Recent advances in QM/MM free energy calculations using reference potentials

Human indoleamine-2,3-dioxygenase 2 cofactor lability and low substrate affinity explained by homology modeling, molecular dynamics and molecular docking

The human indoleamine-2,3-dioxygenase 2 (hIDO2) protein is growing of interest as it is increasingly implicated in multiple diseases (cancer, autoimmune diseases, COVID-19). However, it is only poorly reported in the literature. Its mode of action remains unknown because it does not seem to catalyze the reaction for which it is attributed: the degradation of the L-Tryptophan into N-formyl-kynurenine. This contrasts with its paralog, the human indoleamine-2,3-dioxygenase 1 (hIDO1), which has been extensively studied in the literature and for which several inhibitors are already in clinical trials. Yet, the recent failure of one of the most advanced hIDO1 inhibitors, the Epacadostat, could be caused by a still unknown interaction between hIDO1 and hIDO2. In order to better understand the mechanism of hIDO2, and in the absence of experimental structural data, a computational study mixing homology modeling, Molecular Dynamics, and molecular docking was conducted. The present article highlights an exacerbated lability of the cofactor as well as an inadequate positioning of the substrate in the active site of hIDO2, which might bring part of an answer to its lack of activity.Communicated by Ramaswamy H. Sarma.

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.

Development of analytic gradients for the Huzinaga quantum embedding method and its applications to large-scale hybrid and double hybrid DFT forces

The theory of analytic gradients is presented for the projector-based density functional theory (DFT) embedding approach utilizing the Huzinaga-equation. The advantages of the Huzinaga-equation-based formulation are demonstrated. In particular, it is shown that the projector employed does not appear in the Lagrangian, and the potential risk of numerical problems is avoided at the evaluation of the gradients. The efficient implementation of the analytic gradient theory is presented for approaches where hybrid DFT, second-order Møller-Plesset perturbation theory, or double hybrid DFT are embedded in lower-level DFT environments. To demonstrate the applicability of the method and to gain insight into its accuracy, it is applied to equilibrium geometry optimizations, transition state searches, and potential energy surface scans. Our results show that bond lengths and angles converge rapidly with the size of the embedded system. While providing structural parameters close to high-level quality for the embedded atoms, the embedding approach has the potential to relax the coordinates of the environment as well. Our demonstrations on a 171-atom zeolite and a 570-atom protein system show that the Huzinaga-equation-based embedding can accelerate (double) hybrid gradient computations by an order of magnitude with sufficient active regions and enables affordable force evaluations or geometry optimizations for molecules of hundreds of atoms.

Computational Investigation of a Series of Small Molecules as Potential Compounds for Lysyl Hydroxylase-2 (LH2) Inhibition

The catalytic function of lysyl hydroxylase-2 (LH2), a member of the Fe(II)/αKG-dependent oxygenase superfamily, is to catalyze the hydroxylation of lysine to hydroxylysine in collagen, resulting in stable hydroxylysine aldehyde-derived collagen cross-links (HLCCs). Reports show that high amounts of LH2 lead to the accumulation of HLCCs, causing fibrosis and specific types of cancer metastasis. Some members of the Fe(II)/αKG-dependent family have also been reported to have intramolecular O2 tunnels, which aid in transporting one of the required cosubstrates into the active site. While LH2 can be a promising target to combat these diseases, efficacious inhibitors are still lacking. We have used computational simulations to investigate a series of 44 small molecules as lead compounds for LH2 inhibition. Tunneling analyses indicate the existence of several intramolecular tunnels. The lengths of the calculated O2-transporting tunnels in holoenzymes are relatively longer than those in the apoenzyme, suggesting that the ligands may affect the enzyme's structure and possibly block (at least partially) the tunnels. The sequence alignment analysis between LH enzymes from different organisms shows that all of the amino acid residues with the highest occurrence rate in the oxygen tunnels are conserved. Our results suggest that the enolate form of diketone compounds establishes stronger interactions with the Fe(II) in the active site. Branching the enolate compounds with functional groups such as phenyl and pyridinyl enhances the interaction with various residues around the active site. Our results provide information about possible leads for further LH2 inhibition design and development.

Predicting Effects of Site-Directed Mutagenesis on Enzyme Kinetics by QM/MM and QM Calculations: A Case of Glutamate Carboxypeptidase II

Quantum and molecular mechanics (QM/MM) and QM-only (cluster model) modeling techniques represent the two workhorses in mechanistic understanding of enzyme catalysis. One of the stringent tests for QM/MM and/or QM approaches is to provide quantitative answers to real-world biochemical questions, such as the effect of single-point mutations on enzyme kinetics. This translates into predicting the relative activation energies to 1-2 kcal·mol^-1 accuracy; such predictions can be used for the rational design of novel enzyme variants with desired/improved characteristics. Herein, we employ glutamate carboxypeptidase II (GCPII), a dizinc metallopeptidase, also known as the prostate specific membrane antigen, as a model system. The structure and activity of this major cancer antigen have been thoroughly studied, both experimentally and computationally, which makes it an ideal model system for method development. Its reaction mechanism is quite well understood: the reaction coordinate comprises a "tetrahedral intermediate" and two transition states and experimental activation Gibbs free energy of ∼17.5 kcal·mol^-1 can be inferred for the known k_cat ≈ 1 s^-1. We correlate experimental kinetic data (including the E424H variant, newly characterized in this work) for various GCPII mutants (k_cat = 8.6 × 10^-5 s^-1 to 2.7 s^-1) with the energy profiles calculated by QM/MM and QM-only (cluster model) approaches. We show that the near-quantitative agreement between the experimental values and the calculated activation energies (ΔH^⧧) can be obtained and recommend the combination of the two protocols: QM/MM optimized structures and cluster model (QM) energetics. The trend in relative activation energies is mostly independent of the QM method (DFT functional) used. Last but not least, a satisfactory correlation between experimental and theoretical data allows us to provide qualitative and fairly simple explanations of the observed kinetic effects which are thus based on a rigorous footing.

Affordable Ab Initio Path Integral for Thermodynamic Properties via Molecular Dynamics Simulations Using Semiempirical Reference Potential

Path integral molecular dynamics (PIMD) is becoming a routinely applied method for incorporating the nuclear quantum effect in computer simulations. However, direct PIMD simulations at an ab initio level of theory are formidably expensive. Using the protonated 1,8-bis(dimethylamino)naphthalene molecule as an example, we show in this work that the computational expense for the intramolecular proton transfer between the two nitrogen atoms can be remarkably reduced by implementing the idea of reference-potential methods. The simulation time can be easily extended to a scale of nanoseconds while maintaining the accuracy on an ab initio level of theory for thermodynamic properties. In addition, postprocessing can be carried out in parallel on massive computer nodes. A 545-fold reduction in the total CPU time can be achieved in this way as compared to a direct PIMD simulation at the same ab initio level of theory.

Hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) Simulation: A Tool for Structure-based Drug Design and Discovery

Quantum mechanics (QM) is physics based theory which explains the physical properties of nature at the level of atoms and sub-atoms. Molecular mechanics (MM) construct molecular systems through the use of classical mechanics. So, hybrid quantum mechanics and molecular mechanics (QM/MM) when combined together can act as computer-based methods which can be used to calculate structure and property data of molecular structures. Hybrid QM/MM combines the strengths of QM with accuracy and MM with speed. QM/MM simulation can also be applied for the study of chemical process in solutions as well as in the proteins, and has a great scope in structure-based drug design (CADD) and discovery. Hybrid QM/MM also applied to HTS, to derive QSAR models and due to availability of many protein crystal structures; it has a great role in computational chemistry, especially in structure- and fragment-based drug design. Fused QM/MM simulations have been developed as a widespread method to explore chemical reactions in condensed phases. In QM/MM simulations, the quantum chemistry theory is used to treat the space in which the chemical reactions occur; however the rest is defined through molecular mechanics force field (MMFF). In this review, we have extensively reviewed recent literature pertaining to the use and applications of hybrid QM/MM simulations for ligand and structure-based computational methods for the design and discovery of therapeutic agents.

Development and application of quantum mechanics/molecular mechanics methods with advanced polarizable potentials

Quantum mechanics/molecular mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and biological systems. The combination of QM and MM methods to represent a system gives rise to several challenges that need to be addressed. The increase in computational speed has allowed the expanded use of more complicated and accurate methods for both QM and MM simulations. Here, we review some approaches that address several common challenges encountered in QM/MM simulations with advanced polarizable potentials, from methods to account for boundary across covalent bonds and long-range effects, to polarization and advanced embedding potentials.

Quantifying Interactions and Solvent Effects Using Molecular Balances and Model Complexes

Where the basic units of molecular chemistry are the bonds within molecules, supramolecular chemistry is based on the interactions that occur between molecules. Understanding the "how" and "why" of the processes that govern molecular self-assembly remains an open challenge to the supramolecular community. While many interactions are readily examined in silico through electronic structure calculations, such insights may not be directly applicable to experimentalists. The practical limitations of computationally accounting for solvation is perhaps the largest bottleneck in this regard, with implicit solvation models failing to comprehensively account for the specific nature of solvent effects and explicit models incurring a prohibitively high computational cost. Since molecular recognition processes usually occur in solution, insight into the nature and effect of solvation is imperative not only for understanding these phenomena but also for the rational design of systems that exploit them.Molecular balances and supramolecular complexes have emerged as useful tools for the experimental dissection of the physicochemical basis of various noncovalent interactions, but they have historically been underexploited as a platform for the evaluation of solvent effects. Contrasting with large biological complexes, smaller synthetic model systems enable combined experimental and computational analyses, often facilitating theoretical analyses that can work in concert with experiment.Our research has focused on the development of supramolecular systems to evaluate the role of solvents in molecular recognition, and further characterize the underlying mechanisms by which molecules associate. In particular, the use of molecular balances has provided a framework to measure the magnitude of solvent effects and to examine the accuracy of solvent models. Such approaches have revealed how solvation can modulate the electronic landscape of a molecule and how competitive solvation and solvent cohesion can provide thermodynamic driving forces for association. Moreover, the use of simple model systems facilitates the interrogation and further dissection of the physicochemical origins of molecular recognition. This tandem experimental/computational approach has married less common computational techniques, like symmetry adapted perturbation theory (SAPT) and natural bonding orbital (NBO) analysis, with experimental observations to elucidate the influence of effects that are difficult to resolve experimentally (e.g., London dispersion and electron delocalization).

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Xanthine oxidoreductase inhibition – A review of computational aspect

Xanthine Oxidoreductase (XOR) exists in a variety of organisms from bacteria to humans and catalyzes the oxidation of hypoxanthine to xanthine and from xanthine to uric acid. Excessive uric acid could lead to gout and hyperuricemia. In this paper, we have reviewed the recent computational studies on xanthine oxidase inhibition. Computational methods, such as molecular dynamics (molecular mechanics), quantum mechanics, and quantum mechanics/molecular mechanics (QM/MM), have been employed to investigate the binding affinity of xanthine oxidase with synthesized and isolated nature inhibitors. The limitations of different computational methods for xanthine oxidase inhibition studies were also discussed. Implications of the computational approach could be used to help to understand the existing arguments on substrate/product orientation in xanthine oxidase inhibition, which allows designing new inhibitors with higher efficacy.

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.

Quantum Chemical and QM/MM Models in Biochemistry

Quantum chemical (QC) calculations provide a basis for deriving a microscopic understanding of enzymes and photobiological systems. Here we describe how QC models can be used to explore the electronic structure, dynamics, and energetics of biomolecules. We introduce the hybrid quantum mechanics/classical mechanics (QM/MM) approach, where a quantum mechanically described system of interest is embedded in a classically described force field representation of the biochemical surroundings. We also discuss the QM cluster model approach, as well as embedding theories, that provide complementary methodologies to model quantum mechanical effects in biomolecules. The chapter also provides some practical guides for building quantum biochemical models using the quinone reduction catalysis in respiratory complex I and a model reaction in solution as examples.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

Accelerating the Calculation of Solute-Solvent Interaction Energies through Systematic Molecular Fragmentation

The method of systematic molecular fragmentation by annihilation (SMFA) is modified to apply to the interaction energy between a solute and solvent, where the solute is a pair of reacting molecules. For NH₃ + CH₃Cl as the solute, it is shown that SMFA can estimate (to chemical accuracy) the average binding energy of the solute in large water clusters containing up to 160 water molecules, at an appropriate level of electronic structure theory. The SMFA calculation can be carried out in a computation time that makes it feasible to estimate the solvation contribution to free energies of activation and reaction by ensemble averaging.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

Use of Interaction Energies in QM/MM Free Energy Simulations

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

Adaptive QM/MM for Molecular Dynamics Simulations: 5. On the Energy-Conserved Permuted Adaptive-Partitioning Schemes

In combined quantum-mechanical/molecular-mechanical (QM/MM) dynamics simulations, the adaptive-partitioning (AP) schemes reclassify atoms on-the-fly as QM or MM in a smooth manner. This yields a mobile QM subsystem with contents that are continuously updated as needed. Here, we tailor the Hamiltonian adaptive many-body correction (HAMBC) proposed by Boreboom et al. [J. Chem. Theory Comput.2016, 12, 3441] to the permuted AP (PAP) scheme. The treatments lead to the HAMBC-PAP method (HPAP), which both conserves energy and produces accurate solvation structures in the test of "water-in-water" model system.

Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

QM/MM methods for free energies and photochemistry

Hybrid computational methods describing a small region of a biomolecular system with quantum mechanics and the bulk with molecular mechanics, referred to as QM/MM methods, are now a central part of computational biochemistry. This review considers developments in the QM/MM approach that make it easier to calculate free energies using accurate QM-based potential energy expressions. We also describe techniques to treat electronic coupling between the core region and the MM environment. Polarizability of the protein matrix is important but so is electronic coupling. Applications of these new methods, especially to photochemistry, are discussed.

Combined Quantum Mechanics and Molecular Mechanics Studies of Enzymatic Reaction Mechanisms

The combined quantum mechanics/molecular mechanics (QM/MM) methods have become a valuable tool in computational biochemistry and received versatile applications for studying the reaction mechanisms of enzymes. The approach combines the calculations of the electronic structure of the active site by QM, with modeling of the protein environment using MM force field, which allows the long-range electrostatics and steric effects on the enzyme reactivity to be accounted for. In this review, we review some key theoretical and computational aspects of the method and we also present some applications to particular enzymatic reactions such as tryptophan-7-halogenase, cyclooxygenase-1, and the epidermal growth factor receptor.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

Coupled Valence-Bond State Molecular Dynamics Description of an Enzyme-Catalyzed Reaction in a Non-Aqueous Organic Solvent

Enzymes are widely used in nonaqueous solvents to catalyze non-natural reactions. While experimental measurements showed that the solvent nature has a strong effect on the reaction kinetics, the molecular details of the catalytic mechanism in nonaqueous solvents have remained largely elusive. Here we study the transesterification reaction catalyzed by the paradigm subtilisin Carlsberg serine protease in an organic apolar solvent. The rate-limiting acylation step involves a proton transfer between active-site residues and the nucleophilic attack of the substrate to form a tetrahedral intermediate. We design the first coupled valence-bond state model that simultaneously describes both reactions in the enzymatic active site. We develop a new systematic procedure to parametrize this model on high-level ab initio QM/MM free energy calculations that account for the molecular details of the active site and for both substrate and protein conformational fluctuations. Our calculations show that the reaction energy barrier changes dramatically with the solvent and protein conformational fluctuations. We find that the mechanism of the tetrahedral intermediate formation during the acylation step is similar to that determined under aqueous conditions, and that the proton transfer and nucleophilic attack reactions occur concertedly. We identify the reaction coordinate to be mostly due to the rearrangement of some residual water molecules close to the active site.

Molecular Mechanism of the Reaction Specificity in Threonine Synthase: Importance of the Substrate Conformations

Threonine synthase (ThrS) catalyzes the final chemical reaction of l-threonine biosynthesis from its precursor, O-phospho-l-homoserine. As the phosphate ion generated in its former half reaction assists its latter reaction, ThrS is recognized as one of the best examples of product-assisted catalysis. In our previous QM/MM study, the chemical reactions for the latter half reactions, which are critical for the product-assisted catalysis, were revealed. However, accurate free energy changes caused by the conformational ensembles and entrance of water molecules into the active site are unknown. In the present study, by performing long-time scale MD simulations, the free energy changes by the divalent anions (phosphate or sulfate ions) and conformational states of the intermediate states were theoretically investigated. We found that the calculated free energy double differences are in good agreement with the experimental results. We also revealed that the phosphate ion contributes to forming hydrogen bonds that are suitable for the main reaction progress. This means that the conformation of the active site amino acid residues and the substrate, and hence, the tunable catalysis, are controlled by the product phosphate ion, and this clearly demonstrates a molecular mechanism of the product-assisted catalysis in ThrS.

Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Challenges in modelling nanoparticles for drug delivery

Although there have been significant advances in the fields of theoretical condensed matter and computational physics, when confronted with the complexity and diversity of nanoparticles available in conventional laboratories a number of modeling challenges remain. These challenges are generally shared among application domains, but the impacts of the limitations and approximations we make to overcome them (or circumvent them) can be more significant one area than another. In the case of nanoparticles for drug delivery applications some immediate challenges include the incompatibility of length-scales, our ability to model weak interactions and solvation, the complexity of the thermochemical environment surrounding the nanoparticles, and the role of polydispersivity in determining properties and performance. Some of these challenges can be met with existing technologies, others with emerging technologies including the data-driven sciences; some others require new methods to be developed. In this article we will briefly review some simple methods and techniques that can be applied to these (and other) challenges, and demonstrate some results using nanodiamond-based drug delivery platforms as an exemplar.