The empirical valence bond model: theory and applications

Diabatic States of Charge Transfer with Constrained Charge Equilibration

Charge transfer (CT) processes that are electronically nonadiabatic are ubiquitous in chemistry, biology, and materials science, but their theoretical description requires diabatic states or adiabatic excited states. For complex systems, these latter states are more difficult to calculate than the adiabatic ground state. Here, we propose a simple method to obtain diabatic states, including energies and charges, by constraining the atomic charges within the charge equilibration framework. For two-state systems, the exact diabatic coupling can be determined, from which the adiabatic excited-state energy can also be calculated. The method can be viewed as an affordable alternative to constrained density functional theory (CDFT), and so we call it constrained charge equilibration (CQEq). We test the CQEq method on the anthracene-tetracyanoethylene CT complex and the reductive decomposition of ethylene carbonate on a lithium metal surface. We find that CQEq predicts diabatic energies, charges, and adiabatic excitation energies in good agreement with CDFT, and we propose that CQEq is promising for combination with machine learning force fields to study nonadiabatic CT in the condensed phase.

Engineering Dehalogenase Enzymes Using Variational Autoencoder-Generated Latent Spaces and Microfluidics

Enzymes play a crucial role in sustainable industrial applications, with their optimization posing a formidable challenge due to the intricate interplay among residues. Computational methodologies predominantly rely on evolutionary insights of homologous sequences. However, deciphering the evolutionary variability and complex dependencies among residues presents substantial hurdles. Here, we present a new machine-learning method based on variational autoencoders and evolutionary sampling strategy to address those limitations. We customized our method to generate novel sequences of model enzymes, haloalkane dehalogenases. Three design-build-test cycles improved the solubility of variants from 11% to 75%. Thorough experimental validation including the microfluidic device MicroPEX resulted in 20 multiple-point variants. Nine of them, sharing as little as 67% sequence similarity with the template, showed a melting temperature increase of up to 9 °C and an average improvement of 3 °C. The most stable variant demonstrated a 3.5-fold increase in activity compared to the template. High-quality experimental data collected with 20 variants represent a valuable data set for the critical validation of novel protein design approaches. Python scripts, jupyter notebooks, and data sets are available on GitHub (https://github.com/loschmidt/vae-dehalogenases), and interactive calculations will be possible via https://loschmidt.chemi.muni.cz/fireprotasr/.

Biochemical and Computational Characterization of Haloalkane Dehalogenase Variants Designed by Generative AI: Accelerating the SN2 Step

Generative artificial intelligence (AI) models trained on natural protein sequences have been used to design functional enzymes. However, their ability to predict individual reaction steps in enzyme catalysis remains unclear, limiting the potential use of sequence information for enzyme engineering. In this study, we demonstrated that sequence information can predict the rate of the SN2 step of a haloalkane dehalogenase using a generative maximum-entropy (MaxEnt) model. We then designed lower-order protein variants of haloalkane dehalogenase using the model. Kinetic measurements confirmed the successful design of protein variants that enhance catalytic activity, above that of the wild type, in the overall reaction and in particular in the SN2 step. On the simulation side, we provided molecular insights into these designs for the SN2 step using the empirical valence bond (EVB) and metadynamics simulations. The EVB calculations showed activation barriers consistent with experimental reaction rates, while examining the effect of amino acid replacements on the electrostatic effect on the activation barrier and the consequence of water penetration, as well as the extent of ground state destabilization/stabilization. Metadynamics simulations emphasize the importance of the substrate positioning in enzyme catalysis. Overall, our AI-guided approach successfully enabled the design of a variant with a faster rate for the SN2 step than the wild-type enzyme, despite haloalkane dehalogenase being extensively optimized through natural evolution.

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.

Molecular Dynamics Simulation of Complex Reactivity with the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) Software Package

Simulating chemically reactive phenomena such as proton transport on nanosecond to microsecond and beyond time scales is a challenging task. Ab initio methods are unable to currently access these time scales routinely, and traditional molecular dynamics methods feature fixed bonding arrangements that cannot account for changes in the system's bonding topology. The Multiscale Reactive Molecular Dynamics (MS-RMD) method, as implemented in the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) software package for the LAMMPS molecular dynamics code, offers a method to routinely sample longer time scale reactive simulation data with statistical precision. RAPTOR may also be interfaced with enhanced sampling methods to drive simulations toward the analysis of reactive rare events, and a number of collective variables (CVs) have been developed to facilitate this. Key advances to this methodology, including GPU acceleration efforts and novel CVs to model water wire formation are reviewed, along with recent applications of the method which demonstrate its versatility and robustness.

Evidence and Practical Applications of Site Occupancy Theory (SOT) of Eu3+ in Scheelite Compounds

The determination of the site occupancy of activators in phosphors is essential for precise synthesis, understanding the relationship between their luminescence properties and crystal structure, and tailoring their properties by modifying the host composition. Herein, one simple method was proposed to help determine the sites at which the doping of rare earth ions or transition metal ions occupies in the host lattice through site occupancy theory (SOT) for ions doped into the matrix lattice. SOT was established based on the fact that doping ions preferentially occupy the sites with the lowest bonding energy deviations. In order to provide detailed experimental evidence to prove the feasibility of SOT, several scheelite-type compounds were successfully synthesized using a high-temperature solid-phase method. When Eu3+ ions occupy a similar surrounding environment site, the photoluminescence spectra of the activators Eu3+ are similar. Therefore, by comparing the intensity ratio of photoluminescence spectra and the mechanism of all transitions of KEu(WO4)2, KY(WO4)2:Eu3+, Na5Eu(WO4)4, and Na5Y(WO4)4:Eu3+, it was proved that SOT can successfully confirm the site occupation when doped ions enter the matrix lattice. SOT was further applied to the sites occupied by Eu3+ ion-doped LiAl(MoO4)2 and LiLu(MoO4)2.

Assessing the Catalytic Role of Native Glucagon Amyloid Fibrils

Glucagon stands out as a pivotal peptide hormone, instrumental in controlling blood glucose levels and lipid metabolism. While the formation of glucagon amyloid fibrils has been documented, their biological functions remain enigmatic. Recently, we demonstrated experimentally that glucagon amyloid fibrils can act as catalysts in several biological reactions including esterolysis, lipid hydrolysis, and dephosphorylation. Herein, we present a multiscale quantum mechanics/molecular mechanics (QM/MM) simulation of the acylation step in the esterolysis of para-nitrophenyl acetate (p-NPA), catalyzed by native glucagon amyloid fibrils, serving as a model system to elucidate their catalytic function. This step entails a concerted mechanism, involving proton transfer from serine to histidine, followed by the nucleophilic attack of the serine oxy anion on the carbonyl carbon of p-NPA. We computed the binding energy and free-energy profiles of this reaction using the protein-dipole Langevin-dipole (PDLD) within the linear response approximation (LRA) framework (PDLD/S-LRA-2000) and the empirical valence bond (EVB) methods. This included simulations of the reaction in an aqueous environment and in the fibril, enabling us to estimate the catalytic effect of the fibril. Our EVB calculations obtained a barrier of 23.4 kcal mol-1 for the enzyme-catalyzed reaction compared to the experimental value of 21.9 kcal mol-1 (and a calculated catalytic effect of 3.2 kcal mol-1 compared to the observed effect of 4.7 kcal mol-1). This close agreement together with the barrier reduction when transitioning from the reference solution reaction to the amyloid fibril provides supporting evidence to the catalytic role of glucagon amyloid fibrils. Moreover, employing the PDLD/S-LRA-2000 approach further reinforced exclusively the enzyme's catalytic role. The results presented in this study contribute significantly to our understanding of the catalytic role of glucagon amyloid fibrils, marking, to the best of our knowledge, the first-principles mechanistic investigation of fibrils using QM/MM methods. Therefore, our findings offer fruitful insights for future research into the mechanisms of related amyloid catalysis.

Best Practices on QM/MM Simulations of Biological Systems

During the second half of the 20th century, following structural biology hallmark works on DNA and proteins, biochemists shifted their questions from "what does this molecule look like?" to "how does this process work?". Prompted by the theoretical and practical developments in computational chemistry, this led to the emergence of biomolecular simulations and, along with the 2013 Nobel Prize in Chemistry, to the development of hybrid QM/MM methods. QM/MM methods are necessary whenever the problem we want to address involves chemical reactivity and/or a change in the system's electronic structure, with archetypal examples being the studies of an enzyme's reaction mechanism and a metalloprotein's active site. In the last decades QM/MM methods have seen an increasing adoption driven by their incorporation in widely used biomolecular simulation software. However, properly setting up a QM/MM simulation is not an easy task, and several issues need to be properly addressed to obtain meaningful results. In the present work, we describe both the theoretical concepts and practical issues that need to be considered when performing QM/MM simulations. We start with a brief historical perspective on the development of these methods and describe when and why QM/MM methods are mandatory. Then we show how to properly select and analyze the performance of the QM level of theory, the QM system size, and the position and type of the boundaries. We show the relevance of performing prior QM model system (or QM cluster) calculations in a vacuum and how to use the corresponding results to adequately calibrate those derived from QM/MM. We also discuss how to prepare the starting structure and how to select an adequate simulation strategy, including those based on geometry optimizations as well as free energy methods. In particular, we focus on the determination of free energy profiles using multiple steered molecular dynamics (MSMD) combined with Jarzynski's equation. Finally, we describe the results for two illustrative and complementary examples: the reaction performed by chorismate mutase and the study of ligand binding to hemoglobins. Overall, we provide many practical recommendations (or shortcuts) together with important conceptualizations that we hope will encourage more and more researchers to incorporate QM/MM studies into their research projects.

AsiteDesign: a Semirational Algorithm for an Automated Enzyme Design

With advances in protein structure predictions, the number of available high-quality structures has increased dramatically. In light of these advances, structure-based enzyme engineering is expected to become increasingly important for optimizing biocatalysts for industrial processes. Here, we present AsiteDesign, a Monte Carlo-based protocol for structure-based engineering of active sites. AsiteDesign provides a framework for introducing new catalytic residues in a given binding pocket to either create a new catalytic activity or alter the existing one. AsiteDesign is implemented using pyRosetta and incorporates enhanced sampling techniques to efficiently explore the search space. The protocol was tested by designing an alternative catalytic triad in the active site of Pseudomonas fluorescens esterase (PFE). The designed variant was experimentally verified to be active, demonstrating that AsiteDesign can find alternative catalytic triads. Additionally, the AsiteDesign protocol was employed to enhance the hydrolysis of a bulky chiral substrate (1-phenyl-2-pentyl acetate) by PFE. The experimental verification of the designed variants demonstrated that F158L/F198A and F125A/F158L mutations increased the hydrolysis of 1-phenyl-2-pentyl acetate from 8.9 to 66.7 and 23.4%, respectively, and reversed the enantioselectivity of the enzyme from (R) to (S)-enantiopreference, with 32 and 55% enantiomeric excess (ee), respectively.

Geometry of Charge Density as a Reporter on the Role of the Protein Scaffold in Enzymatic Catalysis: Electrostatic Preorganization and Beyond

Enzymes host active sites inside protein macromolecules, which have diverse, often incredibly complex, and atom-expensive structures. It is an outstanding question what the role of these expensive scaffolds might be in enzymatic catalysis. Answering this question is essential to both enzymology and the design of artificial enzymes with proficiencies that will match those of the best natural enzymes. Protein rigidifying the active site, contrasted with the dynamics and vibrational motion promoting the reaction, as well as long-range electrostatics (also known as electrostatic preorganization) were all proposed as central contributions of the scaffold to the catalysis. Here, we show that all these effects inevitably produce changes in the quantum mechanical electron density in the active site, which in turn defines the reactivity. The phenomena are therefore fundamentally inseparable. The geometry of the electron density-a scalar field characterized by a number of mathematical features such as critical points-is a rigorous and convenient descriptor of enzymatic catalysis and a reporter on the role of the protein. We show how this geometry can be analyzed, linked to the reaction barriers, and report in particular on intramolecular electric fields in enzymes. We illustrate these tools on the studies of electrostatic preorganization in several representative enzyme classes, both natural and artificial. We highlight the forward-looking aspects of the approach.

OntoPESScan: An Ontology for Potential Energy Surface Scans

In this work, a new OntoPESScan ontology is developed for the semantic representation of one-dimensional potential energy surface (PES) scans, a central concept in computational chemistry. This ontology is developed in line with knowledge graph principles and The World Avatar (TWA) project. OntoPESScan is linked to other ontologies for chemistry in TWA, including OntoSpecies, which helps uniquely identify species along the PES and access their properties, and OntoCompChem, which allows the association of potential energy surfaces with quantum chemical calculations and the concepts used to derive them. A force-field fitting agent is also developed that makes use of the information in the OntoPESScan ontology to fit force fields to reactive surfaces of interest on the fly by making use of the empirical valence bond methodology. This agent is demonstrated to successfully parametrize two cases, namely, a PES scan on ethanol and a PES scan on a localized π-radical PAH hypothesized to play a role in soot formation during combustion. OntoPESScan is an extension to the capabilities of TWA and, in conjunction with potential further ontological support for molecular dynamics and reactions, will further progress toward an open, continuous, and self-growing knowledge graph for chemistry.

Flexible Polarizable Water Model Parameterized via Gaussian Process Regression

Water is one of the most common components in molecular dynamics (MD) simulations. Using Gaussian process regression for predicting the properties of a water model without the need of running a simulation whenever the parameters are changed, we obtained a flexible polarizable water model, named SWM4/Fw, that is able to reproduce many reference water properties. The added flexibility is critical for modeling chemical reactions in which chemical bonds can be stretched or even broken and for directly calculating vibrational spectra. In addition to being one of the few water models that are both flexible and polarizable, SWM4/Fw is also efficient thanks to the extended Lagrangian scheme with Drude oscillators. The overall accuracy is on par with or better than the related SWM4-NDP model.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Why Monoamine Oxidase B Preferably Metabolizes N-Methylhistamine over Histamine: Evidence from the Multiscale Simulation of the Rate-Limiting Step

Histamine levels in the human brain are controlled by rather peculiar metabolic pathways. In the first step, histamine is enzymatically methylated at its imidazole N^τ atom, and the produced N-methylhistamine undergoes an oxidative deamination catalyzed by monoamine oxidase B (MAO-B), as is common with other monoaminergic neurotransmitters and neuromodulators of the central nervous system. The fact that histamine requires such a conversion prior to oxidative deamination is intriguing since MAO-B is known to be relatively promiscuous towards monoaminergic substrates; its in-vitro oxidation of N-methylhistamine is about 10 times faster than that for histamine, yet this rather subtle difference appears to be governing the decomposition pathway. This work clarifies the MAO-B selectivity toward histamine and N-methylhistamine by multiscale simulations of the rate-limiting hydride abstraction step for both compounds in the gas phase, in aqueous solution, and in the enzyme, using the established empirical valence bond methodology, assisted by gas-phase density functional theory (DFT) calculations. The computed barriers are in very good agreement with experimental kinetic data, especially for relative trends among systems, thereby reproducing the observed MAO-B selectivity. Simulations clearly demonstrate that solvation effects govern the reactivity, both in aqueous solution as well as in the enzyme although with an opposing effect on the free energy barrier. In the aqueous solution, the transition-state structure involving histamine is better solvated than its methylated analog, leading to a lower barrier for histamine oxidation. In the enzyme, the higher hydrophobicity of N-methylhistamine results in a decreased number of water molecules at the active side, leading to decreased dielectric shielding of the preorganized catalytic electrostatic environment provided by the enzyme. This renders the catalytic environment more efficient for N-methylhistamine, giving rise to a lower barrier relative to histamine. In addition, the transition state involving N-methylhistamine appears to be stabilized by the surrounding nonpolar residues to a larger extent than with unsubstituted histamine, contributing to a lower barrier with the former.

Property Map Collective Variable as a Useful Tool for a Force Field Correction

The accuracy of biomolecular simulations depends on the accuracy of an empirical molecular mechanics potential known as a force field: a set of parameters and expressions to estimate the potential from atomic coordinates. Accurate parametrization of force fields for small organic molecules is a challenge due to their high diversity. One of the possible approaches is to apply a correction to the existing force fields. Here, we propose an approach to estimate the density functional theory (DFT)-derived force field correction which is calculated during the run of molecular dynamics without significantly affecting its speed. Using the formula known as a property map collective variable, we approximate the force field correction by a weighted average of this force field correction calculated only for a small series of reference structures. To validate this method, we used seven AMBER force fields, and we show how it is possible to convert one force field to behave like the other one. We also present the force field correction for the important anticancer drug Imatinib as a use case example. Our method appears to be suitable for adjusting the force field for general drug-like molecules. We provide a pipeline that generates the correction; this pipeline is available at https://pmcvff-correction.cerit-sc.cz/.

Predicting Effects of Site-Directed Mutagenesis on Enzyme Kinetics by QM/MM and QM Calculations: A Case of Glutamate Carboxypeptidase II

Quantum and molecular mechanics (QM/MM) and QM-only (cluster model) modeling techniques represent the two workhorses in mechanistic understanding of enzyme catalysis. One of the stringent tests for QM/MM and/or QM approaches is to provide quantitative answers to real-world biochemical questions, such as the effect of single-point mutations on enzyme kinetics. This translates into predicting the relative activation energies to 1-2 kcal·mol^-1 accuracy; such predictions can be used for the rational design of novel enzyme variants with desired/improved characteristics. Herein, we employ glutamate carboxypeptidase II (GCPII), a dizinc metallopeptidase, also known as the prostate specific membrane antigen, as a model system. The structure and activity of this major cancer antigen have been thoroughly studied, both experimentally and computationally, which makes it an ideal model system for method development. Its reaction mechanism is quite well understood: the reaction coordinate comprises a "tetrahedral intermediate" and two transition states and experimental activation Gibbs free energy of ∼17.5 kcal·mol^-1 can be inferred for the known k_cat ≈ 1 s^-1. We correlate experimental kinetic data (including the E424H variant, newly characterized in this work) for various GCPII mutants (k_cat = 8.6 × 10^-5 s^-1 to 2.7 s^-1) with the energy profiles calculated by QM/MM and QM-only (cluster model) approaches. We show that the near-quantitative agreement between the experimental values and the calculated activation energies (ΔH^⧧) can be obtained and recommend the combination of the two protocols: QM/MM optimized structures and cluster model (QM) energetics. The trend in relative activation energies is mostly independent of the QM method (DFT functional) used. Last but not least, a satisfactory correlation between experimental and theoretical data allows us to provide qualitative and fairly simple explanations of the observed kinetic effects which are thus based on a rigorous footing.

Extended Mulliken-Hush Method with Applications to the Theoretical Study of Electron Transfer

A novel adiabatic-to-diabatic (ATD) transformation strategy, namely, the extended Mulliken-Hush (XMH) method, is proposed to evaluate diabatic properties including electronic couplings, potential energy surfaces, and their crossings. The XMH method is developed by adopting our recently proposed ATD transformation formula of a general vectorial physical observable, in which a useful ATD transformation is further determined by using an auxiliary dipole between localized frontier orbitals as a simple approximation of the diabatic transition dipole. The XMH method is simple and practical that provides a flexible way to construct diabatic states. To some extent, it can be regarded as an extension of the generalized Mulliken-Hush (GMH) method since the latter takes a stronger approximation, in which the diabatic transition dipole is assumed to be vanishing. Test calculations on the HeH₂⁺ system show that the electronic couplings predicted by the XMH method are closer to the ones calculated by the valence bond block-diagonalization approach than the GMH ones since the XMH method takes into account both the magnitude and direction of the diabatic transition dipole, which is consistent with the properties of this molecule. In the study of electron transfer in the two kinds of donor-bridge-acceptor systems, the XMH method maintains the simplicity of the GMH method and gives reasonable results even when the latter fails, wherein the diabatic transition dipole is nearly perpendicular to the difference of the initial and final adiabatic dipoles. More importantly, the XMH method can be easily combined with high-level electronic structure methods, in which the properties of the ground and excited states may be more accurately calculated, and hence, one may expect that further development of the XMH method would result in a general computational model for studying electron transfer reactions.

The future of biomolecular simulation in the pharmaceutical industry: what we can learn from aerodynamics modelling and weather prediction. Part 1. understanding the physical and computational complexity of in silico drug design

The predictive power of simulation has become embedded in the infrastructure of modern economies. Computer-aided design is ubiquitous throughout industry. In aeronautical engineering, built infrastructure and materials manufacturing, simulations are routinely used to compute the performance of potential designs before construction. The ability to predict the behaviour of products is a driver of innovation by reducing the cost barrier to new designs, but also because radically novel ideas can be piloted with relatively little risk. Accurate weather forecasting is essential to guide domestic and military flight paths, and therefore the underpinning simulations are critical enough to have implications for national security. However, in the pharmaceutical and biotechnological industries, the application of computer simulations remains limited by the capabilities of the technology with respect to the complexity of molecular biology and human physiology. Over the last 30 years, molecular-modelling tools have gradually gained a degree of acceptance in the pharmaceutical industry. Drug discovery has begun to benefit from physics-based simulations. While such simulations have great potential for improved molecular design, much scepticism remains about their value. The motivations for such reservations in industry and areas where simulations show promise for efficiency gains in preclinical research are discussed. In this, the first of two complementary papers, the scientific and technical progress that needs to be made to improve the predictive power of biomolecular simulations, and how this might be achieved, is firstly discussed (Part 1). In Part 2, the status of computer simulations in pharma is contrasted with aerodynamics modelling and weather forecasting, and comments are made on the cultural changes needed for equivalent computational technologies to become integrated into life-science industries.

Two Sides of Quantum-Based Modeling of Enzyme-Catalyzed Reactions: Mechanistic and Electronic Structure Aspects of the Hydrolysis by Glutamate Carboxypeptidase

We report the results of a computational study of the hydrolysis reaction mechanism of N-acetyl-l-aspartyl-l-glutamate (NAAG) catalyzed by glutamate carboxypeptidase II. Analysis of both mechanistic and electronic structure aspects of this multistep reaction is in the focus of this work. In these simulations, model systems are constructed using the relevant crystal structure of the mutated inactive enzyme. After selection of reaction coordinates, the Gibbs energy profiles of elementary steps of the reaction are computed using molecular dynamics simulations with ab initio type QM/MM potentials (QM/MM MD). Energies and forces in the large QM subsystem are estimated in the DFT(PBE0-D3/6-31G**) approximation. The established mechanism includes four elementary steps with the activation energy barriers not exceeding 7 kcal/mol. The models explain the role of point mutations in the enzyme observed in the experimental kinetic studies; namely, the Tyr552Ile substitution disturbs the "oxyanion hole", and the Glu424Gln replacement increases the distance of the nucleophilic attack. Both issues diminish the substrate activation in the enzyme active site. To quantify the substrate activation, we apply the QTAIM-based approaches and the NBO analysis of dynamic features of the corresponding enzyme-substrate complexes. Analysis of the 2D Laplacian of electron density maps allows one to define structures with the electron density deconcentration on the substrate carbon atom, i.e., at the electrophilic site of reactants. The similar electronic structure element in the NBO approach is a lone vacancy on the carbonyl carbon atom in the reactive species. The electronic structure patterns revealed in the NBO and QTAIM-based analyses consistently clarify the reactivity issues in this system.

Physics-based, neural network force fields for reactive molecular dynamics: Investigation of carbene formation from [EMIM+][OAc-]

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol^-1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

Loop Dynamics and Enzyme Catalysis in Protein Tyrosine Phosphatases

Protein tyrosine phosphatases (PTPs) play an important role in cellular signaling and have been implicated in human cancers, diabetes, and obesity. Despite shared catalytic mechanisms and transition states for the chemical steps of catalysis, catalytic rates within the PTP family vary over several orders of magnitude. These rate differences have been implied to arise from differing conformational dynamics of the closure of a protein loop, the WPD-loop, which carries a catalytically critical residue. The present work reports computational studies of the human protein tyrosine phosphatase 1B (PTP1B) and YopH from Yersinia pestis, for which NMR has demonstrated a link between their respective rates of WPD-loop motion and catalysis rates, which differ by an order of magnitude. We have performed detailed structural analysis, both conventional and enhanced sampling simulations of their loop dynamics, as well as empirical valence bond simulations of the chemical step of catalysis. These analyses revealed the key residues and structural features responsible for these differences, as well as the residues and pathways that facilitate allosteric communication in these enzymes. Curiously, our wild-type YopH simulations also identify a catalytically incompetent hyper-open conformation of its WPD-loop, sampled as a rare event, previously only experimentally observed in YopH-based chimeras. The effect of differences within the WPD-loop and its neighboring loops on the modulation of loop dynamics, as revealed in this work, may provide a facile means for the family of PTP enzymes to respond to environmental changes and regulate their catalytic activities.

Protonation Dynamics in the K-Channel of Cytochrome c Oxidase Estimated from Molecular Dynamics Simulations

Proton transfer reactions are one of the most fundamental processes in biochemistry. We present a simplistic approach for estimating proton transfer probabilities in a membrane protein, cytochrome c oxidase. We combine short molecular dynamics simulations at discrete protonation states with a Monte Carlo approach to exchange between those states. Requesting for a proton transfer the existence of a hydrogen-bonded connection between the two source and target residues of the exchange, restricts the acceptance of transfers to only those in which a proton-relay is possible. Together with an analysis of the hydrogen-bonded connectivity in one of the proton-conducting channels of cytochrome c oxidase, this approach gives insight into the protonation dynamics of the hydrogen-bonded networks. The connectivity and directionality of the networks are coupled to the conformation of an important protein residue in the channel, K362, rendering proton transfer in the entire channel feasible in only one of the two major conformations. Proton transport in the channel can thus be regulated by K362 not only through its possible role as a proton carrier itself, but also by allowing or preventing proton transport via water residues.

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.

The Effects of the Metal Ion Substitution into the Active Site of Metalloenzymes: A Theoretical Insight on Some Selected Cases

A large number of enzymes need a metal ion to express their catalytic activity. Among the different roles that metal ions can play in the catalytic event, the most common are their ability to orient the substrate correctly for the reaction, to exchange electrons in redox reactions, to stabilize negative charges. In many reactions catalyzed by metal ions, they behave like the proton, essentially as Lewis acids but are often more effective than the proton because they can be present at high concentrations at neutral pH. In an attempt to adapt to drastic environmental conditions, enzymes can take advantage of the presence of many metal species in addition to those defined as native and still be active. In fact, today we know enzymes that contain essential bulk, trace, and ultra-trace elements. In this work, we report theoretical results obtained for three different enzymes each of which contains different metal ions, trying to highlight any differences in their working mechanism as a function of the replacement of the metal center at the active site.

Oxide Relay: An Efficient Mechanism for Catalytic Water Oxidation at Hydrophobic Electrode Surfaces

In order to combine the advantages of molecular catalysts with the stability of solid-state catalysts, hybrid systems with catalysts immobilized on carbon nanotubes are prominent candidates. Here we explore our recent mechanistic proposal for Ru(tda)(py)₂, the oxide relay mechanism, in a hybrid system from an experimental study. It reacts with the same efficiency but with increased stability compared to the homogeneous molecular catalyst. We used the empirical valence bond method and molecular dynamics with enhanced sampling approaches to investigate the two key steps in the mechanism: the intramolecular O-O bond formation and the OH^- nucleophilic attack. The results on these calculations show that the oxide relay mechanism remains unaltered in the new environment. We believe that the principles should apply to other oxide containing dangling groups and to other metal centers, opening new possibilities of future developments on hybrid molecular catalyst-based water splitting devices.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Exploring the Proteolysis Mechanism of the Proteasomes

The proteasome is a key protease in the eukaryotic cells which is responsible for various important cellular processes such as the control of the cell cycle, immune responses, protein homeostasis, inflammation, apoptosis, and the response to proteotoxic stress. Acting as a major molecular machine for protein degradation, proteasome first identifies damaged or obsolete regulatory proteins by attaching ubiquitin chains and subsequently utilizes conserved pore loops of the heterohexameric ring of AAA+ (ATPases associated with diverse cellular activities) to pull and mechanically unfold and translocate the misfolded protein to the active site for proteolysis. A detailed knowledge of the reaction mechanism for this proteasomal proteolysis is of central importance, both for fundamental understanding and for drug discovery. The present study investigates the mechanism of the proteolysis by the proteasome with full consideration of the protein's flexibility and its impact on the reaction free energy. Major attention is paid to the role of the protein electrostatics in determining the activation barriers. The reaction mechanism is studied by considering a small artificial fluorogenic peptide substrate (Suc-LLVY-AMC) and evaluating the activation barriers and reaction free energies for the acylation and deacylation steps, by using the empirical valence bond method. Our results shed light on the proteolysis mechanism and thus should be important for further studies of the proteasome action.

Combinatorial Approach for Exploring Conformational Space and Activation Barriers in Computer-Aided Enzyme Design

Computer-aided enzyme design is a field of great potential importance for biotechnological applications, medical advances, and a fundamental understanding of enzyme action. However, reaching a predictive ability in this direction is extremely challenging. It requires both the ability to predict quantitatively the activation barriers in cases where the structure and sequence are known and the ability to predict the effect of different mutations. In this work, we propose a protocol for predicting reasonable starting structures of mutants of proteins with known structures and for calculating the activation barriers of the generated mutants. Our approach also allows us to use the predicted structures of the generated mutant to predict structures and activation barriers for subsequent set of mutations. This protocol is used to examine the reliability of the in silico directed evolution of Kemp eliminase and haloalkane dehalogenase. We also used the results of single and double mutations as a base for predicting the effect of transition-state stabilization by multiple concurrent mutations. This strategy seems to be useful in creating an activity funnel that provides a qualitative ranking of the catalytic power of different mutants.

Cascading proton transfers are a hallmark of the catalytic mechanism of SAM-dependent methyltransferases

The S-adenosyl methionine (SAM)-dependent methyltransferases attach a methyl group to the deprotonated methyl lysine using SAM as a donor. An intriguing, yet unanswered, question is how the deprotonation takes place. PRDM9 with well-defined enzyme activity is a good representative of the methyltransferase family to study the deprotonation and subsequently the methyl transfer. Our study has found that the pKa of Tyr357 is low enough to make it an ideal candidate for proton abstraction from the methyl lysine. The partially deprontonated Tyr357 is able to change its H-bond pattern thus bridging two proton tunneling states and providing a cascading proton transfer. We have uncovered a new catalytic mechanism for the deprotonation of the methyl lysine in methyltransferases.

The role of ligand-gated conformational changes in enzyme catalysis

Structural and biochemical studies on diverse enzymes have highlighted the importance of ligand-gated conformational changes in enzyme catalysis, where the intrinsic binding energy of the common phosphoryl group of their substrates is used to drive energetically unfavorable conformational changes in catalytic loops, from inactive open to catalytically competent closed conformations. However, computational studies have historically been unable to capture the activating role of these conformational changes. Here, we discuss recent experimental and computational studies, which can remarkably pinpoint the role of ligand-gated conformational changes in enzyme catalysis, even when not modeling the loop dynamics explicitly. Finally, through our joint analyses of these data, we demonstrate how the synergy between theory and experiment is crucial for furthering our understanding of enzyme catalysis.

Design and SAR Analysis of Covalent Inhibitors Driven by Hybrid QM/MM Simulations

Quantum mechanics/molecular mechanics (QM/MM) hybrid technique is emerging as a reliable computational method to investigate and characterize chemical reactions occurring in enzymes. From a drug discovery perspective, a thorough understanding of enzyme catalysis appears pivotal to assist the design of inhibitors able to covalently bind one of the residues belonging to the enzyme catalytic machinery. Thanks to the current advances in computer power, and the availability of more efficient algorithms for QM-based simulations, the use of QM/MM methodology is becoming a viable option in the field of covalent inhibitor design. In the present review, we summarized our experience in the field of QM/MM simulations applied to drug design problems which involved the optimization of agents working on two well-known drug targets, namely fatty acid amide hydrolase (FAAH) and epidermal growth factor receptor (EGFR). In this context, QM/MM simulations gave valuable information in terms of geometry (i.e., of transition states and metastable intermediates) and reaction energetics that allowed to correctly predict inhibitor binding orientation and substituent effect on enzyme inhibition. What is more, enzyme reaction modelling with QM/MM provided insights that were translated into the synthesis of new covalent inhibitor featured by a unique combination of intrinsic reactivity, on-target activity, and selectivity.

Path Integral Calculation of the Hydrogen/Deuterium Kinetic Isotope Effect in Monoamine Oxidase A-Catalyzed Decomposition of Benzylamine

Monoamine oxidase A (MAO A) is a well-known enzyme responsible for the oxidative deamination of several important monoaminergic neurotransmitters. The rate-limiting step of amine decomposition is hydride anion transfer from the substrate α–CH2 group to the N5 atom of the flavin cofactor moiety. In this work, we focus on MAO A-catalyzed benzylamine decomposition in order to elucidate nuclear quantum effects through the calculation of the hydrogen/deuterium (H/D) kinetic isotope effect. The rate-limiting step of the reaction was simulated using a multiscale approach at the empirical valence bond (EVB) level. We applied path integral quantization using the quantum classical path method (QCP) for the substrate benzylamine as well as the MAO cofactor flavin adenine dinucleotide. The calculated H/D kinetic isotope effect of 6.5 ± 1.4 is in reasonable agreement with the available experimental values.

Unified Model for Photophysical and Electro-Optical Properties of Green Fluorescent Proteins

Green fluorescent proteins (GFPs) have become indispensable imaging and optogenetic tools. Their absorption and emission properties can be optimized for specific applications. Currently, no unified framework exists to comprehensively describe these photophysical properties, namely the absorption maxima, emission maxima, Stokes shifts, vibronic progressions, extinction coefficients, Stark tuning rates, and spontaneous emission rates, especially one that includes the effects of the protein environment. In this work, we study the correlations among these properties from systematically tuned GFP environmental mutants and chromophore variants. Correlation plots reveal monotonic trends, suggesting that all these properties are governed by one underlying factor dependent on the chromophore's environment. By treating the anionic GFP chromophore as a mixed-valence compound existing as a superposition of two resonance forms, we argue that this underlying factor is defined as the difference in energy between the two forms, or the driving force, which is tuned by the environment. We then introduce a Marcus-Hush model with the bond length alternation vibrational mode, treating the GFP absorption band as an intervalence charge transfer band. This model explains all of the observed strong correlations among photophysical properties; related subtopics are extensively discussed in the Supporting Information. Finally, we demonstrate the model's predictive power by utilizing the additivity of the driving force. The model described here elucidates the role of the protein environment in modulating the photophysical properties of the chromophore, providing insights and limitations for designing new GFPs with desired phenotypes. We argue that this model should also be generally applicable to both biological and nonbiological polymethine dyes.

Networked Communication between Polymerase and Exonuclease Active Sites in Human Mitochondrial DNA Polymerase

High fidelity human mitochondrial DNA polymerase (Pol γ) contains two active sites, a DNA polymerization site (pol) and a 3'-5' exonuclease site (exo) for proofreading. Although separated by 35 Å, coordination between the pol and exo sites is crucial to high fidelity replication. The biophysical mechanisms for this coordination are not completely understood. To understand the communication between the two active sites, we used a statistical-mechanical model of the protein ensemble to calculate the energetic landscape and local stability. We compared a series of structures of Pol γ, complexed with primer/template DNA, and either a nucleotide substrate or a series of nucleotide analogues, which are differentially incorporated and excised by pol and exo activity. Despite the nucleotide or its analogues being bound in the pol, Pol γ residue stability varied across the protein, particularly in the exo domain. This suggests that substrate presence in the pol can be "sensed" in the exo domain. Consistent with this hypothesis, in silico mutations made in one active site mutually perturbed the energetics of the other. To identify specific regions of the polymerase that contributed to this communication, we constructed an allosteric network connectivity map that further demonstrates specific pol-exo cooperativity. Thus, a cooperative network underlies energetic connectivity. We propose that Pol γ and other dual-function polymerases exploit an energetic coupling network that facilitates domain-domain communication to enhance discrimination between correct and incorrect nucleotides.

Modeling Charge Flux by Interpolating Atomic Partial Charges

Although the charge flux effect or the geometric dependence of the atomic partial charges have been known for a long time, how it can be effectively handled is not yet established. Here, we present a charge interpolation scheme as a new general tool for representing the charge flux in an analytically well-defined manner. By applying it to the anionic GFP chromophore with the diabatically represented atomic charges, we show that the charge interpolation provides a substantial improvement on the accuracy of the geometry-dependent changes in the molecular dipole moments in the gas phase. We also test the scheme toward describing the electrostatic term in the solvation energy in the aqueous environment and observe that it is also improved but that the extent of the improvement is somewhat limited. We show that the remaining errors can be largely corrected by introducing atomic polarizabilities. Overall, our results show that charge interpolation is an amenable approach for describing the charge flux effect and that its description in the condensed phase should be accompanied by proper treatments of polarization effects.

Molecular Mechanisms of DNA Replication and Repair Machinery: Insights from Microscopic Simulations

Reproduction, the hallmark of biological activity, requires making an accurate copy of the genetic material to allow the progeny to inherit parental traits. In all living cells, the process of DNA replication is carried out by a concerted action of multiple protein species forming a loose protein-nucleic acid complex, the replisome. Proofreading and error correction generally accompany replication but also occur independently, safeguarding genetic information through all phases of the cell cycle. Advances in biochemical characterization of intracellular processes, proteomics and the advent of single-molecule biophysics have brought about a treasure trove of information awaiting to be assembled into an accurate mechanistic model of the DNA replication process. In this review, we describe recent efforts to model elements of DNA replication and repair processes using computer simulations, an approach that has gained immense popularity in many areas of molecular biophysics but has yet to become mainstream in the DNA metabolism community. We highlight the use of diverse computational methods to address specific problems of the fields and discuss unexplored possibilities that lie ahead for the computational approaches in these areas.

Protein Flexibility and Stiffness Enable Efficient Enzymatic Catalysis

The enormous rate accelerations observed for many enzyme catalysts are due to strong stabilizing interactions between the protein and reaction transition state. The defining property of these catalysts is their specificity for binding the transition state with a much higher affinity than substrate. Experimental results are presented which show that the phosphodianion-binding energy of phosphate monoester substrates is used to drive conversion of their protein catalysts from flexible and entropically rich ground states to stiff and catalytically active Michaelis complexes. These results are generalized to other enzyme-catalyzed reactions. The existence of many enzymes in flexible, entropically rich, and inactive ground states provides a mechanism for utilization of ligand-binding energy to mold these catalysts into stiff and active forms. This reduces the substrate-binding energy expressed at the Michaelis complex, while enabling the full and specific expression of large transition-state binding energies. Evidence is presented that the complexity of enzyme conformational changes increases with increases in the enzymatic rate acceleration. The requirement that a large fraction of the total substrate-binding energy be utilized to drive conformational changes of floppy enzymes is proposed to favor the selection and evolution of protein folds with multiple flexible unstructured loops, such as the TIM-barrel fold. The effect of protein motions on the kinetic parameters for enzymes that undergo ligand-driven conformational changes is considered. The results of computational studies to model the complex ligand-driven conformational change in catalysis by triosephosphate isomerase are presented.

In Silico-Directed Evolution Using CADEE

Recent years have seen an explosion of interest in both sequence- and structure-based approaches toward in silico-directed evolution. We recently developed a novel computational toolkit, CADEE, which facilitates the computer-aided directed evolution of enzymes. Our initial work (Amrein et al., IUCrJ 4:50-64, 2017) presented a pedagogical example of the application of CADEE to triosephosphate isomerase, to illustrate the CADEE workflow. In this contribution, we describe this workflow in detail, including code input/output snippets, in order to allow users to set up and execute CADEE simulations on any system of interest.

Exploring the challenges of computational enzyme design by rebuilding the active site of a dehalogenase

Rational enzyme design presents a major challenge that has not been overcome by computational approaches. One of the key challenges is the difficulty in assessing the magnitude of the maximum possible catalytic activity. In an attempt to overcome this challenge, we introduce a strategy that takes an active enzyme (assuming that its activity is close to the maximum possible activity), design mutations that reduce the catalytic activity, and then try to restore that catalysis by mutating other residues. Here we take as a test case the enzyme haloalkane dehalogenase (DhlA), with a 1,2-dichloroethane substrate. We start by demonstrating our ability to reproduce the results of single mutations. Next, we design mutations that reduce the enzyme activity and finally design double mutations that are aimed at restoring the activity. Using the computational predictions as a guide, we conduct an experimental study that confirms our prediction in one case and leads to inconclusive results in another case with 1,2-dichloroethane as substrate. Interestingly, one of our predicted double mutants catalyzes dehalogenation of 1,2-dibromoethane more efficiently than the wild-type enzyme.

Loop Motion in Triosephosphate Isomerase Is Not a Simple Open and Shut Case

Conformational changes are crucial for the catalytic action of many enzymes. A prototypical and well-studied example is loop opening and closure in triosephosphate isomerase (TIM), which is thought to determine the rate of catalytic turnover in many circumstances. Specifically, TIM loop 6 "grips" the phosphodianion of the substrate and, together with a change in loop 7, sets up the TIM active site for efficient catalysis. Crystal structures of TIM typically show an open or a closed conformation of loop 6, with the tip of the loop moving ∼7 Å between conformations. Many studies have interpreted this motion as a two-state, rigid-body transition. Here, we use extensive molecular dynamics simulations, with both conventional and enhanced sampling techniques, to analyze loop motion in apo and substrate-bound TIM in detail, using five crystal structures of the dimeric TIM from Saccharomyces cerevisiae. We find that loop 6 is highly flexible and samples multiple conformational states. Empirical valence bond simulations of the first reaction step show that slight displacements away from the fully closed-loop conformation can be sufficient to abolish most of the catalytic activity; full closure is required for efficient reaction. The conformational change of the loops in TIM is thus not a simple "open and shut" case and is crucial for its catalytic action. Our detailed analysis of loop motion in a highly efficient enzyme highlights the complexity of loop conformational changes and their role in biological catalysis.