transition between a low density insulating molecular phase and a conducting polymeric phase has been experimentally established. In this Letter, we model this transition by an ab initio quality molecular dynamics simulation and explore a large portion of the liquid section of the phase diagram. We draw the liquid-liquid coexistence curve and determine that it terminates into a second-order critical point. Close to the critical point, large coupled structure and electronic structure fluctuations are observed.

Confinement effects and acid strength in zeolites

Chemical reactivity and sorption in zeolites are coupled to confinement and-to a lesser extent-to the acid strength of Brønsted acid sites (BAS). In presence of water the zeolite Brønsted acid sites eventually convert into hydronium ions. The gradual transition from zeolite Brønsted acid sites to hydronium ions in zeolites of varying pore size is examined by ab initio molecular dynamics combined with enhanced sampling based on Well-Tempered Metadynamics and a recently developed set of collective variables. While at low water content (1-2 water/BAS) the acidic protons prefer to be shared between zeolites and water, higher water contents (n > 2) invariably lead to solvation of the protons within a localized water cluster adjacent to the BAS. At low water loadings the standard free energy of the formed complexes is dominated by enthalpy and is associated with the acid strength of the BAS and the space around the site. Conversely, the entropy increases linearly with the concentration of waters in the pores, favors proton solvation and is independent of the pore size/shape.

A combined molecular dynamics and experimental study of two-step process enabling low-temperature formation of phase-pure α-FAPbI3

It is well established that the lack of understanding the crystallization process in a two-step sequential deposition has a direct impact on efficiency, stability, and reproducibility of perovskite solar cells. Here, we try to understand the solid-solid phase transition occurring during the two-step sequential deposition of methylammonium lead iodide and formamidinium lead iodide. Using metadynamics, x-ray diffraction, and Raman spectroscopy, we reveal the microscopic details of this process. We find that the formation of perovskite proceeds through intermediate structures and report polymorphs found for methylammonium lead iodide and formamidinium lead iodide. From simulations, we discover a possible crystallization pathway for the highly efficient metastable α phase of formamidinium lead iodide. Guided by these simulations, we perform experiments that result in the low-temperature crystallization of phase-pure α-formamidinium lead iodide.

The role of water in host-guest interaction

One of the main applications of atomistic computer simulations is the calculation of ligand binding free energies. The accuracy of these calculations depends on the force field quality and on the thoroughness of configuration sampling. Sampling is an obstacle in simulations due to the frequent appearance of kinetic bottlenecks in the free energy landscape. Very often this difficulty is circumvented by enhanced sampling techniques. Typically, these techniques depend on the introduction of appropriate collective variables that are meant to capture the system's degrees of freedom. In ligand binding, water has long been known to play a key role, but its complex behaviour has proven difficult to fully capture. In this paper we combine machine learning with physical intuition to build a non-local and highly efficient water-describing collective variable. We use it to study a set of host-guest systems from the SAMPL5 challenge. We obtain highly accurate binding free energies and good agreement with experiments. The role of water during the binding process is then analysed in some detail.

Tautomeric Equilibrium in Condensed Phases

We present an ab initio molecular dynamics (MD) investigation of the tautomeric equilibrium for the aqueous solutions of glycine and acetone under realistic experimental conditions. Metadynamics is used to accelerate proton migration among tautomeric centers. Due to the formation of complex water-ion structures involved in the proton dynamics in the aqueous environment, standard enhanced sampling approaches may face severe limitations in providing a general description of the phenomenon. Recently, we have developed a set of collective variables (CVs) designed to study protons transfer reactions in complex condensed systems [Grifoni, E. Proc. Natl. Acad. Sci. U.S.A. 2019, 116, 4054 4057]. In this work, we applied this approach to study proton dissociation dynamics leading to tautomeric interconversion of biologically and chemically relevant prototypical systems, namely, glycine and acetone in water. Although relatively simple from a chemical point of view, the results show that even for these small systems, complex reaction pathways and nontrivial conversion dynamics are observed. The generality of our method allows obtaining these results without providing any prior information on the dissociation dynamics but only the atomic species that can exchange protons in the process. Our results agree with literature estimates and demonstrate the general applicability of this method in the study of tautomeric reactions.

Erratum: Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations [Phys. Rev. Lett. 119, 015701 (2017)]

This corrects the article DOI: 10.1103/PhysRevLett.119.015701.

Molecular Mechanism of Gas Solubility in Liquid: Constant Chemical Potential Molecular Dynamics Simulations

Accurate prediction of gas solubility in a liquid is crucial in many areas of chemistry, and a detailed understanding of the molecular mechanism of the gas solvation continues to be an active area of research. Here, we extend the idea of the constant chemical potential molecular dynamics (CμMD) approach to the calculation of the gas solubility in the liquid under constant gas chemical potential conditions. As a representative example, we utilize this method to calculate the isothermal solubility of carbon dioxide in water. Additionally, we provide microscopic insight into the mechanism of solvation that preferentially occurs in areas of the surface where the hydrogen network is broken.

Accuracy of Molecular Simulation-Based Predictions of koff Values: A Metadynamics Study

The k_off values of ligands unbinding to proteins are key parameters for drug discovery. Their predictions based on molecular simulation may under- or overestimate experiment in a system- and/or technique-dependent way. Here we use an established method-infrequent metadynamics, based on the AMBER force field-to compute the k_off of the ligand iperoxo (in clinical use) targeting the muscarinic receptor M₂. The ligand charges are calculated by either (i) the Amber standard procedure or (ii) B3LYP-DFT. The calculations using (i) turn out not to provide a reasonable estimation of the transition-state free energy. Those using (ii) differ from experiment by 2 orders of magnitude. On the basis of B3LYP DFT QM/MM simulations, we suggest that the observed discrepancy in (ii) arises, at least in part, from the lack of electronic polarization and/or charge transfer in biomolecular force fields. These issues might be present in other systems, such as DNA-protein complexes.

Metadynamics of Paths

We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time correlation functions are conveniently computed via reweighted averages along a single trajectory and kinetic rates are accessed at no additional cost. These abilities are illustrated analyzing a model potential and the umbrella inversion of NH_{3} in water. The algorithm allows a parallel implementation and promises to be a powerful tool for the study of rare events.

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.

Rethinking Metadynamics: From Bias Potentials to Probability Distributions

Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is a function of a selected number of collective variables. We propose here a change in perspective that shifts the focus from the bias to the probability distribution reconstruction while retaining some of the key characteristics of metadynamics, such as flexible on-the-fly adjustments to the free energy estimate. The result is an enhanced sampling method that presents a drastic improvement in convergence speed, especially when dealing with suboptimal and/or multidimensional sets of collective variables. The method is especially robust and easy to use and in fact requires only a few simple parameters to be set, and it has a straightforward reweighting scheme to recover the statistics of the unbiased ensemble. Furthermore, it gives more control of the desired exploration of the phase space since the deposited bias is not allowed to grow indefinitely and it does not push the simulation to uninteresting high free energy regions. We demonstrate the performance of the method in a number of representative examples.

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.

Kinetics of Aqueous Media Reactions via Ab Initio Enhanced Molecular Dynamics: The Case of Urea Decomposition

Aqueous solutions provide a medium for many important reactions in chemical synthesis, industrial processes, environmental chemistry, and biological functions. It is an accepted fact that aqueous solvents can be direct participants in the reaction process and not act only as simple passive dielectrics. Assisting water molecules and proton wires are thus essential for the efficiency of many reactions. Here, we study the decomposition of urea into ammonia and isocyanic acid by means of enhanced ab initio molecular dynamics simulations. We highlight the role of the solvent molecules and their interactions with the reactants providing a proper description of the reaction mechanism and how the water hydrogen-bond network affects the reaction dynamics. Reaction free energy and rates have been calculated taking into account this important effect.

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.

Calculation of phase diagrams in the multithermal-multibaric ensemble

From the Ising model and the Lennard-Jones fluid to water and the iron-carbon system, phase diagrams are an indispensable tool to understand phase equilibria. Despite the effort of the simulation community, the calculation of a large portion of a phase diagram using computer simulation is still today a significant challenge. Here, we propose a method to calculate phase diagrams involving liquid and solid phases by the reversible transformation of the liquid and the solid. To this end, we introduce an order parameter that breaks the rotational symmetry and we leverage our recently introduced method to sample the multithermal-multibaric ensemble. In this way, in a single molecular dynamics simulation, we are able to compute the liquid-solid coexistence line for entire regions of the temperature and pressure phase diagram. We apply our approach to the bcc-liquid phase diagram of sodium and the fcc-bcc-liquid phase diagram of aluminum.

Temperature Dependence of Homogeneous Nucleation in Ice

Ice nucleation is a process of great relevance in physics, chemistry, technology, and environmental sciences; much theoretical effort has been devoted to its understanding, but it still remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom transferable intermolecular potential with 4 points/ice (TIP4P/ice) model, and the features of the critical nucleus of nucleation at the microscopic level are revealed. We have also estimated the ice nucleation rates along with other nucleation parameters at different undercoolings. Our results are in agreement with recent experimental and other theoretical works, and they confirm that nucleation is preceded by a large increase in tetrahedrally coordinated water molecules.

Exhaustive Search of Ligand Binding Pathways via Volume-Based Metadynamics

Determining the complete set of ligands' binding-unbinding pathways is important for drug discovery and for rational interpretation of mutation data. Here we have developed a metadynamics-based technique that addresses this issue and allows estimating affinities in the presence of multiple escape pathways. Our approach is shown on a lysozyme T4 variant in complex with a benzene molecule. The calculated binding free energy is in agreement with experimental data. Remarkably, not only were we able to find all the previously identified ligand binding pathways, but also we identified three pathways previously not identified as such. These results were obtained at a small computational cost, making this approach valuable for practical applications, such as screening of small compound libraries.