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.

Supramolecular Capsule-Catalyzed Highly ß-Selective Furanosylation Independent of the SN1/SN2 Reaction Pathway.

The resorcin[4]arene capsule was found to catalyze ß-selective furanosylation reactions for a variety of different furanosyl donors: α-d- and α-l-arabinosyl-, α-l-fucosyl-, α-d-ribosyl-, α-d-xylosyl-, and even α-d-lyxosyl fluorides. The scope is only limited by the inherently finite volume inside the closed capsular catalyst. The catalyst is readily available on a multi-100 g scale and can be recycled for at least seven rounds without significant loss in activity, yield, and selectivity. The mechanistic investigations indicated that the furanosylation mechanism is shifted toward an SN1 reaction on the mechanistic continuum between the prototypical SN1 and SN2 substitution types, as compared to the pyranosylation reaction inside the same catalyst. This is especially true for the lyxosyl donor, as indicated by the nucleophile reaction order of 0.26, and supported by metadynamics calculations. The mechanistic shift toward SN1 is of high interest as it indicates that this catalyst not only enables ß-selective furanosylations and pyranoslyations independently of the substrate configuration but in addition also independently of the operating mechanism. To our knowledge, there is no alternative catalyst available that displays such properties.

Physical Chemistry of Chloroquine Permeation through the Cell Membrane with Atomistic Detail.

We provide a molecular-level description of the thermodynamics and mechanistic aspects of drug permeation through the cell membrane. As a case study, we considered the antimalaria FDA approved drug chloroquine. Molecular dynamics simulations of the molecule (in its neutral and protonated form) were performed in the presence of different lipid bilayers, with the aim of uncovering key aspects of the permeation process, a fundamental step for the drug's action. Free energy values obtained by well-tempered metadynamics simulations suggest that the neutral form is the only permeating protomer, consistent with experimental data. H-bond interactions of the drug with water molecules and membrane headgroups play a crucial role for permeation. The presence of the transmembrane potential, investigated here for the first time in a drug permeation study, does not qualitatively affect these conclusions.

Molecular Dynamics and Structural Studies of Zinc Chloroquine Complexes.

Chloroquine (CQ) is a first-choice drug against malaria and autoimmune diseases. It has been co-administered with zinc against SARS-CoV-2 and soon dismissed because of safety issues. The structural features of Zn-CQ complexes and the effect of CQ on zinc distribution in cells are poorly known. In this study, state-of-the-art computations combined with experiments were leveraged to solve the structural determinants of zinc-CQ interactions in solution and the solid state. NMR, ESI-MS, and X-ray absorption and diffraction methods were combined with ab initio molecular dynamics calculations to address the kinetic lability of this complex. Within the physiological pH range, CQ binds Zn2+ through the quinoline ring nitrogen, forming [Zn(CQH)Clx(H2O)3-x](3+)-x (x = 0, 1, 2, and 3) tetrahedral complexes. The Zn(CQH)Cl3 species is stable at neutral pH and at high chloride concentrations typical of the extracellular medium, but metal coordination is lost at a moderately low pH as in the lysosomal lumen. The pentacoordinate complex [Zn(CQH)(H2O)4]3+ may exist in the absence of chloride. This in vitro/in silico approach can be extended to other metal-targeting drugs and bioinorganic systems.

Microscopic description of acid-base equilibrium.

Acid-base reactions are ubiquitous in nature. Understanding their mechanisms is crucial in many fields, from biochemistry to industrial catalysis. Unfortunately, experiments give only limited information without much insight into the molecular behavior. Atomistic simulations could complement experiments and shed precious light on microscopic mechanisms. The large free-energy barriers connected to proton dissociation, however, make the use of enhanced sampling methods mandatory. Here we perform an ab initio molecular dynamics (MD) simulation and enhance sampling with the help of metadynamics. This has been made possible by the introduction of descriptors or collective variables (CVs) that are based on a conceptually different outlook on acid-base equilibria. We test successfully our approach on three different aqueous solutions of acetic acid, ammonia, and bicarbonate. These are representative of acid, basic, and amphoteric behavior.

Enantioselective Tail-to-Head Terpene Cyclizations by Optically Active Hexameric Resorcin[4]arene Capsule Derivatives.

Molecular capsules enable the conversion of substrates inside a closed cavity, mimicking to some extent enzymatic catalysis. Chirality transfer from the molecular capsule onto the encapsulated substrate has been only studied in a few cases. Here we demonstrate that chirality transfer is possible inside a rather large molecular container of approximately 1400 Å3 . Specifically, we present 1) the first examples of optically active hexameric resorcin[4]arene capsules, 2) their ability to enantioselectively catalyze tail-to-head terpene cyclizations, and 3) the surprisingly high sensitivity of enantioselectivity on the structural modifications.

Understanding the binding properties of phosphorylated glycoluril-derived molecular tweezers and selective nanomolar binding of natural polyamines in aqueous solution.

A modular synthetic platform for the construction of flexible glycoluril-derived molecular tweezers was developed. The binding properties of four exemplary supramolecular hosts obtained via this approach towards 16 organic amines were investigated by means of 1H NMR titration. In this work, we compare the Ka values obtained this way with those of three structurally related molecular tweezers and provide a computational approach towards an explanation of the observed behavior of those novel hosts. The results showcase that certain structural modifications lead to very potent and selective binders of natural polyamines, with observed binding of spermine below 10 nM.

Requirements for Terpene Cyclizations inside the Supramolecular Resorcinarene Capsule: Bound Water and Its Protonation Determine the Catalytic Activity.

The elucidation of the requirements for efficient catalysis within supramolecular host systems is an important prerequisite for developing novel supramolecular catalysts. The resorcinarene hexamer has recently been shown to be the first supramolecular catalyst to promote the tail-to-head terpene cyclization in a biomimetic fashion. We herein present the synthesis of a number of resorcinarene-based macrocycles composed of different ratios of resorcinol and pyrogallol units capable of self-assembly and compare the corresponding assemblies regarding their catalytic activity in the cyclization of monoterpenes. The assemblies were investigated in detail with respect to a number of properties including the encapsulation of substrate and ion pairs, the structural incorporation of water, and the response to externally added acid (HCl). The results obtained strongly indicate that water incorporated into the hydrogen-bond network of the self-assembled structure plays an integral role for catalysis, effectively acting as a proton shuttle to activate the encapsulated substrate. These findings are also supported by molecular dynamics simulations, providing further insight into the protonation pathway and the relative energies of the intermediates involved.

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.

Including dispersion in density functional theory for adsorption on flat oxide surfaces, in metal-organic frameworks and in acidic zeolites.

We examine the performance of nine commonly used methods for including dispersion interactions in density functional theory (DFT): three different parametrizations of damped 1/Rn terms (n = 6, 8, …) added to the DFT energy (Grimme's D2 and D3 parameterizations as well as that of Tkatchenko and Scheffler), three different implementations of the many-body dispersion approach (MBD, MBD/HI and MBD/FI), the density-dependent energy correction, called dDsC, and two "first generation" van der Waals density functionals, revPBE-vdW and optB86b-vdW. As test set we use eight molecule-surface systems for which agreement has been reached between experiment and hybrid QM:QM calculations within chemical accuracy limits (±4.2 kJ mol-1). It includes adsorption of carbon monoxide and dioxide in the Mg2(2,5-dioxido-1,4-benzenedicarboxylate) metal-organic framework (Mg-MOF-74, CPO-27-Mg), adsorption of carbon monoxide as well as of monolayers of methane and ethane on the MgO(001) surface, as well as adsorption of methane, ethane and propane in H-chabazite (H-CHA). D2 with Ne parameters for Mg2+, D2(Ne), MBD/HI and MBD/FI perform best. With the PBE functional, the mean unsigned errors are 6.1, 5.6 and 5.4 kJ mol-1, respectively.

The reaction mechanism of the azide-alkyne Huisgen cycloaddition.

The azide-alkyne Huisgen cycloaddition has a key role in click chemistry and is configured as a powerful tool in pharmaceutical and medicinal chemistry. Although this reaction has already been largely studied, there is an ongoing debate about its mechanism. In this work we study the dynamical aspects of the process using metadynamics computer simulations. We focus on the conformational aspects that determine the course of the reaction and characterize its free energy landscape. To properly capture the thermodynamics of the process we select optimal collective variables using harmonic linear discriminant analysis. The results qualitatively confirm and explain the experimental evidence and give insights into the role of the substituents and the possible transition mechanisms.

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.

Ab initio study of methanol and ethanol adsorption on Brønsted sites in zeolite H-MFI.

We examine the interaction of methanol and ethanol with a bridging OH group of H-MFI (Al12-O20(H)-Si3 site). The computational standard approach for molecule-surface interaction uses density functional theory with inclusion of dispersion for energies and harmonic vibrational frequencies for entropies and finite temperature effects for enthalpies. At 300 K, this yields -117 and -135 kJ mol-1 for adsorption enthalpies of methanol and ethanol, respectively, and 59 and 61 kJ mol-1, respectively for their entropy terms -T·ΔS. To reach chemical accuracy (±4 kJ mol-1) we go beyond this approach. The energies are calculated using a hybrid QM:QM scheme (QM - quantum mechanics) which combines plane-wave density functional theory accounting for the periodicity of the system with wave function-based methods (Møller-Plesset perturbation and Coupled Cluster theories). Finite temperature and entropy contributions are calculated from anharmonic vibrational partition functions. This yields as final predictions for methanol and ethanol -84 and -104 kJ mol-1, respectively, for the enthalpies of adsorption, 56 and 48 kJ mol-1, respectively, for the -T·ΔS term, and -28 and -56 kJ mol-1, respectively, for the Gibbs free energies at 300 K.

Folding a small protein using harmonic linear discriminant analysis.

Many processes of scientific importance are characterized by time scales that extend far beyond the reach of standard simulation techniques. To circumvent this impediment, a plethora of enhanced sampling methods has been developed. One important class of such methods relies on the application of a bias that is a function of a set of collective variables specially designed for the problem under consideration. The design of good collective variables can be challenging and thereby constitutes the main bottle neck in the application of these methods. To address this problem, recently we have introduced Harmonic Linear Discriminant Analysis, a method to systematically construct collective variables as linear combinations of a set of descriptors. The method uses input information that can be gathered in short unbiased molecular dynamics simulations in which the system is trapped in the metastable states. Here, to scale up our examination of the method's efficiency, we applied it to the folding of chignolin in water. Interestingly, already before any biased simulations were run, the constructed one-dimensional collective variable revealed much of the physics that underlies the folding process. In addition, using it in metadynamics, we were able to run simulations in which the system goes from the folded state to the unfolded one and back, where to get fully converged results, we combined metadynamics with parallel tempering. Finally, we examined how the collective variable performs when different sets of descriptors are used in its construction.

Ab Initio Prediction of Adsorption Isotherms for Small Molecules in Metal-Organic Frameworks.

For CO and N2 on Mg2+ sites of the metal-organic framework CPO-27-Mg (Mg-MOF-74), ab initio calculations of Gibbs free energies of adsorption have been performed. Combined with the Bragg-Williams/Langmuir model and taking into account the experimental site availability (76.5%), we obtained adsorption isotherms in close agreement with those in experiment. The remaining deviations in the Gibbs free energy (about 1 kJ/mol) are significantly smaller than the "chemical accuracy" limit of about 4 kJ/mol. The presented approach uses (i) a DFT dispersion method (PBE+D2) to optimize the structure and to calculate anharmonic frequencies for vibrational partition functions and (ii) a "hybrid MP2:(PBE+D2)+ΔCCSD(T)" method to determine electronic energies. With the achieved accuracy (estimated uncertainty ±1.4 kJ/mol), the ab initio energies become useful benchmarks for assessing different DFT + dispersion methods (PBE+D2, B3LYP+D*, and vdW-D2), whereas the ab initio heats, entropies, and Gibbs free energies of adsorption are used to assess the reliability of experimental values derived from fitting isotherms or from variable-temperature IR studies.

Ab†Initio Calculation of Rate Constants for Molecule-Surface Reactions with Chemical Accuracy.

The ab initio prediction of reaction rate constants for systems with hundreds of atoms with an accuracy that is comparable to experiment is a challenge for computational quantum chemistry. We present a divide-and-conquer strategy that departs from the potential energy surfaces obtained by standard density functional theory with inclusion of dispersion. The energies of the reactant and transition structures are refined by wavefunction-type calculations for the reaction site. Thermal effects and entropies are calculated from vibrational partition functions, and the anharmonic frequencies are calculated separately for each vibrational mode. This method is applied to a key reaction of an industrially relevant catalytic process, the methylation of small alkenes over zeolites. The calculated reaction rate constants (free energies), pre-exponential factors (entropies), and enthalpy barriers show that our computational strategy yields results that agree with experiment within chemical accuracy limits (less than one order of magnitude).

Window[1]resorcin[3]arenes: A Novel Macrocycle Able to Self-Assemble to a Catalytically Active Hexameric Cage.

The hexameric resorcin[4]arene capsule has been utilized as one of the most versatile supramolecular capsule catalysts. Enlarging its size would enable expansion of the substrate size scope. However, no larger catalytically active versions have been reported. Herein, we introduce a novel class of macrocycles, named window[1]resorcin[3]arene (wRS), that assemble to a cage-like hexameric host. The new host was studied by NMR, encapsulation experiments, and molecular dynamics simulations. The cage is able to bind tetraalkylammonium ions that are too large for encapsulation inside the hexameric resorcin[4]arene capsule. Most importantly, it retained its catalytic activity, and the accelerated conversion of a large substrate that does not fit the closed hexameric resorcin[4]arene capsule was observed. Thus, it will help to expand the limited substrate size scope of the closed hexameric resorcin[4]arene capsule.

Mimicry of the proton wire mechanism of enzymes inside a supramolecular capsule enables ß-selective O-glycosylations.

Enzymes achieve high substrate and product selectivities by orientating and activating the substrate(s) appropriately inside a confined and finely optimized binding pocket. Although some basic aspects of enzymes have already been mimicked successfully with man-made catalysts, substrate activation by proton wires inside enzyme pockets has not been recreated with man-made catalysts so far. A proton wire facilitates the dual activation of a nucleophile and an electrophile via a reciprocal proton transfer, enabling highly stereoselective reactions under mild conditions. Here we present evidence for such an activation mode inside the supramolecular resorcin[4]arene capsule and demonstrate that it enables catalytic and highly ß-selective glycosylation reactions-still a major challenge in glycosylation chemistry. Extensive control experiments provide very strong evidence that the reactions take place inside the molecular container. We show that this activation strategy is compatible with a broad scope of glycoside donors and nucleophiles, and is only limited by the cavity size.

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.

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.