Multiscale analysis of enantioselectivity in enzyme-catalysed 'lethal synthesis' using projector-based embedding

Static embedding with pair coupled cluster doubles based methods

Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.

On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry

In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol^-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

Electronic structure benchmark calculations of CO2 fixing elementary chemical steps in RuBisCO using the projector-based embedding approach

Ribulose 1,5-bisphosphate carboxylase-oxygenase (RuBisCO) is the main enzyme involved in atmospheric carbon dioxide (CO₂ ) fixation in the biosphere. This enzyme catalyzes a set of five chemical steps that take place in the same active-site within magnesium (II) coordination sphere. Here, a set of electronic structure benchmark calculations have been carried out on a reaction path proposed by Gready et al. by means of the projector-based embedding approach. Activation and reaction energies for all main steps catalyzed by RuBisCO have been calculated at the MP2, SCS-MP2, CCSD, and CCSD(T)/aug-cc-pVDZ and cc-pVDZ levels of theory. The treatment of the magnesium cation with post-HF methods is explored to determine the nature of its involvement in the mechanism. With the high-level ab initio values as a reference, we tested the performance of a set of density functional theory (DFT) exchange-correlation (xc) functionals in reproducing the reaction energetics of RuBisCO carboxylase activity on a set of model fragments. Different DFT xc-functionals show large variation in activation and reaction energies. Activation and reaction energies computed at the B3LYP level are close to the reference SCS-MP2 results for carboxylation, hydration and protonation reactions. However, for the carbon-carbon bond dissociation reaction, B3LYP and other functionals give results that differ significantly from the ab initio reference values. The results show the applicability of the projector-based embedding approach to metalloenzymes. This technique removes the uncertainty associated with the selection of different DFT xc-functionals and so can overcome some of inherent limitations of DFT calculations, complementing, and potentially adding to modeling of enzyme reaction mechanisms with DFT methods.

Embedded Mean-Field Theory for Solution-Phase Transition-Metal Polyolefin Catalysis

Decreasing the wall-clock time of quantum mechanics/molecular mechanics (QM/MM) calculations without sacrificing accuracy is a crucial prerequisite for widespread simulation of solution-phase dynamical processes. In this work, we demonstrate the use of embedded mean-field theory (EMFT) as the QM engine in QM/MM molecular dynamics (MD) simulations to examine polyolefin catalysts in solution. We show that employing EMFT in this mode preserves the accuracy of hybrid-functional DFT in the QM region, while providing up to 20-fold reductions in the cost per SCF cycle, thereby increasing the accessible simulation time-scales. We find that EMFT reproduces DFT-computed binding energies and optimized bond lengths to within chemical accuracy, as well as consistently ranking conformer stability. Furthermore, solution-phase EMFT/MM simulations provide insight into the interaction strength of strongly coordinating and bulky counterions.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wave function method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.

Projection-Based Wavefunction-in-DFT Embedding

Complex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems. This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method. Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations. Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.

Acetyl Coenzyme A Analogues as Rationally Designed Inhibitors of Citrate Synthase

In this study, we probed the inhibition of pig heart citrate synthase (E.C. 4.1.3.7) by synthesising seven analogues either designed to mimic the proposed enolate intermediate in this enzyme reaction or developed from historical inhibitors. The most potent inhibitor was fluorovinyl thioether 9 (K_i =4.3 μm), in which a fluorine replaces the oxygen atom of the enolate. A comparison of the potency of 9 with that of its non-fluorinated vinyl thioether analogue 10 (K_i =68.3 μm) revealed a clear "fluorine effect" favouring 9 by an order of magnitude. The dethia analogues of 9 and 10 proved to be poor inhibitors. A methyl sulfoxide analogue was a moderate inhibitor (K_i =11.1 μm), thus suggesting hydrogen bonding interactions in the enolate site. Finally, E and Z propenoate thioether isomers were explored as conformationally constrained carboxylates, but these were not inhibitors. All compounds were prepared by the synthesis of the appropriate pantetheinyl diol and then assembly of the coenzyme A structure according to a three-enzyme biotransformation protocol. A quantum mechanical study, modelling both inhibitors 9 and 10 into the active site indicated short CF⋅⋅⋅H contacts of ≈2.0 Å, consistent with fluorine making two stabilising hydrogen bonds, and mimicking an enolate rather than an enol intermediate. Computation also indicated that binding of 9 to citrate synthase increases the basicity of a key aspartic acid carboxylate, which becomes protonated.

Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures

Drug action is inherently multiscale: it connects molecular interactions to emergent properties at cellular and larger scales. Simulation techniques at each of these different scales are already central to drug design and development, but methods capable of connecting across these scales will extend understanding of complex mechanisms and the ability to predict biological effects. Improved algorithms, ever-more-powerful computing architectures and the accelerating growth of rich datasets are driving advances in multiscale modeling methods capable of bridging chemical and biological complexity from the atom to the cell. Particularly exciting is the development of highly detailed, structure-based, physical simulations of biochemical systems, which are now able to access experimentally relevant timescales for large systems and, at the same time, achieve unprecedented accuracy. In this Perspective, we discuss how emerging data-rich, physics-based multiscale approaches are of the cusp of realizing long-promised impact in the discovery, design and development of novel therapeutics. We highlight emerging methods and applications in this growing field, and outline how different scales can be combined in practical modelling and simulation strategies.

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.