Multilevel Framework for Analysis of Protein Folding Involving Disulfide Bond Formation

In this study, a three-layered multicenter ONIOM approach is implemented to characterize the naive folding pathway of bovine pancreatic trypsin inhibitor (BPTI). Each layer represents a distinct level of theory, where the initial layer, encompassing the entire protein, is modeled by a general all-atom force-field GFN-FF. An intermediate electronic structure layer consisting of three multicenter fragments is introduced with the state-of-the-art semiempirical tight-binding method GFN2-xTB. Higher accuracy, specifically addressing the breaking and formation of the three disulfide bonds, is achieved at the innermost layer using the composite DFT method r2SCAN-3c. Our analysis sheds light on the structural stability of BPTI, particularly the significance of interlinking disulfide bonds. The accuracy and efficiency of the multicenter QM/SQM/MM approach are benchmarked using the oxidative formation of cystine. For the folding pathway of BPTI, relative stabilities are investigated through the calculation of free energy contributions for selected intermediates, focusing on the impact of the disulfide bond. Our results highlight the intricate trade-off between accuracy and computational cost, demonstrating that the multicenter ONIOM approach provides a well-balanced and comprehensive solution to describe electronic structure effects in biomolecular systems. We conclude that multiscale energy landscape exploration provides a robust methodology for the study of intriguing biological targets.

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

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

A quantum mechanical approach to the oxidation mechanism of graphene oxide (GO)

Elucidation of the reaction mechanism concerning the oxidation above the face and at the edge of a large, oxidized graphene (GO) cluster, namely C80H22O, by molecular oxygen in the first excited state (1Δg) was achieved with quantum mechanical calculations using the ONIOM two-layer method. Oxidation on the face of the aforementioned cluster leads to the formation of an ozone molecule, whereas oxygen molecule attack at the edge of the oxidized graphene surface either launches an ozonide -a five-membered ring species- formation during its outward approach or an 1,3-dioxetane -a four-membered ring species- production along its inward invasion. A detailed examination of the proposed pathways suggests that the ozonide formation should overcome almost one and a half times an adiabatic energy barrier with respect to the ozone production and is strongly exergonic by up to -50.1 kcal mol-1, supporting the experimental findings that both compounds are critically involved in the explosive deoxygenation of GO. On the other hand, the 1,3-dioxetane alternative pathway is considered even more exergonic, although it requires an overwhelming adiabatic energy barrier of 29.8 kcal mol-1 to accomplish its target.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.

Mechanism of Selective Aromatic Hydroxylation in the Metabolic Transformation of Paclitaxel Catalyzed by Human CYP3A4

Paclitaxel (PTX) is heralded as one of the most successful natural-product drugs for the treatment of refractory cancers. In humans, the hepatic metabolic transformation of PTX is primarily mediated by two cytochrome P450 enzymes (P450s): CYP3A4 and CYP2C8. The impact of P450 metabolism on the anticancer effectiveness of PTX is significant. However, the precise mechanism underlying selective P450-catalyzed reactions in PTX metabolism remains elusive. To address this knowledge gap, we conducted molecular docking and molecular dynamics simulations using multiple crystal structures of CYP3A4, which originally contained other ligands. These methods enabled us to determine the most plausible binding structure of PTX within the enzyme. By further employing hybrid quantum mechanics and molecular mechanics calculations, we successfully identified two primary pathways for the reaction between compound I (Cpd I) of CYP3A4 and PTX. One of these pathways involves the formation of an epoxide, while the other proceeds through a ketone intermediate.

Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning

The accurate and efficient study of the interactions of organic matter with the surface of water is critical to a wide range of applications. For example, environmental studies have found that acidic polyfluorinated alkyl substances, especially perfluorooctanoic acid (PFOA), have spread throughout the environment and bioaccumulate into human populations residing near contaminated watersheds, leading to many systemic maladies. Thus, the study of the interactions of PFOA with water surfaces became important for the mitigation of their activity as pollutants and threats to public health. However, theoretical study of the interactions of such organic adsorbates on the surface of water, and their bulk concerted properties, often necessitates the use of ab initio methods to properly incorporate the long-range electronic properties that govern these extended systems. Notable theoretical treatments of "on-water" reactions thus far have employed hybrid DFT and semilocal DFT, but the interactions involved are weak interactions that may be best described using post-Hartree-Fock theory. Here, we aim to demonstrate the utility of a graph-theoretic approach to molecular fragmentation that accurately captures the critical "weak" interactions while maintaining an efficient ab initio treatment of the long-range periodic interactions that underpin the physics of extended systems. We apply this graph-theoretical treatment to study PFOA on the surface of water as a model system for the study of weak interactions seen in the wide range of surface interactions and reactions. The approach divides a system into a set of vertices, that are then connected through edges, faces, and higher order graph theoretic objects known as simplexes, to represent a collection of locally interacting subsystems. These subsystems are then used to construct ab initio molecular dynamics simulations and for computing multidimensional potential energy surfaces. To further improve the computational efficiency of our graph theoretic fragmentation method, we use a recently developed transfer learning protocol to construct the full system potential energy from a family of neural networks each designed to accurately model the behavior of individual simplexes. We use a unique multidimensional clustering algorithm, based on the k-means clustering methodology, to define our training space for each separate simplex. These models are used to extrapolate the energies for molecular dynamics trajectories at PFOA water interfaces, at less than one-tenth the cost as compared to a regular molecular fragmentation-based dynamics calculation with excellent agreement with couple cluster level of full system potential energies.

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

A mechanistic insight for the biosynthesis of N,N-dimethyltryptamine: An ONIOM theoretical approach

Psychoactive natural products are potent serotonergic agonists capable of modulating brain functions such as memory and cognition. These substances have shown therapeutic potential for treating various mental disorders. The fact that N,N-dimethyltryptamine (DMT) is produced endogenously in several plants and animals, including humans, makes it particularly attractive. As an amino acid-derived alkaloid, the DMT biosynthetic pathway is part of the L-tryptophan biochemical cascade and can be divided into the decarboxylation by an aromatic L-amino acid decarboxylase (AADC) for tryptamine formation and the subsequent double-methylation by the indolethylamine-N-methyltransferase (INMT) through the cofactor S-adenosyl-L-methionine (SAM), a methyl donor. Unlike the decarboxylation mechanism of L-tryptophan, the molecular details of the double methylation of tryptamine have not been elucidated. Therefore, we propose an in silico model using molecular dynamics (MD), non-covalent interaction index (NCI) and density functional theory (DFT) calculations with the ONIOM QM:MM B3LYP/6-31+G(d,p):MM/UFF level of theory. Based on the obtained energetic data, the potential energy surface (PES) indicates an SN2 mechanism profile, with the second methylation energy barrier being the rate-limiting step with δG‡=60kJ∙mol-1 larger than the previous methylation, following the NCI analysis showing more repulsive interactions for the second transition state. In addition, the hybridization information of each reaction step provides geometric details about the double-methylation.

Automated, Consistent, and Even-Handed Selection of Active Orbital Spaces for Quantum Embedding

A widely used strategy to reduce the computational cost of quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts, and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in orbital space can lead to unpredictable errors on the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the subsystem projected atomic orbital decomposition algorithm that allows us to ensure automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.

Roles of Amides on the Formation of Atmospheric HONO and the Nucleation of Nitric Acid Hydrates

Nitrous acid (HONO) is hazardous to the human respiratory system, and the hydrolysis of NO₂ is the source of HONO. Hence, the investigation on the removal and transformation of HONO is urgently established. The effects of amide on the mechanism and kinetics of the formation of HONO with acetamide, formamide, methylformamide, urea, and its clusters of the catalyst were studied theoretically. The results show that amide and its small clusters reduce the energy barrier, the substituent improves the catalytic efficiency, and the catalytic effect order is dimer > monohydrate > monomer. Meanwhile, the clusters composed of nitric acid (HNO₃), amides, and 1-6 water molecules were investigated in the amide-assisted nitrogen dioxide (NO₂) hydrolysis reaction after HONO decomposes by combining the system sampling technique and density functional theory. The study on thermodynamics, intermolecular forces, optics properties of the clusters, as well as the influence of humidity, temperature, atmospheric pressure, and altitude shows that amide molecules promote the clustering and enhance the optical properties. The substituent facilitates the clustering of amide and nitric acid hydrate and lowers the humidity sensitivity of the clusters. The findings will help to control the atmospheric aerosol particle and then reduce the harm of poisonous organic chemicals on human health.

Unraveling the Mechanism of ACQ-to-AIE Transformation of Fluorescein Derivatives

Although fluorescein derivatives have excellent properties and strong practicability, they are typical aggregation-induced quenching (ACQ) molecules, which are not conducive to working in the solid state. Recently, the fluorescein derivative Fl-Me with aggregation-induced emission (AIE) property was synthesized, which brought a new dawn for the research and development of fluorescein-based materials. In this study, the AIE mechanism of Fl-Me was investigated based on time-dependent density functional theory and the ONIOM method. The results revealed that an effective dark-state deactivation pathway leads to the fluorescence quenching of Fl-Me in a solution environment. Accordingly, the AIE phenomenon originates from the closure of the dark-state quenching channel. It is worth emphasizing that we found that the carbonyl group of molecular Fl-Me has intermolecular hydrogen bonding interaction with the adjacent molecules, which caused the increase of the dark-state energy in the crystalline state. Moreover, the restriction of the rotational motion and the nonexistence of the π-π stacking interaction are beneficial to the enhancement of fluorescence upon aggregation. Finally, the ACQ-to-AIE transformation mechanisms of fluorescein derivatives have been discussed. This work provides deeper insight into the photophysical mechanism for the fluorescein derivatives Fl-Me with AIE feature and eventually is expected to help researchers to develop more fluorescein-based AIE materials with remarkable properties for various fields.

Rational Engineering of (S)-Norcoclaurine Synthase for Efficient Benzylisoquinoline Alkaloids Biosynthesis

(S)-Norcoclaurine is synthesized in vivo through a metabolic pathway that ends with (S)-norcoclaurine synthase (NCS). The former constitutes the scaffold for the biosynthesis of all benzylisoquinoline alkaloids (BIAs), including many drugs such as the opiates morphine and codeine and the semi-synthetic opioids oxycodone, hydrocodone, and hydromorphone. Unfortunately, the only source of complex BIAs is the opium poppy, leaving the drug supply dependent on poppy crops. Therefore, the bioproduction of (S)-norcoclaurine in heterologous hosts, such as bacteria or yeast, is an intense area of research nowadays. The efficiency of (S)-norcoclaurine biosynthesis is strongly dependent on the catalytic efficiency of NCS. Therefore, we identified vital NCS rate-enhancing mutations through the rational transition-state macrodipole stabilization method at the Quantum Mechanics/Molecular Mechanics (QM/MM) level. The results are a step forward for obtaining NCS variants able to biosynthesize (S)-norcoclaurine on a large scale.

Self-Consistent Quantum Mechanics/Embedded Charge Study on Aggregation-Enhanced Delayed Fluorescence of Cu(I) Complexes: Luminescence Mechanism and Molecular Design Strategy

To elucidate the luminescence mechanism of highly efficient blue Cu(N^N)(POP)⁺-type thermally activated delayed fluorescence (TADF) materials, we have selected Cu(pytfmpz)(POP)⁺ (1) and Cu(pympz)(POP)⁺ (2) as targets to investigate the photophysical properties in both solution and solid phases. The self-consistent electrostatic potential (ESP) embedded charge within the quantum mechanics/molecular mechanics (QM/MM) method demonstrates a greater advantage over the charge equilibrium (QEQ) in accurately calculating atomic charges and reasonably describing the polarization effect, ultimately resulting in a favorable consistency between simulation and experimental measurements. After systematic and quantitative simulation, it has been found that complex 2, with an electron-donating group of -CH₃, exhibits a much more blue-shifted spectrum and a significantly enhanced efficiency in comparison to complex 1 with -CF₃. This is due to the widened HOMO-LUMO gap as well as the narrowed energy gap between the lowest singlet and triplet excited states (ΔE_ST), respectively. Then, the designed complex 3 is introduced with a stronger electron donor and larger tert-butyl group, which plays a key role in simultaneously suppressing the structural distortion and reducing the ΔE_ST. This leads to a faster reverse intersystem crossing process than that of the two experimental complexes in solution, turning out to be a new deep-blue-emitting material with excellent TADF performance.

Reactivity and Selectivity of the Diels-Alder Reaction of Anthracene in [Pd6L4]12+ Supramolecular Cages: A Computational Study

The field of supramolecular metal-organic cage catalysis has grown rapidly in recent years. However, theoretical studies regarding the reaction mechanism and reactivity and selectivity controlling factors for supramolecular catalysis are still underdeveloped. Herein, we demonstrate a detailed density functional theory study on the mechanism, catalytic efficiency, and regioselectivity of the Diels-Alder reaction in bulk solution and within two [Pd₆L₄]¹²⁺ supramolecular cages. Our calculations are consistent with experiments. The origins of the catalytic efficiency of the bowl-shaped cage 1 have been elucidated to be the host-guest stabilization of the transition states and the favorable entropy effect. The reasons for the switch of the regioselectivity from 9,10-addition to 1,4-addition within the octahedral cage 2 were attributed to the confinement effect and the noncovalent interactions. This work would shed light on the understanding of [Pd₆L₄]¹²⁺ metallocage-catalyzed reactions and provide a detailed mechanistic profile otherwise difficult to obtain from experiments. The findings of this study could also aid to the improvement and development of more efficient and selective supramolecular catalysis.

Quantum computing in pharma: A multilayer embedding approach for near future applications

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F₂ in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

Cofactor-Free Dioxygenases-Catalyzed Reaction Pathway via Proton-Coupled Electron Transfer

Understanding the general mechanism of the metal-free and cofactor-free oxidases and oxygenases catalyzed activation of triplet O₂ is one of the most challenging questions in the field of enzymatic catalysis. Herein, we have performed Quantum Mechanics/Molecular Mechanics (QM/MM) multiscale simulations to reveal the detailed mechanism of the HOD catalyzed (i.e., 1-H-3-hydroxy-4-oxoquinaldine 2,4-dioxygenase from Arthrobacter nitroguajacolicus Rü61a) decomposition of N-heteroaromatic compounds. The complete catalytic mechanism includes four steps: (1) proton transfer from 1-H-3-hydroxy-4-oxoquinaldine (QND) substrate to His251 residue coupled with an electron transfer from QND to triplet O₂ (i.e., PCET), (2) formation of C-O bond via an open-shell singlet diradical recombination pathway, (3) ring-closure to form a bicyclic ring, and (4) dissociation of CO. The dissociation of CO is determined as the rate-limiting step, and its calculated energy barrier of 14.9 kcal/mol is consistent with the 15.5 kcal/mol barrier derived from experimental kinetic data. The mechanistic profile is not only valuable for understanding the fundamental pathway of cofactor-free oxidases and oxygenases-catalyzed reactions involving the triplet O₂ activation but also discloses a new pathway that undergoes the processes of PCET and open-shell singlet transition state.

Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics

Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.

Detecting the Hydrogen Bond Cooperativity in a Protein β-Sheet by H/D Exchange

The hydrogen bond (H-bond) cooperativity in the β-sheet of GB3 is investigated by a NMR hydrogen/deuterium (H/D) exchange method. It is shown that the weakening of one backbone N-H…O=C H-bond between two β-strands, β1 and β2, due to the exchange of NH to ND of the H-bond donor in β1, perturbs the chemical shift of ¹³C_α, ¹³C_β, ¹H_α, ¹H_N, and ¹⁵N of the H-bond acceptor and its following residue in β2. Quantum mechanical calculations suggest that the -H-bond chemical shift isotope effect is caused by the structural reorganization in response to the H-bond weakening. This structural reorganization perturbs four neighboring H-bonds, with three being weaker and one being stronger, indicating that three H-bonds are cooperative and one is anticooperative with the perturbed H-bond. The sign of the cooperativity depends on the relative position of the H-bonds. This H-bond cooperativity, which contributes to β-sheet stability overall, can be important for conformational coupling across the β-sheet.

Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a family of neural networks that act in parallel to represent, efficiently, the post-Hartree-Fock electronic structure energy contributions for all simplexes (fragments), and (b) a new k-means-based tessellation strategy to glean training data for high-dimensional molecular spaces and minimize the extent of training needed to construct this family of neural networks. The approach is particularly useful when coupled cluster accuracy is desired and when fragment sizes grow in order to capture nonlocal interactions accurately. The unique multidimensional k-means tessellation/clustering algorithm used to determine our training data for all fragments is shown to be extremely efficient and reduces the needed training to only 10% of data for all fragments to obtain accurate neural networks for each fragment. These fully connected dense neural networks are then used to extrapolate the potential energy surface for all molecular fragments, and these are then combined as per our graph-theoretic procedure to transfer the learning process to a full system energy for the entire AIMD trajectory at less than one-tenth the cost as compared to a regular fragmentation-based AIMD calculation.

Improving the Accuracy of Quantum Mechanics/Molecular Mechanics (QM/MM) Models with Polarized Fragment Charges

This paper introduces an economical approach for improving the accuracy and convergence of quantum mechanics/molecular mechanics (QM/MM) models. The approach is tested on a series of neutral and charged amino acids embedded in a 160-water cluster, where their intramolecular proton transfer energies (neutral amino acid → zwitterionic amino acid) were previously obtained at the ωB97X-D/6-31G(d) level of theory. When the charges on the MM atoms were replaced with those obtained at the same QM level of theory used to treat the QM atoms, this significantly improved the accuracy and convergence of the QM/MM models. In particular, the QM/MM model converged to within 1.4 kcal mol^-1 of directly calculated DFT energies for smaller (by as many as 20 waters) QM regions. The use of atomic charges obtained from the natural population analysis yielded the most significant improvement, while other charge schemes such as Mulliken, electrostatic potential, or CM5 led to poorer outcomes. It is further demonstrated that the QM atomic charges can be accurately estimated in a highly efficient manner using an iterative fragmentation approach based on the moving-domain QM/MM method. Similar observations were made when the approach was used to predict the barrier of an S_N2 reaction. Thus, the use of QM-quality atomic charges on MM atoms represents a simple and easy-to-implement strategy for improving the accuracy of QM/MM models.

Multiscale molecular modelling: from electronic structure to dynamics of nanosystems and beyond

Important contemporary biological and materials problems often depend on interactions that span orders of magnitude differences in spatial and temporal dimensions. This Tutorial Review attempts to provide an introduction to such fascinating problems through a series of case studies, aimed at beginning researchers, graduate students, postdocs and more senior colleagues who are changing direction to focus on multiscale aspects of their research. The choice of specific examples is highly personal, with examples either chosen from our own work or outstanding multiscale efforts from the literature. I start with various embedding schemes, as exemplified by polarizable continuum models, 3-D RISM, molecular DFT and frozen-density embedding. Next, QM/MM (quantum mechanical/molecular mechanical) techniques are the workhorse of pm-to-nm/ps-to-ns simulations; examples are drawn from enzymes and from nanocatalysis for oil-sands upgrading. Using polarizable force-fields in the QM/MM framework represents a burgeoning subfield; with examples from ion channels and electron dynamics in molecules subject to strong external fields, probing the atto-second dynamics of the electrons with RT-TDDFT (real-time - time-dependent density functional theory) eventually coupled with nuclear motion through the Ehrenfest approximation. This is followed by a section on coarse graining, bridging dimensions from atoms to cells. The penultimate chapter gives a quick overview of multiscale approaches that extend into the meso- and macro-scales, building on atomistic and coarse-grained techniques to enter the world of materials engineering, on the one hand, and cell biology, on the other. A final chapter gives just a glimpse of the burgeoning impact of machine learning on the structure-dynamics front. I aim to capture the excitement of contemporary leading-edge breakthroughs in the description of physico-chemical systems and processes in complex environments, with only enough historical content to provide context and aid the next generation of methodological development. While I aim also for a clear description of the essence of methodological breakthroughs, equations are kept to a minimum and detailed formalism and implementation details are left to the references. My approach is very selective (case studies) rather than exhaustive. I think that these case studies should provide fodder to build as complete a reference tree on multiscale modelling as the reader may wish, through forward and backward citation analysis. I hope that my choices of cases will excite interest in newcomers and help to fuel the growth of multiscale modelling in general.

Review on the QM/MM Methodologies and Their Application to Metalloproteins

The multiscaling quantum mechanics/molecular mechanics (QM/MM) approach was introduced in 1976, while the extensive acceptance of this methodology started in the 1990s. The combination of QM/MM approach with molecular dynamics (MD) simulation, otherwise known as the QM/MM/MD approach, is a powerful and promising tool for the investigation of chemical reactions’ mechanism of complex molecular systems, drug delivery, properties of molecular devices, organic electronics, etc. In the present review, the main methodologies in the multiscaling approaches, i.e., density functional theory (DFT), semiempirical methodologies (SE), MD simulations, MM, and their new advances are discussed in short. Then, a review on calculations and reactions on metalloproteins is presented, where particular attention is given to nitrogenase that catalyzes the conversion of atmospheric nitrogen molecules N₂ into NH₃ through the process known as nitrogen fixation and the FeMo-cofactor.

Casiopeinas® as SARS-CoV-2 main protease (Mpro) inhibitors: a combined DFT, molecular docking and ONIOM approach

Computational combined protocols suggest that Casiopeinas can block the active site of Mpro SARS-CoV-2 by binding to its main amino acids.

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

On the Accuracy of QM/MM Models: A Systematic Study of Intramolecular Proton Transfer Reactions of Amino Acids in Water

This work presents a systematic assessment of QM/QM' and QM/MM models with respect to direct QM calculations for the tautomerization (neutral to zwitterion) reactions of amino acids (glycine, alanine, valine, aspartate, and neutral and protonated histidine) solvated in a 160 water cluster. The effect of varying QM region size and choice of embedding potentials, including fixed-charge and polarizable molecular mechanics force fields (TIP3P and EFP) and various semiempirical QM methods (PM7, GFN2-xTB, DFTBA, DFTB3, HF-3c, and PBEh-3c), on the accuracy of the models was examined. A surprising finding was that molecular mechanics force fields outperformed many of the semiempirical methods. Generally, the errors in the QM/QM' and QM/MM models converge slowly with respect to the QM region size, requiring 50 or more waters to be included in the QM region before the error in the model falls below 1 kcal mol^-1 of its pure QM result. Different QM region selection schemes were also compared, and it was found that selection based on Natural Population Analysis (NPA) atomic charges significantly reduced the error in the QM/QM' and QM/MM models particularly if a low-quality embedding potential was used. It is envisaged that these results will be useful for the development of future hybrid QM models.

Multiscale Quantum Refinement Approaches for Metalloproteins

Biomolecules with metal ion(s) (e.g., metalloproteins) play many important biological roles. However, accurate structural determination of metalloproteins, particularly those containing transition metal ion(s), is challenging due to their complicated electronic structure, complex bonding of metal ions, and high number of conformations in biomolecules. Quantum refinement, which was proposed to combine crystallographic data with computational chemistry methods by several groups, can improve the local structures of some proteins. In this study, a quantum refinement method combining several multiscale computational schemes with experimental (X-ray diffraction) information was developed for metalloproteins. Various quantum refinement approaches using different ONIOM (our own N-layered integrated molecular orbital and molecular mechanics) combinations of quantum mechanics (QM), semiempirical (SE), and molecular mechanics (MM) methods were conducted to assess the performance and reliability on the refined local structure in two metalloproteins. The structures for two (Cu- or Zn-containing) metalloproteins were refined by combining two-layer ONIOM2(QM1/QM2) and ONIOM2(QM/MM) and three-layer ONIOM3(QM1/QM2/MM) schemes with experimental data. The accuracy of the quantum-refined metal binding sites was also examined and compared in these multiscale quantum refinement calculations. ONIOM3(QM/SE/MM) schemes were found to give good results with lower computational costs and were proposed to be a good choice for the multiscale computational scheme for quantum refinement calculations of metal binding site(s) in metalloproteins with high efficiency. Additionally, a two-center ONIOM approach was employed to speed up the quantum refinement calculations for the Zn metalloprotein with two remote active sites/ligands. Moreover, a recent quantum-embedding wavefunction-in-density functional theory (WF-in-DFT) method was also adopted as the high-level method in unprecedented ONIOM2(CCSD-in-B3LYP/MM) and ONIOM3(CCSD-in-B3LYP/SE/MM) calculations, which can be regarded as novel pseudo-three- and pseudo-four-layer ONIOM methods, respectively, to refine the key Zn binding site at the coupled-cluster singles and doubles (CCSD) level. These refined results indicate that multiscale quantum refinement schemes can be used to improve the structural accuracy obtained for local metal binding site(s) in metalloproteins with high efficiency.

Native and substituted cyclodextrins as chiral selectors for capillary electrophoresis enantioseparations: Structures, features, application, and molecular modeling

CDs are cyclic oligosaccharides consisting of α-d-glucopyranosyl units linked through 1,4-linkages, which are obtained from enzymatic degradation of starch. The coexistence of hydrophilic and hydrophobic regions in the same structure makes these macrocycles extremely versatile as complexing host with application in food, cosmetics, environmental, agriculture, textile, pharmaceutical, and chemical industries. Due to their inherent chirality, CDs have been also successfully used as chiral selectors in enantioseparation science, in particular, for CE enantioseparations. In the last decades, multidisciplinary approaches based on CE, NMR spectroscopy, X-ray crystallography, microcalorimetry, and molecular modeling have shed light on some aspects of recognition mechanisms underlying enantiodiscrimination. With the ever growing improvement of computer facilities, hardware and software, computational techniques have become a useful tool to model at molecular level the dynamics of diastereomeric associate formation to sample low-energy conformations, the binding energies between the enantiomer and the CD, and to profile noncovalent interactions contributing to the stability of CD/enantiomer association. On this basis, the aim of this review is to provide the reader with a critical overview on the applications of CDs in CE. In particular, the contemporary theory of the electrophoretic technique and the main structural features of CDs are described, with a specific focus on techniques, methods, and approaches to model CE enantioseparations promoted by native and substituted CDs. A systematic compilation of all published literature has not been attempted.

Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms

We present a weighted-graph-theoretic approach to adaptively compute contributions from many-body approximations for smooth and accurate post-Hartree-Fock (pHF) ab initio molecular dynamics (AIMD) of highly fluxional chemical systems. This approach is ONIOM-like, where the full system is treated at a computationally feasible quality of treatment (density functional theory (DFT) for the size of systems considered in this publication), which is then improved through a perturbative correction that captures local many-body interactions up to a certain order within a higher level of theory (post-Hartree-Fock in this publication) described through graph-theoretic techniques. Due to the fluxional and dynamical nature of the systems studied here, these graphical representations evolve during dynamics. As a result, energetic "hops" appear as the graphical representation deforms with the evolution of the chemical and physical properties of the system. In this paper, we introduce dynamically weighted, linear combinations of graphs, where the transition between graphical representations is smoothly achieved by considering a range of neighboring graphical representations at a given instant during dynamics. We compare these trajectories with those obtained from a set of trajectories where the range of local many-body interactions considered is increased, sometimes to the maximum available limit, which yields conservative trajectories as the order of interactions is increased. The weighted-graph approach presents improved dynamics trajectories while only using lower-order many-body interaction terms. The methods are compared by computing dynamical properties through time-correlation functions and structural distribution functions. In all cases, the weighted-graph approach provides accurate results at a lower cost.

Computational Investigation of Structural and Spectroscopic Properties of LOV-Based Proteins with Improved Fluorescence

Flavin-based fluorescent proteins are a class of fluorescent reporters derived from light, oxygen, and voltage (LOV) sensing proteins. Through mutagenesis, natural LOV proteins have been engineered to obtain improved fluorescence properties. In this study, we combined extended classical Molecular Dynamics simulations and multiscale Quantum Mechanics/Molecular Mechanics methods to clarify the relationship between structural and dynamic changes induced by specific mutations and the spectroscopic response. To reach this goal we compared two LOV variants, one obtained by the single mutation needed to photochemically inactivate the natural system, and the other (iLOV) obtained through additional mutations and characterized by a significantly improved fluorescence. Our simulations confirmed the "flipping and crowding" effect induced in iLOV by the additional mutations and revealed its mechanism of action. We also showed that these mutations, and the resulting differences in the composition and flexibility of the binding pockets, are not reflected in significant shifts of the excitation and emission energies, in agreement with the similarity of the spectra measured for the two systems. However, a small but consistent reduction was found in the Stokes shift of iLOV, suggesting a reduction of the intermolecular reorganization experienced by the chromophore after excitation, which could slow down its internal conversion to the ground state and improve the fluorescence.

A conserved asparagine in a ubiquitin-conjugating enzyme positions the substrate for nucleophilic attack

The mechanism used by the ubiquitin-conjugating enzyme, Ubc13, to catalyze ubiquitination is probed with three computational techniques: Born-Oppenheimer molecular dynamics, single point quantum mechanics/molecular mechanics energies, and classical molecular dynamics. These simulations support a long-held hypothesis and show that Ubc13-catalyzed ubiquitination uses a stepwise, nucleophilic attack mechanism. Furthermore, they show that the first step-the formation of a tetrahedral, zwitterionic intermediate-is rate limiting. However, these simulations contradict another popular hypothesis that supposes that the negative charge on the intermediate is stabilized by a highly conserved asparagine (Asn79 in Ubc13). Instead, calculated reaction profiles of the N79A mutant illustrate how charge stabilization actually increases the barrier to product formation. Finally, an alternate role for Asn79 is suggested by simulations of wild-type, N79A, N79D, and H77A Ubc13: it stabilizes the motion of the electrophile prior to the reaction, positioning it for nucleophilic attack. © 2019 Wiley Periodicals, Inc.

How Chorismatases Regulate Distinct Reaction Channels in a Single Conserved Active Pocket: Mechanistic Analysis with QM/MM (ONIOM) Investigations

The FkbO and Hyg5 subfamilies of chorismatases share the same active-site architectures, but perform distinct reaction mechanisms, that is, FkbO employs a hydrolysis reaction whereas Hyg5 proceeds through an intramolecular mechanism. Despite extensive research efforts, the detailed mechanism of the product selectivity in chorismatases need to be further unmasked. In this study, the effects of the A/G residue group (A244^FkbO /G240^Hyg5 ) and the V/Q residue group (V209^FkbO /Q201^Hyg5 ) on the catalytic mechanisms are investigated by employing molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical (QM/MM) calculations of the two wild-type models (FkbO/CHO and Hyg5/CHO; CHO=chorismate) and four mutants models (A244G-FkbO/CHO and G240A-Hyg5/CHO; V209Q-FkbO/CHO and Q201V-Hyg5/CHO). Our results showed that the A/G residue group mentioned by previous works would cause changes in the binding states of the substrate and the orientation of the catalytic glutamate, but only these changes affect the product selectivity in chorismatases limitedly. Interestingly, the distal V/Q residue group, which determines the internal water self-regulating ability at the active site, has significant impact on the selectivity of the catalytic mechanisms. The V/Q residue group is suggested to be an important factor to control the catalytic activities in chorismatases. The results are consistent with biochemical and structural experiments, providing novel insight into the mechanism of product selectivity in chorismatases.

Methanol, ethanol, propanol, and butanol adsorption on H-ZSM-5 zeolite: an ONIOM study

The search for renewable raw materials less harmful to the environment, such as methanol, ethanol, 1-propanol, and 1-butanol has become attractive. These products are obtained more rapidly and efficiently by specific solid catalysts, mainly the zeolites. The Brønsted acid sites distributed over the sinusoidal and the straight channels are important for the alcohol dehydration reaction that produces widely used chemicals. Therefore, the ONIOM method was used to study methanol, ethanol, propanol, and butanol adsorption in H-ZSM-5 zeolite. PM6 and DFT levels were used for the high layer ONIOM, while the low layer was calculated using the UFF force field. DFT was calculated using the B3LYP global hybrid GGA, M06-2X hybrid meta-GGA, and the hybrid range separated ωB97X-D functionals at 6-31+G(d) basis set. The high layer ONIOM was completely relaxed. The binding energy shows dependence on the relaxed tetrahedra and position of acid site. The Si/Al ratio was also studied. Graphical Abstract HOMO orbital of adsorbed alcohols showing the main contribution of zeolite for small alcohols.

Computational Understanding of the Selectivities in Metalloenzymes

Metalloenzymes catalyze many different types of biological reactions with high efficiency and remarkable selectivity. The quantum chemical cluster approach and the combined quantum mechanics/molecular mechanics methods have proven very successful in the elucidation of the reaction mechanism and rationalization of selectivities in enzymes. In this review, recent progress in the computational understanding of various selectivities including chemoselectivity, regioselectivity, and stereoselectivity, in metalloenzymes, is discussed.