Ambient-Potential Composite Ewald Method for ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation

PyDFT-QMMM: A modular, extensible software framework for DFT-based QM/MM molecular dynamics

PyDFT-QMMM is a Python-based package for performing hybrid quantum mechanics/molecular mechanics (QM/MM) simulations at the density functional level of theory. The program is designed to treat short-range and long-range interactions through user-specified combinations of electrostatic and mechanical embedding procedures within periodic simulation domains, providing necessary interfaces to external quantum chemistry and molecular dynamics software. To enable direct embedding of long-range electrostatics in periodic systems, we have derived and implemented force terms for our previously described QM/MM/PME approach [Pederson and McDaniel, J. Chem. Phys. 156, 174105 (2022)]. Communication with external software packages Psi4 and OpenMM is facilitated through Python application programming interfaces (APIs). The core library contains basic utilities for running QM/MM molecular dynamics simulations, and plug-in entry-points are provided for users to implement custom energy/force calculation and integration routines, within an extensible architecture. The user interacts with PyDFT-QMMM primarily through its Python API, allowing for complex workflow development with Python scripting, for example, interfacing with PLUMED for free energy simulations. We provide benchmarks of forces and energy conservation for the QM/MM/PME and alternative QM/MM electrostatic embedding approaches. We further demonstrate a simple example use case for water solute in a water solvent system, for which radial distribution functions are computed from 100 ps QM/MM simulations; in this example, we highlight how the solvation structure is sensitive to different basis-set choices due to under- or over-polarization of the QM water molecule's electron density.

Software Infrastructure for Next-Generation QM/MM-ΔMLP Force Fields

We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM-ΔMLP) force fields for a wide range of applications. The software integrates Amber's molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM-ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein-ligand binding.

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.

Analytic Gradients for the Electrostatic Embedding QM/MM Model in Periodic Boundary Conditions Using Particle-Mesh Ewald Sums and Electrostatic Potential Fitted Charge Operators

Long-range electrostatic effects are fundamental for describing chemical reactivity in the condensed phase. Here, we present the methodology of an efficient quantum mechanical/molecular mechanical (QM/MM) model in periodic boundary conditions (PBC) compatible with QM/MM boundaries at chemical bonds. The method combines electrostatic potential fitted charge operators and electrostatic potentials derived from the smooth particle-mesh Ewald (PME) sum approach. The total energy and its analytic first derivatives with respect to QM, MM, and lattice vectors allow QM/MM molecular dynamics (MD) in the most common thermodynamic ensembles. We demonstrate the robustness of the method by performing a QM/MM MD equilibration of methanol in water. We simulate the cis/trans isomerization free-energy profiles in water of proline amino acid and a proline-containing oligopeptide, showing a correct description of the reaction barrier. Our PBC-compatible QM/MM model can efficiently be used to study the chemical reactivity in the condensed phase and enzymatic catalysis.

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

Catalytic mechanism and pH dependence of a methyltransferase ribozyme (MTR1) from computational enzymology

A methyltransferase ribozyme (MTR1) was selected in vitro to catalyze alkyl transfer from exogenous O6-methylguanine (O6mG) to a target adenine N1, and recently, high-resolution crystal structures have become available. We use a combination of classical molecular dynamics, ab initio quantum mechanical/molecular mechanical (QM/MM) and alchemical free energy (AFE) simulations to elucidate the atomic-level solution mechanism of MTR1. Simulations identify an active reactant state involving protonation of C10 that hydrogen bonds with O6mG:N1. The deduced mechanism involves a stepwise mechanism with two transition states corresponding to proton transfer from C10:N3 to O6mG:N1 and rate-controlling methyl transfer (19.4  kcal·mol-1 barrier). AFE simulations predict the pKa for C10 to be 6.3, close to the experimental apparent pKa of 6.2, further implicating it as a critical general acid. The intrinsic rate derived from QM/MM simulations, together with pKa calculations, enables us to predict an activity-pH profile that agrees well with experiment. The insights gained provide further support for a putative RNA world and establish new design principles for RNA-based biochemical tools.

QDπ: A Quantum Deep Potential Interaction Model for Drug Discovery

We report QDπ-v1.0 for modeling the internal energy of drug molecules containing H, C, N, and O atoms. The QDπ model is in the form of a quantum mechanical/machine learning potential correction (QM/Δ-MLP) that uses a fast third-order self-consistent density-functional tight-binding (DFTB3/3OB) model that is corrected to a quantitatively high-level of accuracy through a deep-learning potential (DeepPot-SE). The model has the advantage that it is able to properly treat electrostatic interactions and handle changes in charge/protonation states. The model is trained against reference data computed at the ωB97X/6-31G* level (as in the ANI-1x data set) and compared to several other approximate semiempirical and machine learning potentials (ANI-1x, ANI-2x, DFTB3, MNDO/d, AM1, PM6, GFN1-xTB, and GFN2-xTB). The QDπ model is demonstrated to be accurate for a wide range of intra- and intermolecular interactions (despite its intended use as an internal energy model) and has shown to perform exceptionally well for relative protonation/deprotonation energies and tautomers. An example application to model reactions involved in RNA strand cleavage catalyzed by protein and nucleic acid enzymes illustrates QDπ has average errors less than 0.5 kcal/mol, whereas the other models compared have errors over an order of magnitude greater. Taken together, this makes QDπ highly attractive as a potential force field model for drug discovery.

TeraChem protocol buffers (TCPB): Accelerating QM and QM/MM simulations with a client-server model

The routine use of electronic structures in many chemical simulation applications calls for efficient and easy ways to access electronic structure programs. We describe how the graphics processing unit (GPU) accelerated electronic structure program TeraChem can be set up as an electronic structure server, to be easily accessed by third-party client programs. We exploit Google's protocol buffer framework for data serialization and communication. The client interface, called TeraChem protocol buffers (TCPB), has been designed for ease of use and compatibility with multiple programming languages, such as C++, Fortran, and Python. To demonstrate the ease of coupling third-party programs with electronic structures using TCPB, we have incorporated the TCPB client into Amber for quantum mechanics/molecular mechanics (QM/MM) simulations. The TCPB interface saves time with GPU initialization and I/O operations, achieving a speedup of more than 2× compared to a prior file-based implementation for a QM region with ∼250 basis functions. We demonstrate the practical application of TCPB by computing the free energy profile of p-hydroxybenzylidene-2,3-dimethylimidazolinone (p-HBDI^-)-a model chromophore in green fluorescent proteins-on the first excited singlet state using Hamiltonian replica exchange for enhanced sampling. All calculations in this work have been performed with the non-commercial freely-available version of TeraChem, which is sufficient for many QM region sizes in common use.

An efficient electrostatic embedding QM/MM method using periodic boundary conditions based on particle-mesh Ewald sums and electrostatic potential fitted charge operators

Hybrid quantum mechanics/molecular mechanics (QM/MM) models are successful at describing the properties and reactivity of biological macromolecules. Combining ab initio QM/MM methods and periodic boundary conditions (PBC) is currently the optimal approach for modeling chemical processes in an infinite environment, but frequently, these models are too time-consuming for general applicability to biological systems in a solution. Here, we define a simple and efficient electrostatic embedding QM/MM model in PBC, combining the benefits of electrostatic potential fitted atomic charges and particle-mesh Ewald sums, which can efficiently treat systems of an arbitrary size at a reasonable computational cost. To illustrate this, we apply our scheme to extract the lowest singlet excitation energies from a model for Arabidopsis thaliana cryptochrome 1 containing circa 93 000 atoms, accurately reproducing the experimental absorption maximum.

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.

Who stole the proton? Suspect general base guanine found with a smoking gun in the pistol ribozyme

The pistol ribozyme (Psr) is one among the most recently discovered classes of small nucleolytic ribozymes that catalyze site-specific RNA self-cleavage through 2'-O-transphosphorylation. The Psr contains a conserved guanine (G40) that in crystal structures is in a position suggesting it plays the role of the general base to abstract a proton from the nucleophile to activate the reaction. Although some functional data is consistent with this mechanistic role, a notable exception is 2-aminopurine (2AP) substitution which has no effect on the rate, unlike similar substitutions across other so-called "G + M" and "G + A" ribozyme classes. Herein we postulate that an alternate conserved guanine, G42, is the primary general base, and provide evidence from molecular simulations that the active site of Psr can undergo local refolding into a structure that is consistent with the common "L-platform/L-scaffold" architecture identified in G + M and G + A ribozyme classes with Psr currently the notable exception. We summarize the key currently available experimental data and present new classical and combined quantum mechanical/molecular mechanical simulation results that collectively suggest a new hypothesis. We hypothesize that there are two available catalytic pathways supported by different conformational states connected by a local refolding of the active site: (1) a primary pathway with an active site architecture aligned with the L-platform/L-scaffold framework where G42 acts as a general base, and (2) a secondary pathway with the crystallographic active site architecture where G40 acts as a general base. We go on to make several experimentally testable predictions, and suggest specific experiments that would ultimately bring closure to the mystery as to "who stole the proton in the pistol ribozyme?".

Combined QM/MM, Machine Learning Path Integral Approach to Compute Free Energy Profiles and Kinetic Isotope Effects in RNA Cleavage Reactions

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2'-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM+DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/MM surfaces with and without weighted thermodynamic perturbation corrections. 18O and 34S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

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

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

DFT-based QM/MM with Particle-Mesh Ewald for Direct, Long-Range Electrostatic Embedding

We present a DFT-based, QM/MM implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid, from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections, and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages, as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and BMIM/BF4 ionic liquid were considered as ``simple' and ``complex' solvents respectively, with water and p-phenylenediamine (PPD) solute molecules treated at QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible error for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF4 for which real-space truncation produces severe error even at 2-3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms, with our presented algorithm providing a general and robust approach.

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.

Development and application of quantum mechanics/molecular mechanics methods with advanced polarizable potentials

Quantum mechanics/molecular mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and biological systems. The combination of QM and MM methods to represent a system gives rise to several challenges that need to be addressed. The increase in computational speed has allowed the expanded use of more complicated and accurate methods for both QM and MM simulations. Here, we review some approaches that address several common challenges encountered in QM/MM simulations with advanced polarizable potentials, from methods to account for boundary across covalent bonds and long-range effects, to polarization and advanced embedding potentials.

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.

Exploring the Minimum-Energy Pathways and Free-Energy Profiles of Enzymatic Reactions with QM/MM Calculations

Understanding molecular mechanisms of enzymatic reactions is of vital importance in biochemistry and biophysics. Here, we introduce new functions of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in the GENESIS program to compute the minimum-energy pathways (MEPs) and free-energy profiles of enzymatic reactions. For this purpose, an interface in GENESIS is developed to utilize a highly parallel electronic structure program, QSimulate-QM (https://qsimulate.com), calling it as a shared library from GENESIS. Second, algorithms to search the MEP are implemented, combining the string method (E et al. J. Chem. Phys. 2007, 126, 164103) with the energy minimization of the buffer MM region. The method implemented in GENESIS is applied to an enzyme, triosephosphate isomerase, which converts dihyroxyacetone phosphate to glyceraldehyde 3-phosphate in four proton-transfer processes. QM/MM-molecular dynamics simulations show performances of greater than 1 ns/day with the density functional tight binding (DFTB), and 10-30 ps/day with the hybrid density functional theory, B3LYP-D3. These performances allow us to compute not only MEP but also the potential of mean force (PMF) of the enzymatic reactions using the QM/MM calculations. The barrier height obtained as 13 kcal mol-1 with B3LYP-D3 in the QM/MM calculation is in agreement with the experimental results. The impact of conformational sampling in PMF calculations and the level of electronic structure calculations (DFTB vs B3LYP-D3) suggests reliable computational protocols for enzymatic reactions without high computational costs.

Open-Source Multi-GPU-Accelerated QM/MM Simulations with AMBER and QUICK

The quantum mechanics/molecular mechanics (QM/MM) approach is an essential and well-established tool in computational chemistry that has been widely applied in a myriad of biomolecular problems in the literature. In this publication, we report the integration of the QUantum Interaction Computational Kernel (QUICK) program as an engine to perform electronic structure calculations in QM/MM simulations with AMBER. This integration is available through either a file-based interface (FBI) or an application programming interface (API). Since QUICK is an open-source GPU-accelerated code with multi-GPU parallelization, users can take advantage of "free of charge" GPU-acceleration in their QM/MM simulations. In this work, we discuss implementation details and give usage examples. We also investigate energy conservation in typical QM/MM simulations performed at the microcanonical ensemble. Finally, benchmark results for two representative systems in bulk water, the N-methylacetamide (NMA) molecule and the photoactive yellow protein (PYP), show the performance of QM/MM simulations with QUICK and AMBER using a varying number of CPU cores and GPUs. Our results highlight the acceleration obtained from a single or multiple GPUs; we observed speedups of up to 53× between a single GPU vs a single CPU core and of up to 2.6× when comparing four GPUs to a single GPU. Results also reveal speedups of up to 3.5× when the API is used instead of FBI.

Proton transfer in bulk water using the full adaptive QM/MM method: integration of solute- and solvent-adaptive approaches

The quantum mechanical/molecular mechanical (QM/MM) method is a hybrid molecular simulation technique that increases the accessibility of local electronic structures of large systems. The technique combines the benefit of accuracy found in the QM method and that of cost efficiency found in the MM method. However, it is difficult to directly apply the QM/MM method to the dynamics of solution systems, particularly for proton transfer. As explained in the Grotthuss mechanism, proton transfer is a structural interconversion between hydronium ions and solvent water molecules. Hence, when the QM/MM method is applied, an adaptive treatment, namely on-the-fly revisions on molecular definitions, is required for both the solute and solvent. Although several solvent-adaptive methods have been proposed, a full adaptive framework, which is an approach that also considers adaptation for solutes, remains untapped. In this paper, we propose a new numerical expression for the coordinates of the excess proton and its control algorithm. Furthermore, we confirm that this method can stably and accurately simulate proton transfer dynamics in bulk water.

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

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

The hydrolytic water molecule of Class A β-lactamase relies on the acyl-enzyme intermediate ES* for proper coordination and catalysis

Serine-based β-lactamases of Class A, C and D all rely on a key water molecule to hydrolyze and inactivate β-lactam antibiotics. This process involves two conserved catalytic steps. In the first acylation step, the β-lactam antibiotic forms an acyl-enzyme intermediate (ES*) with the catalytic serine residue. In the second deacylation step, an activated water molecule serves as nucleophile (WAT_Nu) to attack ES* and release the inactivated β-lactam. The coordination and activation of WAT_Nu is not fully understood. Using time-resolved x-ray crystallography and QM/MM simulations, we analyzed three intermediate structures of Class A β-lactamase PenP as it slowly hydrolyzed cephaloridine. WAT_Nu is centrally located in the apo structure but becomes slightly displaced away by ES* in the post-acylation structure. In the deacylation structure, WAT_Nu moves back and is positioned along the Bürgi–Dunitz trajectory with favorable energetic profile to attack ES*. Unexpectedly, WAT_Nu is also found to adopt a catalytically incompetent conformation in the deacylation structure forming a hydrogen bond with ES*. Our results reveal that ES* plays a significant role in coordinating and activating WAT_Nu through subtle yet distinct interactions at different stages of the catalytic process. These interactions may serve as potential targets to circumvent β-lactamase-mediated antibiotic resistance.

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

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.

Cleaning Up Mechanistic Debris Generated by Twister Ribozymes Using Computational RNA Enzymology

The catalytic properties of RNA have been a subject of fascination and intense research since their discovery over 30 years ago. Very recently, several classes of nucleolytic ribozymes have emerged and been characterized structurally. Among these, the twister ribozyme has been center-stage, and a topic of debate about its architecture and mechanism owing to conflicting interpretations of different crystal structures, and in some cases conflicting interpretations of the same functional data. In the present work, we attempt to clean up the mechanistic "debris" generated by twister ribozymes using a comprehensive computational RNA enzymology approach aimed to provide a unified interpretation of existing structural and functional data. Simulations in the crystalline environment and in solution provide insight into the origins of observed differences in crystal structures, and coalesce on a common active site architecture, and dynamical ensemble in solution. We use GPU-accelerated free energy methods with enhanced sampling to ascertain microscopic nucleobase pK a values of the implicated general acid and base, from which predicted activity-pH profiles can be compared directly with experiments. Next, ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with full dynamic solvation under periodic boundary conditions are used to determine mechanistic pathways through multi-dimensional free energy landscapes for the reaction. We then characterize the rate-controlling transition state, and make predictions about kinetic isotope effects and linear free energy relations. Computational mutagenesis is performed to explain the origin of rate effects caused by chemical modifications and make experimentally testable predictions. Finally, we provide evidence that helps to resolve conflicting issues related to the role of metal ions in catalysis. Throughout each stage, we highlight how a conserved L-platform structural motif, to- gether with a key L-anchor residue, forms the characteristic active site scaffold enabling each of the catalytic strategies to come together not only for the twister ribozyme, but the majority of the known small nucleolytic ribozyme classes.

Prediction of Excited-State Properties of Oligoacene Crystals Using Fragment-Based Quantum Mechanical Method

A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S₁) and triplet excitation energies (T₁), in excellent agreement with the full-system quantum mechanical calculations. Using this method, we also investigated the performance of different density functionals in predicting the excited-state properties of the oligoacene crystals. Among the 13 tested functionals, B3LYP and MN15 give the two lowest overall mean unsigned errors with reference to the experimental S₁ and T₁ excitation energies. The EE-GMF approach can be readily utilized for studying the excited-state properties of large-scale organic solids at diverse ab initio levels.

LICHEM 1.1: Recent Improvements and New Capabilities

The QM/MM method has become a useful tool to investigate various properties of complex systems. We previously introduced the layered interacting chemical models (LICHEM) package to enable QM/MM simulations with advanced potentials by combining various (unmodified) QM and MM codes ( J. Comp. Chem., 2016, 37, 1019). LICHEM provides several capabilities such as the ability to use polarizable force fields, such as AMOEBA, for the MM environment. Here, we describe an updated version of LICHEM (v1.1), which includes several new functionalities including a new method to account for long-range electrostatic effects in QM/MM (QM/MM-LREC), a new implementation for QM/MM with the Gaussian electrostatic model (GEM), and new capabilities for path optimizations using the quadratic string model (QSM) coupled with restrained MM environment optimization.

Two symmetric arginine residues play distinct roles in Thermus thermophilus Argonaute DNA guide strand-mediated DNA target cleavage

Bacterium Thermus thermophilus Argonaute (Ago; TtAgo) is a prokaryotic Ago (pAgo) that acts as the host defense against the uptake and propagation of foreign DNA by catalyzing the DNA cleavage reaction. The TtAgo active site consists of a plugged-in glutamate finger with two arginine residues (R545 and R486) located symmetrically around it. An interesting challenge is to understand how they can collaboratively facilitate enzymatic catalysis. In Kluyveromyces polysporus Ago, a eukaryotic Ago, the evolutionarily symmetrical residues are arginine and histidine, both of which function to stabilize the plugged-in catalytic tetrad conformation. Surprisingly, our simulation results indicated that, in TtAgo, only R545 is involved in the cleavage reaction by serving as a critical structural anchor to stabilize the catalytic tetrad Asp-Glu-Asp-Asp that is completed by the insertion of the glutamate finger, whereas R486 is not involved in target cleavage. The TtAgo-mediated target DNA cleavage occurs in a substrate-assisted mechanism, in which the pro-Rp (Rp, a tetrahedral phosphorus center with "R-type" chirality) oxygen of scissile phosphate acts as a general base to activate the nucleophilic water. Our unexpected theoretical findings on distinct roles played by R545 and R486 in TtAgo catalysis have been validated by single-point site-mutagenesis experiments, wherein the target cleavage is abolished for all mutants of R545. In sharp contrast, the cleavage activity is maintained for all mutants of R486. Our work provides mechanistic insights on the catalytic specificity of Ago proteins and could facilitate the design of new gene-editing tools in the long term.

Representation of the QM Subsystem for Long-Range Electrostatic Interaction in Non-Periodic Ab Initio QM/MM Calculations

In QM/MM calculations, it is essential to handle electrostatic interactions between the QM and MM subsystems accurately and efficiently. To achieve maximal efficiency, it is convenient to adopt a hybrid scheme, where the QM electron density is used explicitly in the evaluation of short-range QM/MM electrostatic interactions, while a multipolar representation for the QM electron density is employed to account for the long-range QM/MM electrostatic interactions. In order to avoid energy discontinuity at the cutoffs, which separate the short- and long-range QM/MM electrostatic interactions, a switching function should be utilized to ensure a smooth potential energy surface. In this study, we benchmarked the accuracy of such hybrid embedding schemes for QM/MM electrostatic interactions using different multipolar representations, switching functions and cutoff distances. For test systems (neutral and anionic oxyluciferin in MM (aqueous and enzyme) environments), the best accuracy was acquired with a combination of QM electrostatic potential (ESP) charges and dipoles and two switching functions (long-range electrostatic corrections (LREC) and Switch) in the treatment of long-range QM/MM electrostatics. It allowed us to apply a 10Å distance cutoff and still obtain QM/MM electrostatics/polarization energies within 0.1 kcal/mol and time-dependent density functional theory (TDDFT)/MM vertical excitation energies within 10-3 eV from theoretical reference values.

A GPU-Accelerated Parameter Interpolation Thermodynamic Integration Free Energy Method

There has been a resurgence of interest in free energy methods motivated by the performance enhancements offered by molecular dynamics (MD) software written for specialized hardware, such as graphics processing units (GPUs). In this work, we exploit the properties of a parameter-interpolated thermodynamic integration (PI-TI) method to connect states by their molecular mechanical (MM) parameter values. This pathway is shown to be better behaved for Mg2+ → Ca2+ transformations than traditional linear alchemical pathways (with and without soft-core potentials). The PI-TI method has the practical advantage that no modification of the MD code is required to propagate the dynamics, and unlike with linear alchemical mixing, only one electrostatic evaluation is needed (e.g., single call to particle-mesh Ewald) leading to better performance. In the case of AMBER, this enables all the performance benefits of GPU-acceleration to be realized, in addition to unlocking the full spectrum of features available within the MD software, such as Hamiltonian replica exchange (HREM). The TI derivative evaluation can be accomplished efficiently in a post-processing step by reanalyzing the statistically independent trajectory frames in parallel for high throughput. We also show how one can evaluate the particle mesh Ewald contribution to the TI derivative evaluation without needing to perform two reciprocal space calculations. We apply the PI-TI method with HREM on GPUs in AMBER to predict p Ka values in double stranded RNA molecules and make comparison with experiments. Convergence to under 0.25 units for these systems required 100 ns or more of sampling per window and coupling of windows with HREM. We find that MM charges derived from ab initio QM/MM fragment calculations improve the agreement between calculation and experimental results.

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.

Divalent Metal Ion Activation of a Guanine General Base in the Hammerhead Ribozyme: Insights from Molecular Simulations

The hammerhead ribozyme is a well-studied nucleolytic ribozyme that catalyzes the self-cleavage of the RNA phosphodiester backbone. Despite experimental and theoretical efforts, key questions remain about details of the mechanism with regard to the activation of the nucleophile by the putative general base guanine (G12). Straightforward interpretation of the measured activity-pH data implies the pK_a value of the N1 position in the G12 nucleobase is significantly shifted by the ribozyme environment. Recent crystallographic and biochemical work has identified pH-dependent divalent metal ion binding at the N7/O6 position of G12, leading to the hypothesis that this binding mode could induce a pK_a shift of G12 toward neutrality. We present computational results that support this hypothesis and provide a model that unifies the interpretation of available structural and biochemical data and paints a detailed mechanistic picture of the general base step of the reaction. Experimentally testable predictions are made for mutational and rescue effects on G12, which will give further insights into the catalytic mechanism. These results contribute to our growing knowledge of the potential roles of divalent metal ions in RNA catalysis.

Long-range electrostatic corrections in multipolar/polarizable QM/MM simulations

Taking long-range electrostatic effects into account in classical and hybrid quantum mechanics-molecular mechanics (QM/MM) simulations is necessary for an accurate description of the system under study. We have recently developed a method, termed long-range electrostatic corrections (LREC), for monopolar QM/MM calculations. Here, we present an extension of LREC for multipolar/polarizable QM/MM simulations within the LICHEM software package. Reaction barriers and QM-MM interaction energies converge with a LREC cutoff between 20 and 25 Å, in agreement with our previous results. Additionally, the LREC approach for the QM-MM interactions can be smoothly combined with standard shifting or Ewald summation methods in the MM calculations. We recommend the use of QM(LREC)/MM(PME), where the QM region is treated with LREC and the MM region is treated with particle mesh Ewald (PME) summation. This combination is an excellent compromise between simplicity, speed, and accuracy for large QM/MM simulations.