Insights into enzyme catalysis from QM/MM modelling: transition state stabilization in chorismate mutase

Assessment of Embedding Schemes in a Hybrid Machine Learning/Classical Potentials (ML/MM) Approach

Machine learning (ML) methods have reached high accuracy levels for the prediction of in vacuo molecular properties. However, the simulation of large systems solely through ML methods (such as those based on neural network potentials) is still a challenge. In this context, one of the most promising frameworks for integrating ML schemes in the simulation of complex molecular systems are the so-called ML/MM methods. These multiscale approaches combine ML methods with classical force fields (MM), in the same spirit as the successful hybrid quantum mechanics-molecular mechanics methods (QM/MM). The key issue for such ML/MM methods is an adequate description of the coupling between the region of the system described by ML and the region described at the MM level. In the context of QM/MM schemes, the main ingredient of the interaction is electrostatic, and the state of the art is the so-called electrostatic-embedding. In this study, we analyze the quality of simpler mechanical embedding-based approaches, specifically focusing on their application within a ML/MM framework utilizing atomic partial charges derived in vacuo. Taking as reference electrostatic embedding calculations performed at a QM(DFT)/MM level, we explore different atomic charges schemes, as well as a polarization correction computed using atomic polarizabilites. Our benchmark data set comprises a set of about 80k small organic structures from the ANI-1x and ANI-2x databases, solvated in water. The results suggest that the minimal basis iterative stockholder (MBIS) atomic charges yield the best agreement with the reference coupling energy. Remarkable enhancements are achieved by including a simple polarization correction.

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

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

Exploration of biochemical reactivity with a QM/MM growing string method

In this work, we have implemented the single-ended growing string method using a hybrid internal/Cartesian coordinate scheme within our in-house QM/MM package, QoMMMa, representing the first implementation of the growing string method in the QM/MM framework. The goal of the implementation was to facilitate generation of QM/MM reaction pathways with minimal user input, and also to improve the quality of the pathways generated as compared to the widely used adiabatic mapping approach. We have validated the algorithm against a reaction which has been studied extensively in previous computational investigations - the Claisen rearrangement catalysed by chorismate mutase. The nature of the transition state and the height of the barrier was predicted well using our algorithm, where more than 88% of the pathways generated were deemed to be of production quality. Directly compared to using adiabatic mapping, we found that while our QM/MM single-ended growing string method is slightly less efficient, it readily produces reaction pathways with fewer discontinuites and thus minimises the need for involved remapping of unsatisfactory energy profiles.

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

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.

QM/MM Simulations Reveal the Determinants of Carbapenemase Activity in Class A β-Lactamases

β-lactam antibiotic resistance in Gram-negative bacteria, primarily caused by β-lactamase enzymes that hydrolyze the β-lactam ring, has become a serious clinical problem. Carbapenems were formerly considered "last resort" antibiotics because they escaped breakdown by most β-lactamases, due to slow deacylation of the acyl-enzyme intermediate. However, an increasing number of Gram-negative bacteria now produce β-lactamases with carbapenemase activity: these efficiently hydrolyze the carbapenem β-lactam ring, severely limiting the treatment of some bacterial infections. Here, we use quantum mechanics/molecular mechanics (QM/MM) simulations of the deacylation reactions of acyl-enzyme complexes of eight β-lactamases of class A (the most widely distributed β-lactamase group) with the carbapenem meropenem to investigate differences between those inhibited by carbapenems (TEM-1, SHV-1, BlaC, and CTX-M-16) and those that hydrolyze them (SFC-1, KPC-2, NMC-A, and SME-1). QM/MM molecular dynamics simulations confirm the two enzyme groups to differ in the preferred acyl-enzyme orientation: carbapenem-inhibited enzymes favor hydrogen bonding of the carbapenem hydroxyethyl group to deacylating water (DW). QM/MM simulations of deacylation give activation free energies in good agreement with experimental hydrolysis rates, correctly distinguishing carbapenemases. For the carbapenem-inhibited enzymes, free energies for deacylation are significantly higher than for the carbapenemases, even when the hydroxyethyl group was restrained to prevent interaction with the DW. Analysis of these simulations, and additional simulations of mutant enzymes, shows how factors including the hydroxyethyl orientation, the active site volume, and architecture (conformations of Asn170 and Asn132; organization of the oxyanion hole; and the Cys69-Cys238 disulfide bond) collectively determine catalytic efficiency toward carbapenems.

Accelerating Ab Initio Quantum Mechanical and Molecular Mechanical (QM/MM) Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semiempirical QM/MM Hamiltonian

Molecular dynamics (MD) simulations employing ab initio quantum mechanical and molecular mechanical (ai-QM/MM) potentials are considered to be the state of the art, but the high computational cost associated with the ai-QM calculations remains a theoretical challenge for their routine application. Here, we present a modified protocol of the multiple time step (MTS) method for accelerating ai-QM/MM MD simulations of condensed-phase reactions. Within a previous MTS protocol [Nam J. Chem. Theory Comput. 2014, 10, 4175], reference forces are evaluated using a low-level (semiempirical QM/MM) Hamiltonian and employed at inner time steps to propagate the nuclear motions. Correction forces, which arise from the force differences between high-level (ai-QM/MM) and low-level Hamiltonians, are applied at outer time steps, where the MTS algorithm allows the time-reversible integration of the correction forces. To increase the outer step size, which is bound by the highest-frequency component in the correction forces, the semiempirical QM Hamiltonian is recalibrated in this work to minimize the magnitude of the correction forces. The remaining high-frequency modes, which are mainly bond stretches involving hydrogen atoms, are then removed from the correction forces. When combined with a Langevin or SIN(R) thermostat, the modified MTS-QM/MM scheme remains robust with an up to 8 (with Langevin) or 10 fs (with SIN(R)) outer time step (with 1 fs inner time steps) for the chorismate mutase system. This leads to an over 5-fold speedup over standard ai-QM/MM simulations, without sacrificing the accuracy in the predicted free energy profile of the reaction.

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.

Combined Quantum Mechanics and Molecular Mechanics Studies of Enzymatic Reaction Mechanisms

The combined quantum mechanics/molecular mechanics (QM/MM) methods have become a valuable tool in computational biochemistry and received versatile applications for studying the reaction mechanisms of enzymes. The approach combines the calculations of the electronic structure of the active site by QM, with modeling of the protein environment using MM force field, which allows the long-range electrostatics and steric effects on the enzyme reactivity to be accounted for. In this review, we review some key theoretical and computational aspects of the method and we also present some applications to particular enzymatic reactions such as tryptophan-7-halogenase, cyclooxygenase-1, and the epidermal growth factor receptor.

Quantum chemical modeling of the reaction path of chorismate mutase based on the experimental substrate/product complex

Chorismate mutase is a well-known model enzyme, catalyzing the Claisen rearrangement of chorismate to prephenate. Recent high-resolution crystal structures along the reaction coordinate of this enzyme enabled computational analyses at unprecedented detail. Using quantum chemical simulations, we investigated how the catalytic reaction mechanism is affected by electrostatic and hydrogen-bond interactions. Our calculations showed that the transition state (TS) was mainly stabilized electrostatically, with Arg90 playing the leading role. The effect was augmented by selective hydrogen-bond formation to the TS in the wild-type enzyme, facilitated by a small-scale local induced fit. We further identified a previously underappreciated water molecule, which separates the negative charges during the reaction. The analysis includes the wild-type enzyme and a non-natural enzyme variant, where the catalytic arginine was replaced with an isosteric citrulline residue.

Mechanisms for Two-Step Proton Transfer Reactions in the Outward-Facing Form of MATE Transporter

Bacterial pathogens or cancer cells can acquire multidrug resistance, which causes serious clinical problems. In cells with multidrug resistance, various drugs or antibiotics are extruded across the cell membrane by multidrug transporters. The multidrug and toxic compound extrusion (MATE) transporter is one of the five families of multidrug transporters. MATE from Pyrococcus furiosus uses H(+) to transport a substrate from the cytoplasm to the outside of a cell. Crystal structures of MATE from P. furiosus provide essential information on the relevant H(+)-binding sites (D41 and D184). Hybrid quantum mechanical/molecular mechanical simulations and continuum electrostatic calculations on the crystal structures predict that D41 is protonated in one structure (Straight) and, both D41 and D184 protonated in another (Bent). All-atom molecular dynamics simulations suggest a dynamic equilibrium between the protonation states of the two aspartic acids and that the protonation state affects hydration in the substrate binding cavity and lipid intrusion in the cleft between the N- and C-lobes. This hypothesis is examined in more detail by quantum mechanical/molecular mechanical calculations on snapshots taken from the molecular dynamics trajectories. We find the possibility of two proton transfer (PT) reactions in Straight: the 1st PT takes place between side-chains D41 and D184 through a transient formation of low-barrier hydrogen bonds and the 2nd through another H(+) from the headgroup of a lipid that intrudes into the cleft resulting in a doubly protonated (both D41 and D184) state. The 1st PT affects the local hydrogen bond network and hydration in the N-lobe cavity, which would impinge on the substrate-binding affinity. The 2nd PT would drive the conformational change from Straight to Bent. This model may be applicable to several prokaryotic H(+)-coupled MATE multidrug transporters with the relevant aspartic acids.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

QM/MM free-energy simulations of reaction in Serratia marcescens Chitinase B reveal the protonation state of Asp142 and the critical role of Tyr214

Serratia marcescens Chitinase B (ChiB), belonging to the glycosidase family 18 (GH18), catalyzes the hydrolysis of β-1,4-glycosidic bond, with retention of configuration, via an unusual substrate-assisted mechanism, in which the substrate itself acts as an intramolecular nucleophile. Here, both elementary steps (glycosylation and deglycosylation) of the ChiB-catalyzed reaction are investigated by means of combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations at the SCC-DFTB/CHARMM22 level of theory. We examine the influence of the Asp142 protonation state on the reaction and the role that this residue performs in the reaction. Our simulations show that reaction with a neutral Asp142 is preferred and demonstrate that this residue provides electrostatic stabilization of the oxazolinium ion intermediate formed in the reaction. Insight into the conformational itinerary ((1,4)B↔(4)H5↔(4)C1) adopted by the substrate (bound in subsite -1) along the preferred reaction pathway is also provided by the simulations. The relative energies of the stationary points found along the reaction pathway calculated with SCC-DFTB and B3LYP were compared. The results suggest that SCC-DFTB is an accurate method for estimating the relative barriers for both steps of the reaction; however, it was found to overestimate the relative energy of an intermediate formed in the reaction when compared with the higher level of theory. Glycosylation is suggested to be a rate-determining step in the reaction with calculated overall reaction free-energy barrier of 20.5 kcal/mol, in a reasonable agreement with the 16.1 kcal/mol barrier derived from the experiment. The role of Tyr214 in catalysis was also investigated with the results, indicating that the residue plays a critical role in the deglycosylation step of the reaction. Simulations of the enzyme-product complex were also performed with an unbinding event suggested to have been observed, affording potential new mechanistic insight into the release of the product of ChiB.

Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.

Quantum mechanical methods for the investigation of metalloproteins and related bioinorganic compounds

It is well known that transition metal ions are often bound to proteins, conveying very specific functional properties. In fact, metalloproteins play crucial biological roles in the transport and activation of small molecules such as H2, O2, and N2, as well as in several other biochemical processes. However, even if the presence of transition metals in the active site of proteins allows a very rich biochemistry, the experimental disclosure of structure-activity relationships in metalloproteins is generally difficult exactly because of the presence of transition metals, which are intrinsically characterized by a very versatile and often elusive chemistry. For this reason, computational methods are becoming very popular tools in the characterization of metalloproteins. In particular, since computing power is becoming less and less expensive, due to the continuous technological development of CPUs, the computational tools suited to investigate metalloproteins are becoming more accessible and therefore more commonly used also in molecular biology and biochemistry laboratories. Here, we present the main procedures and computational methods based on quantum mechanics, which are commonly used to study the structural, electronic, and reactivity properties of metalloproteins and related bioinspired compounds, with a specific focus on the practical and technical aspects that must be generally tackled to properly study such biomolecular systems.

Mapping enzymatic catalysis using the effective fragment molecular orbital method: towards all ab initio biochemistry

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We determine the reaction barrier of chorismate mutase to be kcal mol⁻¹ for MP2/cc-pVDZ and for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.

Combined quantum mechanics/molecular mechanics (QM/MM) methods in computational enzymology

Computational enzymology is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/molecular mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mechanical method (i.e., a method that calculates the electronic structure of the active site) and including the enzyme environment with simpler molecular mechanical methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymology. A range of QM/MM methods is available, from cheaper and more approximate methods, which can be used for molecular dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymology, e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.

Mechanism of C-terminal intein cleavage in protein splicing from QM/MM molecular dynamics simulations

Protein splicing is a post-translational process in which a biologically inactive protein is activated by the release of a segment denoted as an intein. The process involves four steps. In the third, the scission of the intein takes place after the cyclization of the last amino acid of the segment, an asparagine. Little is known about the chemical reaction necessary for this cyclization. Experiments demonstrate that two histidines (the penultimate amino acid of the intein, and a histidine located 10 amino acids upstream) are relevant in the cyclization of the asparagine. We have investigated the mechanism and determinants of reaction in the GyrA intein focusing on the requirements for asparagine activation for its cyclization. First, the influence that the protonation states of these two histidines have on the orientation of the asparagine side chain is investigated by means of molecular dynamics simulation. Molecular dynamics simulations using the CHARMM27 force field were carried out on the three possible protonation states for each of these two histidines. The results indicate that the only protonation state in which the conformation of the system is suitable for cyclization is when the penultimate histidine is fully protonated (positively charged), and the upstream histidine is in the His(ε) neutral tautomeric form. The free energy profile for the reaction in which the asparagine is activated by a proton transfer to the upstream histidine is presented, computed by hybrid quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics at the SCCDFTB/CHARMM27 level of theory. The calculated free energy barrier for the reaction is 19.0 kcal mol(-1). B3LYP/6-31+G(d) QM/MM single-point calculations give a qualitatively a similar energy profile, although with somewhat higher energy barriers, in good agreement with the value derived from experiment of 25 kcal mol(-1) at 60 °C. QM/MM molecular dynamics simulations of the reactant, activated reactant and intermediate states highlight the importance of the Arg181-Val182-Asp183 segment in catalysing the reaction. Overall, the results indicate that nucleophilic activation of the asparagine for its cyclization by the upstream histidine acting as the base is a plausible mechanism for the C-terminal cleavage in protein splicing.

MECHANISTIC STUDY OF HIV-1 REVERSE TRANSCRIPTASE AT THE ACTIVE SITE BASED ON QM/MM METHOD

HIV-1 RT catalyses the reverse transcription of viral genetic material (RNA) into double-stranded DNA, and is an important target of antiviral therapy in the treatment of AIDS. Better understanding of the structure, mechanism and functional role of residues involved in the resistance of HIV-1 RT against nucleoside-analog drugs may assist in the development of improved inhibitors, and also in understanding the effects of genetic variation on RT specificity and activity. In this study, firstly, molecular dynamics simulations (with CHARMM27) have been used to investigate binding interactions at the active site and the conformational behavior of the enzyme, then, mechanisms of deprotonation and DNA polymerization reactions have been modelled by the QM/MM method. A combined quantum mechanical and molecular mechanical (QM/MM) method (AM1/CHARMM) has been used to study the triphosphate substrate and the active site of HIV-1 reverse transcriptase complex structure, a virally-encoded enzyme. Free energy profiles for the reaction are also calculated. The obtained results provide important insight into the mechanistic activity of HIV-1 RT.

Analysis of chorismate mutase catalysis by QM/MM modelling of enzyme-catalysed and uncatalysed reactions

Chorismate mutase is at the centre of current controversy about fundamental features of biological catalysts. Some recent studies have proposed that catalysis in this enzyme does not involve transition state (TS) stabilization but instead is due largely to the formation of a reactive conformation of the substrate. To understand the origins of catalysis, it is necessary to compare equivalent reactions in different environments. The pericyclic conversion of chorismate to prephenate catalysed by chorismate mutase also occurs (much more slowly) in aqueous solution. In this study we analyse the origins of catalysis by comparison of multiple quantum mechanics/molecular mechanics (QM/MM) reaction pathways at a reliable, well tested level of theory (B3LYP/6-31G(d)/CHARMM27) for the reaction (i) in Bacillus subtilis chorismate mutase (BsCM) and (ii) in aqueous solvent. The average calculated reaction (potential energy) barriers are 11.3 kcal mol(-1) in the enzyme and 17.4 kcal mol(-1) in water, both of which are in good agreement with experiment. Comparison of the two sets of reaction pathways shows that the reaction follows a slightly different reaction pathway in the enzyme than in it does in solution, because of a destabilization, or strain, of the substrate in the enzyme. The substrate strain energy within the enzyme remains constant throughout the reaction. There is no unique reactive conformation of the substrate common to both environments, and the transition state structures are also different in the enzyme and in water. Analysis of the barrier heights in each environment shows a clear correlation between TS stabilization and the barrier height. The average differential TS stabilization is 7.3 kcal mol(-1) in the enzyme. This is significantly higher than the small amount of TS stabilization in water (on average only 1.0 kcal mol(-1) relative to the substrate). The TS is stabilized mainly by electrostatic interactions with active site residues in the enzyme, with Arg90, Arg7 and Glu78 generally the most important. Conformational effects (e.g. strain of the substrate in the enzyme) do not contribute significantly to the lower barrier observed in the enzyme. The results show that catalysis is mainly due to better TS stabilization by the enzyme.

Testing high-level QM/MM methods for modeling enzyme reactions: acetyl-CoA deprotonation in citrate synthase

Combined quantum mechanics/molecular mechanics (QM/MM) calculations with high levels of correlated ab initio theory can now provide benchmarks for enzyme-catalyzed reactions. Here, we use such methods to test various QM/MM methods and the sensitivity of the results to details of the models for an important enzyme reaction, proton abstraction from acetyl-coenzyme A in citrate synthase. We calculate multiple QM/MM potential energy surfaces up to the local coupled cluster theory (LCCSD(T0)) level, with structures optimized at hybrid density functional theory and Hartree-Fock levels. The influence of QM methods, basis sets, and QM region size is shown to be significant. Correlated ab initio QM/MM calculations give barriers in agreement with experiment for formation of the acetyl-CoA enolate intermediate. In contrast, B3LYP fails to identify the enolate as an intermediate, whereas BH&HLYP does. The results indicate that QM/MM methods and setup should be tested, ideally using high-level calculations, to draw reliable mechanistic conclusions.

A comparative QM/MM study of the reaction mechanism of the Hepatitis C virus NS3/NS4A protease with the three main natural substrates NS5A/5B, NS4B/5A and NS4A/4B

The reaction mechanism of the NS3/NS4A protease with the NS4B/5A and NS4A/4B natural substrates has been investigated using the QM/MM (quantum mechanics/molecular mechanics) approach, and some calculations have been performed on the reaction with the NS5A/5B natural substrate. This study widely extends a previous contribution of our group on the reaction mechanism with the NS5A/5B substrate, the main goal here being to understand the differences found between the reaction mechanism of each natural substrate and the role played by the enzymatic residues in the catalytic cycle. This knowledge will ultimately help in developing new NS3/NS4A protease inhibitors. The two first steps of the mechanism have been considered: Acylation and breaking of the peptide bond, with emphasis on the former one (rate limiting process). Energy and free energy profiles for both steps have been calculated at the AM1/MM level and corrected by means of MP2 ab initio calculations, being evident the importance of correlation energy. Acylation is the rate limiting step in all cases and occurs through a tetracoordinated intermediate, as previously suggested for other serine proteases. Specificities in the NS4B/5A mechanism can be attributed to the presence of a Proline residue in the substrate P2 position. The analysis of structures and energies confirm the importance of the oxyanion hole in the electrostatic stabilization of the tetracoordinated intermediate. Finally, the role of other residues, e.g., Arg-155 and Asp-79, has been explained, and the viability of Arg-155 mutants and its resistance to some protease inhibitors has been understood thanks to virtual mutation studies.

Combined QM/MM mechanistic study of the acylation process in furin complexed with the H5N1 avian influenza virus hemagglutinin's cleavage site

Combined quantum mechanical/molecular mechanical (QM/MM) techniques have been applied to investigate the detailed reaction mechanism of the first step of the acylation process by furin in which the cleavage site of the highly pathogenic avian influenza virus subtype H5N1 (HPH5) acts as its substrate. The energy profile shows a simultaneous mechanism, known as a concerted reaction, of the two subprocesses: the proton transfer from Ser368 to His194 and the nucleophilic attack on the carbonyl carbon of the scissile peptide of the HPH5 cleavage site with a formation of tetrahedral intermediate (INT). The calculated energy barrier for this reaction is 16.2 kcal.mol(-1) at QM/MM B3LYP/6-31+G*//PM3-CHARMM22 level of theory. Once the reaction proceeds, the ordering of the electrostatic stabilization by protein environment is of the enzyme-substrate < transition state < INT complexes. Asp153 was found to play the most important role in the enzymatic reaction by providing the highest degree of intermediate complex stabilization. In addition, the negatively charged carbonyl oxygen of INT is well stabilized by the oxyanion hole constructed by Asn295's carboxamide and Ser368's backbone.

QM/MM methods for biomolecular systems

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

Biomolecular simulation and modelling: status, progress and prospects

Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.

Towards understanding phosphonoacetaldehyde hydrolase: an alternative mechanism involving proton transfer that triggers P-C bond cleavage

The theoretical QM/MM study of the reaction catalysed by phosphonoacetaldehyde hydrolase indicates a possible alternative mechanism of the P-C bond cleavage: as opposed to the mechanism proposed earlier and that involved formation of a covalently bound intermediate (Schiff-base), in the new mechanism, the bond breaking process is facilitated by proton transfer from catalytic lysine residue to the substrate.

Analysis of Classical and Quantum Paths for Deprotonation of Methylamine by Methylamine Dehydrogenase

The hydrogen-transfer reaction catalysed by methylamine dehydrogenase (MADH) with methylamine (MA) as substrate is a good model system for studies of proton tunnelling in enzyme reactions--an area of great current interest--for which atomistic simulations will be vital. Here, we present a detailed analysis of the key deprotonation step of the MADH/MA reaction and compare the results with experimental observations. Moreover, we compare this reaction with the related aromatic amine dehydrogenase (AADH) reaction with tryptamine, recently studied by us, and identify possible causes for the differences observed in the measured kinetic isotope effects (KIEs) of the two systems. We have used combined quantum mechanics/molecular mechanics (QM/MM) techniques in molecular dynamics simulations and variational transition state theory with multidimensional tunnelling calculations averaged over an ensemble of paths. The results reveal important mechanistic complexity. We calculate activation barriers and KIEs for the two possible proton transfers identified-to either of the carboxylate oxygen atoms of the catalytic base (Asp428beta)-and analyse the contributions of quantum effects. The activation barriers and tunnelling contributions for the two possible proton transfers are similar and lead to a phenomenological activation free energy of 16.5+/-0.9 kcal mol(-1) for transfer to either oxygen (PM3-CHARMM calculations applying PM3-SRP specific reaction parameters), in good agreement with the experimental value of 14.4 kcal mol(-1). In contrast, for the AADH system, transfer to the equivalent OD1 was found to be preferred. The structures of the enzyme complexes during reaction are analysed in detail. The hydrogen bond of Thr474beta(MADH)/Thr172beta(AADH) to the catalytic carboxylate group and the nonconserved active site residue Tyr471beta(MADH)/Phe169beta(AADH) are identified as important factors in determining the preferred oxygen acceptor. The protein environment has a significant effect on the reaction energetics and hence on tunnelling contributions and KIEs. These environmental effects, and the related clearly different preferences for the two carboxylate oxygen atoms (with different KIEs) in MADH/MA and AADH/tryptamine, are possible causes of the differences observed in the KIEs between these two important enzyme reactions.

Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations

A hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy function with Hartree-Fock, density functional theory (DFT), and post-HF (RIMP2, MP2, CCSD) capability has been implemented in the CHARMM and Q-Chem software packages. In addition, we have modified CHARMM and Q-Chem to take advantage of the newly introduced replica path and the nudged elastic band methods, which are powerful techniques for studying reaction pathways in a highly parallel (i.e., parallel/parallel) fashion, with each pathway point being distributed to a different node of a large cluster. To test our implementation, a series of systems were studied and comparisons were made to both full QM calculations and previous QM/MM studies and experiments. For instance, the differences between HF, DFT, MP2, and CCSD QM/MM calculations of H2O...H2O, H2O...Na+, and H2O...Cl- complexes have been explored. Furthermore, the recently implemented polarizable Drude water model was used to make comparisons to the popular TIP3P and TIP4P water models for doing QM/MM calculations. We have also computed the energetic profile of the chorismate mutase catalyzed Claisen rearrangement at various QM/MM levels of theory and have compared the results with previous studies. Our best estimate for the activation energy is 8.20 kcal/mol and for the reaction energy is -23.1 kcal/mol, both calculated at the MP2/6-31+G(d)//MP2/6-31+G(d)/C22 level of theory.

Exploring SCC-DFTB paths for mapping QM/MM reaction mechanisms

A new first-order procedure for locating transition structures (TS) that employs hybrid quantum mechanical/molecular mechanical (QM/MM) potentials has been developed. This new technique (RPATh+RESD) combines the replica path method (RPATh) and standard reaction coordinate driving (RCD) techniques in an approach that both efficiently determines reaction barriers and successfully eliminates two key weaknesses of RCD calculations (i.e., hysteresis/discontinuities in the path and the sequential nature of the RCD procedure). In addition, we have extended CHARMM's QM/MM reaction pathway methods, the RPATh and nudged elastic band (NEB) methods, to incorporate SCC-DFTB wave functions. This newly added functionality has been applied to the chorismate mutase-catalyzed interconversion of chorismate to prephenate, which is a key step in the shikimate pathway of bacteria, fungi, and other higher plants. The RPATh+RESD barrier height (DeltaE=5.7 kcal/mol) is in good agreement with previous results from full-energy surface mapping studies (Zhang, X.; Zhang, X.; Bruice, T. C. Biochemistry 2005, 44, 10443-10448). Full reaction paths were independently mapped with RPATh and NEB methods and showed good agreement with the final transition state from the RPATh+RESD "gold standard" and previous high-level QM/MM transition states (Woodcock, H. L.; Hodoscek, M.; Gilbert, T. B.; Gill, P. M. W.; Schaefer, H. F.; Brooks, B. R. J. Comput. Chem. 2007, 28, 1485-1502). The SCC-DFTB TS geometry most closely approximates the MP2/6-31+G(d) QM/MM result. However, the barrier height is underestimated and possibly points to an area for improvement in SCC-DFTB parametrization. In addition, the steepest descents (SD) minimizer for the NEB method was modified to uncouple the in-path and off-path degrees of freedom during the minimization, which significantly improved performance. The convergence behavior of the RPATh and NEB was examined for SCC-DFTB wave functions, and it was determined that, in general, both methods converge at about the same rate, although the techniques used for convergence may be different. For instance, RPATh can effectively use the adopted basis Newton-Raphson (ABNR) minimizer, where NEB seems to require a combination of SD and ABNR.

A Transition Path Sampling Study of the Reaction Catalyzed by the Enzyme Chorismate Mutase

The study of the chemical steps in enzyme-catalyzed reactions represents a challenge for molecular simulation techniques. One concern is how to calculate paths for the reaction. Common techniques include the definition of a reaction coordinate in terms of a small set of (normally) geometrical variables or the determination of minimum energy paths on the potential energy surface of the reacting system. Both have disadvantages, the former because it presupposes knowledge of which variables are likely to be important for reaction and the latter because it provides a static picture and dynamical effects are ignored. In this paper, we employ the transition path sampling method developed by Chandler and co-workers, which overcomes some of these limitations. The reaction that we have chosen is the chorismate-mutase-catalyzed conversion of chorismate into prephenate, which has become something of a test case for simulation studies of enzyme mechanisms. We generated an ensemble of approximately 1000 independent transition paths for the reaction in the enzyme and another approximately 500 for the corresponding reaction in solution. A large variety of analyses of these paths was performed, but we have concentrated on characterizing the transition state ensemble, particularly the flexibility of its structures with respect to other ligands of the enzyme and the time evolution of various geometrical and energetic properties as the reaction proceeds. We have also devised an approximate technique for locating transition state structures along the paths.