Mixed Quantum Mechanics Research Articles

Completeness of Graphical Languages for Mixed State Quantum Mechanics

There exist several graphical languages for quantum information processing, like quantum circuits, ZX-calculus, ZW-calculus, and so on. Each of these languages forms a †-symmetric monoidal category (†-SMC) and comes with an interpretation functor to the †-SMC of finite-dimensional Hilbert spaces. In recent years, one of the main achievements of the categorical approach to quantum mechanics has been to provide several equational theories for most of these graphical languages, making them complete for various fragments of pure quantum mechanics. We address the question of how to extend these languages beyond pure quantum mechanics to reason about mixed states and general quantum operations, i.e., completely positive maps. Intuitively, such an extension relies on the axiomatisation of a discard map that allows one to get rid of a quantum system, an operation that is not allowed in pure quantum mechanics. We introduce a new construction, the discard construction , which transforms any †-symmetric monoidal category into a symmetric monoidal category equipped with a discard map. Roughly speaking this construction consists in making any isometry causal. Using this construction, we provide an extension for several graphical languages that we prove to be complete for general quantum operations. However, this construction fails for some fringe cases like Clifford+T quantum mechanics, as the category does not have enough isometries.

Using Atomic Confining Potentials for Geometry Optimization and Vibrational Frequency Calculations in Quantum-Chemical Models of Enzyme Active Sites.

Quantum-chemical studies of enzymatic reaction mechanisms sometimes use truncated active-site models as simplified alternatives to mixed quantum mechanics molecular mechanics (QM/MM) procedures. Eliminating the MM degrees of freedom reduces the complexity of the sampling problem, but the trade-off is the need to introduce geometric constraints in order to prevent structural collapse of the model system during geometry optimizations that do not contain a full protein backbone. These constraints may impair the efficiency of the optimization, and care must be taken to avoid artifacts such as imaginary vibrational frequencies. We introduce a simple alternative in which terminal atoms of the model system are placed in soft harmonic confining potentials rather than being rigidly constrained. This modification is simple to implement and straightforward to use in vibrational frequency calculations, unlike iterative constraint-satisfaction algorithms, and allows the optimization to proceed without constraint even though the practical result is to fix the anchor atoms in space. The new approach is more efficient for optimizing minima and transition states, as compared to the use of fixed-atom constraints, and also more robust against unwanted imaginary frequencies. We illustrate the method by application to several enzymatic reaction pathways where entropy makes a significant contribution to the relevant reaction barriers. The use of confining potentials correctly describes reaction paths and facilitates calculation of both vibrational zero-point and finite-temperature entropic corrections to barrier heights.

QM Calculations in ADMET Prediction.

In recent years, there has been an increase in the application of quantum mechanics (QM) methods to describe properties related to the ADMET profile of small molecules. The application of these methods allows calculating useful descriptors and physiochemical properties contributing to ADMET prediction. Considering that QM methods are the only one that describe the electronic state of a molecules, such methods are particularly useful for studying the metabolism of drugs; furthermore, the introduction of mixed QM and molecular mechanics (QM/MM) is also increasing the understanding of drug interaction with cytochromes from a mechanistic point of view. Finally, combining the increase number of experimental data with machine learning algorithms and QM-derived descriptors allowed the creation of an end-user software capable of affecting the drug discovery process.

Analytic QM/MM atomic charge derivatives avoiding the scaling of coupled perturbed equations with the MM subsystem size.

In electrostatic embedding mixed quantum and molecular mechanics (QM/MM) approaches, the QM charge distribution is polarized by the electrostatic interaction with the MM environment. Analytic derivatives of expectation values of operators are required to extract properties such as vibrational spectra. These derivatives usually require solving a set of coupled perturbed equations for each nucleus/atom in the system, thus becoming prohibitive when the MM subsystem contains thousands of atoms. In the context of Electrostatic Potential Fitting (ESPF) QM/MM, we can easily overcome this bottleneck by defining a set of auxiliary coupled perturbed equations called the Q-vector equations. The Q-vector method scales only with the size of the QM subsystem, producing an effective charge tensor that leads to the atomic charge derivative after contraction with the MM electrostatic potential gradient. As an example, we use the charge derivatives as an analysis tool to identify the most important chromophore-polarizing amino-acids in plant cryptochrome. This finding opens up the route of defining polarizable force fields and simulating vibrational spectroscopy using ESPF QM/MM electrostatic embedding at an affordable computational cost.

Asymmetric biodegradation of the nerve agents Sarin and VX by human dUTPase: chemometrics, molecular docking and hybrid QM/MM calculations

Organophosphorus compounds (OP) nerve agents are among the most toxic chemical substances known. Their toxicity is due to their ability to bind to acetylcholinesterase. Currently, some enzymes, such as phosphotriesterase, human serum paraoxonase 1 and diisopropyl fluorophosphatase, capable of degrading OP, have been characterized. Regarding the importance of bioremediation methods for detoxication of OP, this work aims to study the interaction modes between the human human deoxyuridine triphosphate nucleotidohydrolase (dUTPase) and Sarin and VX, considering their Rp and Sp enantiomers, to evaluate the asymmetric catalysis of those compounds. In previous work, this enzyme has shown good potential to degrade phosphotriesters, and based on this characteristic, we have applied the human dUTPase to the OP degradation. Molecular docking, chemometrics and mixed quantum and molecular mechanics calculations have been employed, showing a good interaction between dUTPase and OP. Two possible reaction mechanisms were tested, and according to our theoretical results, the catalytic degradation of OP by dUTPase can take place via both mechanisms, beyond being stereoselective, that is, dUTPase cleaves one enantiomer preferentially in relation to other. Chemometric techniques provided excellent assistance for performing this theoretical investigation. The dUTPase study shows importance by the fact of it being a human enzyme.Communicated by Ramaswamy H. Sarma

Large scale Full QM-MD investigation of small peptides and insulin adsorption on ideal and defective TiO2 (1 0 0) surfaces. Influence of peptide size on interfacial bonds

Large biomolecule interaction with oxide surface has attracted a lot of attention because it drives behavior of implanted devices in the living body. To investigate the role of TiO2 surface structure on a large polypeptide (insulin) adsorption, we use a homemade mixed Molecular Dynamics-Full large scale Quantum Mechanics code. A specific re-parameterized (Ti) and globally convergent NDDO method fitted on high level ab initio method (coupled cluster CCSD(T) and DFT) allows us to safely describe the electronic structure of the whole insulin-TiO2 surface system (up to 4000 atoms). Looking specifically at carboxylate residues, we demonstrate in this work that specific interfacial bonds are obtained from the insulin/TiO2 system that are not observed in the case of smaller peptides (tripeptides, insulin segment chains with different configurations). We also demonstrate that a large part of the adsorption energy is compensated by insulin conformational energy changes and surface defects enhanced this trend. Large slab dimensions allow us to take into account surface defects that are actually beyond ab initio capabilities owing to size effect. These results highlight the influence of the surface structure on the conformation and therefore of the possible inactivity of an adsorbed polypeptides.

The Role of Water in the Catalyst-Free Aldol Reaction of Water-Insoluble N-Methyl-2,4-thiazolidinedione with N-Methylisatin from QM/MM Monte Carlo Simulations.

The role of water in the uncatalyzed aldol reaction of N-methyl-2,4-thiazolidinedione with N-methylisatin is investigated through Monte Carlo statistical mechanics simulations that utilize free energy perturbation theory and the mixed quantum mechanics and molecular mechanics (QM/MM) model with PDDG/PM3 for the QM method in "on-water" and DMSO environments. There are several conceivable orientations between thiazolidinedione and isatin in the process of C-C bond formation. However, the formation of the C-C bond takes place between the re face of isatin and the si face of (E)-enol of the thiazolidinedione to form the preferred anti-type product, which results from enhanced hydrogen-bonding interactions between water molecules and the oxygen atoms undergoing bond breakage and bond formation during the reaction. Novel insights into the effect of water on the aldol reaction are presented herein.

The role of hydrogen bond interaction on molecular orientation of alkanolamines through temperature and pressure variation: A mixed molecular dynamics and quantum mechanics study

The role of hydrogen bond interaction on the structural orientation of pure alkanolamines, monoethanolamine (MEA), diethanolamine (DEA), and methyl diethanolamine (MDEA), was under consideration by computer simulation, molecular dynamics simulation as well as density functional theory. Molecular dynamics simulations were carried out at different pressures and temperatures to discover structural stability. A comprehensive force field validation was performed to obtain accurate density. It was also observed that independent of pressure and temperature, MEA molecules prefer head-tail parallel orientation, DEA molecules show both vertical and parallel orientation, and MDEA molecules favor parallel arrangement in liquid state. The probability of hydrogen bond as a substantial intermolecular interaction was also investigated and substantial sites were evaluated. Intermolecular and intramolecular energy, hydrogen bond strength, and transport properties, as well as cluster formation, were investigated to offer an irrefutable proof on structural orientation. Ab initio computation by analyzing frequency, stabilization energy, and electron location function confirmed similar orientation, proposed by molecular dynamics simulation.

Efficient parallelization of perturbative Monte Carlo QM/MM simulations in heterogeneous platforms

A novel perturbative Monte Carlo mixed quantum mechanics (QM)/molecular mechanics (MM) approach has been recently developed to simulate molecular systems in complex environments. However, the required accuracy to efficiently simulate such complex molecular systems is usually granted at the cost of long executing times. To alleviate this problem, a new parallelization strategy of multi-level Monte Carlo molecular simulations is herein proposed for heterogeneous systems. It simultaneously exploits fine-grained (at the data level), coarse-grained (at the Markov chain level) and task-grained (pure QM, pure MM and QM/MM procedures) parallelism to ensure an efficient execution in heterogeneous systems composed of central processing units and multiple and possibly different graphical processing units. This is achieved by making use of the OpenCL library, together with appropriate dynamic load balancing schemes. From the conducted evaluation with real benchmarking data, a speed-up of 56x in the computational bottleneck part was observed, which results in a global speed-up of 38x for the whole simulation, reducing the time of a typical simulation from 80 hours to only 2 hours.

Mechanistic studies of new oximes reactivators of human butyryl cholinesterase inhibited by cyclosarin and sarin

Butyryl cholinesterase (BChE) has been seen as a key enzyme in the search for new strategies in the treatment of poisoning by organophosphates (OPs), since human BChE (HssBChE), complexed with the appropriate oxime, can be a suitable scavenger and deactivator for OPs in the blood stream. However, the efficacy of HssBChE is limited by its strict stoichiometric scavenging, slow reactivation, and propensity for aging. The improvement of the reactivation rate by new and more efficient oximes could contribute to mitigate this problem and increase the HssBChE efficiency as scavenger. Several oximes have been synthesized and tested with this goal, some with promising results, but the mechanistic aspects of the reactivation reaction are not fully understood yet. In order to better investigate this mechanism, docking and mixed quantum and molecular mechanics combined with principal components analysis were performed here to evaluate the capacity of reactivation and determine the preferred route for the reactivation reaction of two new oximes on HssBChE inhibited by the neurotoxic agents cyclosarin and sarin. Plots of potential energies were calculated and all the transition states of the reactional mechanism were determined. Our results showed a good correlation with experimental data and pointed to the most efficient oxime with both OPs. The protocol used could be a suitable tool for a preliminary evaluation of the HssBChE reactivation rates by new oximes.

A Bestiary of Sets and Relations

Building on established literature and recent developments in the graph-theoretic characterisation of its CPM category, we provide a treatment of pure state and mixed state quantum mechanics in the category fRel of finite sets and relations. On the way, we highlight the wealth of exotic beasts that hide amongst the extensive operational and structural similarities that the theory shares with more traditional arenas of categorical quantum mechanics, such as the category fdHilb. We conclude our journey by proving that fRel is local, but not without some unexpected twists.

Anatomy of an iron-sulfur cluster scaffold protein: Understanding the determinants of [2Fe–2S] cluster stability on IscU

Protein-bound iron sulfur clusters are prosthetic groups involved in several metabolic pathways. Understanding how they interact with the host protein and which factors influence their stability is therefore an important goal in biology. Here, we have addressed this question by studying the determinants of the 2Fe–2S cluster stability in the IscU/Isu protein scaffold. Through a detailed computational study based on a mixed quantum and classical mechanics approach, we predict that the simultaneous presence of two conserved residues, D39 and H105, has a conflicting role in cluster coordination which results in destabilizing cluster-loaded IscU/Isu according to a ‘tug-of-war’ mechanism. The effect is absent in the D39A mutant already known to host the cluster more stably. Our theoretical conclusions are directly supported by experimental data, also obtained from the H105A mutant, which has properties intermediate between the wild-type and the D39A mutant. This article is part of a Special Issue entitled: Fe/S proteins: Analysis, structure, function, biogenesis and diseases.

State-dependent molecular dynamics.

This paper proposes a new mixed quantum mechanics (QM)—molecular mechanics (MM) approach, where MM is replaced by quantum Hamilton mechanics (QHM), which inherits the modeling capability of MM, while preserving the state-dependent nature of QM. QHM, a single mechanics playing the roles of QM and MM simultaneously, will be employed here to derive the three-dimensional quantum dynamics of diatomic molecules. The resulting state-dependent molecular dynamics including vibration, rotation and spin are shown to completely agree with the QM description and well match the experimental vibration-rotation spectrum. QHM can be incorporated into the framework of a mixed quantum-classical Bohmian method to enable a trajectory interpretation of orbital-spin interaction and spin entanglement in molecular dynamics.

A sugar isomerization reaction established on various ( )8-barrel scaffolds is based on substrate-assisted catalysis

In the course of tryptophan biosynthesis, the isomerization of phosphoribosylanthranilate (PRA) is catalyzed by the (βα)₈-barrel enzyme TrpF. The reaction occurs via a general acid-base mechanism with an aspartate and a cysteine residue acting as acid and base, respectively. PRA isomerase activity could be established on two (βα)₈-barrel enzymes involved in histidine biosynthesis, namely HisA and HisF, and on a HisAF chimera, by introducing two aspartate-to-valine substitutions. We have analyzed the reaction mechanism underlying this engineered activity by measuring its pH dependence, solving the crystal structure of a HisF variant with bound product analogue, and applying molecular dynamics simulations and mixed quantum and molecular mechanics calculations. The results suggest that PRA is anchored by the C-terminal phosphate-binding sites of HisA, HisF and HisAF. As a consequence, a conserved aspartate residue, which is equivalent to Cys7 from TrpF, is properly positioned to act as catalytic base. However, no obvious catalytic acid corresponding to Asp126 from TrpF could be identified in the three proteins. Instead, this role appears to be carried out by the carboxylate group of the anthranilate moiety of PRA. Thus, the engineered PRA isomerization activity is based on a reaction mechanism including substrate-assisted catalysis and thus differs substantially from the naturally evolved reaction mechanism used by TrpF.

Using QM/MM Methods for the Exploration of Electron Transfer Pathways

Many proteins are known for their ability to perform several functions such as oxidation/reduction, gas transport or storage and electron transfer depending on the active site’s environment or on the available ligands. Consequently, the interest in an atomic (and electronic) description of these functions’ mechanism is very high. However, obtaining such detailed information is not a trivial task. The continued growth of computer power and the development of theoretical techniques, such as mixed quantum mechanics and molecular mechanics, permit the atomistic study of complex biological systems. Here, recent computational advances in protein electron transfer studies on our group are reviewed. We centered our attention on long distance electron transfer processes and the application of the QM/MM e-pathway method to protein systems.

Two Tyrosyl Radicals Stabilize High Oxidation States in Cytochrome c Oxidase for Efficient Energy Conservation and Proton Translocation

The reaction of oxidized bovine cytochrome c oxidase (bCcO) with hydrogen peroxide (H(2)O(2)) was studied by electron paramagnetic resonance (EPR) to determine the properties of radical intermediates. Two distinct radicals with widths of 12 and 46 G are directly observed by X-band EPR in the reaction of bCcO with H(2)O(2) at pH 6 and pH 8. High-frequency EPR (D-band) provides assignments to tyrosine for both radicals based on well-resolved g-tensors. The wide radical (46 G) exhibits g-values similar to a radical generated on L-Tyr by UV-irradiation and to tyrosyl radicals identified in many other enzyme systems. In contrast, the g-values of the narrow radical (12 G) deviate from L-Tyr in a trend akin to the radicals on tyrosines with substitutions at the ortho position. X-band EPR demonstrates that the two tyrosyl radicals differ in the orientation of their β-methylene protons. The 12 G wide radical has minimal hyperfine structure and can be fit using parameters unique to the post-translationally modified Y244 in bCcO. The 46 G wide radical has extensive hyperfine structure and can be fit with parameters consistent with Y129. The results are supported by mixed quantum mechanics and molecular mechanics calculations. In addition to providing spectroscopic evidence of a radical formed on the post-translationally modified tyrosine in CcO, this study resolves the much debated controversy of whether the wide radical seen at low pH in the bovine enzyme is a tyrosine or tryptophan. The possible role of radical formation and migration in proton translocation is discussed.

Spectral properties of polypyridyl ruthenium complexes intercalated in DNA: theoretical insights into the surrounding effects of [Ru(dppz)(bpy)2]2+

The UV/Visible absorption properties of a polypyridyl ruthenium complex upon intercalation on DNA are studied at the mixed quantum mechanics molecular mechanics level of theory. Vertical excitation transitions are computed by time dependent density functional theory. Particular emphasis is put on the different levels at which the macromolecular environment is treated, and in particular on the analysis of the effect of mechanical, electrostatic and polarizable embedding. We show that with the highest level of theory the experimental absorption wavelengths are reproduced with a difference of only 2 or 3 nm for the low energy bands. The systematic analysis of the individual vertical transitions allows us to get much more insights into the role played by the environment, in particular, in metal to ligand and intra ligand charge transfer transitions that can lead to the production of DNA oxidative lesions exploitable in phototherapy.

Substrate diffusion and oxidation in GMC oxidoreductases: an experimental and computational study on fungal aryl-alcohol oxidase

AAO (aryl-alcohol oxidase) provides H₂O₂ in fungal degradation of lignin, a process of high biotechnological interest. The crystal structure of AAO does not show open access to the active site, where different aromatic alcohols are oxidized. In the present study we investigated substrate diffusion and oxidation in AAO compared with the structurally related CHO (choline oxidase). Cavity finder and ligand diffusion simulations indicate the substrate-entrance channel, requiring side-chain displacements and involving a stacking interaction with Tyr⁹². Mixed QM (quantum mechanics)/MM (molecular mechanics) studies combined with site-directed mutagenesis showed two active-site catalytic histidine residues, whose substitution strongly decreased both catalytic and transient-state reduction constants for p-anisyl alcohol in the H502A (over 1800-fold) and H546A (over 35-fold) variants. Combination of QM/MM energy profiles, protonation predictors, molecular dynamics, mutagenesis and pH profiles provide a robust answer regarding the nature of the catalytic base. The histidine residue in front of the FAD ring, AAO His⁵⁰² (and CHO His⁴⁶⁶), acts as a base. For the two substrates assayed, it was shown that proton transfer preceded hydride transfer, although both processes are highly coupled. No stable intermediate was observed in the energy profiles, in contrast with that observed for CHO. QM/MM, together with solvent KIE (kinetic isotope effect) results, suggest a non-synchronous concerted mechanism for alcohol oxidation by AAO.

Mixed quantum mechanics and molecular mechanics methods: Looking inside proteins

AbstractMixed quantum mechanics and molecular mechanics (QM/MM) techniques, wherein the active site is treated with a robust ab initio quantum mechanics methodology and the remainder of the protein is modeled at the molecular mechanics level, offer a valuable tool for looking inside enzymes. We present here a short summary of recent QM/MM applications. We discuss the capabilities of this technology focusing in the main three steps when modeling enzymes: building a model, conformational sampling, and mapping the chemical process. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 315‐322 DOI: 10.1002/wcms.27This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics

Geometry Optimization with Multilayer Methods Using Least-Squares Minimization.

In this article, we introduce a least-squares minimization scheme for optimizing molecular structures with mixed quantum mechanics (QM) and molecular mechanics (MM) multilayer models. A mixed-coordinate optimization framework was developed. The QM and MM regions are modeled with redundant internal coordinates and Cartesian coordinates, respectively. Within this mixed-coordinate system, a least-squares minimization method using the quasi-Newton step as the evaluation of error is constructed. The couplings between layers are treated rigidly in accordance with the mechanical embedding approach, and the MM Hessian is approximated as a scalar constant of the root-mean-square QM Hessian eigenvalues. Both two-layer and three-layer models were tested. The performance of the method developed herein shows consistently stable and fast convergence.