- Top of page
- Supporting Information
The enzyme chorismate mutase EcCM from Escherichia coli catalyzes one of the few pericyclic reactions in biology, the transformation of chorismate to prephenate. The isochorismate pyruvate lyase PchB from Pseudomonas aeroginosa catalyzes another pericyclic reaction, the isochorismate to salicylate transformation. Interestingly, PchB possesses weak chorismate mutase activity as well thus being able to catalyze two distinct pericyclic reactions in a single active site. EcCM and PchB possess very similar folds, despite their low sequence identity. Using molecular dynamics simulations of four combinations of the two enzymes (EcCM and PchB) with the two substrates (chorismate and isochorismate) we show that the electrostatic field due to EcCM at atoms of chorismate favors the chorismate to prephenate transition and that, analogously, the electrostatic field due to PchB at atoms of isochorismate favors the isochorismate to salicylate transition. The largest differences between EcCM and PchB in electrostatic field strengths at atoms of the substrates are found to be due to residue side chains at distances between 0.6 and 0.8 nm from particular substrate atoms. Both enzymes tend to bring their non-native substrate in the same conformation as their native substrate. EcCM and to a lower extent PchB fail in influencing the forces on and conformations of the substrate such as to favor the other chemical reaction (isochorismate pyruvate lyase activity for EcCM and chorismate mutase activity for PchB). These observations might explain the difficulty of engineering isochorismate pyruvate lyase activity in EcCM by solely mutating active site residues.
- Top of page
- Supporting Information
Elucidation of the driving forces and mechanisms of catalysis by enzymes is one of the intriguing challenges in biochemistry with practical consequences.[1, 2] Obviously, the observed speed-ups of the catalyzed chemical reactions compared to the same reaction in the gas phase or solution phase are due to the environment of the reactant or substrate bound in the active site of the enzyme. In the catalytic process, four phases may be distinguished: (i) Binding of the substrate in the active site of the enzyme, thereby possibly changing its own or the enzyme's conformation as to favor the reaction. (ii) The reactant mounting the activation barrier of the transition state (TS). The activation barrier may be decreased compared to the reaction in vacuo or in aqueous solution by the electrostatic field due to the various residues of the enzyme and by structural changes in the substrate and enzyme. The probability of reaching TS conformations may be enhanced by positional fluctuations of atoms of the enzyme or solvent that induce fluctuations in the forces on the atoms of the substrate, for example, by a fluctuating electrostatic field or through short-range covalent or van der Waals interactions, or originating from motional correlations in the enzymes. (iii) Formation of the product. (iv) Release of the product from its binding pocket in the enzyme.
Experimentally, only a few observable quantities characterizing the catalytic process can be measured: (i) Overall reaction rates. (ii) The free energy or enthalpy of binding of ligand molecules, in particular transition state analogs (TSA), to the enzymes. The binding free energy of a particular substrate A to an enzyme may in some cases be obtained indirectly by measuring the product formation of a substrate B and the inhibition of this process by the presence of substrate A or by inhibiting the conversion of substrate A in one way or the other. (iii) Atomic structure of the enzyme in a particular crystalline form as derived from X-ray or neutron diffraction patterns, or to much less precision in aqueous solution as derived from NMR spectroscopic measurements, but again in general only for the apoenzyme or the enzyme with a ligand bound that is not the substrate, unless the conversion of the substrate can be prevented by inducing particular conditions. These three types of quantities can be measured or derived as a function of (i) the thermodynamic state point, that is, temperature, pressure, pH, ionic strength, or (ii) the composition of the enzyme which is varied in mutant enzymes, enzymes from different organisms, minimum amino acid alphabet enzymes, deuterated enzymes, etc., or (iii) the substrate or ligand composition. As these data are much lower in number than the number of degrees of freedom of an enzyme system, the detailed driving forces and mechanism of the catalytic process can not be unambiguously determined by experimental means. This has led to a variety of descriptions, models, and theories of enzymatic reactions that cannot unambiguously be falsified or repudiated based on experimental data.
From a theoretical and computational point of view, statistical quantum mechanics offers the basic model by which catalytic processes should be explained. In computational practice, though severe simplifications and approximations of the statistical quantum-mechanical (QM) equations have to be invoked in order to obtain a result, even using the fastest computers available. For reviews of the level, we refer to Refs. [3-5]. Time-independent QM models for the electronic degrees of freedom of the substrate and part of the enzyme are used to obtain the energy of the system along a chosen pathway or reaction coordinate connecting the reactant state (RS) configuration with the postulated TS configurations of the enzyme and the ligand. If entropic contributions are estimated in one way or the other, the energy profile becomes a free energy profile. Because of the statistical-mechanical nature of an enzyme in solution, a proper sampling of the configurational Boltzmann ensembles is required to include entropic contributions to the free energy differences that drive the reaction. Due to the severity of the required assumptions and approximations both at the quantum electronic and the classical atomic levels of modelling, the current computational models of enzymatic reactions are rather of qualitative than of quantitative accuracy. On the quantum-chemical side, empirical valence bond, semiempirical, and density-functional methods are rather approximate, while higher level ab initio methods are too expensive to allow for a proper sampling of the many relevant degrees of freedom. On the classical statistical molecular-mechanical (MM) side, biomolecular force fields have a limited accuracy and although the sampling can reach time scales of nanoseconds to microseconds, this may not be sufficient to cover the slow conformational relaxation in enzymes. In addition, in view of the limited set of experimentally observable quantities a proper validation of theoretical-computational models of enzyme catalysis is problematic. The reproduction of a few experimental data for a high-dimensional model of an enzyme that contains many parameters to be chosen does not necessarily imply the correctness of the model or observed mechanism, unfortunately.
The variety of computational approaches to investigate enzyme catalysis can be illustrated by considering this type of work on the enzymes of the chorismate mutase (CM) family.[6, 7] Because hybrid quantum-mechanical molecular-mechanical (QM/MM) simulation of this enzyme in aqueous solution currently only covers tens of picoseconds, too short to surmount the activation barrier, in QM/MM studies of CM the enzyme plus substrate is energy minimized or simulated in conformations along a one8- or two9- dimensional reaction pathway connecting the RS with a hypothetical TS.[10, 11] From the generated configurations, an energy or free energy profile or potential of mean force (PMF) along the pathway can be calculated. This can be done for the reaction inside the enzyme, in solution, and in the gas phase, which allows the analysis of the energetic and geometric differences in these different environments. Such an analysis addresses the rate enhancement by the enzyme over a gas or solvent environment. In this type of approach, it is not well possible to determine the contribution of the different amino acid residues to the catalysis without making assumptions on the insensitivity of the pathway to residue variation, unless the PMF calculation is repeated for each mutant of the enzyme.[12-15]
An alternative type of computational approach in which configurational sampling can be much enhanced is to perform classical molecular dynamics (MD) simulations of the enzyme with substrate, TSA, or product and then evaluate the energy, the structural ensembles, or the forces on atoms of interest, for example, to determine whether the conformation of the substrate is driven toward that of a TS.[16, 17] The averages of different quantities such as forces on atoms or distances between atoms over the generated Boltzmann ensemble are of lesser interest than the distributions of these quantities. The tails of such distributions may contain configurations or forces that are rarely present but may induce the reaction, that is, the electronic rearrangement. This type of computational approach has the advantage that contributions to the forces from the different amino acid residues can be readily determined from a single simulation.
All approaches used so far to elucidate enzyme reaction mechanisms suffer from more or less severe assumptions or limitations. In the quantum-chemical model, these reside in the choice of Hamiltonian basis set and limited number of degrees of freedom. In the MM model, these reside in the choice of force field and degree of sampling of the degrees of freedom. In QM/MM model studies, approximations in the way the QM/MM boundary is treated are additional sources of inaccuracy. Yet, the intriguing catalytic properties of enzymes nevertheless beg for computational investigation, be it only on a qualitative level. In the present article, we address a question that is different from the ones addressed in most QM/MM or MD studies of enzyme reactions.
Two enzymes that adopt very similar folds consisting of α-helices, CM, and isochorismate pyruvate lyase (IPL; Fig. 1) catalyze the transformation of different substrates (Fig. 2), that is, chorismate (chr) and isochorismate (ichr), respectively. This difference must be due to the different forces exerted on the atoms of the bound substrates by the different protein atoms in the similar folds. This raises the question whether such a difference in forces can be detected when modeling the enzyme substrate complexes.
Figure 1. The simulated enzymes. Representative X-ray structures for the EcCM-chr (left) and PchB-ichr (middle) systems together with the substrates. On the right, the CM and IPL enzymes are superimposed. EcCM is shown in orange and PchB in yellow. For the two substrates, carbon atoms are depicted in cyan, oxygen atoms in red, and hydrogen atoms in white.
Download figure to PowerPoint
Figure 2. Schematic diagrams illustrating the transformations of chr to prephenate (CM-catalyzed reaction 1) and ichr to salicylate (IPL-catalyzed reaction 2).
Download figure to PowerPoint
CM catalyzes one of the few pericyclic reactions in biology and is a key enzyme in the biosynthetic pathway leading to the aromatic amino acids phenylalanine and tyrosine in bacteria, fungi, and plants. The transformation of chr to prephenate (Fig. 2), formally a [3,3]-pericyclic rearrangement, also known as a Claisen rearrangement, proceeds in the absence of enzymatic catalysis as a concerted but asynchronous process via a chair-like TS. Natural CMs accelerate the rearrangement of chr more than a million-fold. The structure of the all-helical CM from Escherichia coli (EcCM) has been determined by X-ray crystallography at 2.2 Å resolution.
The IPL from Pseudomonas aeroginusa (PchB) physiologically catalyzes the elimination of the enolpyruvyl side chain from ichr to make salicylate for incorporation into the siderophore pyochelin (Fig. 2). The IPL reaction is a concerted but asynchronous hydrogen transfer, by a proposed [1,5]-sigmatropic reaction mechanism with a pericyclic TS. The structure of PchB has been determined at 1.95 and 2.35 Å resolution, revealing that this enzyme is a structural homolog of EcCM, despite the low sequence identity of 21%.[20, 21] The similarity of their folds is clear from Figure 1. This structural similarity possibly accounts for residual CM activity of PchB, albeit with considerably lower efficiency than EcCM.
PchB has been engineered by mutagenesis to catalyze more efficiently the chr to prephenate rearrangement. CM catalytic activity was improved 43-fold, while IPL catalytic activity was lost. The PchB enzyme's promiscuity in catalyzing the chr to prephenate rearrangement has been the source of inspiration to engineer by mutagenesis a CM into an enzyme catalyzing the transformation of ichr into salicylate. Nevertheless, not a trace of this activity has been detected in CM variants mutated to more closely resemble the IPL active site. It has been recently suggested that unique dynamic properties of chr-utilizing enzymes might be partly responsible for their enzymatic activities. Investigation of the active site participants alone might, therefore, not be enough to understand catalysis in those enzymes. Hence, regions further from the binding pocket might influence catalytic activity in EcCM as well.
Can a model calculation detect reasons for the differential catalytic activity of the enzymes EcCM and PchB with respect to the substrates chr and ichr despite the similar fold of these two enzymes? The key must lie in the different side chains surrounding the active sites. To delineate the differences in the contributions to the forces from these residue side chains, we simulated four enzyme–substrate systems, each of the two enzymes with each of the two substrates, in aqueous solution. As we are interested in the distribution of the forces on the atoms of the substrates originating from residues close to and far from the active site, we restricted the calculations to classical MD simulations of the four enzyme-substrate systems and analyzed the configurational Boltzmann ensembles in terms of particular features of substrate geometry and of electrostatic forces on particular atoms of the substrate due to shells or layers of protein atoms around the substrates.
We do not intend to explain catalytic activity of near attack configurations[17, 25, 26] or differences in (free) energy of the transition versus RS between the enzyme and the solution or gas phase.[27, 28] To that end, we would have to involve QM modeling and to apply umbrella sampling along a hypothetical reaction coordinate leading to a hypothetical TS. We only investigate the four enzyme-substrate complexes to obtain an indication of the effect of the different environments on the substrates and whether such effects can be traced to particular amino acid residues. Our work differs in a number of aspects from other computational studies of CM catalytic activity: (i) we consider IPL from PchB and CM from EcCM, that is, CM from E. coli as in Ref. [17, 27, 28], while most computational studies[5, 8, 10-13, 16, 25, 26, 29-31] consider CM from Bacillus subtilis; (ii) we investigate the difference in substrate binding to IPL and CM, while most other studies aim at explaining CM catalysis, for example, Ref. ; (iii) we do not calculate a PMF along a reaction pathway using QM/MM methodology,[27, 28] but perform long MD simulations of enzymes-substrate complexes and analyze not only the configurations of the substrates but also the electrostatic forces on particular atoms of the substrates.