Quantum Mechanical Region Research Articles

Quantum mechanics/molecular mechanics (QM/MM) methods in drug design: a comprehensive review of development and applications

The integration of quantum mechanics (QM) and molecular mechanics (MM) methods, known as QM/MM, has emerged as a powerful computational approach in drug design. This hybrid technique combines the accuracy of QM calculations for the reactive region with the computational efficiency of MM methods for the surrounding environment. QM/MM methods have proven invaluable in studying chemical reactions, exploring enzyme mechanisms, and investigating ligand-protein interactions, all of which are crucial for rational drug design. This review provides a comprehensive overview of the QM/MM methodology, its theoretical foundations, and its applications in various aspects of drug design. We discussed the key components, such as QM and MM region partitioning, link atom schemes, and boundary treatments. Additionally, we highlight recent advancements and challenges in QM/MM methods, including polarizable force fields, implicit solvation models, and enhanced sampling techniques. Furthermore, we present illustrative examples showcasing the successful application of QM/MM methods in lead optimization, virtual screening, and the elucidation of biochemical mechanisms relevant to drug targets. Finally, we provide perspectives on future developments and the potential impact of QM/MM methods on the drug discovery pipeline.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol.

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Time-dependent Kohn-Sham electron dynamics coupled with nonequilibrium plasmonic response via atomistic electromagnetic model.

Computational modeling of plasmon-mediated molecular photophysical and photochemical behaviors can help us better understand and tune the bound molecular properties and reactivity and make better decisions to design and control nanostructures. However, computational investigations of coupled plasmon-molecule systems are challenging due to the lack of accurate and efficient protocols to simulate these systems. Here, we present a hybrid scheme by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency dependent fluctuating charge (TD-ωFQ) model. At first, we transform ωFQ in the frequency-domain, an atomistic electromagnetic model for the plasmonic response of plasmonic metal nanoparticles (PMNPs), into the time-domain and derive its equation-of-motion formulation. The TD-ωFQ introduces the nonequilibrium plasmonic response of PMNPs and atomistic interactions to the electronic excitation of the quantum mechanical (QM) region. Then, we combine TD-ωFQ with RT-TDDFT. The derived RT-TDDFT/TD-ωFQ scheme allows us to effectively simulate the plasmon-mediated "real-time" electronic dynamics and even the coupled electron-nuclear dynamics by combining them with the nuclear dynamics approaches. As a first application of the RT-TDDFT/TD-ωFQ method, we study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs. Thanks to the atomistic nature of the ωFQ model, the edge effect of MNP on absorption enhancement has also been investigated and unveiled.

Level-Shifted Embedded Cluster Method for Modeling the Chemistry of Metal Oxides.

The embedded cluster method has been used extensively in the study of the chemical and physical properties of metal oxides. This method has been a popular tool due to its relatively high accuracy and low computational cost. An even more promising option may entail integrating the embedded cluster method with the combined quantum mechanical and molecular mechanical (QM/MM) approach, thereby enabling further consideration of interactions within the entire system for superior results. We aim to accurately model the chemistry of metal oxides using this combined scheme. Here, using the prototypical MgO(100) surface as a test system, with Mg9O14 as the cluster in the quantum mechanical region, we show that the embedded cluster with untailored boundary effective core potentials (ECPs) can have frontier orbital energy levels that substantially deviate from the quantum mechanical reference results. This occurs even when Mg9O9, which retains the stoichiometry of MgO, is used as the cluster in the quantum mechanical region. As a result, the chemical properties of the embedded cluster models differ from those of the quantum mechanical reference model. To address this issue, we propose a new variant of the embedded cluster method called the level-shifted embedded cluster (LSEC) method, which allows the energy levels to be shifted to match the reference levels by tuning the boundary ECPs. Our validation calculations on the adsorption of various adsorbates with different properties on the MgO(100) surface show that the overall performance of QM/MM with the LSEC method is excellent for the adsorption energies, geometries, and charge properties. The excellent performance holds for both the nonstoichiometric and stoichiometric clusters (i.e., Mg9O14 and Mg9O9, respectively), demonstrating the robustness of the LSEC method. We expect that the LSEC method can be combined with QM/MM or used separately for future chemical studies of metal oxides and other ionically bonded systems.

Embedding Beyond Electrostatics: The Extended Polarizable Density Embedding Model.

The polarizable density embedding (PDE) model is a focused QM/QM fragment-based embedding model designed to model solvation effects on molecular properties. We extend the PDE model to include exchange and nonadditive exchange-correlation (for DFT) in the embedding potential in addition to the existing electrostatic, polarization, and nonelectrostatic effects already present. The resulting model, termed PDE-X, yields localized electronic excitation energies that accurately capture the range dependence of the solvent interaction and gives close agreement with full quantum mechanical (QM) results, even when using minimal QM regions. We show that the PDE-X embedding description consistently improves the accuracy of excitation energies for a diverse set of organic chromophores. The improved embedding description leads to systematic solvent effects that do not average out when applying configurational sampling.

CHARMM-GUI QM/MM interfacer for the hybrid QM/MM molecular dynamics simulations.

Molecular mechanical (MM) force fields are constructed based on the empirical potentials, describing intramolecular and intermolecular potentials. Molecular dynamics (MD) simulation utilizing MM force fields is a robust tool to investigate large biomolecular systems, but the changes in electronic structures during a chemical process are overlooked in classical mechanics. Quantum mechanical (QM) treatments are needed for such changes including bond forming/breaking and charge transfers, but a high computational cost limits its usages with up to hundreds of atoms or less. A hybrid QM/MM approach, where the reactive part of the system is treated with QM and the remainder by cheap MM potentials, can effectively capture the reaction without significantly increasing the computational cost. For the different nature of the QM versus MM theories, however, the setup of biomolecular QM/MM simulation is known to be time consuming even to QM/MM experts. We present CHARMM-GUI QM/MM Interfacer that prepares QM/MM simulations with a user-selected QM region and various QM theories in multiple simulation packages. A non-trivial and error-prone QM/MM simulation setup involving link-atom insertion and charge distribution can be seamlessly prepared in QM/MM Interfacer. A few representative systems are simulated to delineate the robustness of QM/MM Interfacer. We hope both QM/MM beginners and experts to find the module's quick and accurate QM/MM simulation setup useful for their important applications.

Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model.

We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

Irregular structure of the hydrated Ag+ in aqueous solution and its Dynamics: An insight from perturbation theory hybrid forces molecular dynamics simulation

The structural and dynamical properties of hydrated Ag+ in a water solution were investigated theoretically using hybrid forces molecular dynamics simulation. The quantum mechanical region was treated using the resolution of identity MP2 (RI-MP2) level of a theory enabling the description of the properties of the hydration shell accurately.In contrast to the previously reported linear configuration, the first hydration shell had an irregular shape, with an average coordination number of 5.5. The Ag+–O distance in the first hydration shell was 2.59 Å. The mean residence time of water molecules in the first hydration shell was 0.89 ps, indicating that Ag+ acted as a structure-breaking agent.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges.

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Influence of the Greater Protein Environment on the Electrostatic Potential in Metalloenzyme Active Sites: The Case of Formate Dehydrogenase.

The Mo/W-containing metalloenzyme formate dehydrogenase (FDH) is an efficient and selective natural catalyst that reversibly converts CO2 to formate under ambient conditions. In this study, we investigate the impact of the greater protein environment on the electrostatic potential (ESP) of the active site. To model the enzyme environment, we used a combination of classical molecular dynamics and multiscale quantum-mechanical (QM)/molecular-mechanical (MM) simulations. We leverage charge shift analysis to systematically construct QM regions and analyze the electronic environment of the active site by evaluating the degree of charge transfer between the core active site and the protein environment. The contribution of the terminal chalcogen ligand to the ESP of the metal center is substantial and dependent on the chalcogen identity, with similar, less negative ESPs for Se and S terminal chalcogens in comparison to O regardless of whether the metal is Mo or W. The orientation of the side chains and conformations of the cofactor also affect the ESP, highlighting the importance of sampling dynamic fluctuations in the protein. Overall, our observations suggest that the terminal chalcogen ligand identity plays an important role in the enzymatic activity of FDH, suggesting opportunities for a rational bioinspired catalyst design.

Fragmentation Method for Computing Quantum Mechanics and Molecular Mechanics Gradients for Force Matching: Validation with Hydration Free Energy Predictions Using Adaptive Force Matching.

A fragmentation approach referred to as a simple overlapping region method for force matching (SORForM) is presented. SORForM is designed to enable efficient computation of quantum mechanical (QM) forces for large molecules and is validated in the framework of adaptive force matching (AFM) to develop solute models in water. The SORForM method divides a molecule into overlapping QM regions with each region containing a gradient zone and a buffer zone. The buffer zone ensures that the atoms in the gradient zone have their surroundings unchanged with fragmentation. The performance of the method is validated with mefenamic acid and linalyl acetate by comparing the hydration free energies of AFM models developed with and without SORForM. The AFM hydration free energies are also compared with that of the experiments. The models developed with B3LYP-D3(BJ) and def2-TZVP are in excellent agreement with experiments. Our work shows that PBE-D3(BJ) provides less satisfactory results when compared to B3LYP-D3(BJ). The def2-TZVP basis set is found to greatly improve the agreement with experiments when compared to a double-zeta quality basis set.

Factors That Determine the Variation of Equilibrium and Kinetic Properties of QM/MM Enzyme Simulations: QM Region, Conformation, and Boundary Condition.

To analyze the impact of various technical details on the results of quantum mechanical (QM)/molecular mechanical (MM) enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ∼100 to ∼500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

QM/MM Energy Decomposition Using the Interacting Quantum Atoms Approach.

The interacting quantum atoms (IQA) method decomposes the quantum mechanical (QM) energy of a molecular system in terms of one- and two-center (atomic) contributions within the context of the quantum theory of atoms in molecules. Here, we demonstrate that IQA, enhanced with molecular mechanics (MM) and Poisson–Boltzmann surface-area (PBSA) solvation methods, is naturally extended to the realm of hybrid QM/MM methodologies, yielding intra- and inter-residue energy terms that characterize all kinds of covalent and noncovalent bonding interactions. To test the robustness of this approach, both metal–water interactions and QM/MM boundary artifacts are characterized in terms of the IQA descriptors derived from QM regions of varying size in Zn(II)– and Mg(II)–water clusters. In addition, we analyze a homologous series of inhibitors in complex with a matrix metalloproteinase (MMP-12) by carrying out QM/MM–PBSA calculations on their crystallographic structures followed by IQA energy decomposition. Overall, these applications not only show the advantages of the IQA QM/MM approach but also address some of the challenges lying ahead for expanding the QM/MM methodology.

Using bio/cheminformatics in atomistic quantum mechanical enzyme simulations

Enzyme simulations are notoriously challenging as their large size prevents modeling the whole enzyme with highly accurate but computationally expensive quantum mechanical (QM) methods. Currently, only the chemically important “active site” residues/substrates/cofactors are modeled with QM-cluster or QM/MM methods. However, determining which biological sub-units necessarily should be included in the QM region remains ambiguous. Current practices for model construction typically suffer from human bias and unclear methodology.

BAR‐Based Multi‐Dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscapes: Varying the QM Region

AbstractThe indirect free energy simulation at quantum mechanics (QM)/ molecular mechanics (MM) levels provides a feasible alternative to direct QM/MM simulations. The main idea under the indirect method is constructing a thermodynamic cycle, exploring the configurational space under a cheaper but less accurate QM level, and performing an alchemical correction to obtain the thermodynamics under an accurate but computationally demanding QM level. In the authors' previous works, a multi‐dimensional nonequilibrium free energy simulation framework was developed to obtain QM/MM free energy landscapes indirectly, where the QM theory is varied but the other details of the multi‐scale treatment remain unchanged. In this work, the possibility of changing the region for electronic structure calculations in the multi‐scale treatment is explored. Numerical tests are performed for the conformational change in a biologically relevant peptide in vacuo and in solution, and the QM region and QM level are varied simultaneously. Unidirectional and bidirectional equilibrium perturbations are also performed for comparison. The indirect estimates from the nonequilibrium perturbation framework are almost identical to the direct results, while the indirect equilibrium estimates show obvious deviations from the direct references. They further derive the acceleration ratio of the indirect scheme to understand when the indirect scheme prevails.

Influence of the quantum mechanical region size in QM/MM modelling: A case study of fluoroacetate dehalogenase catalyzed C[sbnd]F bond cleavage

Quantum Mechanics/Molecular Mechanics method is a robust tool in exploring enzymatic processes. Here we explore the influence of the energetic and structural properties with respect to the QM size by studying fluoroacetate dehalogenase, a metal-free enzyme that can catalyze the CF bond cleavage of a small compound fluoroacetate. By expanding the QM sizes from 14 atoms to 723 atoms, we determined the variations of energies and key structural parameters. Using M06-2X functional to calculate energies, an excellent agreement between the “by radius” strategy and “by functional group” strategy was found.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions.

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Combining Evolutionary Conservation and Quantum Topological Analyses To Determine Quantum Mechanics Subsystems for Biomolecular Quantum Mechanics/Molecular Mechanics Simulations.

Selection of residues and other molecular fragments for inclusion in the quantum mechanics (QM) region for QM/molecular mechanics (MM) simulations is an important step for these calculations. Here, we present an approach that combines protein sequence/structure evolution and electron localization function (ELF) analyses. The combination of these two analyses allows the determination of whether a residue needs to be included in the QM subsystem or can be represented by the MM environment. We have applied this approach on two systems previously investigated by QM/MM simulations, 4-oxalocrotonate tautomerase (4OT) and ten-eleven translocation-2 (TET2), that provide examples where fragments may or may not need to be included in the QM subsystem. Subsequently, we present the use of this approach to determine the appropriate QM subsystem to calculate the minimum energy path (MEP) for the reaction catalyzed by human DNA polymerase λ (Polλ) with a third cation in the active site. Our results suggest that the combination of protein evolutionary and ELF analyses provides insights into residue/molecular fragment selection for QM/MM simulations.

Automated Construction of Quantum-Classical Hybrid Models.

We present a protocol for the fully automated construction of quantum mechanical (QM)-classical hybrid models by extending our previously reported approach on self-parametrizing system-focused atomistic models (SFAMs) [Brunken, C.; Reiher, M. J. Chem. Theory Comput. 2020, 16, 3, 1646-1665]. In this QM/SFAM approach, the size and composition of the QM region are evaluated in an automated manner based on first principles so that the hybrid model describes the atomic forces in the center of the QM region accurately. This entails the automated construction and evaluation of differently sized QM regions with a bearable computational overhead that needs to be paid for automated validation procedures. Applying SFAM for the classical part of the model eliminates any dependence on pre-existing parameters due to its system-focused quantum mechanically derived parametrization. Hence, QM/SFAM is capable of delivering high fidelity and complete automation. Furthermore, since SFAM parameters are generated for the whole system, our ansatz allows for a convenient redefinition of the QM region during a molecular exploration. For this purpose, a local reparametrization scheme is introduced, which efficiently generates additional classical parameters on the fly when new covalent bonds are formed (or broken) and moved to the classical region.

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations.

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions.