Enzyme catalysis by entropy without Circe effect

Solution Ionic Strength Can Modulate Functional Loop Conformations in E. coli Dihydrofolate Reductase

The observation of multiple conformations of a functional loop (termed M20) in the Escherichia coli dihydrofolate reductase (ecDHFR) enzyme triggered the proposition that large-scale motions of protein structural elements contribute to enzyme catalysis. The transition of the M20 loop from a closed conformation to an occluded conformation was thought to aid the rate-limiting release of the products. However, the influence of charged species in the solution environment on the observed M20 loop conformations, independent of charged ligands bound to the enzyme, had not been considered. Molecular dynamics simulations of ecDHFR in model CaCl2 solutions of varying molar ionic strengths IM reveal a substantial free energy barrier between occluded and closed M20 loop states at IM exceeding the E. coli threshold (∼0.24 M). This barrier may facilitate crystallization of ecDHFR in the occluded state, consistent with ecDHFR structures obtained at IM exceeding 0.3 M. At lower IM (≤0.15 M), the M20 loop can explore the occluded state, but prefers an open/partially closed conformation, again consistent with ecDHFR structures. Our findings caution against using ecDHFR structures obtained at nonphysiological ionic strengths in interpreting catalytic events or in structure-based drug design.

Why Do Empirical Valence Bond Simulations Yield Accurate Arrhenius Plots?

Computer simulations of the temperature dependence of enzyme reactions using the empirical valence bond (EVB) method have proven to give very accurate results in terms of the thermodynamic activation parameters. Here, we analyze the reasons for why such simulations are able to correctly capture activation enthalpies and entropies and how sensitive these quantities are to parametrization of the reactive potential energy function. We examine first the solution reference reaction for the enzyme ketosteroid isomerase, which corresponds to the acetate catalyzed deprotonation of the steroid in water. The experimentally determined activation parameters for this reaction turn out to be remarkably well reproduced by the calculations. By modifying the EVB potential so that the activation and reaction free energies become significantly shifted, we show that the activation entropy is basically invariant to such changes and that ΔS⧧ is instead determined by the specific mixture of the underlying force fields in the transition state region. The coefficients of this mixture do not change appreciably when the EVB potential is modified within reasonable limits, and hence, the estimate of ΔS⧧ becomes very robust. This is further verified by examining a more complex concerted hydride and proton transfer reaction in the enzyme hydroxybutyrate dehydrogenase.

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.

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.

Enzyme dynamics-a brief review

Debate has been simmering for some years regarding the importance of internal thermal motions of enzymes to catalysis. Recent developments in protein design may bring resolution of the more contentious points a little closer.

The Quantum Chemical Cluster Approach in Biocatalysis

ConspectusThe quantum chemical cluster approach has been used for modeling enzyme active sites and reaction mechanisms for more than two decades. In this methodology, a relatively small part of the enzyme around the active site is selected as a model, and quantum chemical methods, typically density functional theory, are used to calculate energies and other properties. The surrounding enzyme is modeled using implicit solvation and atom fixing techniques. Over the years, a large number of enzyme mechanisms have been solved using this method. The models have gradually become larger as a result of the faster computers, and new kinds of questions have been addressed. In this Account, we review how the cluster approach can be utilized in the field of biocatalysis. Examples from our recent work are chosen to illustrate various aspects of the methodology. The use of the cluster model to explore substrate binding is discussed first. It is emphasized that a comprehensive search is necessary in order to identify the lowest-energy binding mode(s). It is also argued that the best binding mode might not be the productive one, and the full reactions for a number of enzyme-substrate complexes have therefore to be considered to find the lowest-energy reaction pathway. Next, examples are given of how the cluster approach can help in the elucidation of detailed reaction mechanisms of biocatalytically interesting enzymes, and how this knowledge can be exploited to develop enzymes with new functions or to understand the reasons for lack of activity toward non-natural substrates. The enzymes discussed in this context are phenolic acid decarboxylase and metal-dependent decarboxylases from the amidohydrolase superfamily. Next, the application of the cluster approach in the investigation of enzymatic enantioselectivity is discussed. The reaction of strictosidine synthase is selected as a case study, where the cluster calculations could reproduce and rationalize the selectivities of both the natural and non-natural substrates. Finally, we discuss how the cluster approach can be used to guide the rational design of enzyme variants with improved activity and selectivity. Acyl transferase from Mycobacterium smegmatis serves as an instructive example here, for which the calculations could pinpoint the factors controlling the reaction specificity and enantioselectivity. The cases discussed in this Account highlight thus the value of the cluster approach as a tool in biocatalysis. It complements experiments and other computational techniques in this field and provides insights that can be used to understand existing enzymes and to develop new variants with tailored properties.

Theoretical Kinetic Isotope Effects in Establishing the Precise Biodegradation Mechanisms of Organic Pollutants

Compound-specific isotope analysis (CSIA) for natural isotope ratios has been recognized as a promising tool to elucidate biodegradation pathways of organic pollutants by microbial enzymes by relating reported kinetic isotope effects (KIEs) to apparent KIEs (AKIEs) derived from bulk isotope fractionations (ε_bulk). However, for many environmental reactions, neither are the reference KIE ranges sufficiently narrow nor are the mechanisms elucidated to the point that rate-determining steps have been identified unequivocally. In this work, besides providing reference KIEs and rationalizing AKIEs, good relationships have been explained by DFT computations for diverse biodegradation pathways with known enzymatic models between the theoretical isotope fractionations (ε_bulk^') from intrinsic KIEs on the rate-determining steps and the observed ε_bulk. (1) To confirm the mechanistic details of previously reported pathway-dependent CSIA, it includes isotope changes in MTBE biodegradation between hydroxylation by CYP450 and S_N2 reaction by cobalamin-dependent methyltransferase, the regioselectivity of toluene biodegradation by CYP450, and the rate-determining step in toluene biodegradation by benzylsuccinate synthase. (2) To yield new fundamental insights into some unclear biodegradation pathways, it consists of the oxidative function of toluene dioxygenase in biodegradation of TCE, the epoxidation mode in biodegradation of TCE by toluene 4-monooxygenase, and the weighted average mechanism in biodegradation of cDCE by CYP450.

Analyzing the Reaction of Orotidine 5'-Phosphate Decarboxylase as a Way to Examine Some Key Catalytic Proposals

This study analyzes the origin of enzyme catalysis by focusing on the reaction of orotidine 5'-phosphate decarboxylase (ODCase). This reaction involves an enormous catalytic effect of 23 kcal/mol that has been attributed to reactant state destabilization associated with the use of binding energy through the so-called Circe effect. However, our early studies and subsequent key experiments have shown that the presumed effect of the binding energy (namely, the strain exerted by a bond to a phosphate group) does not contribute to the catalysis. In this study, we perform quantitative empirical valence bond calculations that reproduce the catalytic effect of ODCase and the effect of removing the phosphate side chain. The calculations demonstrate that the effect of the phosphate is due to a change in reorganization energy and should not be described as an induced fit effect. Similarly, we show that the overall catalytic effect is due to electrostatic transition state stabilization, which again reflects the smaller reorganization energy in the enzyme than in water. We also elaborate on the problems with the induced fit proposal, including the fact that it does not serve to tell us what the actual origin of the action of the catalytic effect is. In addition to the above points, we use this paper to discuss misconceptions about the meaning of the preorganization effect, as well as other misunderstandings of what is being done in consistent calculations of enzyme catalysis.

Revisiting the Burden Borne by Fumarase: Enzymatic Hydration of an Olefin

Fumarate hydratase (FH) is a remarkable catalyst that decreases the free energy of the catalyzed reaction by 30 kcal mol^-1, much larger than most exceptional enzymes with extraordinary catalytic rates. Two classes of FH are observed in nature: class-I and class-II, which have different folds, yet catalyze the same reversible hydration/dehydration reaction of the dicarboxylic acids fumarate/malate, with equal efficiencies. Using class-I FH from the hyperthermophilic archaeon Methanocaldococcus jannaschii (Mj) as a model along with comparative analysis with the only other available class-I FH structure from Leishmania major (Lm), we provide insights into the molecular mechanism of catalysis in this class of enzymes. The structure of MjFH apo-protein has been determined, revealing that large intersubunit rearrangements occur across apo- and holo-protein forms, with a largely preorganized active site for substrate binding. Site-directed mutagenesis of active site residues, kinetic analysis, and computational studies, including density functional theory (DFT) and natural population analysis, together show that residues interacting with the carboxylate group of the substrate play a pivotal role in catalysis. Our study establishes that an electrostatic network at the active site of class-I FH polarizes the substrate fumarate through interactions with its carboxylate groups, thereby permitting an easier addition of a water molecule across the olefinic bond. We propose a mechanism of catalysis in FH that occurs through transition-state stabilization involving the distortion of the electronic structure of the substrate olefinic bond mediated by the charge polarization of the bound substrate at the enzyme active site.

Structural dynamics support electrostatic interactions in the active site of Adenylate Kinase

Electrostatic preorganization as well as structural and dynamic heterogeneity are often used to rationalize the remarkable catalytic efficiency of enzymes. However, they are often presented as incompatible because the generation of permanent electrostatic effects implies that the protein structure remains rigid. Here, we use a metric, electric fields, that can treat electrostatic contributions and dynamics effects on equal footing, for a unique perspective on enzymatic catalysis. We find that the residues that contribute the most to electrostatic interactions with the substrate in the active site of Adenylate Kinase (our working example) are also the most flexible residues. Further, entropy-tuning mutations raise flexibility at the picosecond timescale where more conformations can be visited on short time periods, thereby softening the sharp heterogeneity normally visible at the microsecond timescale.

From quantum-derived principles underlying cysteine reactivity to combating the COVID-19 pandemic

The COVID‐19 pandemic poses a challenge in coming up with quick and effective means to counter its cause, the SARS‐CoV‐2. Here, we show how the key factors governing cysteine reactivity in proteins derived from combined quantum mechanical/continuum calculations led to a novel multi‐targeting strategy against SARS‐CoV‐2, in contrast to developing potent drugs/vaccines against a single viral target such as the spike protein. Specifically, they led to the discovery of reactive cysteines in evolutionary conserved Zn²⁺‐sites in several SARS‐CoV‐2 proteins that are crucial for viral polypeptide proteolysis as well as viral RNA synthesis, proofreading, and modification. These conserved, reactive cysteines, both free and Zn²⁺‐bound, can be targeted using the same Zn‐ejector drug (disulfiram/ebselen), which enables the use of broad‐spectrum anti‐virals that would otherwise be removed by the virus's proofreading mechanism. Our strategy of targeting multiple, conserved viral proteins that operate at different stages of the virus life cycle using a Zn‐ejector drug combined with other broad‐spectrum anti‐viral drug(s) could enhance the barrier to drug resistance and antiviral effects, as compared to each drug alone. Since these functionally important nonstructural proteins containing reactive cysteines are highly conserved among coronaviruses, our proposed strategy has the potential to tackle future coronaviruses.

This article is categorized under:

Structure and Mechanism > Reaction Mechanisms and Catalysis

Structure and Mechanism > Computational Biochemistry and Biophysics

Electronic Structure Theory > Density Functional Theory

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

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

Mechanisms of metal-dependent non-redox decarboxylases from quantum chemical calculations

Quantum chemical calculations are today an extremely valuable tool for studying enzymatic reaction mechanisms. In this mini-review, we summarize our recent work on several metal-dependent decarboxylases, where we used the so-called cluster approach to decipher the details of the reaction mechanisms, including elucidation of the identity of the metal cofactors and the origins of substrate specificity.

Decarboxylases are of growing potential for biocatalytic applications, as they can be used in the synthesis of novel compounds of, e.g., pharmaceutical interest. They can also be employed in the reverse direction, providing a strategy to synthesize value‐added chemicals by CO₂ fixation. A number of non-redox metal-dependent decarboxylases from the amidohydrolase superfamily have been demonstrated to have promiscuous carboxylation activities and have attracted great attention in the recent years. The computational mechanistic studies provide insights that are important for the further modification and utilization of these enzymes in industrial processes. The discussed enzymes are: 5‐carboxyvanillate decarboxylase, γ‐resorcylate decarboxylase, 2,3‐dihydroxybenzoic acid decarboxylase, and iso-orotate decarboxylase.

Alkaline Phosphatases: in Silico Study on the Catalytic Effect of Conserved Active Site Residues Using Human Placental Alkaline Phosphatase (PLAP) As a Model Protein

The metalloenzymes from the alkaline phosphatase (AP) superfamily catalyze the hydrolysis and transphosphorylation of phosphate monoesters. The role of several amino acids highly conserved in the active site of this family of enzymes was examined, using human placental AP (PLAP) as a model protein. By employing an active-site model based on the X-ray crystal structure of PLAP, mutations of several key residues were modeled by quantum mechanical methods in order to determine their impact on the catalytic activity. Kinetic and thermodynamic estimations were achieved for each reaction step of the catalytic mechanism by characterization of the intermediates and transition states on the reaction pathway, and the effects of mutations on the activation barriers were analyzed. A good accordance was observed between the present computational results and experimental measurements reported in the literature.

Hydrogen-Deuterium Exchange within Adenosine Deaminase, a TIM Barrel Hydrolase, Identifies Networks for Thermal Activation of Catalysis

Proteins are intrinsically flexible macromolecules that undergo internal motions with time scales spanning femtoseconds to milliseconds. These fluctuations are implicated in the optimization of reaction barriers for enzyme catalyzed reactions. Time, temperature, and mutation dependent hydrogen-deuterium exchange coupled to mass spectrometry (HDX-MS) has been previously employed to identify spatially resolved, catalysis-linked dynamical regions of enzymes. We now extend this technique to pursue the correlation of protein flexibility and chemical reactivity within the diverse and widespread TIM barrel proteins, targeting murine adenosine deaminase (mADA) that catalyzes the irreversible deamination of adenosine to inosine and ammonia. Following a structure-function analysis of rate and activation energy for a series of mutations at a second sphere phenylalanine positioned in proximity to the bound substrate, the catalytically impaired Phe61Ala with an elevated activation energy (Ea = 7.5 kcal/mol) and the wild type (WT) mADA (Ea = 5.0 kcal/mol) were selected for HDX-MS experiments. The rate constants and activation energies of HDX for peptide segments are quantified and used to assess mutation-dependent changes in local and distal motions. Analyses reveal that approximately 50% of the protein sequence of Phe61Ala displays significant changes in the temperature dependence of HDX behaviors, with the dominant change being an increase in protein flexibility. Utilizing Phe61Ile, which displays the same activation energy for k_cat as WT, as a control, we were able to further refine the HDX analysis, highlighting the regions of mADA that are altered in a functionally relevant manner. A map is constructed that illustrates the regions of protein that are proposed to be essential for the thermal optimization of active site configurations that dominate reaction barrier crossings in the native enzyme.

Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide

Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.

Temperature, Dynamics, and Enzyme-Catalyzed Reaction Rates

We review the adaptations of enzyme activity to different temperatures. Psychrophilic (cold-adapted) enzymes show significantly different activation parameters (lower activation enthalpies and entropies) from their mesophilic counterparts. Furthermore, there is increasing evidence that the temperature dependence of many enzyme-catalyzed reactions is more complex than is widely believed. Many enzymes show curvature in plots of activity versus temperature that is not accounted for by denaturation or unfolding. This is explained by macromolecular rate theory: A negative activation heat capacity for the rate-limiting chemical step leads directly to predictions of temperature optima; both entropy and enthalpy are temperature dependent. Fluctuations in the transition state ensemble are reduced compared to the ground state. We show how investigations combining experiment with molecular simulation are revealing fundamental details of enzyme thermoadaptation that are relevant for understanding aspects of enzyme evolution. Simulations can calculate relevant thermodynamic properties (such as activation enthalpies, entropies, and heat capacities) and reveal the molecular mechanisms underlying experimentally observed behavior.

Using Atomic Confining Potentials for Geometry Optimization and Vibrational Frequency Calculations in Quantum-Chemical Models of Enzyme Active Sites

Quantum-chemical studies of enzymatic reaction mechanisms sometimes use truncated active-site models as simplified alternatives to mixed quantum mechanics molecular mechanics (QM/MM) procedures. Eliminating the MM degrees of freedom reduces the complexity of the sampling problem, but the trade-off is the need to introduce geometric constraints in order to prevent structural collapse of the model system during geometry optimizations that do not contain a full protein backbone. These constraints may impair the efficiency of the optimization, and care must be taken to avoid artifacts such as imaginary vibrational frequencies. We introduce a simple alternative in which terminal atoms of the model system are placed in soft harmonic confining potentials rather than being rigidly constrained. This modification is simple to implement and straightforward to use in vibrational frequency calculations, unlike iterative constraint-satisfaction algorithms, and allows the optimization to proceed without constraint even though the practical result is to fix the anchor atoms in space. The new approach is more efficient for optimizing minima and transition states, as compared to the use of fixed-atom constraints, and also more robust against unwanted imaginary frequencies. We illustrate the method by application to several enzymatic reaction pathways where entropy makes a significant contribution to the relevant reaction barriers. The use of confining potentials correctly describes reaction paths and facilitates calculation of both vibrational zero-point and finite-temperature entropic corrections to barrier heights.

GTP Hydrolysis Without an Active Site Base: A Unifying Mechanism for Ras and Related GTPases

GTP hydrolysis is a biologically crucial reaction, being involved in regulating almost all cellular processes. As a result, the enzymes that catalyze this reaction are among the most important drug targets. Despite their vital importance and decades of substantial research effort, the fundamental mechanism of enzyme-catalyzed GTP hydrolysis by GTPases remains highly controversial. Specifically, how do these regulatory proteins hydrolyze GTP without an obvious general base in the active site to activate the water molecule for nucleophilic attack? To answer this question, we perform empirical valence bond simulations of GTPase-catalyzed GTP hydrolysis, comparing solvent- and substrate-assisted pathways in three distinct GTPases, Ras, Rab, and the G_αi subunit of a heterotrimeric G-protein, both in the presence and in the absence of the corresponding GTPase activating proteins. Our results demonstrate that a general base is not needed in the active site, as the preferred mechanism for GTP hydrolysis is a conserved solvent-assisted pathway. This pathway involves the rate-limiting nucleophilic attack of a water molecule, leading to a short-lived intermediate that tautomerizes to form H₂PO₄^- and GDP as the final products. Our fundamental biochemical insight into the enzymatic regulation of GTP hydrolysis not only resolves a decades-old mechanistic controversy but also has high relevance for drug discovery efforts. That is, revisiting the role of oncogenic mutants with respect to our mechanistic findings would pave the way for a new starting point to discover drugs for (so far) "undruggable" GTPases like Ras.

Thermodynamic analysis of remote substrate binding energy in 3α-hydroxysteroid dehydrogenase/carbonyl reductase catalysis

The binding energy of enzyme and substrate is used to lower the activation energy for the catalytic reaction. 3α-HSD/CR uses remote binding interactions to accelerate the reaction of androsterone with NAD⁺. Here, we examine the enthalpic and entropic components of the remote binding energy in the 3α-HSD/CR-catalyzed reaction of NAD⁺ with androsterone versus the substrate analogs, 2-decalol and cyclohexanol, by analyzing the temperature-dependent kinetic parameters through steady-state kinetics. The effects of temperature on k_cat/K_m for 3α-HSD/CR acting on androsterone, 2-decalol, and cyclohexanol show the reactions are entropically favorable but enthalpically unfavorable. Thermodynamic analysis from the temperature-dependent values of K_m and k_cat shows the binding of the E-NAD⁺ complex with either 2-decalol or cyclohexanol to form the ternary complex is endothermic and entropy-driven, and the subsequent conversion to the transition state is both enthalpically and entropically unfavorable. Hence, solvation entropy may play an important role in the binding process through both the desolvation of the solute molecules and the release of bound water molecules from the active site into bulk solvent. As compared to the thermodynamic parameters of 3α-HSD/CR acting on cyclohexanol, the hydrophobic interaction of the B-ring of steroids with the active site of 3α-HSD/CR contributes to catalysis by increasing exclusively the entropy of activation (ΔTΔS^‡ = 1.8 kcal/mol), while the BCD-ring of androsterone significantly lowers ΔΔH^‡ by 10.4 kcal/mol with a slight entropic penalty of -1.9 kcal/mol. Therefore, the remote non-reacting sites of androsterone may induce a conformational change of the substrate binding loop with an entropic cost for better interaction with the transition state to decrease the enthalpy of activation, significantly increasing catalytic efficiency.

Understanding the entropic effect in chorismate mutase reaction catalyzed by isochorismate-pyruvate lyase fromPseudomonas aeruginosa(PchB)

The substrate preorganization process in the entropically driven PchB-catalyzed chorismate mutase reaction leads to a remarkable apparent entropic effect.

Conversion mechanism of enoyl thioesters into acyl thioesters catalyzed by 2-enoyl-thioester reductases from Candida Tropicalis

Enoyl thioester reductase from Candida tropicalis (Etr1p) catalyzes the NADPH-dependent conversion of enoyl thioesters into acyl thioesters, which are essential in fatty acid and second metabolite biosynthesis.

Influence of Dlutaraldehyde Cross-Linking Modes on the Recyclability of Immobilized Lipase B from Candida antarctica for Transesterification of Soy Bean Oil

Lipase B from Candida antarctica (CAL-B) is largely employed as a biocatalyst for hydrolysis, esterification, and transesterification reactions. CAL-B is a good model enzyme to study factors affecting the enzymatic structure, activity and/or stability after an immobilization process. In this study, we analyzed the immobilization of CAL-B enzyme on different magnetic nanoparticles, synthesized by the coprecipitation method inside inverse micelles made of zwitterionic surfactants, with distinct carbon chain length: 4 (ImS4), 10 (ImS10) and 18 (ImS18) carbons. Magnetic nanoparticles ImS4 and ImS10 were shown to cross-link to CAL-B enzyme via a Michael-type addition, whereas particles with ImS18 were bond via pyridine formation after glutaraldehyde cross-coupling. Interestingly, the Michael-type cross-linking generated less stable immobilized CAL-B, revealing the influence of a cross-linking mode on the resulting biocatalyst behavior. Curiously, a direct correlation between nanoparticle agglomerate sizes and CAL-B enzyme reuse stability was observed. Moreover, free CAL-B enzyme was not able to catalyze transesterification due to the high methanol concentration; however, the immobilized CAL-B enzyme reached yields from 79.7 to 90% at the same conditions. In addition, the transesterification of lipids isolated from oleaginous yeasts achieved 89% yield, which confirmed the potential of immobilized CAL-B enzyme in microbial production of biodiesel.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

A Theoretical Study of the Benzoylformate Decarboxylase Reaction Mechanism

Density functional theory calculations are used to investigate the detailed reaction mechanism of benzoylformate decarboxylase, a thiamin diphosphate (ThDP)-dependent enzyme that catalyzes the nonoxidative decarboxylation of benzoylformate yielding benzaldehyde and carbon dioxide. A large model of the active site is constructed on the basis of the X-ray structure, and it is used to characterize the involved intermediates and transition states and evaluate their energies. There is generally good agreement between the calculations and available experimental data. The roles of the various active site residues are discussed and the results are compared to mutagenesis experiments. Importantly, the calculations identify off-cycle intermediate species of the ThDP cofactor that can have implications on the kinetics of the reaction.

Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures

Drug action is inherently multiscale: it connects molecular interactions to emergent properties at cellular and larger scales. Simulation techniques at each of these different scales are already central to drug design and development, but methods capable of connecting across these scales will extend understanding of complex mechanisms and the ability to predict biological effects. Improved algorithms, ever-more-powerful computing architectures and the accelerating growth of rich datasets are driving advances in multiscale modeling methods capable of bridging chemical and biological complexity from the atom to the cell. Particularly exciting is the development of highly detailed, structure-based, physical simulations of biochemical systems, which are now able to access experimentally relevant timescales for large systems and, at the same time, achieve unprecedented accuracy. In this Perspective, we discuss how emerging data-rich, physics-based multiscale approaches are of the cusp of realizing long-promised impact in the discovery, design and development of novel therapeutics. We highlight emerging methods and applications in this growing field, and outline how different scales can be combined in practical modelling and simulation strategies.

Multiscale analysis of enantioselectivity in enzyme-catalysed 'lethal synthesis' using projector-based embedding

The action of fluoroacetate as a broad-spectrum mammalian pesticide depends on the 'lethal synthesis' of fluorocitrate by citrate synthase, through a subtle enantioselective enolization of fluoroacetyl-coenzyme A. In this work, we demonstrate how a projection-based embedding method can be applied to calculate coupled cluster (CCSD(T)) reaction profiles from quantum mechanics/molecular mechanics optimized pathways for this enzyme reaction. Comparison of pro-R and pro-S proton abstraction in citrate synthase at the CCSD(T)-in-DFT//MM level yields the correct enantioselectivity. We thus demonstrate the potential of projection-based embedding for determining stereoselectivity in enzymatic systems. We further show that the method is simple to apply, eliminates variability due to the choice of density functional theory functional and allows the efficient calculation of CCSD(T) quality enzyme reaction barriers.

Ab Initio QM/MM Modeling of the Rate-Limiting Proton Transfer Step in the Deamination of Tryptamine by Aromatic Amine Dehydrogenase

Aromatic amine dehydrogenase (AADH) and related enzymes are at the heart of debates on the roles of quantum tunneling and protein dynamics in catalysis. The reaction of tryptamine in AADH involves significant quantum tunneling in the rate-limiting proton transfer step, shown by large H/D primary kinetic isotope effects (KIEs), with unusual temperature dependence. We apply correlated ab initio combined quantum mechanics/molecular mechanics (QM/MM) methods, at levels up to local coupled cluster theory (LCCSD(T)/(aug)-cc-pVTZ), to calculate accurate potential energy surfaces for this reaction, which are necessary for quantitative analysis of tunneling contributions and reaction dynamics. Different levels of QM/MM treatment are tested. Multiple pathways are calculated with fully flexible transition state optimization by the climbing-image nudged elastic band method at the density functional QM/MM level. The average LCCSD(T) potential energy barriers to proton transfer are 16.7 and 14.0 kcal/mol for proton transfer to the two carboxylate atoms of the catalytic base, Asp128β. The results show that two similar, but distinct pathways are energetically accessible. These two pathways have different barriers, exothermicity and curvature, and should be considered in analyses of the temperature dependence of reaction and KIEs in AADH and other enzymes. These results provide a benchmark for this prototypical enzyme reaction and will be useful for developing empirical models, and analyzing experimental data, to distinguish between different conceptual models of enzyme catalysis.

Cold Adaptation of Triosephosphate Isomerase

The main problem for enzymes from psychrophilic species, which need to work near the freezing point of liquid water, is the exponential decay of reaction rates as the temperature is decreased. Cold-adapted enzymes have solved this problem by shifting the activation enthalpy-entropy balance for the catalyzed reaction compared to those of their mesophilic orthologs. To understand the structural basis of this universal feature, it is necessary to examine pairs of such orthologous enzymes, with known three-dimensional structures, at the microscopic level. Here, we use molecular dynamics free energy calculations in combination with the empirical valence bond method to evaluate the temperature dependence of the activation free energy for differently adapted triosephosphate isomerases. The results show that the enzyme from the psychrophilic bacterium Vibrio marinus indeed displays the characteristic shift in enthalpy-entropy balance, compared to that of the yeast ortholog. The origin of this effect is found to be located in a few surface-exposed protein loops that show differential mobilities in the two enzymes. Key mutations render these loops more mobile in the cold-adapted triosephosphate isomerase, which explains both the reduced activation enthalpy contribution from the protein surface and the lower thermostability.

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.

Mechanistic Explanation of the Weak Carbonic Anhydrase's Esterase Activity

In order to elucidate the elementary mechanism of the promiscuous esterase activity of human carbonic anhydrase (h-CA), we present an accurate theoretical investigation on the hydrolysis of fully-acetylated d-glucose functionalized as sulfamate. This h-CA's inhibitor is of potential relevance in cancer therapy. The study has been performed within the framework of three-layer ONIOM (QM-high:QM'-medium:MM-low) hybrid approach. The computations revealed that the hydrolysis process is not energetically favored, in agreement with the observed weak carbonic anhydrase's esterase activity.

Enzyme activation through the utilization of intrinsic dianion binding energy

43

We consider 'the proposition that the intrinsic binding energy that results from the noncovalent interaction of a specific substrate with the active site of the enzyme is considerably larger than is generally believed. An important part of this binding energy may be utilized to provide the driving force for catalysis, so that the observed binding energy represents only what is left over after this utilization' [Jencks,W.P. (1975) Adv. Enzymol. Relat. Areas. Mol. Biol. , , 219-410]. The large ~12 kcal/mol intrinsic substrate phosphodianion binding energy for reactions catalyzed by triosephosphate isomerase (TIM), orotidine 5'-monophosphate decarboxylase and glycerol-3-phosphate dehydrogenase is divided into 4-6 kcal/mol binding energy that is expressed on the formation of the Michaelis complex in anchoring substrates to the respective enzyme, and 6-8 kcal/mol binding energy that is specifically expressed at the transition state in activating the respective enzymes for catalysis. A structure-based mechanism is described where the dianion binding energy drives a conformational change that activates these enzymes for catalysis. Phosphite dianion plays the active role of holding TIM in a high-energy closed active form, but acts as passive spectator in showing no effect on transition-state structure. The result of studies on mutant enzymes is presented, which support the proposal that the dianion-driven enzyme conformational change plays a role in enhancing the basicity of side chain of E167, the catalytic base, by clamping the base between a pair of hydrophobic side chains. The insight these results provide into the architecture of enzyme active sites and the development of strategies for the de novo design of protein catalysts is discussed.

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.

Recent Trends in Quantum Chemical Modeling of Enzymatic Reactions

The quantum chemical cluster approach is a powerful method for investigating enzymatic reactions. Over the past two decades, a large number of highly diverse systems have been studied and a great wealth of mechanistic insight has been developed using this technique. This Perspective reviews the current status of the methodology. The latest technical developments are highlighted, and challenges are discussed. Some recent applications are presented to illustrate the capabilities and progress of this approach, and likely future directions are outlined.

Entropy and Enzyme Catalysis

The role played by entropy for the enormous rate enhancement achieved by enzymes has been debated for many decades. There are, for example, several confirmed cases where the activation free energy is reduced by around 10 kcal/mol due to entropic effects, corresponding to a rate enhancement of ∼10⁷ compared to the uncatalyzed reaction. However, despite substantial efforts from both the experimental and theoretical side, no real consensus has been reached regarding the origin of such large entropic contributions to enzyme catalysis. Another remarkable instance of entropic effects is found in enzymes that are adapted by evolution to work at low temperatures, near the freezing point of water. These cold-adapted enzymes invariably show a more negative entropy and a lower enthalpy of activation than their mesophilic orthologs, which counteracts the exponential damping of reaction rates at lower temperature. The structural origin of this universal phenomenon has, however, remained elusive. The basic problem with connecting macroscopic thermodynamic quantities, such as activation entropy and enthalpy derived from Arrhenius plots, to the 3D protein structure is that the underlying detailed (microscopic) energetics is essentially inaccessible to experiment. Moreover, attempts to calculate entropy contributions by computer simulations have mostly focused only on substrate entropies, which do not provide the full picture. We have recently devised a new approach for accessing thermodynamic activation parameters of both enzyme and solution reactions from computer simulations, which turns out to be very successful. This method is analogous to the experimental Arrhenius plots and directly evaluates the temperature dependence of calculated reaction free energy profiles. Hence, by extensive molecular dynamics simulations and calculations of up to thousands of independent free energy profiles, we are able to extract activation parameters with sufficient precision for making direct comparisons to experiment. We show here that the agreement with the measured quantities, for both enzyme catalyzed and spontaneous solution reactions, is quite remarkable. Importantly, we can now address some of the most spectacular entropy effects in enzymes and clarify their detailed microscopic origin. Herein, we discuss as examples the conversion of cytidine to uridine catalyzed by cytidine deaminase and reactions taking place on the ribosome, namely, peptide bond formation and GTP hydrolysis by elongation factor Tu. It turns out that the large entropy contributions to catalysis in these cases can now be rationalized by our computational approach. Finally, we address the problem of cold adaptation of enzyme reaction rates and prove by computational experiments that the universal activation enthalpy-entropy phenomenon originates from mechanical properties of the outer protein surface.

QM/MM Analysis of Transition States and Transition State Analogues in Metalloenzymes

Enzymology is approaching an era where many problems can benefit from computational studies. While ample challenges remain in quantitatively predicting behavior for many enzyme systems, the insights that often come from computations are an important asset for the enzymology community. Here we provide a primer for enzymologists on the types of calculations that are most useful for mechanistic problems in enzymology. In particular, we emphasize the integration of models that range from small active-site motifs to fully solvated enzyme systems for cross-validation and dissection of specific contributions from the enzyme environment. We then use a case study of the enzyme alkaline phosphatase to illustrate specific application of the methods. The case study involves examination of the binding modes of putative transition state analogues (tungstate and vanadate) to the enzyme. The computations predict covalent binding of these ions to the enzymatic nucleophile and that they adopt the trigonal bipyramidal geometry of the expected transition state. By comparing these structures with transition states found through free energy simulations, we assess the degree to which the transition state analogues mimic the true transition states. Technical issues worth treating with care as well as several remaining challenges to quantitative analysis of metalloenzymes are also highlighted during the discussion.

Enzyme surface rigidity tunes the temperature dependence of catalytic rates

The structural origin of enzyme adaptation to low temperature, allowing efficient catalysis of chemical reactions even near the freezing point of water, remains a fundamental puzzle in biocatalysis. A remarkable universal fingerprint shared by all cold-active enzymes is a reduction of the activation enthalpy accompanied by a more negative entropy, which alleviates the exponential decrease in chemical reaction rates caused by lowering of the temperature. Herein, we explore the role of protein surface mobility in determining this enthalpy-entropy balance. The effects of modifying surface rigidity in cold- and warm-active trypsins are demonstrated here by calculation of high-precision Arrhenius plots and thermodynamic activation parameters for the peptide hydrolysis reaction, using extensive computer simulations. The protein surface flexibility is systematically varied by applying positional restraints, causing the remarkable effect of turning the cold-active trypsin into a variant with mesophilic characteristics without changing the amino acid sequence. Furthermore, we show that just restraining a key surface loop causes the same effect as a point mutation in that loop between the cold- and warm-active trypsin. Importantly, changes in the activation enthalpy-entropy balance of up to 10 kcal/mol are almost perfectly balanced at room temperature, whereas they yield significantly higher rates at low temperatures for the cold-adapted enzyme.

A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase

Projector-based embedding has recently emerged as a robust multiscale method for the calculation of various electronic molecular properties. We present the coupling of projector embedding with quantum mechanics/molecular mechanics modeling and apply it for the first time to an enzyme-catalyzed reaction. Using projector-based embedding, we combine coupled-cluster theory, density-functional theory (DFT), and molecular mechanics to compute energies for the proton abstraction from acetyl-coenzyme A by citrate synthase. By embedding correlated ab initio methods in DFT we eliminate functional sensitivity and obtain high-accuracy profiles in a procedure that is straightforward to apply.

Understanding the Mechanism of the Hydrogen Abstraction from Arachidonic Acid Catalyzed by the Human Enzyme 15-Lipoxygenase-2. A Quantum Mechanics/Molecular Mechanics Free Energy Simulation

Lipoxygenases (LOXs) are a family of enzymes involved in the biosynthesis of several lipid mediators. In the case of human 15-LOX, the 15-LOX-1 and 15-LOX-2 isoforms show slightly different reaction regiospecificity and substrate specificity, indicating that substrate binding and recognition may be different, a fact that could be related to their different biological role. Here, we have used long molecular dynamics simulations, QM(DFT)/MM potential energy and free energy calculations (using the newly developed DHAM method), to investigate the binding mode of the arachidonic acid (AA) substrate into 15-LOX-2 and the rate-limiting hydrogen-abstraction reaction 15-LOX-2 catalyzes. Our results strongly indicate that hydrogen abstraction from C13 in 15-LOX-2 is only consistent with the "tail-first" orientation of AA, with its carboxylate group interacting with Arg429, and that only the pro-S H13 hydrogen will be abstracted (being the pro-R H13 and H10 too far from the acceptor oxygen atom). At the B3LYP/6-31G(d) level the potential and free energy barriers for the pro-S H13 abstraction of AA by 15-LOX-2 are 18.0 and 18.6 kcal/mol, respectively. To analyze the kinetics of the hydrogen abstraction process, we determined a Markov model corresponding to the unbiased simulations along the state-discretized reaction coordinate. The calculated rates based on the second largest eigenvalue of the Markov matrices agree well with experimental measurements, and also provide the means to directly determine the pre-exponential factor for the reaction by comparing with the free energy barrier height. Our calculated pre-exponential factor is close to the value of kBT/h. On the other hand, our results suggest that the spin inversion of the complete system (including the O2 molecule) that is required to happen at some point along the full process to lead to the final hydroperoxide product, is likely to take place during the hydrogen transfer, which is a proton coupled electron transfer. Overall, a different binding mode from the one accepted for 15-LOX-1 is proposed, which provides a molecular basis for 15-LOX-2 exclusive 15-HPETE production in front of the double (although highly 15-) 12/15 regiospecificity of 15-LOX-1. Understanding how these different isoenzymes achieve their regiospecificity is expected to help in specific inhibitor design.