QM/MM free energy simulations: recent progress and challenges

Machine learning in molecular biophysics: Protein allostery, multi-level free energy simulations, and lipid phase transitions

Machine learning (ML) techniques have been making major impacts on all areas of science and engineering, including biophysics. In this review, we discuss several applications of ML to biophysical problems based on our recent research. The topics include the use of ML techniques to identify hotspot residues in allosteric proteins using deep mutational scanning data and to analyze how mutations of these hotspots perturb co-operativity in the framework of a statistical thermodynamic model, to improve the accuracy of free energy simulations by integrating data from different levels of potential energy functions, and to determine the phase transition temperature of lipid membranes. Through these examples, we illustrate the unique value of ML in extracting patterns or parameters from complex data sets, as well as the remaining limitations. By implementing the ML approaches in the context of physically motivated models or computational frameworks, we are able to gain a deeper mechanistic understanding or better convergence in numerical simulations. We conclude by briefly discussing how the introduced models can be further expanded to tackle more complex problems.

Fine-tuning molecular mechanics force fields to experimental free energy measurements

Alchemical free energy methods using molecular mechanics (MM) force fields are essential tools for predicting thermodynamic properties of small molecules, especially via free energy calculations that can estimate quantities relevant for drug discovery such as affinities, selectivities, the impact of target mutations, and ADMET properties. While traditional MM forcefields rely on hand-crafted, discrete atom types and parameters, modern approaches based on graph neural networks (GNNs) learn continuous embedding vectors that represent chemical environments from which MM parameters can be generated. Excitingly, GNN parameterization approaches provide a fully end-to-end differentiable model that offers the possibility of systematically improving these models using experimental data. In this study, we treat a pretrained GNN force field-here, espaloma-0.3.2-as a foundation simulation model and fine-tune its charge model using limited quantities of experimental hydration free energy data, with the goal of assessing the degree to which this can systematically improve the prediction of other related free energies. We demonstrate that a highly efficient "one-shot fine-tuning" method using an exponential (Zwanzig) reweighting free energy estimator can improve prediction accuracy without the need to resimulate molecular configurations. To achieve this "one-shot" improvement, we demonstrate the importance of using effective sample size (ESS) regularization strategies to retain good overlap between initial and fine-tuned force fields. Moreover, we show that leveraging low-rank projections of embedding vectors can achieve comparable accuracy improvements as higher-dimensional approaches in a variety of data-size regimes. Our results demonstrate that linearly-perturbative fine-tuning of foundation model electrostatic parameters to limited experimental data offers a cost-effective strategy that achieves state-of-the-art performance in predicting hydration free energies on the FreeSolv dataset.

Catalytic Role of Methanol in Anodic Coupling Reactions Involving Alcohol Trapping of Cation Radicals

In anodic electrosynthesis, cation radicals are often key intermediates that can be highly susceptible to nucleophilic attack and/or deprotonation, with the selectivity of competing pathways dictating product yield. In this work, we computationally investigate the role of methanol in alcohol trapping of enol ether cation radicals for which substantial modulation of the reaction yield by the solvent environment was previously observed. Reaction free energies computed for intramolecular coupling unequivocally demonstrate that the key intramolecular alcohol attack on the oxidized enol ether group is catalyzed by methanol, proceeding through overall second-order kinetics. Methanol complexation with the formed oxonium ion group gives rise to a "Zundel-like", shared proton conformation, providing a critical driving force for the intramolecular alcohol attack. Free energies computed for methanol solvent attack of enol ether cation radicals demonstrate an analogous mechanism and overall third-order kinetics, due to similar complexation from a secondary methanol molecule to form the "Zundel-like", shared proton conformation. As catalyzed by methanol, both intramolecular alcohol attack and methanol attack on the oxidized enol ether group are barrierless or low-barrier reactions, with kinetic competition dictated by the conformational free energy profile of the cation radical substrate and the difference in reaction rate orders.

Protocols for Metallo- and Serine-β-Lactamase Free Energy Predictions: Insights from Cross-Class Inhibitors

While relative binding free energy (RBFE) calculations using alchemical methods are routinely carried out for many pharmaceutically relevant protein targets, challenges remain. For example, open-source tools do not support the easy setup and simulation of metalloproteins, particularly when ligands directly coordinate to the metal site. Here, we evaluate the performance of RBFE methods for KPC-2, a serine-β-lactamase (SBL), and two nonbonded metal parameter setups for VIM-2, a metallo-β-lactamase (MBL) with two active site zinc ions. We tested two different ways of modeling the ligand-zinc interactions. First, a restraint-based approach, in which FF14SB zinc parameters are combined with harmonic restraints between the zincs and their coordinating residues. The second approach uses an upgraded Amber force field (UAFF) for zinc-metalloproteins with adjusted partial charges and nonbonded terms of zinc-coordinating residues. Molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) simulations show that the crystallographically observed zinc coordination is not retained in MM simulations with either zinc parameter set for a series of known phosphonic acid-based inhibitors bound to VIM-2. These phosphonic acid-based inhibitors exhibit known cross-class affinity for SBLs and MBLs and serve as a benchmark for RBFE calculations for VIM-2, after validation with KPC-2. The KPC-2 free energy of binding estimates are within expected literature accuracies for the ligand series with a mean absolute error of 0.45 0.28 0.66 kcal/mol and a Pearson's correlation coefficient of 0.93 0.85 0.98 . For VIM-2, the UAFF approach has improved correlation from 0.55 - 0.04 0.88 to 0.78 0.38 0.92 , compared to the restraint approach. The presented strategies for handling ligands coordinating to metal sites highlight that simple metal parameter models can provide some predictive free energy estimates for metalloprotein-ligand systems, but leave room for improvement in their ease of use, modeling of coordination sites and as a result, their accuracy.

Nuclear Quantum Effects in Quantum Mechanical/Molecular Mechanical Free Energy Simulations of Ribonucleotide Reductase

The enzyme ribonucleotide reductase plays a critical role in DNA synthesis and repair. Its mechanism requires long-range radical transfer through a series of proton-coupled electron transfer (PCET) steps. Nuclear quantum effects such as zero-point energy, proton delocalization, and hydrogen tunneling are known to be important in PCET. We present a strategy for efficiently incorporating nuclear quantum effects into multidimensional free energy surfaces and real-time dynamical simulations for condensed-phase systems such as enzymes. This strategy is based on the nuclear-electronic orbital (NEO) method, which treats specified protons quantum mechanically on the same level as the electrons. NEO density functional theory (NEO-DFT) is combined with the quantum mechanical/molecular mechanical finite temperature string method with umbrella sampling via a simple reweighting procedure. Application of this strategy to PCET between two tyrosines, Y731 and Y730, in ribonucleotide reductase illustrates that nuclear quantum effects could either raise or lower the free energy barrier, leading to a range of possible kinetic isotope effects. Real-time time-dependent DFT (RT-NEO-TDDFT) simulations highlight nuclear-electronic quantum dynamics. These approaches enable the incorporation of nuclear quantum effects into a wide range of chemically and biologically important processes.

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.

Insights and Challenges in Correcting Force Field Based Solvation Free Energies Using a Neural Network Potential

We present a comprehensive study investigating the potential gain in accuracy for calculating absolute solvation free energies (ASFE) using a neural network potential to describe the intramolecular energy of the solute. We calculated the ASFE for most compounds from the FreeSolv database using the Open Force Field (OpenFF) and compared them to earlier results obtained with the CHARMM General Force Field (CGenFF). By applying a nonequilibrium (NEQ) switching approach between the molecular mechanics (MM) description (either OpenFF or CGenFF) and the neural net potential (NNP)/MM level of theory (using ANI-2x as the NNP potential), we attempted to improve the accuracy of the calculated ASFEs. The predictive performance of the results did not change when this approach was applied to all 589 small molecules in the FreeSolv database that ANI-2x can describe. When selecting a subset of 156 molecules, focusing on compounds where the force fields performed poorly, we saw a slight improvement in the root-mean-square error (RMSE) and mean absolute error (MAE). The majority of our calculations utilized unidirectional NEQ protocols based on Jarzynski's equation. Additionally, we conducted bidirectional NEQ switching for a subset of 156 solutes. Notably, only a small fraction (10 out of 156) exhibited statistically significant discrepancies between unidirectional and bidirectional NEQ switching free energy estimates.

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

The catalytic mechanism of the RNA methyltransferase METTL3

The complex of methyltransferase-like proteins 3 and 14 (METTL3-14) is the major enzyme that deposits N6-methyladenosine (m6A) modifications on messenger RNA (mRNA) in humans. METTL3-14 plays key roles in various biological processes through its methyltransferase (MTase) activity. However, little is known about its substrate recognition and methyl transfer mechanism from its cofactor and methyl donor S-adenosylmethionine (SAM). Here, we study the MTase mechanism of METTL3-14 by a combined experimental and multiscale simulation approach using bisubstrate analogues (BAs), conjugates of a SAM-like moiety connected to the N6-atom of adenosine. Molecular dynamics simulations based on crystal structures of METTL3-14 with BAs suggest that the Y406 side chain of METTL3 is involved in the recruitment of adenosine and release of m6A. A crystal structure with a BA representing the transition state of methyl transfer shows a direct involvement of the METTL3 side chains E481 and K513 in adenosine binding which is supported by mutational analysis. Quantum mechanics/molecular mechanics (QM/MM) free energy calculations indicate that methyl transfer occurs without prior deprotonation of adenosine-N6. Furthermore, the QM/MM calculations provide further support for the role of electrostatic contributions of E481 and K513 to catalysis. The multidisciplinary approach used here sheds light on the (co)substrate binding mechanism, catalytic step, and (co)product release, and suggests that the latter step is rate-limiting for METTL3. The atomistic information on the substrate binding and methyl transfer reaction of METTL3 can be useful for understanding the mechanisms of other RNA MTases and for the design of transition state analogues as their inhibitors.

Development of a QM/MM(ABEEM) method for the deprotonation of neutral and cation radicals in the G-tetrad and GGX(8-oxo-G) tetrad

The rapid deprotonation of G˙+ in the DNA strand impedes positive charge (hole) transfer, whereas the slow deprotonation rate of G˙+ in the G-tetrad makes it a more suitable carrier for hole conduction. The QM/MM(ABEEM) combined method, which involves the integration of QM and the ABEEM polarizable force field (ABEEM PFF), was developed to investigate the deprotonation of neutral and cation free radicals in the G-tetrad and GGX(8-oxo-G) tetrad (xanthine and 8-oxoguanine dual substituted G-tetrad). By incorporating valence-state electronegativity piecewise functions χ*(r) and implementing charge local conservation conditions, QM/MM(ABEEM) possesses the advantage of accurately simulating charge transfer and polarization effect during deprotonation. The activation energy calculated by the QM method of X˙ is the lowest among other bases in the GGX(8-oxo-G) tetrad, which is supported by the computation of the average electronegativity calculated by ABEEM PFF. By utilizing QM/MM(ABEEM) with a two-way free energy perturbation method, the deprotonation activation energy of X˙ in the GGX(8-oxo-G) tetrad is determined to be 33.0 ± 2.1 kJ mol-1, while that of G˙+ in the G-tetrad is 20.7 ± 0.6 kJ mol-1, consistent with the experimental measurement of 20 ± 1.0 kJ mol-1. These results manifest that X˙ in the GGX(8-oxo-G) tetrad exhibits a slower deprotonation rate than G˙+ in the G-tetrad, suggesting that the GGX(8-oxo-G) tetrad may serve as a more favorable hole transport carrier. Furthermore, the unequal average electronegativities of bases in the GGX(8-oxo-G) tetrad impede the deprotonation rate. This study provides a potential foundation for investigating the microscopic mechanism of DNA electronic devices.

The catalytic mechanism of the RNA methyltransferase METTL3

The complex of methyltransferase-like proteins 3 and 14 (METTL3-14) is the major enzyme that deposits N6-methyladenosine (m6A) modifications on mRNA in humans. METTL3-14 plays key roles in various biological processes through its methyltransferase (MTase) activity. However, little is known about its substrate recognition and methyl transfer mechanism from its cofactor and methyl donor S-adenosylmethionine (SAM). Here, we study the MTase mechanism of METTL3-14 by a combined experimental and multiscale simulation approach using bisubstrate analogues (BAs), conjugates of a SAM-like moiety connected to the N6-atom of adenosine. Molecular dynamics simulations based on crystal structures of METTL3-14 with BAs suggest that the Y406 side chain of METTL3 is involved in the recruitment of adenosine and release of m6A. A crystal structure with a bisubstrate analogue representing the transition state of methyl transfer shows a direct involvement of the METTL3 side chains E481 and K513 in adenosine binding which is supported by mutational analysis. Quantum mechanics/molecular mechanics (QM/MM) free energy calculations indicate that methyl transfer occurs without prior deprotonation of adenosine-N6. Furthermore, the QM/MM calculations provide further support for the role of electrostatic contributions of E481 and K513 to catalysis. The multidisciplinary approach used here sheds light on the (co)substrate binding mechanism, catalytic step, and (co)product release catalysed by METTL3, and suggests that the latter step is rate-limiting. The atomistic information on the substrate binding and methyl transfer reaction of METTL3 can be useful for understanding the mechanisms of other RNA MTases and for the design of transition state analogues as their inhibitors.

Accurate and Efficient Multilevel Free Energy Simulations with Neural Network-Assisted Enhanced Sampling

Free energy differences (ΔF) are essential to quantitative characterization and understanding of chemical and biological processes. Their direct estimation with an accurate quantum mechanical potential is of great interest and yet impractical due to high computational cost and incompatibility with typical alchemical free energy protocols. One promising solution is the multilevel free energy simulation in which the estimate of ΔF at an inexpensive low level of theory is combined with the correction toward a higher level of theory. The poor configurational overlap generally expected between the two levels of theory, however, presents a major challenge. We overcome this challenge by using a deep neural network model and enhanced sampling simulations. An adversarial autoencoder is used to identify a low-dimensional (latent) space that compactly represents the degrees of freedom that encode the distinct distributions at the two levels of theory. Enhanced sampling in this latent space is then used to drive the sampling of configurations that predominantly contribute to the free energy correction. Results for both gas phase and condensed phase systems demonstrate that this data-driven approach offers high accuracy and efficiency with great potential for scalability to complex systems.

Emerging Trends of Computational Chemistry and Molecular Modeling in Froth Flotation: A Review

Froth flotation is the most versatile process in mineral beneficiation, extensively used to concentrate a wide range of minerals. This process comprises mixtures of more or less liberated minerals, water, air, and various chemical reagents, involving a series of intermingled multiphase physical and chemical phenomena in the aqueous environment. Today's main challenge facing the froth flotation process is to gain atomic-level insights into the properties of its inherent phenomena governing the process performance. While it is often challenging to determine these phenomena via trial-and-error experimentations, molecular modeling approaches not only elicit a deeper understanding of froth flotation but can also assist experimental studies in saving time and budget. Thanks to the rapid development of computer science and advances in high-performance computing (HPC) infrastructures, theoretical/computational chemistry has now matured enough to successfully and gainfully apply to tackle the challenges of complex systems. In mineral processing, however, advanced applications of computational chemistry are increasingly gaining ground and demonstrating merit in addressing these challenges. Accordingly, this contribution aims to encourage mineral scientists, especially those interested in rational reagent design, to become familiarized with the necessary concepts of molecular modeling and to apply similar strategies when studying and tailoring properties at the molecular level. This review also strives to deliver the state-of-the-art integration and application of molecular modeling in froth flotation studies to assist either active researchers in this field to disclose new directions for future research or newcomers to the field to initiate innovative works.

In silico characterization of nanoparticles

Nanoparticles (NPs) make for intriguing heterogeneous catalysts due to their large active surface area and excellent and often size-dependent catalytic properties that emerge from a multitude of chemically different surface reaction sites. NP catalysts are, in principle, also highly tunable: even small changes to the NP size or surface facet composition, doping with heteroatoms, or changes of the supporting material can significantly alter their physicochemical properties. Because synthesis of size- and shape-controlled NP catalysts is challenging, the ability to computationally predict the most favorable NP structures for a catalytic reaction of interest is an in-demand skill that can help accelerate and streamline the material optimization process. Fundamentally, simulations of NP model systems present unique challenges to computational scientists. Not only must considerable methodological hurdles be overcome in performing calculations with hundreds to thousands of atoms while retaining appropriate accuracy to be able to probe the desired properties. Also, the data generated by simulations of NPs are typically more complex than data from simulations of, for example, single crystal surface models, and therefore often require different data analysis strategies. To this end, the present work aims to review analytical methods and data analysis strategies that have proven useful in extracting thermodynamic trends from NP simulations.

MoBioTools: A toolkit to setup quantum mechanics/molecular mechanics calculations

We present a toolkit that allows for the preparation of QM/MM input files from a conformational ensemble of molecular geometries. The package is currently compatible with trajectory and topology files in Amber, CHARMM, GROMACS and NAMD formats, and has the possibility to generate QM/MM input files for Gaussian (09 and 16), Orca (≥4.0), NWChem and (Open)Molcas. The toolkit can be used in command line, so that no programming experience is required, although it presents some features that can also be employed as a python application programming interface. We apply the toolkit in four situations in which different electronic-structure properties of organic molecules in the presence of a solvent or a complex biological environment are computed: the reduction potential of the nucleobases in acetonitrile, an energy decomposition analysis of tyrosine interacting with water, the absorption spectrum of an azobenzene derivative integrated into a voltage-gated ion channel, and the absorption and emission spectra of the luciferine/luciferase complex. These examples show that the toolkit can be employed in a manifold of situations for both the electronic ground state and electronically excited states. It also allows for the automatic correction of the active space in the case of CASSCF calculations on an ensemble of geometries, as it is shown for the azobenzene derivative photoswitch case.

Recent advances on graphyne and its family members as membrane materials for water purification and desalination

Graphyne and its family members (GFMs) are allotropes of carbon (a class of 2D materials) having unique properties in form of structures, pores and atom hybridizations. Owing to their unique properties, GFMs have been widely utilized in various practical and theoretical applications. In the past decade, GFMs have received considerable attention in the area of water purification and desalination, especially in theoretical and computational aspects. More recently, GFMs have shown greater prospects in achieving optimal separation performance than the experimentally derived commercial polyamide membranes. In this review, recent theoretical and computational advances made in the GFMs research as it relates to water purification and desalination are summarized. Brief details on the properties of GFMs and the commonly used computational methods were described. More specifically, we systematically reviewed the various computational approaches employed with emphasis on the predicted permeability and selectivity of the GFM membranes. Finally, the current challenges limiting their large-scale practical applications coupled with the possible research directions for overcoming the challenges are proposed.

Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications

Computational chemistry is an essential tool in the pharmaceutical industry. Quantum computing is a fast evolving technology that promises to completely shift the computational capabilities in many areas of chemical research by bringing into reach currently impossible calculations. This perspective illustrates the near-future applicability of quantum computation of molecules to pharmaceutical problems. We briefly summarize and compare the scaling properties of state-of-the-art quantum algorithms and provide novel estimates of the quantum computational cost of simulating progressively larger embedding regions of a pharmaceutically relevant covalent protein-drug complex involving the drug Ibrutinib. Carrying out these calculations requires an error-corrected quantum architecture that we describe. Our estimates showcase that recent developments on quantum phase estimation algorithms have dramatically reduced the quantum resources needed to run fully quantum calculations in active spaces of around 50 orbitals and electrons, from estimated over 1000 years using the Trotterization approach to just a few days with sparse qubitization, painting a picture of fast and exciting progress in this nascent field.

Hydrogen Bond Thermodynamics in Aqueous Acid Solutions: A Combined DFT and Classical Force-Field Approach

The thermodynamics of hydrogen bonds in aqueous and acidic solutions significantly impacts the kinetics and thermodynamics of acid reaction chemistry. We utilize in this work a multiscale approach, combining density functional theory (DFT) with classical molecular dynamics (MD) to model hydrogen bond thermodynamics in an acidic solution. Using thermodynamic cycles, we split the solution phase free energy into its gas phase counterpart plus solvation free energies. We validate this DFT/MD approach by calculating the aqueous phase hydrogen bond free energy between two water molecules (H₂O-···-H₂O), the free energy to transform an H₃O⁺ cation into an H₅O₂⁺ cation, and the hydrogen bond free energy of protonated water clusters (H₃O⁺-···-H₂O and H₅O₂⁺-···-H₂O). The computed equilibrium hydrogen bond free energy of H₂O-···-H₂O is remarkably accurate, especially considering the large individual contributions to the thermodynamic cycle. Turning to cations, we find the ion to be more stable than H₃O⁺ by roughly 1-2 k_BT. This small free energy difference allows for thermal fluctuation between the two idealized motifs, consistent with spectroscopic and simulation studies. Lastly, hydrogen bonding free energies between either H⁺ cation and H₂O in solution were found to be stronger than between two H₂O, though much less so than in vacuum because of dielectric screening in solution. Altogether, our results suggest the DFT/MD approach is promising for application in modeling hydrogen bonding and proton transfer thermodynamics in condensed phases.

Glucosylation mechanism of resveratrol through the mutant Q345F sucrose phosphorylase from the organism Bifidobacterium adolescentis: a computational study

Mainly due to their great antioxidant, anti-inflammatory and anticancer capacities, natural polyphenolic compounds have many properties with important applications in the food, cosmetic and pharmaceutical industries. Unfortunately, these molecules have very low water solubility and bioavailability. Glucosylation of polyphenols is an excellent alternative to overcome these drawbacks. Specifically, for the natural polyphenol resveratrol this process is very inefficiently performed by the native enzyme sucrose phosphorylase (BaSP) from the organism Bifidobacterium adolescentis (4%). However, the Q345F point mutation of the sucrose phosphorylase (BaSP Q345F) has been shown to achieve 97% monoglucosylation for the same substrate and the mechanism is still unknown. This report presents an analysis of MD simulations performed with the BaSP Q345F and BaSP systems in complex with resveratrol monoglucoside, followed by a study of the transglucosylation reaction of the mutant enzyme BaSP Q345F with resveratrol through the QM/MM hybrid method. With respect to the MD simulations, both protein structures showed greater similarity to the phosphate-binding conformation, and a larger active site and conformational changes in certain structures were found for the mutant system compared with the native enzyme; all this is in agreement with experimental data. With regard to the QM/MM calculations, the structure of an oxocarbenium ion-like transition state and the minimum energy adiabatic path (MEP) that connects the reactants with the products were obtained with a 20.3 kcal mol^-1 energy barrier, which fits within the known experimental range for this type of enzyme. Finally, the analyses performed along the MEP suggest a concerted but asynchronous mechanism. In particular, they show that the interactions involving the residues of the catalytic triad (Asp¹⁹², Glu²³², and Asp²⁹⁰) together with two water molecules at the active site strongly contribute to the stabilization of the transition state. The understanding of this glucosylation mechanism of the polyphenol resveratrol carried out by the mutant sucrose phosphorylase enzyme presented in this work could serve as the basis for subsequent studies on related carbohydrate-active enzymes.

Optimizing the Calculation of Free Energy Differences in Nonequilibrium Work SQM/MM Switching Simulations

A key step during indirect alchemical free energy simulations using quantum mechanical/molecular mechanical (QM/MM) hybrid potential energy functions is the calculation of the free energy difference ΔAlow→high between the low level (e.g., pure MM) and the high level of theory (QM/MM). A reliable approach uses nonequilibrium work (NEW) switching simulations in combination with Jarzynski's equation; however, it is computationally expensive. In this study, we investigate whether it is more efficient to use more shorter switches or fewer but longer switches. We compare results obtained with various protocols to reference free energy differences calculated with Crooks' equation. The central finding is that fewer longer switches give better converged results. As few as 200 sufficiently long switches lead to ΔAlow→high values in good agreement with the reference results. This optimized protocol reduces the computational cost by a factor of 40 compared to earlier work. We also describe two tools/ways of analyzing the raw data to detect sources of poor convergence. Specifically, we find it helpful to analyze the raw data (work values from the NEW switching simulations) in a quasi-time series-like manner. Principal component analysis helps to detect cases where one or more conformational degrees of freedom are different at the low and high level of theory.

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

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

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with Quantum Mechanical/Molecular Mechanics (QM/MM) being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g., solvents, if some of them must be included in the QM region, for example, in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will eventually lead to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to an exchange of identical particles. With a careful choice of the biasing potential and the use of a tree algorithm to include only important QM and MM exchanges, we find that the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy, and remarkably, sub-diffusional dynamical quantities in the inner QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

Doubly Polarized QM/MM with Machine Learning Chaperone Polarizability

A major shortcoming of semiempirical (SE) molecular orbital methods is their severe underestimation of molecular polarizability compared with experimental and ab initio (AI) benchmark data. In a combined quantum mechanical and molecular mechanical (QM/MM) treatment of solution-phase reactions, solute described by SE methods therefore tends to generate inadequate electronic polarization response to solvent electric fields, which often leads to large errors in free energy profiles. To address this problem, here we present a hybrid framework that improves the response property of SE/MM methods through high-level molecular-polarizability fitting. Specifically, we place on QM atoms a set of corrective polarizabilities (referred to as chaperone polarizabilities), whose magnitudes are determined from machine learning (ML) to reproduce the condensed-phase AI molecular polarizability along the minimum free energy path. These chaperone polarizabilities are then used in a machinery similar to a polarizable force field calculation to compensate for the missing polarization energy in the conventional SE/MM simulations. Because QM atoms in this treatment host SE wave functions as well as classical polarizabilities, both polarized by MM electric fields, we name this method doubly polarized QM/MM (dp-QM/MM). We demonstrate the new method on the free energy simulations of the Menshutkin reaction in water. Using AM1/MM as a base method, we show that ML chaperones greatly reduce the error in the solute molecular polarizability from 6.78 to 0.03 ų with respect to the density functional theory benchmark. The chaperone correction leads to ∼10 kcal/mol of additional polarization energy in the product region, bringing the simulated free energy profiles to closer agreement with the experimental results. Furthermore, the solute-solvent radial distribution functions show that the chaperone polarizabilities modify the free energy profiles through enhanced solvation corrections when the system evolves from the charge-neutral reactant state to the charge-separated transition and product states. These results suggest that the dp-QM/MM method, enabled by ML chaperone polarizabilities, provides a very physical remedy for the underpolarization problem in SE/MM-based free energy simulations.

Computational investigations of selected enzymes from two iron and α-ketoglutarate-dependent families

DNA alkylation is used as the key epigenetic mark in eukaryotes, however, most alkylation in DNA can result in deleterious effects. Therefore, this process needs to be tightly regulated. The enzymes of the AlkB and Ten-Eleven Translocation (TET) families are members of the Fe and alpha-ketoglutarate-dependent superfamily of enzymes that are tasked with dealkylating DNA and RNA in cells. Members of these families span all species and are an integral part of transcriptional regulation. While both families catalyze oxidative dealkylation of various bases, each has specific preference for alkylated base type as well as distinct catalytic mechanisms. This perspective aims to provide an overview of computational work carried out to investigate several members of these enzyme families including AlkB, ALKB Homolog 2, ALKB Homolog 3 and Ten-Eleven Translocate 2. Insights into structural details, mutagenesis studies, reaction path analysis, electronic structure features in the active site, and substrate preferences are presented and discussed.

O to bR transition in bacteriorhodopsin occurs through a proton hole mechanism

Extensive classical and quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations are used to establish the structural features of the O state in bacteriorhodopsin (bR) and its conversion back to the bR ground state. The computed free energy surface is consistent with available experimental data for the kinetics and thermodynamics of the O to bR transition. The simulation results highlight the importance of the proton release group (PRG, consisting of Glu194/204) and the conserved arginine 82 in modulating the hydration level of the protein cavity. In particular, in the O state, deprotonation of the PRG and downward rotation of Arg82 lead to elevated hydration level and a continuous water network that connects the PRG to the protonated Asp85. Proton exchange through this water network is shown by ∼0.1-μs semiempirical QM/MM free energy simulations to occur through the generation and propagation of a proton hole, which is relayed by Asp212 and stabilized by Arg82. This mechanism provides an explanation for the observation that the D85S mutant of bacteriorhodopsin pumps chloride ions. The electrostatics-hydration coupling mechanism and the involvement of all titration states of water are likely applicable to many biomolecules involved in bioenergetic transduction.

Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force

First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN2 reaction, NH3 + CH3Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B-matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.

Computational Design and Crystal Structure of a Highly Efficient Benzoylecgonine Hydrolase

Benzoylecgonine (BZE) is the major toxic metabolite of cocaine and is responsible for the long-term cocaine-induced toxicity owing to its long residence time in humans. BZE is also the main contaminant following cocaine consumption. Here, we identified the bacterial cocaine esterase (CocE) as a BZE-metabolizing enzyme (BZEase), which can degrade BZE into biological inactive metabolites (ecgonine and benzoic acid). CocE was redesigned by a reactant-state-based enzyme design theory. An encouraging mutant denoted as BZEase2, presented a >400-fold improved catalytic efficiency against BZE compared with wild-type (WT) CocE. In vivo, a single dose of BZEase2 (1 mg kg^-1 , IV) could eliminate nearly all BZE within only two minutes, suggesting the enzyme has the potential for cocaine overdose treatment and BZE elimination in the environment by accelerating BZE clearance. The crystal structure of a designed BZEase was also determined.

Active site dynamics and catalytic mechanism in arabinan hydrolysis catalyzed by GH43 endo-arabinanase from QM/MM molecular dynamics simulation and potential energy surface

The endo-1,5-α-L-arabinanases, belonging to glycoside hydrolase family 43 (GH43), catalyse the hydrolysis of α-1,5-arabinofuranosidic bonds in arabinose-containing polysaccharides. These enzymes are proposed targets for industrial and medical applications. Here, molecular dynamics (MD), potential energy surface and free energy (potential of mean force) simulations are undertaken using hybrid quantum mechanical/molecular mechanical (QM/MM) potentials to understand the active site dynamics, catalytic mechanism and the electrostatic influence of active site residues of the GH43 endo-arabinanase from G. stearothermophilus. The calculated results give support to the single-displacement mechanism proposed for the inverting GH43 enzymes: first a proton is transferred from the general acid E201 to the substrate, followed by a nucleophilic attack by water, activated by the general base D27, on the anomer carbon. A conformational change (²E ↔E₃ ↔ ⁴E) in the -1 sugar ring is observed involving a transition state featuring an oxocarbenium ion character. Residues D87, K106, H271 are highlighted as potential targets for future mutation experiments in order to increase the efficiency of the reaction. To our knowledge, this is the first QM/MM study providing molecular insights into the glycosidic bond hydrolysis of a furanoside substrate by an inverting GH in solution.Communicated by Ramaswamy H. Sarma.

Solvation Induction of Free Energy Barriers of Decarboxylation Reactions in Aqueous Solution from Dual-Level QM/MM Simulations

Carbon dioxide capture, corresponding to the recombination process of decarboxylation reactions of organic acids, is typically barrierless in the gas phase and has a relatively low barrier in aprotic solvents. However, these processes often encounter significant solvent-reorganization-induced barriers in aqueous solution if the decarboxylation product is not immediately protonated. Both the intrinsic stereoelectronic effects and solute-solvent interactions play critical roles in determining the overall decarboxylation equilibrium and free energy barrier. An understanding of the interplay of these factors is important for designing novel materials applied to greenhouse gas capture and storage as well as for unraveling the catalytic mechanisms of a range of carboxy lyases in biological CO₂ production. A range of decarboxylation reactions of organic acids with rates spanning nearly 30 orders of magnitude have been examined through dual-level combined quantum mechanical and molecular mechanical simulations to help elucidate the origin of solvation-induced free energy barriers for decarboxylation and the reverse carboxylation reactions in water.

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.

Computational design of enzymes for biotechnological applications

Enzymes are the natural catalysts that execute biochemical reactions upholding life. Their natural effectiveness has been fine-tuned as a result of millions of years of natural evolution. Such catalytic effectiveness has prompted the use of biocatalysts from multiple sources on different applications, including the industrial production of goods (food and beverages, detergents, textile, and pharmaceutics), environmental protection, and biomedical applications. Natural enzymes often need to be improved by protein engineering to optimize their function in non-native environments. Recent technological advances have greatly facilitated this process by providing the experimental approaches of directed evolution or by enabling computer-assisted applications. Directed evolution mimics the natural selection process in a highly accelerated fashion at the expense of arduous laboratory work and economic resources. Theoretical methods provide predictions and represent an attractive complement to such experiments by waiving their inherent costs. Computational techniques can be used to engineer enzymatic reactivity, substrate specificity and ligand binding, access pathways and ligand transport, and global properties like protein stability, solubility, and flexibility. Theoretical approaches can also identify hotspots on the protein sequence for mutagenesis and predict suitable alternatives for selected positions with expected outcomes. This review covers the latest advances in computational methods for enzyme engineering and presents many successful case studies.

ReaxFF/AMBER-A Framework for Hybrid Reactive/Nonreactive Force Field Molecular Dynamics Simulations

Combined quantum mechanical/molecular mechanical (QM/MM) models using semiempirical and ab initio methods have been extensively reported on over the past few decades. These methods have been shown to be capable of providing unique insights into a range of problems, but they are still limited to relatively short time scales, especially QM/MM models using ab initio methods. An intermediate approach between a QM based model and classical mechanics could help fill this time-scale gap and facilitate the study of a range of interesting problems. Reactive force fields represent the intermediate approach explored in this paper. A widely used reactive model is ReaxFF, which has largely been applied to materials science problems and is generally used as a stand-alone (i.e., the full system is modeled using ReaxFF). We report a hybrid ReaxFF/AMBER molecular dynamics (MD) tool, which introduces ReaxFF capabilities to capture bond breaking and formation within the AMBER MD software package. This tool enables us to study local reactive events in large systems at a fraction of the computational costs of QM/MM models. We describe the implementation of ReaxFF/AMBER, validate this implementation using a benzene molecule solvated in water, and compare its performance against a range of similar approaches. To illustrate the predictive capabilities of ReaxFF/AMBER, we carried out a Claisen rearrangement study in aqueous solution. In a first for ReaxFF, we were able to use AMBER's potential of mean force (PMF) capabilities to perform a PMF study on this organic reaction. The ability to capture local reaction events in large systems using combined ReaxFF/AMBER opens up a range of problems that can be tackled using this model to address both chemical and biological processes.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Recent advances in computational methods for biosensor design

Biosensors are analytical tools with a great application in healthcare, food quality control, and environmental monitoring. They are of considerable interest to be designed by using cost-effective and efficient approaches. Designing biosensors with improved functionality or application in new target detection has been converted to a fast-growing field of biomedicine and biotechnology branches. Experimental efforts have led to valuable successes in the field of biosensor design; however, some deficiencies restrict their utilization for this purpose. Computational design of biosensors is introduced as a promising key to eliminate the gap. A set of reliable structure prediction of the biosensor segments, their stability, and accurate descriptors of molecular interactions are required to computationally design biosensors. In this review, we provide a comprehensive insight into the progress of computational methods to guide the design and development of biosensors, including molecular dynamics simulation, quantum mechanics calculations, molecular docking, virtual screening, and a combination of them as the hybrid methodologies. By relying on the recent advances in the computational methods, an opportunity emerged for them to be complementary or an alternative to the experimental methods in the field of biosensor design.

Differences in the Nature of the Phosphoryl Transfer Transition State in Protein Phosphatase 1 and Alkaline Phosphatase: Insights from QM Cluster Models

Quantum mechanical (QM) cluster models are used to probe effects on the catalytic properties of protein phosphatase 1 (PP1) and alkaline phosphatase (AP) due to metal ions and active site residues. The calculations suggest that the phosphoryl transfer transition states in PP1 are synchronous in nature with a significant degree of P-Olg cleavage, while those in AP are tighter with a modest degree of P-Olg cleavage and a range of P-Onuc formation. Similar to observations made in our recent work, a significant degree of cross talk between the forming and breaking P-O bonds complicates the interpretation of the Brønsted relation, especially in regard to AP for which the computed βlg/βEQ,lg value does not correlate with the degree of P-Olg cleavage regardless of the metal ions in the active site. By comparison, the correlation between βlg/βEQ,lg and the P-Olg bond order is more applicable to PP1, which generally exhibits less variation in the transition state than AP. Results for computational models with swapped metal ions between PP1 and AP suggest that the metal ions modulate both the nature of the transition state and the degrees of sensitivity of the transition state to the leaving group. In the reactant state, the degree of the scissile bond polarization is also different in the two enzymes, although this difference appears to be largely determined by the active site residues rather than the metal ions. Therefore, both the identity of the metal ion and the positioning of polar or charged residues in the active site contribute to the distinct catalytic characteristics of these enzymes. Several discrepancies observed between the QM cluster results and the available experimental data highlight the need for further QM/MM method developments for the quantitative analysis of metalloenzymes that contain open-shell transition metal ions.

Unraveling the energetic significance of chemical events in enzyme catalysis via machine-learning based regression approach

The bacterial enzyme class of β-lactamases are involved in benzylpenicillin acylation reactions, which are currently being revisited using hybrid quantum mechanical molecular mechanical (QM/MM) chain-of-states pathway optimizations. Minimum energy pathways are sampled by reoptimizing pathway geometry under different representative protein environments obtained through constrained molecular dynamics simulations. Predictive potential energy surface models in the reaction space are trained with machine-learning regression techniques. Herein, using TEM-1/benzylpenicillin acylation reaction as the model system, we introduce two model-independent criteria for delineating the energetic contributions and correlations in the predicted reaction space. Both methods are demonstrated to effectively quantify the energetic contribution of each chemical process and identify the rate limiting step of enzymatic reaction with high degrees of freedom. The consistency of the current workflow is tested under seven levels of quantum chemistry theory and three non-linear machine-learning regression models. The proposed approaches are validated to provide qualitative compliance with experimental mutagenesis studies.

Multi-level free energy simulation with a staged transformation approach

Combining multiple levels of theory in free energy simulations to balance computational accuracy and efficiency is a promising approach for studying processes in the condensed phase. While the basic idea has been proposed and explored for quite some time, it remains challenging to achieve convergence for such multi-level free energy simulations as it requires a favorable distribution overlap between different levels of theory. Previous efforts focused on improving the distribution overlap by either altering the low-level of theory for the specific system of interest or ignoring certain degrees of freedom. Here, we propose an alternative strategy that first identifies the degrees of freedom that lead to gaps in the distributions of different levels of theory and then treats them separately with either constraints or restraints or by introducing an intermediate model that better connects the low and high levels of theory. As a result, the conversion from the low level to the high level model is done in a staged fashion that ensures a favorable distribution overlap along the way. Free energy components associated with different steps are mostly evaluated explicitly, and thus, the final result can be meaningfully compared to the rigorous free energy difference between the two levels of theory with limited and well-defined approximations. The additional free energy component calculations involve simulations at the low level of theory and therefore do not incur high computational costs. The approach is illustrated with two simple but non-trivial solution examples, and factors that dictate the reliability of the result are discussed.

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.

Prediction of aqueous free energies of solvation using coupled QM and MM explicit solvent simulations

A method based on molecular dynamics simulations which employ two distinct levels of theory is proposed and tested for the prediction of Gibbs free energies of solvation for non-ionic solutes in water. The method consists of two additive contributions: (i) an evaluation of the free energy of solvation predicted by a computationally efficient molecular mechanics (MM) method; and (ii) an evaluation of the free energy difference between the potential energy surface of the MM method and that of a more computationally intensive first-principles quantum-mechanical (QM) method. The latter is computed by a thermodynamic integration method based on a series of shorter molecular dynamics simulations that employ weighted averages of the QM and MM force evaluations. The combined computational approach is tested against the experimental free energies of aqueous solvation for four solutes. For solute-solvent interactions that are found to be described qualitatively well by the MM method, the QM correction makes a modest improvement in the predicted free energy of aqueous solvation. However, for solutes that are found to not be adequately described by the MM method, the QM correction does not improve agreement with experiment. These preliminary results provide valuable insights into the novel concept of implementing thermodynamic integration between two model chemistries, suggesting that it is possible to use QM methods to improve upon the MM predictions of free energies of aqueous solvation.

Understanding and Controlling Food Protein Structure and Function in Foods: Perspectives from Experiments and Computer Simulations

The structure and interactions of proteins play a critical role in determining the quality attributes of many foods, beverages, and pharmaceutical products. Incorporating a multiscale understanding of the structure-function relationships of proteins can provide greater insight into, and control of, the relevant processes at play. Combining data from experimental measurements, human sensory panels, and computer simulations through machine learning allows the construction of statistical models relating nanoscale properties of proteins to the physicochemical properties, physiological outcomes, and tastes of foods. This review highlights several examples of advanced computer simulations at molecular, mesoscale, and multiscale levels that shed light on the mechanisms at play in foods, thereby facilitating their control. It includes a practical simulation toolbox for those new to in silico modeling.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

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.

Structural and functional insights into the bona fide catalytic state of Streptococcus pyogenes Cas9 HNH nuclease domain

The CRISPR-associated endonuclease Cas9 from Streptococcus pyogenes (SpyCas9), along with a programmable single-guide RNA (sgRNA), has been exploited as a significant genome-editing tool. Despite the recent advances in determining the SpyCas9 structures and DNA cleavage mechanism, the cleavage-competent conformation of the catalytic HNH nuclease domain of SpyCas9 remains largely elusive and debatable. By integrating computational and experimental approaches, we unveiled and validated the activated Cas9-sgRNA-DNA ternary complex in which the HNH domain is neatly poised for cleaving the target DNA strand. In this catalysis model, the HNH employs the catalytic triad of D839-H840-N863 for cleavage catalysis, rather than previously implicated D839-H840-D861, D837-D839-H840, or D839-H840-D861-N863. Our study contributes critical information to defining the catalytic conformation of the HNH domain and advances the knowledge about the conformational activation underlying Cas9-mediated DNA cleavage.

Use of Interaction Energies in QM/MM Free Energy Simulations

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.