Specific Reaction Parametrization of the AM1/d Hamiltonian for Phosphoryl Transfer Reactions: H, O, and P Atoms

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Molecular Basis of the Substrate Specificity of Phosphotriesterase from Pseudomonas diminuta: A Combined QM/MM MD and Electron Density Study

The occurrence of organophosphorus compounds, pesticides, and flame-retardants in wastes is an emerging ecological problem. Bacterial phosphotriesterases are capable of hydrolyzing some of them. We utilize modern molecular modeling tools to study the hydrolysis mechanism of organophosphorus compounds with good and poor leaving groups by phosphotriesterase from Pseudomonas diminuta (Pd-PTE). We compute Gibbs energy profiles for enzymes with different cations in the active site: native Zn2+cations and Co2+cations, which increase the steady-state rate constant. Hydrolysis occurs in two elementary steps via an associative mechanism and formation of the pentacoordinated intermediate. The first step, a nucleophilic attack, occurs with a low energy barrier independently of the substrate. The second step has a low energy barrier and considerable stabilization of products for substrates with good leaving groups. For substrates with poor leaving groups, the reaction products are destabilized relative to the ES complex that suppresses the reaction. The reaction proceeds with low energy barriers for substrates with good leaving groups with both Zn2+and Co2+cations in the active site; thus, the product release is likely to be a limiting step. Electron density and geometry analysis of the QM/MM MD trajectories of the intermediate states with all considered compounds allow us to discriminate substrates by their ability to be hydrolyzed by the Pd-PTE. For hydrolyzable substrates, the cleaving bond between a phosphorus atom and a leaving group is elongated, and electron density depletion is observed on the Laplacian of electron density maps.

Exploring the Reaction Mechanism of Polyethylene Terephthalate Biodegradation through QM/MM Approach

The enzyme PETase fromIdeonella sakaiensis (IsPETase) strain 201-F6 can catalyze the hydrolysis of polyethylene terephthalate (PET), mainly converting it into mono(2-hydroxyethyl) terephthalic acid (MHET). In this study, we used quantum mechanics/molecular mechanics (QM/MM) simulations to explore the molecular details of the catalytic reaction mechanism of IsPETase in the formation of MHET. The QM region was described with AM1d/PhoT and M06-2X/6-31+G(d,p) potential. QM/MM simulations unveil the complete enzymatic PET hydrolysis mechanism and identify two possible reaction pathways for acylation and deacylation steps. The barrier obtained at M06-2X/6-31+G(d,p)/MM potential for the deacylation step corresponds to 20.4 kcal/mol, aligning with the experimental value of 18 kcal/mol. Our findings indicate that deacylation is the rate-limiting step of the process. Furthermore, per-residue interaction energy contributions revealed unfavorable contributions to the transition state of amino acids located at positions 200-230, suggesting potential sites for targeted mutations. These results can contribute to the development of more active and selective enzymes for PET depolymerization.

CHARMM-GUI QM/MM Interfacer for a Quantum Mechanical and Molecular Mechanical (QM/MM) Simulation Setup: 1. Semiempirical Methods

Quantum mechanical (QM) treatments, when combined with molecular mechanical (MM) force fields, can effectively handle enzyme-catalyzed reactions without significantly increasing the computational cost. In this context, we present CHARMM-GUI QM/MM Interfacer, a web-based cyberinfrastructure designed to streamline the preparation of various QM/MM simulation inputs with ligand modification. The development of QM/MM Interfacer has been achieved through integration with existing CHARMM-GUI modules, such as PDB Reader and Manipulator, Solution Builder, and Membrane Builder. In addition, new functionalities have been developed to facilitate the one-stop preparation of QM/MM systems and enable interactive and intuitive ligand modifications and QM atom selections. QM/MM Interfacer offers support for a range of semiempirical QM methods, including AM1(+/d), PM3(+/PDDG), MNDO(+/d, +/PDDG), PM6, RM1, and SCC-DFTB, tailored for both AMBER and CHARMM. A nontrivial setup related to ligand modification, link-atom insertion, and charge distribution is automatized through intuitive user interfaces. To illustrate the robustness of QM/MM Interfacer, we conducted QM/MM simulations of three enzyme-substrate systems: dihydrofolate reductase, insulin receptor kinase, and oligosaccharyltransferase. In addition, we have created three tutorial videos about building these systems, which can be found at https://www.charmm-gui.org/demo/qmi. QM/MM Interfacer is expected to be a valuable and accessible web-based tool that simplifies and accelerates the setup process for hybrid QM/MM simulations.

Amber free energy tools: Interoperable software for free energy simulations using generalized quantum mechanical/molecular mechanical and machine learning potentials

We report the development and testing of new integrated cyberinfrastructure for performing free energy simulations with generalized hybrid quantum mechanical/molecular mechanical (QM/MM) and machine learning potentials (MLPs) in Amber. The Sander molecular dynamics program has been extended to leverage fast, density-functional tight-binding models implemented in the DFTB+ and xTB packages, and an interface to the DeePMD-kit software enables the use of MLPs. The software is integrated through application program interfaces that circumvent the need to perform "system calls" and enable the incorporation of long-range Ewald electrostatics into the external software's self-consistent field procedure. The infrastructure provides access to QM/MM models that may serve as the foundation for QM/MM-ΔMLP potentials, which supplement the semiempirical QM/MM model with a MLP correction trained to reproduce ab initio QM/MM energies and forces. Efficient optimization of minimum free energy pathways is enabled through a new surface-accelerated finite-temperature string method implemented in the FE-ToolKit package. Furthermore, we interfaced Sander with the i-PI software by implementing the socket communication protocol used in the i-PI client-server model. The new interface with i-PI allows for the treatment of nuclear quantum effects with semiempirical QM/MM-ΔMLP models. The modular interoperable software is demonstrated on proton transfer reactions in guanine-thymine mispairs in a B-form deoxyribonucleic acid helix. The current work represents a considerable advance in the development of modular software for performing free energy simulations of chemical reactions that are important in a wide range of applications.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine-Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials

Rare tautomeric forms of nucleobases can lead to Watson-Crick-like (WC-like) mispairs in DNA, but the process of proton transfer is fast and difficult to detect experimentally. NMR studies show evidence for the existence of short-time WC-like guanine-thymine (G-T) mispairs; however, the mechanism of proton transfer and the degree to which nuclear quantum effects play a role are unclear. We use a B-DNA helix exhibiting a wGT mispair as a model system to study tautomerization reactions. We perform ab initio (PBE0/6-31G*) quantum mechanical/molecular mechanical (QM/MM) simulations to examine the free energy surface for tautomerization. We demonstrate that while the ab initio QM/MM simulations are accurate, considerable sampling is required to achieve high precision in the free energy barriers. To address this problem, we develop a QM/MM machine learning potential correction (QM/MM-ΔMLP) that is able to improve the computational efficiency, greatly extend the accessible time scales of the simulations, and enable practical application of path integral molecular dynamics to examine nuclear quantum effects. We find that the inclusion of nuclear quantum effects has only a modest effect on the mechanistic pathway but leads to a considerable lowering of the free energy barrier for the GT*⇌G*T equilibrium. Our results enable a rationalization of observed experimental data and the prediction of populations of rare tautomeric forms of nucleobases and rates of their interconversion in B-DNA.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Landscape of In Silico Tools for Modeling Covalent Modification of Proteins: A Review on Computational Covalent Drug Discovery

Covalent drug discovery has been a challenging research area given the struggle of finding a sweet balance between selectivity and reactivity for these drugs, the lack of which often leads to off-target activities and hence undesirable side effects. However, there has been a resurgence in covalent drug design following the success of several covalent drugs such as boceprevir (2011), ibrutinib (2013), neratinib (2017), dacomitinib (2018), zanubrutinib (2019), and many others. Design of covalent drugs includes many crucial factors, where "evaluation of the binding affinity" and "a detailed mechanistic understanding on covalent inhibition" are at the top of the list. Well-defined experimental techniques are available to elucidate these factors; however, often they are expensive and/or time-consuming and hence not suitable for high throughput screens. Recent developments in in silico methods provide promise in this direction. In this report, we review a set of recent publications that focused on developing and/or implementing novel in silico techniques in "Computational Covalent Drug Discovery (CCDD)". We also discuss the advantages and disadvantages of these approaches along with what improvements are required to make it a great tool in medicinal chemistry in the near future.

The binding mechanism of failed, in processing and succeed inhibitors target SARS-CoV-2 main protease

Since the outbreak of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), several variants have caused a persistent pandemic. Consequently, it is crucial to develop new potential anti-SARS-CoV-2 drugs with specificity. To minimize potential failures and preserve valuable clinical resources for the development of other useful drugs, researchers must enhance their understanding of the interactions between drugs and SARS-CoV-2. While numerous crystal structures of the SARS-CoV-2 main protease (SCM) and its inhibitors have been reported, they provide only static snapshots and fail to capture the dynamic nature of SCM/inhibitor interactions. Herein, we conducted molecular dynamics simulations for five SCM complexes: ritonavir (SCM/RTV), lopinavir (SCM/LPV), the identified inhibitor N3 (SCM/N3), the approved inhibitor ensitrelvir (SCM/ESV), and the approved drug nirmatrelvir (SCM/NMV). Additionally, we explored the potential for covalent bond formation in the N3 and NMV inhibitors through QM/MM calculations using Umbrella sampling. The results show that the binding site is highly flexible to fit those five different inhibitors and each compound has its unique binding mode at the same binding site. Moreover, the binding affinities of positive and negative inhibitors to SCM exhibit significant differences. By gaining insights into the dynamics, we can potentially elucidate why lopinavir/ritonavir, initially considered promising, failed to effectively treat COVID-19. Furthermore, understanding the mechanistic aspects of N3 and NMV inhibition on SCM not only contributes to rational drug discovery against COVID-19 but also aids future studies on the catalytic mechanisms of main proteases in other novel coronaviruses.Communicated by Ramaswamy H. Sarma.

Impact of the Recognition Part of Dipeptidyl Nitroalkene Compounds on the Inhibition Mechanism of Cysteine Proteases Cruzain and Cathepsin L

Cysteine proteases (CPs) are an important class of enzymes, many of which are responsible for several human diseases. For instance, cruzain of protozoan parasite Trypanosoma cruzi is responsible for the Chagas disease, while the role of human cathepsin L is associated with some cancers or is a potential target for the treatment of COVID-19. However, despite paramount work carried out during the past years, the compounds that have been proposed so far show limited inhibitory action against these enzymes. We present a study of proposed covalent inhibitors of these two CPs, cruzain and cathepsin L, based on the design, synthesis, kinetic measurements, and QM/MM computational simulations on dipeptidyl nitroalkene compounds. The experimentally determined inhibition data, together with the analysis and the predicted inhibition constants derived from the free energy landscape of the full inhibition process, allowed describing the impact of the recognition part of these compounds and, in particular, the modifications on the P2 site. The designed compounds and, in particular, the one with a bulky group (Trp) at the P2 site show promising in vitro inhibition activities against cruzain and cathepsin L for use as a starting lead compound in the development of drugs with medical applications for the treatment of human diseases and future designs.

Mechanistic Basis for a Connection between the Catalytic Step and Slow Opening Dynamics of Adenylate Kinase

Escherichia coli adenylate kinase (AdK) is a small, monomeric enzyme that synchronizes the catalytic step with the enzyme's conformational dynamics to optimize a phosphoryl transfer reaction and the subsequent release of the product. Guided by experimental measurements of low catalytic activity in seven single-point mutation AdK variants (K13Q, R36A, R88A, R123A, R156K, R167A, and D158A), we utilized classical mechanical simulations to probe mutant dynamics linked to product release, and quantum mechanical and molecular mechanical calculations to compute a free energy barrier for the catalytic event. The goal was to establish a mechanistic connection between the two activities. Our calculations of the free energy barriers in AdK variants were in line with those from experiments, and conformational dynamics consistently demonstrated an enhanced tendency toward enzyme opening. This indicates that the catalytic residues in the wild-type AdK serve a dual role in this enzyme's function─one to lower the energy barrier for the phosphoryl transfer reaction and another to delay enzyme opening, maintaining it in a catalytically active, closed conformation for long enough to enable the subsequent chemical step. Our study also discovers that while each catalytic residue individually contributes to facilitating the catalysis, R36, R123, R156, R167, and D158 are organized in a tightly coordinated interaction network and collectively modulate AdK's conformational transitions. Unlike the existing notion of product release being rate-limiting, our results suggest a mechanistic interconnection between the chemical step and the enzyme's conformational dynamics acting as the bottleneck of the catalytic process. Our results also suggest that the enzyme's active site has evolved to optimize the chemical reaction step while slowing down the overall opening dynamics of the enzyme.

A specific MNDO parameterization for water

A modified neglect of differential overlap has been parameterized specifically for water and its oligomers with the addition of polarization functions on both hydrogen and oxygen, Feynman dispersion, and a slight modification of the treatment of the hydrogen nucleus. The results show that it is possible to easily obtain good geometries and energies for hydrogen-bonded water aggregates. Data from the Benchmark Energy and Geometry Database water-cluster database were used to parameterize the new Hamiltonian for water clusters from the dimer to the decamer using MP2/aug-cc-pVDZ optimized geometries and CCSD(T)/CBS oligomerization energies. Seventy five oligomerization and rearrangement energies derived from the parameterization data are reproduced with a root mean-square error (RMSE) of 0.79 kcal mol^-1 and the geometries of 38 oligomers with an RMSE of 0.17 Å. Interestingly, the Feynman dispersion term adopts a role different from that intended and tunes the atomic polarizability. The implications of these results in terms of future dedicated neglect of diatomic differential overlap Hamiltonians and those that use force-field-like atom types are discussed.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.

Assessment of Reversibility for Covalent Cysteine Protease Inhibitors Using Quantum Mechanics/Molecular Mechanics Free Energy Surfaces

We have used molecular dynamics (MD) simulations with hybrid quantum mechanics/molecular mechanics (QM/MM) potentials to investigate the reaction mechanism for covalent inhibition of cathepsin K and assess the reversibility of inhibition. The computed free energy profiles suggest that a nucleophilic attack by the catalytic cysteine on the inhibitor warhead and proton transfer from the catalytic histidine occur in a concerted manner. The results indicate that the reaction is more strongly exergonic for the alkyne-based inhibitors, which bind irreversibly to cathepsin K, than for the nitrile-based inhibitor odanacatib, which binds reversibly. Gas-phase energies were also calculated for the addition of methanethiol to structural prototypes for a number of warheads of interest in cysteine protease inhibitor design in order to assess electrophilicity. The approaches presented in this study are particularly applicable to assessment of novel warheads, and computed transition state geometries can be incorporated into molecular models for covalent docking.

Development of Range-Corrected Deep Learning Potentials for Fast, Accurate Quantum Mechanical/Molecular Mechanical Simulations of Chemical Reactions in Solution

We develop a new deep potential─range correction (DPRc) machine learning potential for combined quantum mechanical/molecular mechanical (QM/MM) simulations of chemical reactions in the condensed phase. The new range correction enables short-ranged QM/MM interactions to be tuned for higher accuracy, and the correction smoothly vanishes within a specified cutoff. We further develop an active learning procedure for robust neural network training. We test the DPRc model and training procedure against a series of six nonenzymatic phosphoryl transfer reactions in solution that are important in mechanistic studies of RNA-cleaving enzymes. Specifically, we apply DPRc corrections to a base QM model and test its ability to reproduce free-energy profiles generated from a target QM model. We perform these comparisons using the MNDO/d and DFTB2 semiempirical models because they differ in the way they treat orbital orthogonalization and electrostatics and produce free-energy profiles which differ significantly from each other, thereby providing us a rigorous stress test for the DPRc model and training procedure. The comparisons show that accurate reproduction of the free-energy profiles requires correction of the QM/MM interactions out to 6 Å. We further find that the model's initial training benefits from generating data from temperature replica exchange simulations and including high-temperature configurations into the fitting procedure, so the resulting models are trained to properly avoid high-energy regions. A single DPRc model was trained to reproduce four different reactions and yielded good agreement with the free-energy profiles made from the target QM/MM simulations. The DPRc model was further demonstrated to be transferable to 2D free-energy surfaces and 1D free-energy profiles that were not explicitly considered in the training. Examination of the computational performance of the DPRc model showed that it was fairly slow when run on CPUs but was sped up almost 100-fold when using NVIDIA V100 GPUs, resulting in almost negligible overhead. The new DPRc model and training procedure provide a potentially powerful new tool for the creation of next-generation QM/MM potentials for a wide spectrum of free-energy applications ranging from drug discovery to enzyme design.

Theoretical Studies of the Self Cleavage Pistol Ribozyme Mechanism

Ribozymes are huge complex biological catalysts composed of a combination of RNA and proteins. Nevertheless, there is a reduced number of small ribozymes, the self-cleavage ribozymes, that are formed just by RNA and, apparently, they existed in cells of primitive biological systems. Unveiling the details of these “fossils” enzymes can contribute not only to the understanding of the origins of life but also to the development of new simplified artificial enzymes. A computational study of the reactivity of the pistol ribozyme carried out by means of classical MD simulations and QM/MM hybrid calculations is herein presented to clarify its catalytic mechanism. Analysis of the geometries along independent MD simulations with different protonation states of the active site basic species reveals that only the canonical system, with no additional protonation changes, renders reactive conformations. A change in the coordination sphere of the Mg2+ ion has been observed during the simulations, which allows proposing a mechanism to explain the unique mode of action of the pistol ribozyme by comparison with other ribozymes. The present results are at the center of the debate originated from recent experimental and theoretical studies on pistol ribozyme.

Dynamic Connection between Enzymatic Catalysis and Collective Protein Motions

Enzymes employ a wide range of protein motions to achieve efficient catalysis of chemical reactions. While the role of collective protein motions in substrate binding, product release, and regulation of enzymatic activity is generally understood, their roles in catalytic steps per se remain uncertain. Here, molecular dynamics simulations, enzyme kinetics, X-ray crystallography, and nuclear magnetic resonance spectroscopy are combined to elucidate the catalytic mechanism of adenylate kinase and to delineate the roles of catalytic residues in catalysis and the conformational change in the enzyme. This study reveals that the motions in the active site, which occur on a time scale of picoseconds to nanoseconds, link the catalytic reaction to the slow conformational dynamics of the enzyme by modulating the free energy landscapes of subdomain motions. In particular, substantial conformational rearrangement occurs in the active site following the catalytic reaction. This rearrangement not only affects the reaction barrier but also promotes a more open conformation of the enzyme after the reaction, which then results in an accelerated opening of the enzyme compared to that of the reactant state. The results illustrate a linkage between enzymatic catalysis and collective protein motions, whereby the disparate time scales between the two processes are bridged by a cascade of intermediate-scale motion of catalytic residues modulating the free energy landscapes of the catalytic and conformational change processes.

Elucidating the Dual Mode of Action of Dipeptidyl Enoates in the Inhibition of Rhodesain Cysteine Proteases

A computational study of the two possible inhibition mechanisms of rhodesain cysteine protease by the dipeptidyl enoate Cbz-Phe-Leu-CH=CH-CO₂ C₂ H₅ has been carried out by means of molecular dynamics simulations with hybrid QM/MM potentials. The low free energy barriers confirm that the Cys25 residue can attack both C_β and C1 atoms of the inhibitor, confirming a dual mode of action in the inhibition of the rhodesain by enoates. According to the results, the inhibition process through the Cys25 attack on the C_β atom of the inhibitor is an exergonic and irreversible process, while the inhibition process when Cys25 attacks on the C1 atom of the inhibitor is and exergonic but reversible process. The interactions between the inhibitor and rhodesain suggest that P2 is the most important fragment to consider in the design of new efficient inhibitors of rhodesain. These results may be useful for the design of new inhibitors of rhodesain and other related cysteine proteases based on dipeptidyl enoates scaffolds.

Extension of the Variational Free Energy Profile and Multistate Bennett Acceptance Ratio Methods for High-Dimensional Potential of Mean Force Profile Analysis

We redevelop the variational free energy profile (vFEP) method using a cardinal B-spline basis to extend the method for analyzing free energy surfaces (FESs) involving three or more reaction coordinates. We also implemented software for evaluating high-dimensional profiles based on the multistate Bennett acceptance ratio (MBAR) method which constructs an unbiased probability density from global reweighting of the observed samples. The MBAR method takes advantage of a fast algorithm for solving the unbinned weighted histogram (UWHAM)/MBAR equations which replaces the solution of simultaneous equations with a nonlinear optimization of a convex function. We make use of cardinal B-splines and multiquadric radial basis functions to obtain smooth, differentiable MBAR profiles in arbitrary high dimensions. The cardinal B-spline vFEP and MBAR methods are compared using three example systems that examine 1D, 2D, and 3D profiles. Both methods are found to be useful and produce nearly indistinguishable results. The vFEP method is found to be 150 times faster than MBAR when applied to periodic 2D profiles, but the MBAR method is 4.5 times faster than vFEP when evaluating unbounded 3D profiles. In agreement with previous comparisons, we find the vFEP method produces superior FESs when the overlap between umbrella window simulations decreases. Finally, the associative reaction mechanism of hammerhead ribozyme is characterized using 3D, 4D, and 6D profiles, and the higher-dimensional profiles are found to have smaller reaction barriers by as much as 1.5 kcal/mol. The methods presented here have been implemented into the FE-ToolKit software package along with new methods for network-wide free energy analysis in drug discovery.

Sugar-Pucker Force-Induced Transition in Single-Stranded DNA

The accurate knowledge of the elastic properties of single-stranded DNA (ssDNA) is key to characterize the thermodynamics of molecular reactions that are studied by force spectroscopy methods where DNA is mechanically unfolded. Examples range from DNA hybridization, DNA ligand binding, DNA unwinding by helicases, etc. To date, ssDNA elasticity has been studied with different methods in molecules of varying sequence and contour length. A dispersion of results has been reported and the value of the persistence length has been found to be larger for shorter ssDNA molecules. We carried out pulling experiments with optical tweezers to characterize the elastic response of ssDNA over three orders of magnitude in length (60-14 k bases). By fitting the force-extension curves (FECs) to the Worm-Like Chain model we confirmed the above trend:the persistence length nearly doubles for the shortest molecule (60 b) with respect to the longest one (14 kb). We demonstrate that the observed trend is due to the different force regimes fitted for long and short molecules, which translates into two distinct elastic regimes at low and high forces. We interpret this behavior in terms of a force-induced sugar pucker conformational transition (C3'-endo to C2'-endo) upon pulling ssDNA.

Theoretical characterization of the shikimate 5-dehydrogenase reaction from Mycobacterium tuberculosis by hybrid QC/MM simulations and quantum chemical descriptors

In this study, we have investigated the enzyme shikimate 5-dehydrogenase from the causative agent of tuberculosis, Mycobacterium tuberculosis. We have employed a mixture of computational techniques, including molecular dynamics, hybrid quantum chemical/molecular mechanical potentials, relaxed surface scans, quantum chemical descriptors and free-energy simulations, to elucidate the enzyme's reaction pathway. Overall, we find a two-step mechanism, with a single transition state, that proceeds by an energetically uphill hydride transfer, followed by an energetically downhill proton transfer. Our mechanism and calculated free energy barrier for the reaction, 64.9 kJ mol^- 1, are in good agreement with those predicted from experiment. An analysis of quantum chemical descriptors along the reaction pathway indicated a possibly important, yet currently unreported, role of the active site threonine residue, Thr65.

Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate

Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.

Quantum Mechanics/Molecular Mechanics Studies of the Mechanism of Cysteine Proteases Inhibition by Dipeptidyl Nitroalkenes

In this work a computational study of the mechanism of inhibition of cruzain, rhodesain, and cathepsin L cysteine proteases by the dipeptidyl nitroalkene Cbz-Phe-Ala-CH=CH-NO₂ has been carried out by means of molecular dynamics simulations with hybrid QM/MM potentials. The free-energy surfaces confirmed that the inhibition takes place by the formation of a covalent bond between the protein and the β-carbon atom of the inhibitor. According to the results, the tested inhibitor should be a much more efficient inhibitor of cruzain than of rhodesain, and little activity would be expected against cathepsin L, in total correspondence with the available experimental data. The origin of these differences may lie in the different stabilizing electrostatic interactions established between the inhibitor and the residues of the active site and S2 pocket of these enzymes. These results may be useful for the rational design of new dipeptidyl nitroalkenes with higher and more selective inhibitory activity against cysteine proteases.

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.

QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra

Cyanobacteriochromes are compact and spectrally diverse photoreceptor proteins that are promising candidates for biotechnological applications. Computational studies can contribute to an understanding at a molecular level of their wide spectral tuning and diversity. In this contribution, we benchmark methods to model a 110 nm shift in the UV/Vis absorption spectrum from a red- to a green-absorbing form of the cyanobacteriochrome Slr1393g3. Based on an assessment of semiempirical methods to describe the chromophore geometries of both forms in vacuo, we find that DFTB2+D leads to structures that are the closest to the reference method. The benchmark of the excited state calculations is based on snapshots from quantum mechanics/molecular mechanics molecular dynamics simulations. In our case, the methods RI-ADC(2) and sTD-DFT based on CAM-B3LYP ground state calculations perform the best, whereas no functional can be recommended to simulate the absorption spectra of both forms with time-dependent density functional theory. Furthermore, the difference in absorption for the lowest energy absorption maxima of both forms can already be modelled with optimized structures, but sampling is required to improve the shape of the absorption bands of both forms, in particular for the second band. This benchmark study can guide further computational studies, as it assesses essential components of a protocol to model the spectral tuning of both cyanobacteriochromes and the related phytochromes.

Experimental study and computational modelling of cruzain cysteine protease inhibition by dipeptidyl nitriles

Chagas disease affects millions of people in Latin America. This disease is caused by the protozoan parasite Trypanossoma cruzi. The cysteine protease cruzain is a key enzyme for the survival and propagation of this parasite lifecycle. Nitrile-based inhibitors are efficient inhibitors of cruzain that bind by forming a covalent bond with this enzyme. Here, three nitrile-based inhibitors dubbed Neq0409, Neq0410 and Neq0570 were synthesized, and the thermodynamic profile of the bimolecular interaction with cruzain was determined using isothermal titration calorimetry (ITC). The result suggests the inhibition process is enthalpy driven, with a detrimental contribution of entropy. In addition, we have used hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) and Molecular Dynamics (MD) simulations to investigate the reaction mechanism of reversible covalent modification of cruzain by Neq0409, Neq0410 and Neq0570. The computed free energy profile shows that the nucleophilic attack of Cys25 on the carbon C1 of inhibitiors and the proton transfer from His162 to N1 of the dipeptidyl nitrile inhibitor take place in a single step. The calculated free energy of the inhibiton reaction is in agreement with covalent experimental binding. Altogether, the results reported here suggests that nitrile-based inhibitors are good candidates for the development of reversible covalent inhibitors of cruzain and other cysteine proteases.

Studying the phosphoryl transfer mechanism of the E. coli phosphofructokinase-2: from X-ray structure to quantum mechanics/molecular mechanics simulations

Phosphofructokinases catalyze the ATP-dependent phosphorylation of fructose-6-phosphate and they are highly regulated.

Phosphofructokinases (Pfks) catalyze the ATP-dependent phosphorylation of fructose-6-phosphate (F6P) and they are regulated in a wide variety of organisms. Although numerous aspects of the kinetics and regulation have been characterized for Pfks, the knowledge about the mechanism of the phosphoryl transfer reaction and the transition state lags behind. In this work, we describe the X-ray crystal structure of the homodimeric Pfk-2 from E. coli, which contains products in one site and reactants in the other, as well as an additional ATP molecule in the inhibitory allosteric site adjacent to the reactants. This complex was previously predicted when studying the kinetic mechanism of ATP inhibition. After removing the allosteric ATP, molecular dynamic (MD) simulations revealed conformational changes related to domain packing, as well as stable interactions of Lys27 and Asp256 with donor (ATP) and acceptor (fructose-6-) groups, and of Asp166 with Mg²⁺. The phosphoryl transfer reaction mechanism catalyzed by Pfk-2 was investigated through Quantum Mechanics/Molecular Mechanics (QM/MM) simulations using a combination of the string method and a path-collective variable for the exploration of its free energy surface. The calculated activation free energies showed that a dissociative mechanism, occurring with a metaphosphate intermediate formation followed by a proton transfer to Asp256, is more favorable than an associative one. The structural analysis reveals the role of Asp256 acting as a catalytic base and Lys27 stabilizing the transition state of the dissociative mechanism.

Semi-Empirical Born-Oppenheimer Molecular Dynamics (SEBOMD) within the Amber Biomolecular Package

Semi-empirical quantum methods from the neglect of differential diatomic overlap (NDDO) family such as MNDO, AM1, or PM3 are fast albeit approximate quantum methods. By combining them with linear scaling methods like the divide & conquer (D&C) method, it is possible to quickly evaluate the energy of systems containing hundreds to thousands of atoms. We here present our implementation in the Amber biomolecular package of a SEBOMD module that provides a way to run semi-empirical Born-Oppenheimer molecular dynamics. At each step of a SEBOMD, a fully converged self-consistent field (SCF) calculation is performed to obtain the semiempirical quantum potential energy of a molecular system encaged or not in periodic boundary conditions. We describe the implementation and the features of our SEBOMD implementation. We show the requirements to conserve the total energy in NVE simulations, and how to accelerate SCF convergence through density matrix extrapolation. Specific ways of handling periodic boundary conditions using mechanical embedding or electrostatic embedding through a tailored quantum Ewald summation is developed. The parallel performance of SEBOMD simulations using the D&C scheme are presented for liquid water systems of various sizes, and a comparison between the traditional full diagonalization scheme and the D&C approach for the reproduction of the structure of liquid water illustrates the potentiality of SEBOMD to simulate molecular systems containing several hundreds of atoms for hundreds of picoseconds with a quantum mechanical potential in a reasonable amount of CPU time.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

Intermolecular interactions in the condensed phase: Evaluation of semi-empirical quantum mechanical methods

To facilitate further development of approximate quantum mechanical methods for condensed phase applications, we present a new benchmark dataset of intermolecular interaction energies in the solution phase for a set of 15 dimers, each containing one charged monomer. The reference interaction energy in solution is computed via a thermodynamic cycle that integrates dimer binding energy in the gas phase at the coupled cluster level and solute-solvent interaction with density functional theory; the estimated uncertainty of such calculated interaction energy is ±1.5 kcal/mol. The dataset is used to benchmark the performance of a set of semi-empirical quantum mechanical (SQM) methods that include DFTB3-D3, DFTB3/CPE-D3, OM2-D3, PM6-D3, PM6-D3H+, and PM7 as well as the HF-3c method. We find that while all tested SQM methods tend to underestimate binding energies in the gas phase with a root-mean-squared error (RMSE) of 2-5 kcal/mol, they overestimate binding energies in the solution phase with an RMSE of 3-4 kcal/mol, with the exception of DFTB3/CPE-D3 and OM2-D3, for which the systematic deviation is less pronounced. In addition, we find that HF-3c systematically overestimates binding energies in both gas and solution phases. As most approximate QM methods are parametrized and evaluated using data measured or calculated in the gas phase, the dataset represents an important first step toward calibrating QM based methods for application in the condensed phase where polarization and exchange repulsion need to be treated in a balanced fashion.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Quantum mechanics/molecular mechanics studies of the mechanism of cysteine protease inhibition by peptidyl-2,3-epoxyketones

Cysteine proteases are the most abundant proteases in parasitic protozoa and they are essential enzymes to the life cycle of several of them, thus becoming attractive therapeutic targets for the development of new inhibitors. In this paper, a computational study of the inhibition mechanism of cysteine protease by dipeptidyl-2,3-epoxyketone Cbz-Phe-Hph-(S), a recently proposed inhibitor, has been carried out by means of molecular dynamics (MD) simulations with hybrid QM/MM potentials. The computed free energy surfaces of the inhibition mechanism of cysteine proteases by peptidyl epoxyketones showing how the activation of the epoxide ring and the attack of Cys25 on either C2 or C3 atoms take place in a concerted manner. According to our results, the acid species responsible for the protonation of the oxygen atom of the ring would be able to conserve His159, in contrast to previous studies that proposed a water molecule as the activating species. The low activation free energies for the reaction where Cys25 attacks the C2 atom of the epoxide ring (12.1 kcal mol^-1) or to the C3 atom (15.4 kcal mol^-1), together with the high negative reaction energies suggest that the derivatives of peptidyl-2,3-epoxyketones can be used to develop new potent inhibitors for the treatment of Chagas disease.

Mechanistic Insights on Human Phosphoglucomutase Revealed by Transition Path Sampling and Molecular Dynamics Calculations

Human α-phosphoglucomutase 1 (α-PGM) catalyzes the isomerization of glucose-1-phosphate into glucose-6-phosphate (G6P) through two sequential phosphoryl transfer steps with a glucose-1,6-bisphosphate (G16P) intermediate. Given that the release of G6P in the gluconeogenesis raises the glucose output levels, α-PGM represents a tempting pharmacological target for type 2 diabetes. Here, we provide the first theoretical study of the catalytic mechanism of human α-PGM. We performed transition-path sampling simulations to unveil the atomic details of the two catalytic chemical steps, which could be key for developing transition state (TS) analogue molecules with inhibitory properties. Our calculations revealed that both steps proceed through a concerted S_N 2-like mechanism, with a loose metaphosphate-like TS. Even though experimental data suggests that the two steps are identical, we observed noticeable differences: 1) the transition state ensemble has a well-defined TS region and a late TS for the second step, and 2) larger coordinated protein motions are required to reach the TS of the second step. We have identified key residues (Arg23, Ser117, His118, Lys389), and the Mg²⁺ ion that contribute in different ways to the reaction coordinate. Accelerated molecular dynamics simulations suggest that the G16P intermediate may reorient without leaving the enzymatic binding pocket, through significant conformational rearrangements of the G16P and of specific loop regions of the human α-PGM.

Quantum mechanical force fields for condensed phase molecular simulations

Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.

Theoretical Study of the Phosphoryl Transfer Reaction from ATP to Dha Catalyzed by DhaK from Escherichia coli

Protein kinases, representing one of the largest protein families involved in almost all aspects of cell life, have become one of the most important targets for the development of new drugs to be used in, for instance, cancer treatments. In this article an exhaustive theoretical study of the phosphoryl transfer reaction from adenosine triphosphate (ATP) to dihydroxyacetone (Dha) catalyzed by DhaK from Escherichia coli (E. coli) is reported. Two different mechanisms, previously proposed for the phosphoryl transfer from ATP to the hydroxyl side chain of specific serine, threonine, or tyrosine residues, have been explored based on the generation of free energy surfaces (FES) computed with hybrid QM/MM potentials. The results suggest that the substrate-assisted phosphoryl and proton-transfer mechanism is kinetically more favorable than the mechanism where an aspartate would be activating the Dha. Although the details of the mechanisms appear to be dramatically dependent on the level of theory employed in the calculations (PM3/MM, B3LYP:PM3/MM, or B3LYP/MM), the transition states (TSs) for the phosphoryl transfer step appear to be described as a concerted step with different degrees of synchronicity in the breaking and forming bonds process in both explored mechanisms. Residues of the active site belonging to different subunits of the protein, such as Gly78B, Thr79A, Ser80A, Arg178B, and one Mg²⁺ cation, would be stabilizing the transferred phosphate in the TS. Asp109A would have a structural role by posing the Dha and other residues of the active site in the proper orientation. The information derived from our calculations not only reveals the role of the enzyme and the particular residues of its active site, but it can assist in the rational design of new more specific inhibitors.

A Multidimensional B-Spline Correction for Accurate Modeling Sugar Puckering in QM/MM Simulations

The computational efficiency of approximate quantum mechanical methods allows their use for the construction of multidimensional reaction free energy profiles. It has recently been demonstrated that quantum models based on the neglect of diatomic differential overlap (NNDO) approximation have difficulty modeling deoxyribose and ribose sugar ring puckers and thus limit their predictive value in the study of RNA and DNA systems. A method has been introduced in our previous work to improve the description of the sugar puckering conformational landscape that uses a multidimensional B-spline correction map (BMAP correction) for systems involving intrinsically coupled torsion angles. This method greatly improved the adiabatic potential energy surface profiles of DNA and RNA sugar rings relative to high-level ab initio methods even for highly problematic NDDO-based models. In the present work, a BMAP correction is developed, implemented, and tested in molecular dynamics simulations using the AM1/d-PhoT semiempirical Hamiltonian for biological phosphoryl transfer reactions. Results are presented for gas-phase adiabatic potential energy surfaces of RNA transesterification model reactions and condensed-phase QM/MM free energy surfaces for nonenzymatic and RNase A-catalyzed transesterification reactions. The results show that the BMAP correction is stable, efficient, and leads to improvement in both the potential energy and free energy profiles for the reactions studied, as compared with ab initio and experimental reference data. Exploration of the effect of the size of the quantum mechanical region indicates the best agreement with experimental reaction barriers occurs when the full CpA dinucleotide substrate is treated quantum mechanically with the sugar pucker correction.

Unraveling the Addition-Elimination Mechanism of EPSP Synthase through Computer Modeling

Enolpyruvyl transfer from phosphoenolpyruvate (PEP) to the hydroxyl group of shikimate-5-OH-3-phosphate (S3P) is catalyzed by 5-enolpyruvylshikimate 3-phosphate (EPSP) synthase in a reaction that involves breaking the C-O bond of PEP. Catalysis involves an addition-elimination mechanism with the formation of a tetrahedral intermediate (THI). Experiments have elucidated the mechanism of THI formation and breakdown. However, the catalytic action of EPSP synthase and the individual roles of catalytic residues Asp313 and Glu341 remains unclear. We have used a hybrid quantum mechanical/molecular mechanical (QM/MM) approach to explore the free energy surface in a reaction catalyzed by EPSP synthase. The Glu341 was the most favorable acid/base catalyst. Our results indicate that the protonation of PEP C3 precedes the nucleophilic attack on PEP C2 in the addition mechanism. Also, the breaking of the C-O bond of THI to form an EPSP cation intermediate must occur before proton transfer from PEP C3 to Glu341 in the elimination mechanism. Analysis of the FES supports cationic intermediate formation during the reaction catalyzed by EPSP synthase. Finally, the computational model indicates a proton transfer shift (Hammond shift) from Glu341 to C3 for an enzyme-based reaction with the shifted transition state, earlier than in the reference reaction in water.

Acceleration of Semiempirical QM/MM Methods through Message Passage Interface (MPI), Hybrid MPI/Open Multiprocessing, and Self-Consistent Field Accelerator Implementations

The strategy and implementation of scalable and efficient semiempirical (SE) QM/MM methods in CHARMM are described. The serial version of the code was first profiled to identify routines that required parallelization. Afterward, the code was parallelized and accelerated with three approaches. The first approach was the parallelization of the entire QM/MM routines, including the Fock matrix diagonalization routines, using the CHARMM message passage interface (MPI) machinery. In the second approach, two different self-consistent field (SCF) energy convergence accelerators were implemented using density and Fock matrices as targets for their extrapolations in the SCF procedure. In the third approach, the entire QM/MM and MM energy routines were accelerated by implementing the hybrid MPI/open multiprocessing (OpenMP) model in which both the task- and loop-level parallelization strategies were adopted to balance loads between different OpenMP threads. The present implementation was tested on two solvated enzyme systems (including <100 QM atoms) and an S_N2 symmetric reaction in water. The MPI version exceeded existing SE QM methods in CHARMM, which include the SCC-DFTB and SQUANTUM methods, by at least 4-fold. The use of SCF convergence accelerators further accelerated the code by ∼12-35% depending on the size of the QM region and the number of CPU cores used. Although the MPI version displayed good scalability, the performance was diminished for large numbers of MPI processes due to the overhead associated with MPI communications between nodes. This issue was partially overcome by the hybrid MPI/OpenMP approach which displayed a better scalability for a larger number of CPU cores (up to 64 CPUs in the tested systems).

Understanding in-line probing experiments by modeling cleavage of nonreactive RNA nucleotides

Ribonucleic acid (RNA) is involved in many regulatory and catalytic processes in the cell. The function of any RNA molecule is intimately related with its structure. In-line probing experiments provide valuable structural data sets for a variety of RNAs and are used to characterize conformational changes in riboswitches. However, the structural determinants that lead to differential reactivities in unpaired nucleotides have not been investigated yet. In this work, we used a combination of theoretical approaches, i.e., classical molecular dynamics simulations, multiscale quantum mechanical/molecular mechanical calculations, and enhanced sampling techniques in order to compute and interpret the differential reactivity of individual residues in several RNA motifs, including members of the most important GNRA and UNCG tetraloop families. Simulations on the multinanosecond timescale are required to converge the related free-energy landscapes. The results for uGAAAg and cUUCGg tetraloops and double helices are compared with available data from in-line probing experiments and show that the introduced technique is able to distinguish between nucleotides of the uGAAAg tetraloop based on their structural predispositions toward phosphodiester backbone cleavage. For the cUUCGg tetraloop, more advanced ab initio calculations would be required. This study is the first attempt to computationally classify chemical probing experiments and paves the way for an identification of tertiary structures based on the measured reactivity of nonreactive nucleotides.

Perspective: Quantum mechanical methods in biochemistry and biophysics

In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.