The EVB as a quantitative tool for formulating simulations and analyzing biological and chemical reactions

Toward transferable empirical valence bonds: Making classical force fields reactive

The empirical valence bond technique allows classical force fields to model reactive processes. However, parametrization from experimental data or quantum mechanical calculations is required for each reaction present in the simulation. We show that the parameters present in the empirical valence bond method can be predicted using a neural network model and the SMILES strings describing a reaction. This removes the need for quantum calculations in the parametrization of the empirical valence bond technique. In doing so, we have taken the first steps toward defining a new procedure for enabling reactive atomistic simulations. This procedure would allow researchers to use existing classical force fields for reactive simulations, without performing additional quantum mechanical calculations.

Accurate Computation of Thermodynamic Activation Parameters in the Chorismate Mutase Reaction from Empirical Valence Bond Simulations

Chorismate mutase (CM) enzymes have long served as model systems for benchmarking new methods and tools in computational chemistry. Despite the enzymes' prominence in the literature, the extent of the roles that activation enthalpy and entropy play in catalyzing the conversion of chorismate to prephenate is still subject to debate. Knowledge of these parameters is a key piece in fully understanding the mechanism of chorismate mutases. Within this study, we utilize EVB/MD free energy perturbation calculations at a range of temperatures, allowing us to extract activation enthalpies and entropies from an Arrhenius plot of activation free energies of the reaction catalyzed by a monofunctional Bacillus subtilis CM and the promiscuous enzyme isochorismate pyruvate lyase of Pseudomonas aeruginosa. In comparison to the uncatalyzed reaction, our results show that both enzyme-catalyzed reactions exhibit a substantial reduction in activation enthalpy, while the effect on activation entropy is relatively minor, demonstrating that enzyme-catalyzed CM reactions are enthalpically driven. Furthermore, we observe that the monofunctional CM from B. subtilis more efficiently catalyzes this reaction than its promiscuous counterpart. This is supported by a structural analysis of the reaction pathway at the transition state, from which we identified key residues explaining the enthalpically driven nature of the reactions and also the difference in efficiencies between the two enzymes.

The catalytic mechanism of the mitochondrial methylenetetrahydrofolate dehydrogenase/cyclohydrolase (MTHFD2)

Methylenetetrahydrofolate dehydrogenase/cyclohydrolase (MTHFD2) is a new drug target that is expressed in cancer cells but not in normal adult cells, which provides an Achilles heel to selectively kill cancer cells. Despite the availability of crystal structures of MTHFD2 in the inhibitor- and cofactor-bound forms, key information is missing due to technical limitations, including (a) the location of absolutely required Mg2+ ion, and (b) the substrate-bound form of MTHFD2. Using computational modeling and simulations, we propose that two magnesium ions are present at the active site whereby (i) Arg233, Asp225, and two water molecules coordinate MgA2+, while MgA2+ together with Arg233 stabilize the inorganic phosphate (Pi); (ii) Asp168 and three water molecules coordinate MgB2+, and MgB2+ further stabilizes Pi by forming a hydrogen bond with two oxygens of Pi; (iii) Arg201 directly coordinates the Pi; and (iv) through three water-mediated interactions, Asp168 contributes to the positioning and stabilization of MgA2+, MgB2+ and Pi. Our computational study at the empirical valence bond level allowed us also to elucidate the detailed reaction mechanisms. We found that the dehydrogenase activity features a proton-coupled electron transfer with charge redistribution connected to the reorganization of the surrounding water molecules which further facilitates the subsequent cyclohydrolase activity. The cyclohydrolase activity then drives the hydration of the imidazoline ring and the ring opening in a concerted way. Furthermore, we have uncovered that two key residues, Ser197/Arg233, are important factors in determining the cofactor (NADP+/NAD+) preference of the dehydrogenase activity. Our work sheds new light on the structural and kinetic framework of MTHFD2, which will be helpful to design small molecule inhibitors that can be used for cancer treatment.

Low temperature catalytic hydrodeoxygenation of lignin-derived phenols to cyclohexanols over the Ru/SBA-15 catalyst

Cyclohexanol and its derivatives are widely used as chemical intermediates and fuel additives. Herein, Ru/SBA-15 catalysts were prepared via impregnation, and used for the production of cyclohexanols from lignin-derived phenols. The catalyst samples were characterized by XRD, XPS, TEM, etc., where the Ru⁰ species was speculated as the active phase. 5 wt% Ru/SBA-15 with small Ru particle size (4.99 nm) and high Ru dispersion (27.05%) exhibited an excellent hydrogenation activity. A high cyclohexanol yield of >99.9% was achieved at 20 °C for 5 h in an aqueous phase, and the catalyst indicated stable activity and selectivity after five runs. Crucially, Ru/SBA-15 exhibited a zero-order reaction rate with an apparent activation energy (Ea) as low as 10.88 kJ mol⁻¹ and a TON of 172.84 at 80 °C. Simultaneously, demethoxylation activity was also observed in the hydrodeoxygenation (HDO) of G- and S-type monophenols, and a high yield of 37.4% of cyclohexanol was obtained at 80 °C and 4 h when using eugenol as substrate.

Ru/SBA-15 showed excellent activity for phenol to cyclohexanol at 20 °C and exhibited a zero-order character with low Ea of 10.88 kJ mol⁻¹. A high yield of 37.4% of cyclohexanol was obtained at 80 °C and 4 h when using eugenol as substrate.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

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.

Histidine protonation states are key in the LigI catalytic reaction mechanism

Lignin is one of the world's most abundant organic polymers, and 2-pyrone-4,6-dicarboxylate lactonase (LigI) catalyzes the hydrolysis of 2-pyrone-4,6-dicarboxylate (PDC) in the degradation of lignin. The pH has profound effects on enzyme catalysis and therefore we studied this in the context of LigI. We found that changes of the pH mostly affects surface residues, while the residues at the active site are more subject to changes of the surrounding microenvironment. In accordance with this, a high pH facilitates the deprotonation of the substrate. Detailed free energy calculations by the empirical valence bond (EVB) approach revealed that the overall hydrolysis reaction is more likely when the three active site histidines (His31, His33 and His180) are protonated at the ɛ site, however, protonation at the δ site may be favored during specific steps of the reaction. Our studies have uncovered the determinant role of the protonation state of the active site residues His31, His33 and His180 in the hydrolysis of PDC.

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.

Hydride Abstraction as the Rate-Limiting Step of the Irreversible Inhibition of Monoamine Oxidase B by Rasagiline and Selegiline: A Computational Empirical Valence Bond Study

Monoamine oxidases (MAOs) catalyze the degradation of a very broad range of biogenic and dietary amines including many neurotransmitters in the brain, whose imbalance is extensively linked with the biochemical pathology of various neurological disorders, and are, accordingly, used as primary pharmacological targets to treat these debilitating cognitive diseases. Still, despite this practical significance, the precise molecular mechanism underlying the irreversible MAO inhibition with clinically used propargylamine inhibitors rasagiline and selegiline is still not unambiguously determined, which hinders the rational design of improved inhibitors devoid of side effects current drugs are experiencing. To address this challenge, we present empirical valence bond QM/MM simulations of the rate-limiting step of the MAO inhibition involving the hydride anion transfer from the inhibitor α-carbon onto the N5 atom of the flavin adenin dinucleotide (FAD) cofactor. The proposed mechanism is strongly supported by the obtained free energy profiles, which confirm a higher reactivity of selegiline over rasagiline, while the calculated difference in the activation Gibbs energies of ΔΔG^‡ = 3.1 kcal mol^-1 is found to be in very good agreement with that from the measured literature k_inact values that predict a 1.7 kcal mol^-1 higher selegiline reactivity. Given the similarity with the hydride transfer mechanism during the MAO catalytic activity, these results verify that both rasagiline and selegiline are mechanism-based irreversible inhibitors and offer guidelines in designing new and improved inhibitors, which are all clinically employed in treating a variety of neuropsychiatric and neurodegenerative conditions.

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.

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.

Exploring alternative catalytic mechanisms of the Cas9 HNH domain

Understanding the reaction mechanism of CRISPR-associated protein 9 (Cas9) is crucial for the application of programmable gene editing. Despite the availability of the structures of Cas9 in apo- and substrate-bound forms, the catalytically active structure is still unclear. Our first attempt to explore the catalytic mechanism of Cas9 HNH domain has been based on the reasonable assumption that we are dealing with the same mechanism as endonuclease VII, including the assumption that the catalytic water is in the first shell of the Mg2+ . Trying this mechanism with the cryo-EM structure forced us to induce significant structural change driven by the movement of K848 (or other positively charged residue) close to the active site to facilitate the proton transfer step. In the present study, we explore a second reaction mechanism where the catalytic water is in the second shell of the Mg2+ and assume that the cryo-EM structure by itself is a suitable representation of a catalytic-ready structure. The alternative mechanism indicates that if the active water is from the second shell, then the calculated reaction barrier is lower compared with the corresponding barrier when the water comes from the first shell.

Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wave function method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.

Anharmonic Molecular Mechanics: Ab Initio Based Morse Parametrizations for the Popular MM3 Force Field

Methodologies for creating reactive potential energy surfaces from molecular mechanics force-fields are becoming increasingly popular. To date, molecular mechanics force-fields in biochemistry and small molecule organic chemistry tend to use harmonic expressions to treat bonding stretches, which is a poor approximation in reactive and nonequilibirum molecular dynamics simulations since bonds are often displaced significantly from their equilibrium positions. For such applications there is need for a better treatment of anharmonicity. In this contribution, Morse bonding potentials have been extensively parametrized for the atom types in the MM3 force field of Allinger and co-workers using high level CCSD(T)(F12*) energies. To our knowledge this is among the first instances of a comprehensive parametrization of Morse potentials in a popular organic chemistry force field. In the context of molecular dynamics simulations, these data will: (1) facilitate the fitting of reactive potential energy surfaces using empirical valence bond approaches and (2) enable more accurate treatments of energy transfer.

Exploring the Catalytic Mechanism of Cas9 Using Information Inferred from Endonuclease VII

Elucidating the nature of the gene editing mechanism of CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) is an important task in view of the role of this breakthrough to the advancement of human medicine. In particular, it is crucial to understand the catalytic mechanism of Cas9 (one of the CRISPR associated proteins) and its role in confirming accurate editing. Thus, we focus in this work on an attempt to analyze the catalytic mechanism of Cas9. Considering the absence of detailed structural information on the active form of Cas9, we use an empirical valence bond (EVB) which is calibrated on the closely related mechanism of T4 endonuclease VII. The calibrated EVB is then used in studying the reaction of Cas9, while trying several structural models. It is found that the catalytic activation requires a large conformational change, where K848 or other positively charged group moves from a relatively large distance toward the scissile phosphate. This conformational change leads to the change in position of the Mg²⁺ ion and to a major reduction in the activation barrier for the catalytic reaction. Our finding provides an important clue on the nature of the catalytic activation of CAS9 and thus should help in elucidating a key aspect of the gene editing process. For example, the approach used here should be effective in exploring the nature of off target activation and its relationship to the energetics of the unwinding process. This strategy may offer ways to improve the selectivity of Cas9.

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.

Modulating Enzyme Activity by Altering Protein Dynamics with Solvent

Optimal enzyme activity depends on a number of factors, including structure and dynamics. The role of enzyme structure is well recognized; however, the linkage between protein dynamics and enzyme activity has given rise to a contentious debate. We have developed an approach that uses an aqueous mixture of organic solvent to control the functionally relevant enzyme dynamics (without changing the structure), which in turn modulates the enzyme activity. Using this approach, we predicted that the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase (DHFR) from Escherichia coli in aqueous mixtures of isopropanol (IPA) with water will decrease by ∼3 fold at 20% (v/v) IPA concentration. Stopped-flow kinetic measurements find that the pH-independent k_hydride rate decreases by 2.2 fold. X-ray crystallographic enzyme structures show no noticeable differences, while computational studies indicate that the transition state and electrostatic effects were identical for water and mixed solvent conditions; quasi-elastic neutron scattering studies show that the dynamical enzyme motions are suppressed. Our approach provides a unique avenue to modulating enzyme activity through changes in enzyme dynamics. Further it provides vital insights that show the altered motions of DHFR cause significant changes in the enzyme's ability to access its functionally relevant conformational substates, explaining the decreased k_hydride rate. This approach has important implications for obtaining fundamental insights into the role of rate-limiting dynamics in catalysis and as well as for enzyme engineering.

EF-Tu and EF-G are activated by allosteric effects

Many cellular processes are controlled by GTPases, and gaining quantitative understanding of the activation of such processes has been a major challenge. In particular, it is crucial to obtain reliable free-energy surfaces for the relevant reaction paths both in solution and in GTPases active sites. Here, we revisit the energetics of the activation of EF-G and EF-Tu by the ribosome and explore the nature of the catalysis of the GTPase reaction. The comparison of EF-Tu to EF-G allows us to explore the impact of possible problems with the available structure of EF-Tu. Additionally, mutational effects are used for a careful validation of the emerging conclusions. It is found that the reaction may proceed by both a two-water mechanism and a one-water (GTP as a base) mechanism. However, in both cases, the activation involves a structural allosteric effect, which is likely to be a general-activation mechanism for all GTPases.

Structural Articulation of Biochemical Reactions Using Restrained Geometries and Topology Switching

A strategy named "restrained geometries and topology switching" (RGATS) is presented to obtain detailed trajectories for complex biochemical reactions using molecular mechanics (MM) methods. It enables prediction of realistic dynamical pathways for chemical reactions, especially for accurately characterizing the structural adjustments of highly complex environments to any proximal biochemical reaction. It can be used to generate reactive conformations, model stepwise or concerted reactions in complex environments, and probe the influence of changes in the environment. Its ability to take reactively nonoptimal conformations and generate favorable starting conformations for a biochemical reaction is illustrated for a proton transfer between two model compounds. Its ability to study concerted reactions in explicit solvent is illustrated using proton transfers between an ammonium ion and two conserved histidines in an ammonia transporter channel embedded in a lipid membrane. Its ability to characterize the changes induced by subtle differences in the active site environment is illustrated using nucleotide addition by a DNA polymerase in the presence of two versus three Mg²⁺ ions. RGATS can be employed within any MM program and requires no additional software implementation. This allows the full assortment of computational methods implemented in all available MM programs to be used to tackle virtually any question about biochemical reactions that is answerable without using a quantum mechanical (QM) model. It can also be applied to generate reasonable starting structures for more detailed and expensive QM or QM/MM methods. In particular, this strategy enables rapid prediction of reactant, intermediary, or product state structures in any macromolecular context, with the only requirement being that the structure in any one of these states is either known or can be accurately modeled.

Origins of Enzyme Catalysis: Experimental Findings for C-H Activation, New Models, and Their Relevance to Prevailing Theoretical Constructs

The physical basis for enzymatic rate accelerations is a subject of great fundamental interest and of direct relevance to areas that include the de novo design of green catalysts and the pursuit of new drug regimens. Extensive investigations of C-H activating systems have provided considerable insight into the relationship between an enzyme's overall structure and the catalytic chemistry at its active site. This Perspective highlights recent experimental data for two members of distinct, yet iconic C-H activation enzyme classes, lipoxygenases and prokaryotic alcohol dehydrogenases. The data necessitate a reformulation of the dominant textbook definition of biological catalysis. A multidimensional model emerges that incorporates a range of protein motions that can be parsed into a combination of global stochastic conformational thermal fluctuations and local donor-acceptor distance sampling. These motions are needed to achieve a high degree of precision with regard to internuclear distances, geometries, and charges within the active site. The available model also suggests a physical framework for understanding the empirical enthalpic barrier in enzyme-catalyzed processes. We conclude by addressing the often conflicting interface between computational and experimental chemists, emphasizing the need for computation to predict experimental results in advance of their measurement.

Misunderstanding the preorganization concept can lead to confusions about the origin of enzyme catalysis

Understanding the origin of the catalytic power of enzymes has both conceptual and practical importance. One of the most important finding from computational studies of enzyme catalysis is that a major part of the catalytic power is due to the preorganization of the enzyme active site. Unfortunately, misunderstanding of the nontrivial preorganization idea lead some to assume that it does not consider the effect of the protein residues. This major confusion reflects a misunderstanding of the statement that the interaction energy of the enzyme group and the transition state (TS) is similar to the corresponding interaction between the water molecules (in the reference system) and the TS, and that the catalysis is due to the reorganization free energy of the water molecules. Obviously, this finding does not mean that we do not consider the enzyme groups. Another problem is the idea that catalysis is due to substrate preorganization. This more traditional idea is based in some cases on inconsistent interpretation of the action of model compounds, which unfortunately, do not reflect the actual situation in the enzyme active site. The present article addresses the above problems, clarifying first the enzyme polar preorganization idea and the current misunderstandings. Next we take a specific model compound that was used to promote the substrate preorganization proposal and establish its irrelevance to enzyme catalysis. Overall, we show that the origin of the catalytic power of enzymes cannot be assessed uniquely without computer simulations, since at present this is the only way of relating structure and energetics.

Coupled Valence-Bond State Molecular Dynamics Description of an Enzyme-Catalyzed Reaction in a Non-Aqueous Organic Solvent

Enzymes are widely used in nonaqueous solvents to catalyze non-natural reactions. While experimental measurements showed that the solvent nature has a strong effect on the reaction kinetics, the molecular details of the catalytic mechanism in nonaqueous solvents have remained largely elusive. Here we study the transesterification reaction catalyzed by the paradigm subtilisin Carlsberg serine protease in an organic apolar solvent. The rate-limiting acylation step involves a proton transfer between active-site residues and the nucleophilic attack of the substrate to form a tetrahedral intermediate. We design the first coupled valence-bond state model that simultaneously describes both reactions in the enzymatic active site. We develop a new systematic procedure to parametrize this model on high-level ab initio QM/MM free energy calculations that account for the molecular details of the active site and for both substrate and protein conformational fluctuations. Our calculations show that the reaction energy barrier changes dramatically with the solvent and protein conformational fluctuations. We find that the mechanism of the tetrahedral intermediate formation during the acylation step is similar to that determined under aqueous conditions, and that the proton transfer and nucleophilic attack reactions occur concertedly. We identify the reaction coordinate to be mostly due to the rearrangement of some residual water molecules close to the active site.

Exploring the Drug Resistance of HCV Protease

Hepatitis C virus (HCV) currently affects several million people across the globe. One of the major classes of drugs against HCV inhibits the NS3/4A protease of the polyprotein chain. Efficacy of these drugs is severely limited due to the high mutation rate that results in several genetically related quasispecies. The molecular mechanism of drug resistance is frequently deduced from structural studies and binding free energies. However, prediction of new mutations requires the evaluation of both binding free energy of the drug as well as the parameters (k_cat and K_M) for the natural substrate. The vitality values offer a good approach to investigate and predict mutations that render resistance to the inhibitor. A successful mutation should only affect the binding of the drug and not the catalytic activity and binding of the natural substrate. In this article, we have calculated the vitality values for four known drug inhibitors that are either currently in use or in clinical trials, evaluating binding free energies by the relevant PDLD/S-LRA method and activation barriers by the EVB method. The molecular details pertaining to resistance are also discussed. We show that our calculations are able to reproduce the catalytic effects and binding free energies in a good agreement with the corresponding observed values. Importantly, previous computational approaches have not been able to achieve this task. The trend for the vitality values is in accordance with experimental findings. Finally, we calculate the vitality values for mutations that have either not been studied experimentally or reported for some inhibitors.

Computational Biochemistry-Enzyme Mechanisms Explored

Understanding enzyme mechanisms is a major task to achieve in order to comprehend how living cells work. Recent advances in biomolecular research provide huge amount of data on enzyme kinetics and structure. The analysis of diverse experimental results and their combination into an overall picture is, however, often challenging. Microscopic details of the enzymatic processes are often anticipated based on several hints from macroscopic experimental data. Computational biochemistry aims at creation of a computational model of an enzyme in order to explain microscopic details of the catalytic process and reproduce or predict macroscopic experimental findings. Results of such computations are in part complementary to experimental data and provide an explanation of a biochemical process at the microscopic level. In order to evaluate the mechanism of an enzyme, a structural model is constructed which can be analyzed by several theoretical approaches. Several simulation methods can and should be combined to get a reliable picture of the process of interest. Furthermore, abstract models of biological systems can be constructed combining computational and experimental data. In this review, we discuss structural computational models of enzymatic systems. We first discuss various models to simulate enzyme catalysis. Furthermore, we review various approaches how to characterize the enzyme mechanism both qualitatively and quantitatively using different modeling approaches.

Exploring the Development of Ground-State Destabilization and Transition-State Stabilization in Two Directed Evolution Paths of Kemp Eliminases

Computer-aided enzyme design presents a major challenge since in most cases it has not resulted in an impressive catalytic power. The reasons for the problems with computational design include the use of nonquantitative approaches, but they may also reflect other difficulties that are not completely obvious. Thus, it is very useful to try to learn from the trend in directed evolution experiments. Here we explore the nature of the refinement of Kemp eliminases by directed evolution, trying to gain an understanding of related requirements from computational design. The observed trend in the directed evolution refinement of KE07 and HG3 are reproduced, showing that in the case of KE07 the directed evolution leads to ground-state destabilization, whereas in the case of HG3 the directed evolution leads to transition-state stabilization. The nature of the different paths of the directed evolution is examined and discussed. The present study seems to indicate that computer-aided enzyme design may require more than calculations of the effect of single mutations and should be extended to calculations of the effect of simultaneous multiple mutations (that make a few residues preorganized effectively). However, the analysis of two known evolution paths can still be accomplished using the relevant sequences and structures. Thus, by comparing two directed evolution paths of Kemp eliminases we reached the important conclusion that the more effective path leads to transition-state stabilization.

Simulating the fidelity and the three Mg mechanism of pol η and clarifying the validity of transition state theory in enzyme catalysis

Pol η belongs to the important Y family of DNA polymerases that can catalyze translesion synthesis across sites of damaged DNA. This activity involves the reduced fidelity of Pol η for 8-oxo-7,8-dhyedro-2'-deoxoguanosin(8-oxoG). The fundamental interest in Pol η has grown recently with the demonstration of the importance of a 3rd Mg2+ ion. The current work explores both the fidelity of Pol η and the role of the 3rd metal ion, by using empirical valence bond (EVB) simulations. The simulations reproduce the observed trend in fidelity and shed a new light on the role of the 3rd metal ion. It is found that this ion does not lead to a major catalytic effect, but most probably plays an important role in reducing the product release barrier. Furthermore, it is concluded, in contrast to some implications, that the effect of this metal does not violate transition state theory, and the evaluation of the catalytic effect must conserve the molecular composition upon moving from the reactant to the transition state. Proteins 2017; 85:1446-1453. © 2017 Wiley Periodicals, Inc.

Theoretical estimation of redox potential of biological quinone cofactors

Redox potentials are essential to understand biological cofactor reactivity and to predict their behavior in biological media. Experimental determination of redox potential in biological system is often difficult due to complexity of biological media but computational approaches can be used to estimate them. Nevertheless, the quality of the computational methodology remains a key issue to validate the results. Instead of looking to the best absolute results, we present here the calibration of theoretical redox potential for quinone derivatives in water coupling QM + MM or QM/MM scheme. Our approach allows using low computational cost theoretical level, ideal for long simulations in biological systems, and determination of the uncertainties linked to the calculations. © 2017 Wiley Periodicals, Inc.

Perspective: Quantum mechanical methods in biochemistry and biophysics

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

Perspective: Defining and quantifying the role of dynamics in enzyme catalysis

Enzymes control chemical reactions that are key to life processes, and allow them to take place on the time scale needed for synchronization between the relevant reaction cycles. In addition to general interest in their biological roles, these proteins present a fundamental scientific puzzle, since the origin of their tremendous catalytic power is still unclear. While many different hypotheses have been put forward to rationalize this, one of the proposals that has become particularly popular in recent years is the idea that dynamical effects contribute to catalysis. Here, we present a critical review of the dynamical idea, considering all reasonable definitions of what does and does not qualify as a dynamical effect. We demonstrate that no dynamical effect (according to these definitions) has ever been experimentally shown to contribute to catalysis. Furthermore, the existence of non-negligible dynamical contributions to catalysis is not supported by consistent theoretical studies. Our review is aimed, in part, at readers with a background in chemical physics and biophysics, and illustrates that despite a substantial body of experimental effort, there has not yet been any study that consistently established a connection between an enzyme's conformational dynamics and a significant increase in the catalytic contribution of the chemical step. We also make the point that the dynamical proposal is not a semantic issue but a well-defined scientific hypothesis with well-defined conclusions.

Simulating the dynamics of the mechanochemical cycle of myosin-V

The detailed dynamics of the cycle of myosin-V are explored by simulation approaches, examining the nature of the energy-driven motion. Our study started with Langevin dynamics (LD) simulations on a very coarse landscape with a single rate-limiting barrier and reproduced the stall force and the hand-over-hand dynamics. We then considered a more realistic landscape and used time-dependent Monte Carlo (MC) simulations that allowed trajectories long enough to reproduce the force/velocity characteristic sigmoidal correlation, while also reproducing the hand-over-hand motion. Overall, our study indicated that the notion of a downhill lever-up to lever-down process (popularly known as the powerstroke mechanism) is the result of the energetics of the complete myosin-V cycle and is not the source of directional motion or force generation on its own. The present work further emphasizes the need to use well-defined energy landscapes in studying molecular motors in general and myosin in particular.

CADEE: Computer-Aided Directed Evolution of Enzymes

The tremendous interest in enzymes as biocatalysts has led to extensive work in enzyme engineering, as well as associated methodology development. Here, a new framework for computer-aided directed evolution of enzymes (CADEE) is presented which allows a drastic reduction in the time necessary to prepare and analyze in silico semi-automated directed evolution of enzymes. A pedagogical example of the application of CADEE to a real biological system is also presented in order to illustrate the CADEE workflow.

A multi-resolution model to capture both global fluctuations of an enzyme and molecular recognition in the ligand-binding site

In multi-resolution simulations, different system components are simultaneously modeled at different levels of resolution, these being smoothly coupled together. In the case of enzyme systems, computationally expensive atomistic detail is needed in the active site to capture the chemistry of ligand binding. Global properties of the rest of the protein also play an essential role, determining the structure and fluctuations of the binding site; however, these can be modeled on a coarser level. Similarly, in the most computationally efficient scheme only the solvent hydrating the active site requires atomistic detail. We present a methodology to couple atomistic and coarse-grained protein models, while solvating the atomistic part of the protein in atomistic water. This allows a free choice of which protein and solvent degrees of freedom to include atomistically. This multi-resolution methodology can successfully model stable ligand binding, and we further confirm its validity by exploring the reproduction of system properties relevant to enzymatic function. In addition to a computational speedup, such an approach can allow the identification of the essential degrees of freedom playing a role in a given process, potentially yielding new insights into biomolecular function. Proteins 2016; 84:1902-1913. © 2016 Wiley Periodicals, Inc.

Exploring the Dependence of QM/MM Calculations of Enzyme Catalysis on the Size of the QM Region

Although QM/MM calculations are the primary current tool for modeling enzymatic reactions, the reliability of such calculations can be limited by the size of the QM region. Thus, we examine in this work the dependence of QM/MM calculations on the size of the QM region, using the reaction of catechol-O-methyl transferase (COMT) as a test case. Our study focuses on the effect of adding residues to the QM region on the activation free energy, obtained with extensive QM/MM sampling. It is found that the sensitivity of the activation barrier to the size of the QM is rather limited, while the dependence of the reaction free energy is somewhat larger. Of course, the results depend on the inclusion of the first solvation shell in the QM regions. For example, the inclusion of the Mg²⁺ ion can change the activation barrier due to charge transfer effects. However, such effects can easily be included in semiempirical approaches by proper parametrization. Overall, we establish that QM/MM calculations of activation barriers of enzymatic reactions are not highly sensitive to the size of the QM region, beyond the immediate region that describes the reacting atoms.

Exploring the mechanism of DNA polymerases by analyzing the effect of mutations of active site acidic groups in Polymerase β

Elucidating the catalytic mechanism of DNA polymerase is crucial for a progress in the understanding of the control of replication fidelity. This work tries to advance the mechanistic understanding by analyzing the observed effect of mutations of the acidic groups in the active site of Polymerase β as well as the pH effect on the rate constant. The analysis involves both empirical valence bond (EVB) free energy calculations and considerations of the observed pH dependence of the reaction. The combined analysis indicates that the proton transfer (PT) from the nucleophilic O3' has two possible pathways, one to D256 and the second to the bulk. We concluded based on calculations and the experimental pH profile that the most likely path for the wild-type (WT) and the D256E and D256A mutants is a PT to the bulk, although the WT may also use a PT to Asp 256. Our analysis highlights the need for very extensive sampling in the calculations of the activation barrier and also clearly shows that ab initio QM/MM calculations that do not involve extensive sampling are unlikely to give a clear quantitative picture of the reaction mechanism. Proteins 2016; 84:1644-1657. © 2016 Wiley Periodicals, Inc.

The control of the discrimination between dNTP and rNTP in DNA and RNA polymerase

Understanding the origin of discrimination between rNTP and dNTP by DNA/RNA polymerases is important both for gaining fundamental knowledge on the corresponding systems and for advancing the design of specific drugs. This work explores the nature of this discrimination by systematic calculations of the transition state (TS) binding energy in RB69 DNA polymerase (gp43) and T7 RNA polymerase. The calculations reproduce the observed trend, in particular when they included the water contribution obtained by the water flooding approach. Our detailed study confirms the idea that the discrimination is due to the steric interaction between the 2'OH and Tyr416 in DNA polymerase, while the electrostatic interaction is the source of the discrimination in RNA polymerase. Proteins 2016; 84:1616-1624. © 2016 Wiley Periodicals, Inc.

Quantum Mechanics/Molecular Mechanics Modeling of Enzymatic Processes: Caveats and Breakthroughs

Nature has developed large groups of enzymatic catalysts with the aim to transfer substrates into useful products, which enables biosystems to perform all their natural functions. As such, all biochemical processes in our body (we drink, we eat, we breath, we sleep, etc.) are governed by enzymes. One of the problems associated with research on biocatalysts is that they react so fast that details of their reaction mechanisms cannot be obtained with experimental work. In recent years, major advances in computational hardware and software have been made and now large (bio)chemical systems can be studied using accurate computational techniques. One such technique is the quantum mechanics/molecular mechanics (QM/MM) technique, which has gained major momentum in recent years. Unfortunately, it is not a black-box method that is easily applied, but requires careful set-up procedures. In this work we give an overview on the technical difficulties and caveats of QM/MM and discuss work-protocols developed in our groups for running successful QM/MM calculations.

Catalytic stimulation by restrained active-site floppiness--the case of high density lipoprotein-bound serum paraoxonase-1

Despite the abundance of membrane-associated enzymes, the mechanism by which membrane binding stabilizes these enzymes and stimulates their catalysis remains largely unknown. Serum paraoxonase-1 (PON1) is a lipophilic lactonase whose stability and enzymatic activity are dramatically stimulated when associated with high-density lipoprotein (HDL) particles. Our mutational and structural analyses, combined with empirical valence bond simulations, reveal a network of hydrogen bonds that connect HDL binding residues with Asn168--a key catalytic residue residing >15Å from the HDL contacting interface. This network ensures precise alignment of N168, which, in turn, ligates PON1's catalytic calcium and aligns the lactone substrate for catalysis. HDL binding restrains the overall motion of the active site and particularly of N168, thus reducing the catalytic activation energy barrier. We demonstrate herein that disturbance of this network, even at its most far-reaching periphery, undermines PON1's activity. Membrane binding thus immobilizes long-range interactions via second- and third-shell residues that reduce the active site's floppiness and pre-organize the catalytic residues. Although this network is critical for efficient catalysis, as demonstrated here, unraveling these long-rage interaction networks is challenging, let alone their implementation in artificial enzyme design.