Adrian J. Mulholland

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.

Taking Ockham's razor to enzyme dynamics and catalysis

The role of protein dynamics in enzyme catalysis is a matter of intense current debate. Enzyme-catalysed reactions that involve significant quantum tunnelling can give rise to experimental kinetic isotope effects with complex temperature dependences, and it has been suggested that standard statistical rate theories, such as transition-state theory, are inadequate for their explanation. Here we introduce aspects of transition-state theory relevant to the study of enzyme reactivity, taking cues from chemical kinetics and dynamics studies of small molecules in the gas phase and in solution--where breakdowns of statistical theories have received significant attention and their origins are relatively better understood. We discuss recent theoretical approaches to understanding enzyme activity and then show how experimental observations for a number of enzymes may be reproduced using a transition-state-theory framework with physically reasonable parameters. Essential to this simple model is the inclusion of multiple conformations with different reactivity.

Does Compound I Vary Significantly between Isoforms of Cytochrome P450

The cytochrome P450 (CYP) enzymes are important in many areas, including pharmaceutical development. Subtle changes in the electronic structure of the active species, Compound I, have been postulated previously to account partly for the experimentally observed differences in reactivity between isoforms. Current predictive models of CYP metabolism typically assume an identical Compound I in all isoforms. Here we present a method to calculate the electronic structure and to estimate the Fe–O bond enthalpy of Compound I, and apply it to several human and bacterial CYP isoforms. Conformational flexibility is accounted for by sampling large numbers of structures from molecular dynamics simulations, which are subsequently optimized with density functional theory (B3LYP) based quantum mechanics/molecular mechanics. The observed differences in Compound I between human isoforms are small: They are generally smaller than the spread of values obtained for the same isoform starting from different initial structures. Hence, it is unlikely that the variation in activity between human isoforms is due to differences in the electronic structure of Compound I. A larger difference in electronic structure is observed between the human isoforms and P450cam and may be explained by the slightly different hydrogen-bonding environment surrounding the cysteinyl sulfur. The presence of substrate in the active site of all isoforms studied appears to cause a slight decrease in the Fe–O bond enthalpy, apparently due to displacement of water out of the active site, suggesting that Compound I is less stable in the presence of substrate.

Modelling enzyme reaction mechanisms, specificity and catalysis

Modern modelling methods can now give uniquely detailed understanding of enzyme-catalyzed reactions, including the analysis of mechanisms and the identification of determinants of specificity and catalytic efficiency. A new field of computational enzymology has emerged that has the potential to contribute significantly to structure-based design and to develop predictive models of drug metabolism and, for example, of the effects of genetic polymorphisms. This review outlines important techniques in this area, including quantum-chemical model studies and combined quantum-mechanics and molecular-mechanics (QM/MM) methods. Some recent applications to enzymes of pharmacological interest are also covered, showing the types of problems that can be tackled and the insight they can give.

A practical guide to modelling enzyme-catalysed reactions

Molecular modelling and simulation methods are increasingly at the forefront of elucidating mechanisms of enzyme-catalysed reactions, and shedding light on the determinants of specificity and efficiency of catalysis. These methods have the potential to assist in drug discovery and the design of novel protein catalysts. This Tutorial Review highlights some of the most widely used modelling methods and some successful applications. Modelling protocols commonly applied in studying enzyme-catalysed reactions are outlined here, and some practical implications are considered, with cytochrome P450 enzymes used as a specific example.

Investigations of enzyme-catalysed reactions with combined quantum mechanics/molecular mechanics (QM/MM) methods

Combined quantum mechanics/molecular mechanics (QM/MM or QM-MM) methods are an excellent approach for modelling the mechanisms of enzyme-catalysed reactions. QM/MM methods allow detailed modelling of reactions in enzymes by coupling quantum chemical calculations on the active site with a simpler, empirical ‘molecular mechanics’ treatment of the rest of the protein. Possible reaction mechanisms can be compared and catalytic interactions analysed. QM/MM calculations can now be carried out for enzyme-catalysed reactions with quantum chemical methods of potentially very high accuracy. More approximate QM methods can allow extensive molecular simulations (e.g. molecular dynamics or Monte Carlo simulations). In this review, QM/MM techniques are outlined and some recent applications to enzyme-catalysed reactions are discussed.

Unraveling the role of protein dynamics in dihydrofolate reductase catalysis

Significance The role of protein dynamics in enzyme catalysis remains a topic of considerable debate. Here, we use a combination of experimental and computational methods to identify the origins of the observed changes in reactivity on isotopic substitution of dihydrofolate reductase from Escherichia coli. Isotopic substitution causes differences in environmental coupling to the hydride transfer step and protein dynamics have therefore a small but measurable effect on the chemical reaction rate. Protein dynamics have controversially been proposed to be at the heart of enzyme catalysis, but identification and analysis of dynamical effects in enzyme-catalyzed reactions have proved very challenging. Here, we tackle this question by comparing an enzyme with its heavy (15N, 13C, 2H substituted) counterpart, providing a subtle probe of dynamics. The crucial hydride transfer step of the reaction (the chemical step) occurs more slowly in the heavy enzyme. A combination of experimental results, quantum mechanics/molecular mechanics simulations, and theoretical analyses identify the origins of the observed differences in reactivity. The generally slightly slower reaction in the heavy enzyme reflects differences in environmental coupling to the hydride transfer step. Importantly, the barrier and contribution of quantum tunneling are not affected, indicating no significant role for “promoting motions” in driving tunneling or modulating the barrier. The chemical step is slower in the heavy enzyme because protein motions coupled to the reaction coordinate are slower. The fact that the heavy enzyme is only slightly less active than its light counterpart shows that protein dynamics have a small, but measurable, effect on the chemical reaction rate.

Compound I Reactivity Defines Alkene Oxidation Selectivity in Cytochrome P450cam

Prediction of the chemoselectivity of drug oxidation by the human cytochrome P450 enzymes will aid in the avoidance of adverse drug reactions. The chemoselectivity of alkene oxidation is an important problem to address, as it can result in the formation of epoxides, which can have toxic effects. In this paper the epoxidation and hydroxylation of cyclohexene and propene by the bacterial P450(cam) isoform are modeled with hybrid quantum mechanical/molecular mechanical (QM/MM) methods. Snapshots for QM/MM modeling are chosen from molecular dynamics trajectories, to sample the different conformations of the enzyme-substrate complex. The energy barriers obtained for these processes are in qualitative agreement with experimental work, supporting the use of QM/MM methods in the study of selectivity for this class of enzyme. This work highlights the complexity involved in modeling these systems with QM/MM and the importance in the selection of starting geometries.

Mechanism and structure-reactivity relationships for aromatic hydroxylation by cytochrome P450

Cytochrome P450 enzymes play a central role in drug metabolism, and models of their mechanism could contribute significantly to pharmaceutical research and development of new drugs. The mechanism of cytochrome P450 mediated hydroxylation of aromatics and the effects of substituents on reactivity have been investigated using B3LYP density functional theory computations in a realistic porphyrin model system. Two different orientations of substrate approach for addition of Compound I to benzene, and also possible subsequent rearrangement pathways have been explored. The rate-limiting Compound I addition to an aromatic carbon atom proceeds on the doublet potential energy surface via a transition state with mixed radical and cationic character. Subsequent formation of epoxide, ketone and phenol products is shown to occur with low barriers, especially starting from a cation-like rather than a radical-like tetrahedral adduct of Compound I with benzene. Effects of ring substituents were explored by calculating the activation barriers for Compound I addition in the meta and para-position for a range of monosubstituted benzenes and for more complex polysubstituted benzenes. Two structure-reactivity relationships including 8 and 10 different substituted benzenes have been determined using (i) experimentally derived Hammett sigma-constants and (ii) a theoretical scale based on bond dissociation energies of hydroxyl adducts of the substrates, respectively. In both cases a dual-parameter approach that employs a combination of radical and cationic electronic descriptors gave good relationships with correlation coefficients R2 of 0.96 and 0.82, respectively. These relationships can be extended to predict the reactivity of other substituted aromatics, and thus can potentially be used in predictive drug metabolism models.

An efficient method for the calculation of quantum mechanics/molecular mechanics free energies

The combination of quantum mechanics (QM) with molecular mechanics (MM) offers a route to improved accuracy in the study of biological systems, and there is now significant research effort being spent to develop QM/MM methods that can be applied to the calculation of relative free energies. Currently, the computational expense of the QM part of the calculation means that there is no single method that achieves both efficiency and rigor; either the QM/MM free energy method is rigorous and computationally expensive, or the method introduces efficiency-led assumptions that can lead to errors in the result, or a lack of generality of application. In this paper we demonstrate a combined approach to form a single, efficient, and, in principle, exact QM/MM free energy method. We demonstrate the application of this method by using it to explore the difference in hydration of water and methane. We demonstrate that it is possible to calculate highly converged QM/MM relative free energies at the MP2/aug-cc-pVDZ/OPLS level within just two days of computation, using commodity processors, and show how the method allows consistent, high-quality sampling of complex solvent configurational change, both when perturbing hydrophilic water into hydrophobic methane, and also when moving from a MM Hamiltonian to a QM/MM Hamiltonian. The results demonstrate the validity and power of this methodology, and raise important questions regarding the compatibility of MM and QM/MM forcefields, and offer a potential route to improved compatibility.