Using quantum mechanical approaches to study biological systems

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Elucidation of factors shaping reactivity of 5'-deoxyadenosyl - a prominent organic radical in biology

This study investigates the factors modulating the reactivity of 5'-deoxyadenosyl (5'dAdo˙) radical, a potent hydrogen atom abstractor that forms in the active sites of radical SAM enzymes and that otherwise undergoes a rapid self-decay in aqueous solution. Here, we compare hydrogen atom abstraction (HAA) reactions between native substrates of radical SAM enzymes and 5'dAdo˙ in aqueous solution and in two enzymatic microenvironments. With that we reveal that HAA efficiency of 5'dAdo˙ is due to (i) the in situ formation of 5'dAdo˙ in a pre-ordered complex with a substrate, which attenuates the unfavorable effect of substrate:5'dAdo˙ complex formation, and (ii) the prevention of the conformational changes associated with self-decay by a tight active-site cavity. The enzymatic cavity, however, does not have a strong effect on the HAA activity of 5'dAdo˙. Thus, we performed an analysis of in-water HAA performed by 5'dAdo˙ based on a three-component thermodynamic model incorporating the diagonal effect of the free energy of reaction, and the off-diagonal effect of asynchronicity and frustration. To this aim, we took advantage of the straightforward relationship between the off-diagonal thermodynamic effects and the electronic-structure descriptor - the redistribution of charge between the reactants during the reaction. It allows to access HAA-competent redox and acidobasic properties of 5'dAdo˙ that are otherwise unavailable due to its instability upon one-electron reduction and protonation. The results show that all reactions feature a favourable thermodynamic driving force and tunneling, the latter of which lowers systematically barriers by ∼2 kcal mol-1. In addition, most of the reactions experience a favourable off-diagonal thermodynamic contribution. In HAA reactions, 5'dAdo˙ acts as a weak oxidant as well as a base, also 5'dAdo˙-promoted HAA reactions proceed with a quite low degree of asynchronicity of proton and electron transfer. Finally, the study elucidates the crucial and dual role of asynchronicity. It directly lowers the barrier as a part of the off-diagonal thermodynamic contribution, but also indirectly increases the non-thermodynamic part of the barrier by presumably controlling the adiabatic coupling between proton and electron transfer. The latter signals that the reaction proceeds as a hydrogen atom transfer rather than a proton-coupled electron transfer.

MOFs for next-generation cancer therapeutics through a biophysical approach-a review

Metal-organic frameworks (MOFs) have emerged as promising nanocarriers for cancer treatment due to their unique properties. Featuring high porosity, extensive surface area, chemical stability, and good biocompatibility, MOFs are ideal for efficient drug delivery, targeted therapy, and controlled release. They can be designed to target specific cellular organelles to disrupt metabolic processes in cancer cells. Additionally, functionalization with enzymes mimics their catalytic activity, enhancing photodynamic therapy and overcoming apoptosis resistance in cancer cells. The controllable and regular structure of MOFs, along with their tumor microenvironment responsiveness, make them promising nanocarriers for anticancer drugs. These carriers can effectively deliver a wide range of drugs with improved bioavailability, controlled release rate, and targeted delivery efficiency compared to alternatives. In this article, we review both experimental and computational studies focusing on the interaction between MOFs and drug, explicating the release mechanisms and stability in physiological conditions. Notably, we explore the relationship between MOF structure and its ability to damage cancer cells, elucidating why MOFs are excellent candidates for bio-applicability. By understanding the problem and exploring potential solutions, this review provides insights into the future directions for harnessing the full potential of MOFs, ultimately leading to improved therapeutic outcomes in cancer treatment.

Investigation of protein-protein interactions and hotspot region on the NSP7-NSP8 binding site in NSP12 of SARS-CoV-2

Background: The RNA-dependent RNA polymerase (RdRp) complex, essential in viral transcription and replication, is a key target for antiviral therapeutics. The core unit of RdRp comprises the nonstructural protein NSP12, with NSP7 and two copies of NSP8 (NSP81 and NSP82) binding to NSP12 to enhance its affinity for viral RNA and polymerase activity. Notably, the interfaces between these subunits are highly conserved, simplifying the design of molecules that can disrupt their interaction. Methods: We conducted a detailed quantum biochemical analysis to characterize the interactions within the NSP12-NSP7, NSP12-NSP81, and NSP12-NSP82 dimers. Our objective was to ascertain the contribution of individual amino acids to these protein-protein interactions, pinpointing hotspot regions crucial for complex stability. Results: The analysis revealed that the NSP12-NSP81 complex possessed the highest total interaction energy (TIE), with 14 pairs of residues demonstrating significant energetic contributions. In contrast, the NSP12-NSP7 complex exhibited substantial interactions in 8 residue pairs, while the NSP12-NSP82 complex had only one pair showing notable interaction. The study highlighted the importance of hydrogen bonds and π-alkyl interactions in maintaining these complexes. Intriguingly, introducing the RNA sequence with Remdesivir into the complex resulted in negligible alterations in both interaction energy and geometric configuration. Conclusion: Our comprehensive analysis of the RdRp complex at the protein-protein interface provides invaluable insights into interaction dynamics and energetics. These findings can guide the design of small molecules or peptide/peptidomimetic ligands to disrupt these critical interactions, offering a strategic pathway for developing effective antiviral drugs.

Improving protein-ligand docking results using the Semiempirical quantum mechanics: testing on the PDBbind 2016 core set

Molecular docking techniques are routinely employed for predicting ligand binding conformations and affinities in the in silico phase of the drug design and development process. In this study, a reliable semiempirical quantum mechanics (SQM) method, PM7, was employed for geometry optimization of top-ranked poses obtained from two widely used docking programs, AutoDock4 and AutoDock Vina. The PDBbind core set (version 2016), which contains high-quality crystal protein - ligand complexes with their corresponding experimental binding affinities, was used as an initial dataset in this research. It was shown that docking pose optimization improves the accuracy of pose predictions and is very useful for the refinement of docked complexes via removing clashes between ligands and proteins. It was also demonstrated that AutoDock Vina achieves a higher sampling power than AutoDock4 in generating accurate ligand poses (RMSD ≤ 2.0 Å), while AutoDock4 exhibits a better ranking power than AutoDock Vina. Finally, a new protocol based on a combination of the results obtained from the two docking programs was proposed for structure-based virtual screening studies, which benefits from the robust sampling abilities of AutoDock Vina and the reliable ranking performance of AutoDock4.Communicated by Ramaswamy H. Sarma.

Drug Design in the Exascale Era: A Perspective from Massively Parallel QM/MM Simulations

The initial phases of drug discovery - in silico drug design - could benefit from first principle Quantum Mechanics/Molecular Mechanics (QM/MM) molecular dynamics (MD) simulations in explicit solvent, yet many applications are currently limited by the short time scales that this approach can cover. Developing scalable first principle QM/MM MD interfaces fully exploiting current exascale machines - so far an unmet and crucial goal - will help overcome this problem, opening the way to the study of the thermodynamics and kinetics of ligand binding to protein with first principle accuracy. Here, taking two relevant case studies involving the interactions of ligands with rather large enzymes, we showcase the use of our recently developed massively scalable Multiscale Modeling in Computational Chemistry (MiMiC) QM/MM framework (currently using DFT to describe the QM region) to investigate reactions and ligand binding in enzymes of pharmacological relevance. We also demonstrate for the first time strong scaling of MiMiC-QM/MM MD simulations with parallel efficiency of ∼70% up to >80,000 cores. Thus, among many others, the MiMiC interface represents a promising candidate toward exascale applications by combining machine learning with statistical mechanics based algorithms tailored for exascale supercomputers.

Updates on drug designing approach through computational strategies: a review

The drug discovery and development (DDD) process in pursuit of novel drug candidates is a challenging procedure requiring lots of time and resources. Therefore, computer-aided drug design (CADD) methodologies are used extensively to promote proficiency in drug development in a systematic and time-effective manner. The point in reference is SARS-CoV-2 which has emerged as a global pandemic. In the absence of any confirmed drug moiety to treat the infection, the science fraternity adopted hit and trial methods to come up with a lead drug compound. This article is an overview of the virtual methodologies, which assist in finding novel hits and help in the progression of drug development in a short period with a specific medicinal solution.

MiMiCPy: An Efficient Toolkit for MiMiC-Based QM/MM Simulations

MiMiC is a highly flexible, extremely scalable multiscale modeling framework. It couples the CPMD (quantum mechanics, QM) and GROMACS (molecular mechanics, MM) codes. The code requires preparing separate input files for the two programs with a selection of the QM region. This can be a tedious procedure prone to human error, especially when dealing with large QM regions. Here, we present MiMiCPy, a user-friendly tool that automatizes the preparation of MiMiC input files. It is written in Python 3 with an object-oriented approach. The main subcommand PrepQM can be used to generate MiMiC inputs directly from the command line or through a PyMOL/VMD plugin for visually selecting the QM region. Many other subcommands are also provided for debugging and fixing MiMiC input files. MiMiCPy is designed with a modular structure that allows seamless extensions to new program formats depending on the requirements of MiMiC.

ULYSSES: An Efficient and Easy to Use Semiempirical Library for C+

We introduce ULYSSES, a user-friendly and robust C++ library for semiempirical quantum chemical calculations. In its current version, ULYSSES is equipped with a large set of different semiempirical models, most of which are based on the Neglect of Diatomic Differential Overlap (NDDO) approximation. Empirical corrections for dispersion and hydrogen bonding are available for most methods, so that higher quality is achieved in the calculation of energies of nonbonded complexes. The library is furthermore equipped with geometry optimization, as well as modules for calculating molecular properties of general interest. Ideal gas thermodynamics is available and allows single structure as well as conformer (multistructure) averaged properties to be calculated. We offer the possibility to use several vibrational partition functions according to the nature of interactions being studied: for covalent systems, the traditional harmonic oscillator approximation is available; for nonbonded complexes, we systematically extended the partition function proposed by Grimme for all thermodynamic functions. The library is also capable of running Born-Oppenheimer molecular dynamics.

Computer-aided drug design, quantum-mechanical methods for biological problems

Quantum chemistry enables to study systems with chemical accuracy (<1 kcal/mol from experiment) but is restricted to a handful of atoms due to its computational expense. This has led to ongoing interest to optimize and simplify these methods while retaining accuracy. Implementing quantum mechanical (QM) methods on modern hardware such as multiple-GPUs is one example of how the field is optimizing performance. Multiscale approaches like the so-called QM/molecular mechanical method are gaining popularity in drug discovery because they focus the application of QM methods on the region of choice (e.g., the binding site), while using efficient MM models to represent less relevant areas. The creation of simplified QM methods is another example, including the use of machine learning to create ultra-fast and accurate QM models. Herein, we summarize recent advancements in the development of optimized QM methods that enhance our ability to use these methods in computer aided drug discovery.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Quantum simulations of SARS-CoV-2 main protease Mpro enable high-quality scoring of diverse ligands

The COVID-19 pandemic has led to unprecedented efforts to identify drugs that can reduce its associated morbidity/mortality rate. Computational chemistry approaches hold the potential for triaging potential candidates far more quickly than their experimental counterparts. These methods have been widely used to search for small molecules that can inhibit critical proteins involved in the SARS-CoV-2 replication cycle. An important target is the SARS-CoV-2 main protease Mpro, an enzyme that cleaves the viral polyproteins into individual proteins required for viral replication and transcription. Unfortunately, standard computational screening methods face difficulties in ranking diverse ligands to a receptor due to disparate ligand scaffolds and varying charge states. Here, we describe full density functional quantum mechanical (DFT) simulations of Mpro in complex with various ligands to obtain absolute ligand binding energies. Our calculations are enabled by a new cloud-native parallel DFT implementation running on computational resources from Amazon Web Services (AWS). The results we obtain are promising: the approach is quite capable of scoring a very diverse set of existing drug compounds for their affinities to M pro and suggest the DFT approach is potentially more broadly applicable to repurpose screening against this target. In addition, each DFT simulation required only ~ 1 h (wall clock time) per ligand. The fast turnaround time raises the practical possibility of a broad application of large-scale quantum mechanics in the drug discovery pipeline at stages where ligand diversity is essential.

'All That Glitters Is Not Gold': High-Resolution Crystal Structures of Ligand-Protein Complexes Need Not Always Represent Confident Binding Poses

Our understanding of the structure–function relationships of biomolecules and thereby applying it to drug discovery programs are substantially dependent on the availability of the structural information of ligand–protein complexes. However, the correct interpretation of the electron density of a small molecule bound to a crystal structure of a macromolecule is not trivial. Our analysis involving quality assessment of ~0.28 million small molecule–protein binding site pairs derived from crystal structures corresponding to ~66,000 PDB entries indicates that the majority (65%) of the pairs might need little (54%) or no (11%) attention. Out of the remaining 35% of pairs that need attention, 11% of the pairs (including structures with high/moderate resolution) pose serious concerns. Unfortunately, most users of crystal structures lack the training to evaluate the quality of a crystal structure against its experimental data and, in general, rely on the resolution as a ‘gold standard’ quality metric. Our work aims to sensitize the non-crystallographers that resolution, which is a global quality metric, need not be an accurate indicator of local structural quality. In this article, we demonstrate the use of several freely available tools that quantify local structural quality and are easy to use from a non-crystallographer’s perspective. We further propose a few solutions for consideration by the scientific community to promote quality research in structural biology and applied areas.

Multiscale Quantum Refinement Approaches for Metalloproteins

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

Quantum Chemistry Calculations for Metabolomics

A primary goal of metabolomics studies is to fully characterize the small-molecule composition of complex biological and environmental samples. However, despite advances in analytical technologies over the past two decades, the majority of small molecules in complex samples are not readily identifiable due to the immense structural and chemical diversity present within the metabolome. Current gold-standard identification methods rely on reference libraries built using authentic chemical materials ("standards"), which are not available for most molecules. Computational quantum chemistry methods, which can be used to calculate chemical properties that are then measured by analytical platforms, offer an alternative route for building reference libraries, i.e., in silico libraries for "standards-free" identification. In this review, we cover the major roadblocks currently facing metabolomics and discuss applications where quantum chemistry calculations offer a solution. Several successful examples for nuclear magnetic resonance spectroscopy, ion mobility spectrometry, infrared spectroscopy, and mass spectrometry methods are reviewed. Finally, we consider current best practices, sources of error, and provide an outlook for quantum chemistry calculations in metabolomics studies. We expect this review will inspire researchers in the field of small-molecule identification to accelerate adoption of in silico methods for generation of reference libraries and to add quantum chemistry calculations as another tool at their disposal to characterize complex samples.

Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?

QM/MM simulations have become an indispensable tool in many chemical and biochemical investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chemistry, are there still "burning challenges" in QM/MM methods, especially for biomolecular systems? In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quantitative applicability of QM/MM simulations to many, if not all, biomolecules. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate additional developments that help push the field forward in meaningful directions.

Accurate and cost-effective NMR chemical shift predictions for proteins using a molecules-in-molecules fragmentation-based method

We have developed an efficient protocol using our two-layer Molecules-in-Molecules (MIM2) fragmentation-based quantum chemical method for the prediction of NMR chemical shifts of large biomolecules. To investigate the performance of our fragmentation approach and demonstrate its applicability, MIM-NMR calculations are first calibrated on a test set of six proteins. The MIM2-NMR method yields a mean absolute deviation (MAD) from unfragmented full molecule calculations of 0.01 ppm for 1H and 0.06 ppm for 13C chemical shifts. Thus, the errors from fragmentation are only about 3% of our target accuracy of ∼0.3 ppm for 1H and 2-3 ppm for 13C chemical shifts. To compare with experimental chemical shifts, a standard protocol is first derived using two smaller proteins 2LHY (176 atoms) and 2LI1 (146 atoms) for obtaining an appropriate protein structure for NMR chemical shift calculations. The effect of the solvent environment on the calculated NMR chemical shifts is incorporated through implicit, explicit, or explicit-implicit solvation models. The expensive first solvation shell calculations are replaced by a micro-solvation model in which only the immediate interaction between the protein and the explicit solvation environment is considered. A single explicit water molecule for each amine and amide proton is found to be sufficient to yield accurate results for 1H chemical shifts. The 1H and 13C NMR chemical shifts calculated using our protocol give excellent agreement with experiments for two larger proteins, 2MC5 (the helical part with 265 atoms) and 3UMK (33 residue slice with 547 atoms). Overall, our target accuracy of ∼0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for the larger proteins. The proposed MIM-NMR method is accurate and computationally cost-effective and should be applicable to study a wide range of large proteins.

Polarizable Multipolar Molecular Dynamics Using Distributed Point Charges

Distributed point charge models (DCM) and their minimal variants (MDCM) have been integrated with tools widely used for condensed-phase simulations, including a virial-based barostat and a slow-growth algorithm for thermodynamic integration. Minimal DCM is further developed in a systematic fashion to reduce fitting errors in the electrostatic interaction energy, and a new fragment-based approach offers considerable speedup of the MDCM fitting process for larger molecules with increased numbers of off-centered charged sites. Finally, polarizable (M)DCM is also introduced in the present work. The developments are used in condensed-phase simulations of popular force fields with commonly applied simulation conditions. (M)DCM equivalents for a range of widely used water force fields and for fluorobenzene (PhF) are developed and applied along with the original models to evaluate the impact of reformulating the electrostatic term. Comparisons of the molecular electrostatic potential (MEP), electrostatic interaction energies, and bulk properties from molecular dynamics simulations for a range of models from simple TIPnP (n = 3-5) to the polarizable, multipolar iAMOEBA models for water and an existing quadrupolar model for PhF confirm that DCMs retain the accuracy of the original models, providing a homogeneous, efficient, and generic point charge alternative to a multipolar electrostatic model for force field development and multilevel simulations.

Metabolite Structure Assignment Using In Silico NMR Techniques

A major challenge for metabolomic analysis is to obtain an unambiguous identification of the metabolites detected in a sample. Among metabolomics techniques, NMR spectroscopy is a sophisticated, powerful, and generally applicable spectroscopic tool that can be used to ascertain the correct structure of newly isolated biogenic molecules. However, accurate structure prediction using computational NMR techniques depends on how much of the relevant conformational space of a particular compound is considered. It is intrinsically challenging to calculate NMR chemical shifts using high-level DFT when the conformational space of a metabolite is extensive. In this work, we developed NMR chemical shift calculation protocols using a machine learning model in conjunction with standard DFT methods. The pipeline encompasses the following steps: (1) conformation generation using a force field (FF)-based method, (2) filtering the FF generated conformations using the ASE-ANI machine learning model, (3) clustering of the optimized conformations based on structural similarity to identify chemically unique conformations, (4) DFT structural optimization of the unique conformations, and (5) DFT NMR chemical shift calculation. This protocol can calculate the NMR chemical shifts of a set of molecules using any available combination of DFT theory, solvent model, and NMR-active nuclei, using both user-selected reference compounds and/or linear regression methods. Our protocol reduces the overall computational time by 2 orders of magnitude over methods that optimize the conformations using fully ab initio methods, while still producing good agreement with experimental observations. The complete protocol is designed in such a manner that makes the computation of chemical shifts tractable for a large number of conformationally flexible metabolites.

Quantum Chemical Calculation of Molecular and Periodic Peptide and Protein Structures

Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.

Mechanisms of ATP to cAMP Conversion Catalyzed by the Mammalian Adenylyl Cyclase: A Role of Magnesium Coordination Shells and Proton Wires

We report a mechanism of adenosine triphosphate (ATP) to cyclic adenosine monophosphate (cAMP) conversion by the mammalian type V adenylyl cyclase revealed in molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) simulations. We characterize a set of computationally derived enzyme-substrate (ES) structures showing an important role of coordination shells of magnesium ions in the solvent accessible active site. In the lowest energy ES conformation, the coordination shell of Mg_A²⁺ does not include the O_δ1 atom of the conserved Asp440 residue. Starting from this conformation, a one-step reaction mechanism is characterized that includes proton transfer from the ribose O^3'H^3' group in ATP to Asp440 via a shuttling water molecule concerted with P^A-O^3A bond cleavage and O^3'-P^A bond formation. The energy profile of this route is consistent with the observed reaction kinetics. The computed energy profiles initiated from higher energy ES complexes are characterized by larger energy expenses to complete the reaction. Consistent with experimental data, we show that the Asp440Ala mutant of the enzyme should exhibit a reduced but retained activity. All considered reaction pathways include proton wires from the O^3'H^3' group via shuttling water molecules.

Analyzing Interactions with the Fragment Molecular Orbital Method

Basic concepts in the analysis of binding using the fragment molecular orbital method are discussed at length: polarization, desolvation, and interaction. The components in the pair interaction energy decomposition analysis are introduced, and the analysis is illustrated for a water dimer and a protein-ligand complex.

What Next for Quantum Mechanics in Structure-Based Drug Discovery?

There is significant potential for electronic structure methods to improve the quality of the predictions furnished by the tools of computer-aided drug design, which typically rely on empirically derived functions. In this perspective, we consider some recent examples of how quantum mechanics has been applied in predicting protein-ligand geometries, protein-ligand binding affinities and ligand strain on binding. We then outline several significant developments in quantum mechanics methodology likely to influence these approaches: in particular, we note the advent of more computationally expedient ab initio quantum mechanical methods that can provide chemical accuracy for larger molecular systems than hitherto possible. We highlight the emergence of increasingly accurate semiempirical quantum mechanical methods and the associated role of machine learning and molecular databases in their development. Indeed, the convergence of improved algorithms for solving and analyzing electronic structure, modern machine learning methods, and increasingly comprehensive benchmark data sets of molecular geometries and energies provides a context in which the potential of quantum mechanics will be increasingly realized in driving future developments and applications in structure-based drug discovery.

mTOR–mLST8 interaction: hot spot identification through quantum biochemistry calculations

Quantum calculation of mTOR–mLST8 interaction.

Analysis of Density Functional Tight Binding with Natural Bonding Orbitals

The description of chemical bonding by the density functional tight binding (DFTB) model is analyzed using natural bonding orbitals (NBOs) and compared to results from density functional theory (B3LYP/aug-cc-pVTZ) calculations. Several molecular systems have been chosen to represent fairly diverse bonding scenarios that include standard covalent bonds, hypervalent interactions, multicenter bonds, metal-ligand interactions (with and without the pseudo-Jahn-Teller effect), and through-space donor-acceptor interactions. Overall, the results suggest that DFTB3/3OB provides physically sound descriptions for the different bonding scenarios analyzed here, as reflected by the general agreement between DFTB3 and B3LYP NBO properties, such as the nature of the NBOs, the magnitudes of natural charges and bond orders, and the dominant donor-acceptor interactions. The degree of ligand-to-metal charge transfer and the ionic nature of pentavalent phosphate are overestimated, likely reflecting the minimal-basis nature of DFTB3/3OB. Moreover, certain orbital interactions, such as geminal interactions, are observed to be grossly overestimated by DFTB3 for hypervalent phosphate and several transition metal compounds that involve copper and nickel. The study indicates that results from NBO analysis can be instructive for identifying electronic structure descriptions at the approximate quantum-mechanical level that require improvement and thus for guiding the systematic improvement of these methods.

Understanding Neurobehavioural Dynamics: A Close-Up View on Psychiatry and Quantum Mechanics

Psychiatric disorders are prevalent throughout the world and causes heavy burden on mankind. Alone in US, billions of dollars are used for treatment purposes annually. Although advances in treatment strategies had witnessed recently, however the efficacy and overall outcome weren’t quite promising. In neurobehavioural sciences, old problems survive through ages and with psychiatric disease, the phenomenon turns intensely complex. While our understanding of brain is mostly based on concepts of particle physics, its functions largely follow the principles of quantum mechanics. The current therapeutics relies on understanding of brain as a material entity that turns to be one of the chief reasons for the unsatisfactory therapeutic outcomes. Collectively, as mankind we are suffering huge loss due to the least effective treatment strategies. Even though we just begin to understand about how brain works, we also do not know much about quantum mechanics and how subatomic particles behave with quantum properties. Though it is apparent that quantum properties like particle and wave function duality coincides with the fundamental aspects of brain and mind duality, thus must share some common basis. Here in this article, an opinion is set that quantum mechanics in association with brain and more specifically psychiatry may take us towards a better understanding about brain, behaviour and how we approach towards treatment.

Transferable Machine-Learning Model of the Electron Density

The electronic charge density plays a central role in determining the behavior of matter at the atomic scale, but its computational evaluation requires demanding electronic-structure calculations. We introduce an atom-centered, symmetry-adapted framework to machine-learn the valence charge density based on a small number of reference calculations. The model is highly transferable, meaning it can be trained on electronic-structure data of small molecules and used to predict the charge density of larger compounds with low, linear-scaling cost. Applications are shown for various hydrocarbon molecules of increasing complexity and flexibility, and demonstrate the accuracy of the model when predicting the density on octane and octatetraene after training exclusively on butane and butadiene. This transferable, data-driven model can be used to interpret experiments, accelerate electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems.

Computational Understanding of the Selectivities in Metalloenzymes

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

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Covalent simulations of covalent/irreversible enzyme inhibition in drug discovery: a reliable technical protocol

Aim: Irreversible covalent inhibition of biological targets in disease pathogenesis is an emerging field in drug design. Computational techniques have assumed a critical role in understanding covalent enzyme inhibition. However, a gap currently exists with regards to the reliability and reproducibility of currently available protocols available in literature and open scientific forums. Methodology/results: Appropriate ligand and protein target are selected, docked covalently or noncovalently using respective docking tools. Both components are subjected to premolecular dynamic preparations. This was followed by parameterization of the ligand, protein and covalent complex, respectively. The production runs were initiated and the resulting trajectories are saved and analyzed. Conclusion: This protocol is reliable and reproducible, hence would advance the development of irreversible covalent inhibitors toward disease treatment.

Generation of Pairwise Potentials Using Multidimensional Data Mining

The rapid development of molecular structural databases provides the chemistry community access to an enormous array of experimental data that can be used to build and validate computational models. Using radial distribution functions collected from experimentally available X-ray and NMR structures, a number of so-called statistical potentials have been developed over the years using the structural data mining strategy. These potentials have been developed within the context of the two-particle Kirkwood equation by extending its original use for isotropic monatomic systems to anisotropic biomolecular systems. However, the accuracy and the unclear physical meaning of statistical potentials have long formed the central arguments against such methods. In this work, we present a new approach to generate molecular energy functions using structural data mining. Instead of employing the Kirkwood equation and introducing the "reference state" approximation, we model the multidimensional probability distributions of the molecular system using graphical models and generate the target pairwise Boltzmann probabilities using the Bayesian field theory. Different from the current statistical potentials that mimic the "knowledge-based" PMF based on the 2-particle Kirkwood equation, the graphical-model-based structure-derived potential developed in this study focuses on the generation of lower-dimensional Boltzmann distributions of atoms through reduction of dimensionality. We have named this new scoring function GARF, and in this work we focus on the mathematical derivation of our novel approach followed by validation studies on its ability to predict protein-ligand interactions.

Nanosecond-Scale Isomerization of the 4'-Carboxonium Cation Oxidatively Produced in Pyrimidine Units of DNA

The long-standing puzzle of the chemistry producing the Stubbe-Kozarich abasic site, which is the minor product in the oxidation of 2'-deoxycytidine units of DNA by Fe(II)-bleomycin, has been computationally solved in this study. Scrupulous DFT-based calculations that included extensive screening of the potential energy surface of model-solvated nucleotides and the elucidation of the chemical structure of the located nucleotide cations via natural bond orbital analysis demonstrated that the 2'-deoxycytidine unit bearing the 2'-deoxyribose ring 2e-oxidized at the 4'-position undergoes carboxonium ion- iminium ion (C═O⁺-C → C═N⁺) isomerization. This 1,2-elimination of the carbonyl group 4'-C═O from the carboxonium cation fragment is associated with minimal spatial reorganization of the molecule and appears to be an ultrafast reaction. The calculated barrier Δ G₀^# of 2.7 kcal mol^-1 for this isomerization is lower than that reported for the addition of water to oxocarbenium ions. Thus, this unusual nucleotide transformation is the key chemical reaction that yields the Stubbe-Kozarich product. Such a product cannot be formed for purine nucleotide units in DNA. The isomerization of 4'-dehydro-2'-deoxyribose-4'-carboxonium cations formed in these DNA units is slower because it destroys the purine aromaticity, and the cations are intercepted by water molecules before they isomerize.

Kinetics and pathway of biodegradation of dibutyl phthalate by Pleurotus ostreatus

Dibutyl phthalate (DBP) is a plasticizer, whose presence in the environment as a pollutant has attained a great deal of attention due to its reported association with endocrine system disturbances on animals. Growth parameters, glucose uptake, percentage of removal efficiency (%E) of DBP, biodegradation constant of DBP (k) and half-life of DBP biodegradation (t_1/2) were evaluated for Pleurotus ostreatus grown on media containing glucose and different concentrations of DBP (0, 500 and 1000 mg l^-1). P. ostreatus degraded 99.6 % and 94 % of 500 and 1000 mg of DBP l^-1 after 312 h and 504 h, respectively. The k was 0.0155 h^-1 and 0.0043 h^-1 for 500 and 1000 mg of DBP l^-1, respectively. t_1/2 was 44.7 h and 161 h for 500 and 1000 mg of DBP l^-1, respectively. Intermediate compounds of biodegraded DBP were identified by GC-MS and a DBP biodegradation pathway was proposed using quantum chemical calculation. DBP might be metabolized to benzene and acetyl acetate, the first would be oxidated to muconic acid and the latter would enter into the Krebs cycle. P. ostreatus has the ability to degrade DBP and utilizes it as source of carbon and energy.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

QM Cluster or QM/MM in Computational Enzymology: The Test Case of LigW-Decarboxylase

The catalytic mechanism of the decarboxylation of 5-carboxyvanillate by LigW producing vanillic acid has been studied by using QM cluster and hybrid QM/MM methodologies. In the QM cluster model, the environment of a small QM model is treated with a bulky potential while two QM/MM models studies include partial and full protein with and without explicitly treated water solvent. The studied reaction involves two sequential steps: the protonation of the carbon of the 5-carboxy-vanillate substrate and the decarboxylation of the intermediate from which results deprotonated vanillic acid as product. The structures and energetics obtained by using three structural models and two density functionals are quite consistent to each other. This indicates that the small QM cluster model of the presently considered enzymatic reaction is appropriate enough and the reaction is mainly influenced by the active site.

Automated Fragmentation QM/MM Calculation of NMR Chemical Shifts for Protein-Ligand Complexes

In this study, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method was applied for NMR chemical shift calculations of protein-ligand complexes. In the AF-QM/MM approach, the protein binding pocket is automatically divided into capped fragments (within ~200 atoms) for density functional theory (DFT) calculations of NMR chemical shifts. Meanwhile, the solvent effect was also included using the Poission-Boltzmann (PB) model, which properly accounts for the electrostatic polarization effect from the solvent for protein-ligand complexes. The NMR chemical shifts of neocarzinostatin (NCS)-chromophore binding complex calculated by AF-QM/MM accurately reproduce the large-sized system results. The 1H chemical shift perturbations (CSP) between apo-NCS and holo-NCS predicted by AF-QM/MM are also in excellent agreement with experimental results. Furthermore, the DFT calculated chemical shifts of the chromophore and residues in the NCS binding pocket can be utilized as molecular probes to identify the correct ligand binding conformation. By combining the CSP of the atoms in the binding pocket with the Glide scoring function, the new scoring function can accurately distinguish the native ligand pose from decoy structures. Therefore, the AF-QM/MM approach provides an accurate and efficient platform for protein-ligand binding structure prediction based on NMR derived information.

Determination of accurate backbone chemical shift tensors in microcrystalline proteins by integrating MAS NMR and QM/MM

Chemical shifts are highly sensitive probes of local conformation and overall structure. Both isotropic shifts and chemical shift tensors are readily accessible from NMR experiments but their quantum mechanical calculations remain challenging. In this work, we report and compare accurately measured and calculated 15NH and 13Cα chemical shift tensors in proteins, using the microcrystalline agglutinin from Oscillatoria agardhii (OAA). Experimental 13Cα and 15NH chemical tensors were obtained by solid-state NMR spectroscopy, employing tailored recoupling sequences, and for their quantum mechanics/molecular mechanics (QM/MM) calculations different sets of functionals were evaluated. We show that 13Cα chemical shift tensors are primarily determined by backbone dihedral angles and dynamics, while 15NH tensors mainly depend on local electrostatic contributions from solvation and hydrogen bonding. In addition, the influence of including crystallographic waters, the molecular mechanics geometry optimization protocol, and the level of theory on the accuracy of the calculated chemical shift tensors is discussed. Specifically, the power of QM/MM calculations in accurately predicting the unusually upfield shifted 1HN G26 and G93 resonances is highlighted. Our integrated approach is expected to benefit structure refinement of proteins and protein assemblies.

A novel biodegradation pathway of the endocrine-disruptor di(2-ethyl hexyl) phthalate by Pleurotus ostreatus based on quantum chemical investigation

Di(2-ethyl hexyl) phthalate (DEHP) is a plasticizer that interfere with endocrine systems in mammals. Growth parameters for Pleurotus ostreatus grown on media containing glucose and different concentrations of DEHP (0, 500 and 1000mg/L) were evaluated. The highest biomass production was observed in medium supplemented with 1000mg of DEHP/L. Half-life of DEHP biodegradation, biodegradation constant of DEHP, and percentage of removal efficiency (%E) were also determined. P. ostreatus degraded 100% of DEHP after 504h. %E was 99.3% and 98.4% for 500 and 1000mg of DEHP/L, respectively. Intermediate compounds of biodegraded DEHP were identified by GC-MS and a DEHP biodegradation pathway was proposed using quantum chemical investigation. DEHP might be metabolized through three pathways; a de-esterification pathway, an oxidation pathway and an oxidation-hydrolysis pathway, forming phthalic acid, acetic acid and butanediol, respectively. P. ostreatus degrades and uses (as carbon and energy source) high concentrations of DEHP.

Mineralization of high concentrations of the endocrine disruptor dibutyl phthalate by Fusarium culmorum

Dibutyl phthalate (DBP) is a widely used plasticizer, whose presence in the environment as a pollutant raises concern because of its endocrine-disrupting toxicity. Growth kinetics, glucose uptake, biodegradation constant of DBP (k), half-life of DBP biodegradation (t_1/2) and percentage of removal efficiency (%E) were evaluated for Fusarium culmorum grown on media containing glucose and different concentrations of DBP (500 and 1000 mg/l). Intermediate compounds of biodegraded DBP were identified by GC-MS and a novel DBP biodegradation pathway was proposed on the basis of the intermolecular flow of electrons of the intermediates identified using quantum chemical modeling. F. culmorum degraded 99% of both 1000 and 500 mg of DBP/l after an incubation period of 168 and 228 h, respectively. %E was 99.5 and 99.3 for 1000 and 500 mg of DBP/l, respectively. The k was 0.0164 and 0.0231 h^-1 for 500 and 1000 mg of DBP/l, respectively. DBP was fully metabolized to fumaric and malic acids, which are compounds that enter into the Krebs cycle. F. culmorum has a promising ability for bioremediation of environments polluted with DBP because it efficiently degrades DBP and uses high concentrations of this compound as carbon and energy source.

Toward Closing the Gap: Quantum Mechanical Calculations and Experimentally Measured Chemical Shifts of a Microcrystalline Lectin

NMR chemical shifts are exquisitely sensitive probes for conformation and dynamics in molecules and supramolecular assemblies. Although isotropic chemical shifts are easily measured with high accuracy and precision in conventional NMR experiments, they remain challenging to calculate quantum mechanically, particularly in inherently dynamic biological systems. Using a model benchmark protein, the 133-residue agglutinin from Oscillatoria agardhii (OAA), which has been extensively characterized by us previously, we have explored the integration of X-ray crystallography, solution NMR, MAS NMR, and quantum mechanics/molecular mechanics (QM/MM) calculations for analysis of 13Cα and 15NH isotropic chemical shifts. The influence of local interactions, quaternary contacts, and dynamics on the accuracy of calculated chemical shifts is analyzed. Our approach is broadly applicable and expected to be beneficial in chemical shift analysis and chemical-shift-based structure refinement for proteins and protein assemblies.