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Enzyme mechanisms: interplay of theory and experiment
Journal of Molecular Structure (Theochem) 500 (2000) 157–167 www.elsevier.nl/locate/theochem
Enzyme mechanisms: interplay of theory and experiment G. Na´ray-Szabo´* Department of Theoretical Chemistry, Lora´nd Eo¨tvo¨s University, Pa´zma´ny Pe´ter st. 2, H-1117 Budapest, Hungary
Abstract An overview is given on experimental and theoretical methods applied to the study of enzyme mechanisms. While experiments provide more or less precise data on realistic systems, the obtained information often overlap and a mixture of observations has to be resolved in order to appropriately understand enzymatic processes at the molecular level. On the other hand, computations to be done on adequate models reflecting all important properties of the system, may not provide results that are accurate enough to be compared with experiments. It is stressed that in a computational study the level of sophistication of the model and the method applied to it should be about the same in order to obtain sound results. A case study, the catalytic mechanism of serine proteases, is discussed in detail calling attention to the problems where the interplay between computations and experimental studies was necessary to understand mechanistic details. It is computational chemistry that lead to the discovery of the crucial role of the protein electrostatic field in the acceleration of the enzyme reaction as well as protonation state of the side chains of the active site. We stress that computational studies are especially important in the right interpretation of experimental observations and should replace speculations based on textbook chemistry. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Enzyme mechanism; Mechanistic studies; Serine proteases
1. Introduction The spectacular development of experimental and computational techniques in the last few decades allowed to perform detailed studies on enzyme mechanisms [1,2]. Combination of enzyme kinetics, genetic engineering, protein crystallography, nuclear magnetic resonance spectroscopy, kinetic isotope effects as well as computer modelling provides a powerful arsenal that can be applied to study even subtle details of complicated enzymatic processes. It is important to notice that there is no single method, be it experimental or computational, that provides full and precise information both on structural and kinetic * Tel.: ⫹ 36-1-209-0555; fax: ⫹ 36-1-209-0602. E-mail address: [email protected] (G. Na´ray-Szabo´).
aspects of enzyme action. Thus, the multidisciplinary approach is imperative, a successful research group should include both experimentalists and theorists who are skilled in several techniques complementing each other. In this paper we present an overview on the most important methods for the study of enzyme reactions that should be, and are in fact often, combined in mechanistic studies. A separate section will be devoted to the construction of models that is prerequisite for any structural consideration, especially computational studies. It has to be stressed that model and method should be at about the same level of sophistication in a specific study in order to be able to draw sound conclusions. A rough model, even if combined with the most advanced calculation, cannot provide relevant results while even the most precise
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model may be misleading if the applied computational method is inaccurate. In the last section we present a case study, serine proteases, for which there is probably the largest amount of structural and mechanistic information available. Special attention will be paid to computational studies, especially if they complete results obtained by various experimental techniques that alone are not sufficient to answer some specific questions, e.g. relative stability of protonation states or structure and charge distribution of the transitionstate complex. 2. Models Prerequisite for a mechanistic study on an enzymatic process is a three-dimensional (3D) model of the group of atoms participating in the reaction. In general, enzyme active sites consist of more atoms than the bare substrate and the reacting functional group. Other components, like adjacent side chains, prosthetic group, water molecules and metal ions, even the protein environment and the surrounding biophase, have to be considered in a precise model. In general, this model can be constructed on the basis of experiment though there are some cases where computational methods are also applicable. We discuss the most important methods below. 2.1. Protein crystallography [3] Though proteins are high molecular weight, mobile macromolecules, it is possible to position them in a 3D periodic lattice with great precision, they frequently form regular crystals. In contrast to small molecules, unit cells of many proteins contain 30– 80% (by volume) of water as solvent, which means that there are few contacts between protein molecules, the crystals are stabilised by a few hydrogen bonds and van der Waals contacts. The high proportion of solvent means that the crystal environment is similar to the natural one, thus proteins in crystals are often functional. Growing of crystals is even nowadays more of an art than an established technique; there are dozens of factors, like protein purity, buffer type, pH, temperature, ionic strength or the presence of organic solvents, that strongly influence the success. Once we have appropriate crystals, it is possible to
collect many thousands of X-ray reflections allowing to determine the electron density. In order to do that the so-called phase problem has to be solved which means that not only the directly detectable intensities but also the phases of the reflections have to be known for the evaluation. The isomorphous replacement method may provide a solution when heavy metal ions are introduced into the crystal without changing its structure and the differences in the intensities contain information about the phases. Thus, the electron density map can be obtained which allows to fit a relatively rough model yielding the approximate location of protein atoms. Afterwards atomic positions have to be refined by sophisticated computational methods, making use of standard models of protein backbone and side chains, even molecular dynamics calculations. Finally, a quite precise geometric model of the protein structure is available with an estimated error of 30 pm for the positions of well-defined rigid atoms. While protein crystallography provides reliable positions for heavier atoms, in most of the cases hydrogen atoms cannot be seen because of the small electron density around them. This makes the study of protonation states of side chains, prosthetic groups and substrate very difficult. The problem can be surmounted by the neutron diffraction technique which, however, needs high-intensity neutron beams and these can be obtained only from nuclear reactors. Thus, the method is available only for a limited number of laboratories. A further problem may arise in case of disorder because the electronic density near disordered atomic positions is lower and more spread out which makes evaluation more difficult, sometimes impossible. On the other hand, some of the tightly bound water molecules around the protein can be located that may provide essential information on the enzymatic mechanism. It has to be borne in mind that X-ray crystallography does not allow study of energetic aspects and is essentially limited to static models. 2.2. Nuclear magnetic resonance spectroscopy [4] Complementary to protein crystallography in the experimental derivation of reliable enzyme models is nuclear magnetic resonance (NMR) spectroscopy. NMR measurements are carried out in solution under
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potentially physiological conditions, thus crystallisation is not a problem. On the other hand, strongly aggregated systems are not amenable to study by NMR. Spectra contain structural information through chemical shifts which are sensitive to the local environment, spin–spin coupling constants which are sensitive to dihedral angles and relaxation (Nuclear Overhauser Effect, NOE) which is sensitive to the positions of nearby spins (proton–proton distances). These data provide information that can be converted to 3D structures. In order to determine the structure a protein solution in the range of mM concentration has to be prepared first, then the NMR data can be recorded. This is followed by spectral analysis to yield NMR parameters and subsequently sequence-specific resonance assignments that provided earlier the major hurdle in interpretation. Fortunately, over the past decade spectacular progress has been made through the introduction of multidimensional NMR techniques and advances in spectrometer hardware. The conformational constraints needed as input have to be collected, then the structure can be calculated and refined from these data. In practice these steps are linked and one goes through repeated cycles of data analysis and structure determination. Once sequential resonance assignments have been obtained cross-peaks can be assigned, too, especially those involving residues far apart in the sequence and therefore provide information about the polypeptide fold. With the assignment in hand, a large number of interproton distance restraints can be derived which provide the necessary information to determine the 3D structure of the protein. To do this a number of computational methods can be employed such as distance geometry, minimisation of torsion angles with a variable target function, restrained molecular dynamics and simulated annealing [5]. While X-ray diffraction may yield structures even for quite large systems, like viruses, de novo structure determination with the NMR method is practicable for proteins with a molecular weight of at most 20 kD. New techniques applying 13C and 15N isotope labelling allow to study larger systems, even beyond 100 kD. A further complementary feature of the NMR method is that it provides information on protein dynamics. The precision with which the majority of structures has been determined is around
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100 pm for backbone atoms and 200 pm for all atoms. This limit can be reduced in some cases to 30 pm for backbone atoms and 50 pm for all atoms.
2.3. Homology modelling [6] In the absence of definitive information about the geometric parameters of the 3D model of a protein by X-ray diffraction or NMR spectroscopy prediction is often possible on the basis of the amino-acid sequence alone by detecting similarities between the new structure and the previously solved ones. There are several dozens of thousand sequences available in a database, many of which can be clustered into homologous families. If at least one structure within a family with at least 30% sequence homology is available, modelling of the others becomes a realistic possibility. The main steps of modelling are as follows. A sequence alignment between the protein to be modelled and a protein of known structure has to be established. Obviously, the higher the percentage identity observed in this alignment, and the lower the number of insertions and deletions, the easier the modelling and the better the final result will be. Based on this alignment a backbone has to be generated which is normally the backbone of the most homologous structure. Afterwards side chains have to be placed in the model, normally the side chains of the conserved residues will not be altered. During this process the major problem is that many residues have multiple favourable side chain conformations that may lead to steric conflict which should be avoided by applying Monte Carlo procedures or other algorithms. If the protein to be modelled has insertions or deletions with respect to the known structure, loops have to be re-modelled, or modelled ab initio. Database searches for loops with similar anchoring points in the structure are often used to build these loops, but energy based ab initio modelling techniques can be employed, too. After constructing the initial rough model, it needs to be optimised by some energy minimisation or molecular dynamics technique. Generally, a comparison of the predicted and observed structures shows an average rms superposition error of 100 pm for backbone atoms and 200 pm for all atoms including side chains.
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3. Methods
3.2. Site-directed mutagenesis [7]
3.1. Enzyme kinetics
The best method for altering the covalent structure of a protein for structure–function studies is by mutagenesis of the gene coding for it. In this way, any amino acid of the protein primary structure can be replaced by another one, they can be also deleted or inserted, either individually or collectively. This approach requires that there be available a gene coding for the protein and an expression system for producing the protein from the gene. The technology for cloning and producing the genes became standard by now. The basic principles of oligonucleotide-directed mutagenesis may be summarised as follows. The DNA of interest is cloned into the double-stranded form of a single-stranded bacteriophage, then the DNA carrying the insert is transfected into a bacterial cell line that amplifies it. These single-stranded copies are packaged into phage and excreted from the cell. A mismatch primer, a short oligonucleotide, is used to introduce the desired mutation. The primer is complementary to the target sequence except for the mutated position. The single-stranded recombinant DNA is annealed to the mutated primer, then the primerannealed template is converted to a double-stranded closed circular DNA through the action of a suitable polymerase in the presence of the four deoxynucleoside triphosphates and a ligase. On transfection into a suitable cell line, the desired mutant can be obtained. Site-directed mutagenesis allows to study the specific role of single amino-acid residues or a group of them in the enzymatic process. A point mutation, leading to drastic changes in the catalytic rate, indicates the participation of the corresponding aminoacid residue in the process. Thus, the active site residues can be identified even in the absence of the full 3D structure and an approximate model can be constructed for computational studies.
Kinetic parameters, derived from rate equations which are based on mathematical treatment of enzyme-catalysed reactions, are most important for the characterisation of their mechanism. The exceptionally high rate of enzyme reactions makes it easy to study their kinetic properties. It is the Michaelis–Menten theory that accounts for the kinetic behaviour of very many, but not all, enzymes. The critical feature of this model is that a specific enzyme–substrate complex is a necessary intermediate in catalysis. Two basic reactions are involved in the formation and breakdown of the enzyme–substrate complex: E ⫹ S $ ES and ES $ E ⫹ P with forward and backward reaction rates of k1 and k⫺1 and k2 and k⫺2, respectively. Here E, S, ES and P stand for the enzyme, substrate, enzyme–substrate complex and product, respectively. If we define KM as k2 ⫹ k⫺1 =k1 and Vmax as k2[Et] and derive a double reciprocal plot from the measured rate versus substrate concentration relationship (the Lineweaver–Burk equation) this yields a straight line with slope KM =k2 Et and y-intercept 1/k2[Et]. Here Vmax is the rate when all available E is present in the form of ES. Since the slope and intercept can be readily obtained from the graph, k2 (hereinafter called kcat) and KM can be accurately determined. KM is that concentration of substrate at which half the active sites of the enzyme are filled. It represents the strength of binding or affinity of the substrate for the enzyme. Tightly bound substrates have a low KM e.g. in the mM region and loosely bound substrates have a high KM e.g. in the mM region. The maximal rate, Vmax reveals the turnover number of an enzyme i.e. the number of substrate molecules being catalysed per second. This varies considerably from 10 in the case of lysozyme to 600,000 in the case of carbonic anhydrase. The binding energy of a substrate in the Michaelis-complex and the activation energy of the overall enzymatic reaction are proportional to log KM and log kcat =KM ; respectively. These values can be compared to computationally derived energy quantities, substrate binding energy and activation energy.
3.3. Quantum mechanics Most enzymatic processes involve fission or formation of covalent bonds, therefore high-level quantum mechanical calculations are needed to obtain reliable activation energies that can be compared to data from kinetic measurements. In case of metalloenzymes the
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spin distribution and other properties, characterising free radicals, are also of interest and these can only be calculated using a quantum mechanical method. Present-day computer hardware and software allows to perform both conventional ab initio molecular orbital [8] and density functional [9] calculations on quite large active-site models with up to 200 non-hydrogen atoms. This limit can be extended in case of semi-empirical methods to 600 [10], while recent fast multipole techniques allow to treat systems with as many as 2000 atoms or more [11]. Gradually, geometry optimisation becomes the rate-limiting step of calculations, therefore robust methods are under development [12]. In order to achieve the sufficient accuracy for the calculation of reaction paths electron correlation has to be considered that reduces the size of the applicable model. However, density functional theory seems to overcome this problem and may provide reliable activation energies also for realistic activesite models. Owing to the careful parameterisation of recent semi-empirical methods, these are also acceptable [13]. Active-site models alone, be they quite large, are not complete since they do not consider the distant enzyme environment and the biophase being often of utmost importance in the precise description of an enzymatic process. This is in most cases localised to the active site, which should be treated quantum mechanically, while the surroundings may be described by a simpler quantum mechanical or a molecular orbital method. This is the basis of combined QM/QM [14–16] and QM/MM [17,18] methods that allow to treat the enzyme as a whole. QM/MM methods make possible to treat dynamic aspects of enzyme reactions, too, which may become especially important if, e.g. NMR experiments have to be interpreted. The most precise calculations on enzyme dynamics can be performed with the Carr–Parinello method [19,20] where atoms move classically over a potential energy surface that is calculated by quantum mechanics. The method is very precise, but needs enormous computer times therefore its application to larger systems, like enzymes, is limited to supercomputers.
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3.4. Molecular dynamics [21] Since enzymes are dynamic systems fluctuating quite intensively under physiological conditions, efficient methods are needed to describe this aspect of their action. In a molecular dynamics simulation atoms move according to the laws of classical mechanics, and Newton’s equations of motion have to be integrated over time for the molecular system. Here the potential energy is needed that can be best obtained from some classical force field breaking down the total energy into bond stretching, bending, torsion, and non-bonded (van der Waals and electrostatic) contributions, as well as cross terms. Owing to the mathematical simplicity of the force field and the available effective integration techniques, enzymes with up to 50 kD molecular weight can be fully simulated by molecular dynamics. For smaller proteins, some thousands of water molecules, as well as counter-ions can also be explicitly treated allowing the more appropriate simulation of the biophase. Conventional molecular dynamics calculations have been used to study many aspects of enzyme structure and function at the picosecond time scale, like atomic fluctuations and their correlation with X-ray diffraction and NMR results, the thermodynamics of ligand binding, dynamic aspects of catalysis, conformational transitions and hydrogen exchange reactions. Since application of classical force fields to bond breaking and formation processes is problematic enzymatic reaction paths cannot be treated by ground-state molecular dynamics. Possible ways to do this are the Free Energy Perturbation method [22] and the Car–Parrinello method, the latter has been applied recently to the study of the mononuclear copper enzyme, galactose oxidase [23]. 3.5. Electrostatic calculations [24] There are several enzymatic processes where the time-consuming and complicated quantum mechanical or molecular dynamics methods do not have to be applied. Shift of protonation equilibrium states inside proteins, energetic aspects of ligand binding involving charge–charge interactions or hydrogen bonds, as well as effects of point mutations on reaction rates can be accurately predicted by classical electrostatics alone. While there are several methods available for
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Fig. 1. Schematic diagram of the rate-limiting acylation step in the hydrolysis of the peptide bond by subtilisin. E.S, Michaelis complex; E.S ‡, transition-state complex; E-Ac, acyl-enzyme.
the calculation of protein electrostatic potentials and interaction energies, we mention here only the most popular linearised Poisson–Boltzmann method [25] which is based on the Poisson equation relating the spatial variation of the protein electrostatic potential to the charge density and dielectric constant. It is possible to account for ionic strength effects of the biophase which is an essential improvement over gas-phase models. Numerical solution of the Poisson–Boltzmann equation is quite complicated since they are non-linear, 3D partial differential equations thus finite difference methods should be used. The commercial software DelPhi, developed for largescale applications, makes use of this procedure [26].
4. A case study: serine proteases Serine proteases are probably the most studied enzymes to date (for a review, see Ref. [27]). They are members of a large family of homologous proteins which require a serine side chain for reaction, which forms a so-called catalytic triad with spatially closely located histidine and aspartate side chains. These enzymes catalyse the hydrolysis of ester or amide substrates through an acyl-enzyme intermediate, in which the hydroxyl group of the active serine side chain is acylated by the substrate. The reaction involves proton transfer from the serine to the catalytic histidine side chain, an attack of the serine oxygen
Fig. 2. Space-filling representation of the catalytic triad of subtilisin with substrate. Large grey spheres, oxygen; small grey spheres, hydrogen; white spheres, nitrogen; light grey spheres, carbon. Note the hydrogen bond between the oxyanion and the amino group of Asn-155 (left), the Ser-221 (center) and His-64 side chains (right). Co-ordinates are from Protein Data Bank [32].
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on the carbonyl carbon of the substrate and the formation of a high-energy tetrahedral intermediate. This will break down then the leaving group accepts the proton from the histidine and an acyl enzyme is formed which is then hydrolysed via the reverse route. The mechanism is depicted in Fig. 1. It is interesting to follow, how details of the mechanism were gradually elucidated first by kinetic, X-ray diffraction and NMR spectroscopic, then by computational methods. Experimental methods have been completed by speculations based on chemical evidence that has been drawn from solution experiments on small model molecules. In spite of the wide applicability of such evidences in classical organic chemistry, these were not necessarily valid in the protein. For example, the pKa values of amino-acid residues participating in the reaction may differ strongly from those of the corresponding free amino acids in aqueous solution. The best way to detect and rationalise these changes is to do computations on an adequate model. The amino-acid sequence of the zymogen precursor of bovine a-chymotrypsin has been determined in 1964 [28], then the tertiary structure became available through X-ray diffraction studies [29]. While it has been known earlier that the enzymatic reaction makes use of an active serine side chain, the essential role of the nearby histidine was discovered only later [30]. A reaction mechanism was proposed by Wang and Parker suggesting that it is an alkoxide ion of the active serine that attacks the substrate [31]. Blow and co-workers refined this mechanism suggesting that the Ser, nearby His and Asp side chains form a catalytic triad (see Fig. 2) and a “charge-relay” mechanism will conduct electrons from the buried carboxyl group to hydrogen bonds in the surface. Accordingly, the active serine donates its proton to NE2 of His which, in turn, donates its proton from ND1 to the buried aspartate. The peptide bond will then be cleaved upon attack by the alkoxide and an acylenzyme forms where Asp donates its proton back to ND1 of His, which protonates the leaving group from its NE2 atom. Though the charge-relay mechanism has been questioned quite early by Polga´r and Bender on the basis of kinetic studies stating that the buried aspartate remains charged during the catalytic process [33], it was very popular in the 1970s and early 1980s. 13C
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NMR [34] and infrared spectroscopy [35] assigned high and low pK values to the protonation of Asp102 and His-57, respectively, indicating that the Asp side chain is protonated. Early molecular orbital calculations using semi-empirical methods showed that the proton transfer occurs from His to Asp-102 when Ser donates its proton to the former [36–41]. It seemed that theory and experiment correspond to each other, the enzyme mechanism is well established. The situation changed in the 1980s and it has been recognised gradually that the following points have not been considered to be essential. (i) Protons cannot be seen in X-ray diffraction experiments, which may provide only an indirect answer to the question, where is the proton located between Asp and His? (ii) Signals in NMR spectra are difficult to assign because of the large number of magnetically active nuclei and the influence of the macromolecular environment. (iii) Quantum mechanical methods in the seventies were not reliable enough to provide accurate relative energies of various protonation states. (iv) It is not sufficient to do quantum mechanical calculations, despite being quite precise, on models of limited size. Johannin and Kellersohn were the first who recognised the importance of the protein electrostatic field on the catalytic His·· ·Asp protonation state, their calculated field suggested that the ion pair is favoured in a-chymotrypsin [42]. This suggestion was supported later by a calculation on the full protein model [43] and confirmed by refined calculations that properly represented the protein dielectric [44,45]. Molecular orbital calculations on large models of the active site also provided evidence for the formation of the ion pair [46,47]. On the basis of refined NMR spectroscopic experiments Bachovchin and Roberts concluded that the buried aspartate remains charged during the catalytic process [48]. The strongest argument was provided by Kossiakoff and Spencer [49] who detected the Asp ⫺ –HisH ⫹ couple in monoisopropyl phosphoryl trypsin, a model of the transition-state complex, by neutron diffraction. Since this method is able to locate hydrogen positions, the final answer to the problem of protonation state has been given. However, some still argued that this model is valid only for the ground state, but not necessarily for the transition state, where the charge relay mechanism may still work [50,51].
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Fig. 3. Three-dimensional model of the complex between protease B and its substrate. Hydrogen bonds are indicated by dashed lines.
Furthermore, it was not clear, what is the role, if any, of the buried aspartate in catalysis. Important information has been provided by sitedirected mutagenesis, where Asp-102 of trypsin was replaced by an isosteric but uncharged Asn residue [52,53] and Asp-32 of subtilisin by Ala [54]. In both point mutants the activity decreases by about four orders of magnitude, while the geometric structure remains almost exactly the same as in the wild-type enzyme. This means that the role of the buried aspartate is to stabilise the transition-state complex by electrostatic interaction which leads to rate acceleration. Early molecular orbital calculations already predicted this role, however, the energy effect was severely overestimated because the influence of water solvent around the protein was not considered in the models applied [55–57]. The rate decrease could be quantitatively reproduced by a computational study and the success of the applied method allowed to rule out the double proton transfer mechan-
ism as a possible route for the catalytic reaction [58]. This study provided also very strong argument for the nature of the driving force of the catalytic reaction, which is the electrostatic stabilisation of the polar transition-state complex by the protein environment. The electrostatic effect, also proved to be important by point mutation studies on subtilisin BPN 0 [59], seems to effective in a number of catalytic reactions, be they homogeneous, heterogeneous or enzymatic [60]. The last important question to be answered was related to the rate-limiting step. Kinetic studies indicate that while formation of the acyl-enzyme is slower, thus rate-limiting, for amide substrates, its breakdown becomes slower for ester substrates. Kollman and co-workers [61,62] performed gas-phase semi-empirical calculations on a model of the active site and completed them by molecular mechanics and molecular dynamics calculations on the full enzyme. They state that using the gas-phase active site model implies formation of the first tetrahedral intermediate
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Fig. 4. Electrostatic complementarity between the active site of protease B and its substrate. Dark and light regions on the van der Waals envelope represent negative and positive electrostatic potentials, respectively.
as the rate-limiting step for both amide and ester substrates. However, molecular dynamics calculations provide evidence that protein fluctuations favour deacylation as the rate limiting step for ester substrates in agreement with kinetic studies. This again calls the attention to the crucial role of the model applied, rigid models could not reproduce experimental findings in this case. Combination of experimental and theoretical methods is also important in the study of enzyme–ligand interactions. In case of serine proteases specificity has been extensively studied by site-directed mutagenesis, X-ray diffraction and computational methods. Gra´f and co-workers [63,64] tested the role of Asp-189, buried in the base of the substrate-binding pocket, in determining the specificity of trypsin toward basic substrates. Applying site-directed mutagenesis they
replaced this residue by lysine in the hope that charge specificity will change to the opposite. Surprisingly, they found that, though the mutant does not display catalytic activity toward arginyl and lysyl substrates, there is no specificity change toward aspartyl or glutamyl substrates. Computer modelling studies dissolved this controversy: the extended Lys side chain is most probably directed outside the substrate-binding pocket in the mutant therefore cannot favourably interact with acidic substrates. Electrostatic calculations provided simple relations explaining activity changes of various substrates on point mutants of trypsin and subtilisin [65,66]. In the Asp/Ser-189 mutant it was found that the enzyme–substrate interaction free energy is larger for charged–charged (monopole–monopole) and polar–polar (dipole–dipole) pairs of side chains than
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for charged–polar (monopole–dipole) ones [65,66]. This is in contrast to the situation in the gas phase, but could be interpreted on the basis of hydrophobic complementarity. The similis simili gaudet principle states that molecular regions, characterised by similar values of the hydration ability (e.g. the gradient of the electrostatic potential) tend to associate stronger than dissimilar ones [67]. On the basis of the quantitative measure of hydration ability it was possible to derive a simple quantitative structure-specificity relationship for subtilisin point mutants [68]. An interplay between theory and experiment allowed to explain ligand binding characteristics of oligopeptidase B, an enzyme belonging to a recently discovered new family of serine proteases [69]. We applied homology modelling to determine the structure on the basis of prolyl oligopeptidase for which 3D co-ordinates are already available [70,71]. The model allows to dock substrates in the binding pocket and to construct the enzyme–substrate complex (cf. Fig. 3). Electrostatic complementarity gave an explanation why the doubly charged Z–Arg–Arg (Z benzyloximino-carbonyl) is a better substrate than the monobasic Z–Arg [72] (cf. Fig. 4). The larger negative potential in the active site binds the more positive dibasic substrate better than the monobasic one. Furthermore, molecular basis of the experimentally observed selectivity of oligopeptidase B towards processing at dibasic sites can also be interpreted in terms of electrostatic potentials. We found that the overall binding site of oligopeptidase B is more negative than the binding site of prolyl oligopeptidase, which is in accordance with the increased activity of the former against basic substrates. Considering the amino-acid composition of the binding site of oligopeptidase B and prolyl oligopeptidase the more negative character of the binding site of the latter can be rationalised in terms of some mutations from nonpolar to polar or acidic amino acid residues in OpB with respect to PEP.
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Systems, Scientific Applications, Data Commission of the International Union of Crystallography, Bonn, p. 107, 1984, Protein Data Bank File 1SBN. L. Polga´r, M.L. Bender, Proc. Natl Acad. Sci. USA 64 (1969) 1335. M.W. Hunkapiller, S.H. Smallcombe, D.R. Whitaker, J.H. Richards, Biochemistry 12 (1973) 4732. R.E. Koeppe II, R.M. Stroud, Biochemistry 15 (1976) 3450. H. Umeyama, A. Imamura, C. Nagata, M. Hanano, J. Theor. Biol. 41 (1973) 485. G.L. Amidon, J. Theor. Biol. 46 (1974) 101. S. Scheiner, D.A. Kleier, W.N. Lipscomb, Proc. Natl Acad. Sci. USA 72 (1975) 2606. S. Scheiner, W.N. Lipscomb, Proc. Natl Acad. Sci. USA 73 (1976) 432. H.P. Kitayama, H. Fukutome, J. Theor. Biol. 60 (1976) 1. Y. Beppu, S. Yomosa, J. Phys. Soc. Jpn 42 (1977) 1694. G. Johannin, N. Kellersohn, Biochem. Biophys. Res. Commun. 49 (1972) 321. G. Na´ray-Szabo´, Int. J. Quantum Chem. 16 (1979) 265. A. Warshel, S.T. Russell, R.M. Weiss, in: B.S. Green, Y. Ashani, D. Chipman (Eds.), Chemical Approaches to Understanding Enzyme Catalysis. Biomimetic Chemistry and Transition-State Analogs, Elsevier, Amsterdam, 1982, p. 267. A. Warshel, S.T. Russell, J. Am. Chem. Soc. 108 (1986) 6569. H. Umeyama, S. Nakagawa, T. Kudo, J. Mol. Biol. 150 (1981) 409. E. Longo, F.M.L.G. Stamato, R. Ferreira, O. Tapia, J. Theor. Biol. 112 (1985) 783. W.W. Bachovchin, J.D. Roberts, J. Am. Chem. Soc. 100 (1978) 80421. A.A. Kosiakoff, S.A. Spencer, Nature 288 (1980) 414. M.J.S. Dewar, D.M. Storch, Proc. Natl Acad. Sci. USA 82 (1985) 2225. L.R. Schowen, Molecular structure and energetics, in: J.F. Liebman, A. Greenberg (Eds.), Principles of Enzyme ActivityVCH, Weinheim, 1988. S. Sprang, T. Standing, R.J. Fletterick, R.M. Stroud, J.
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Enzyme mechanisms: interplay of theory and experiment G. Na´ray-Szabo´* Department of Theoretical Chemistry, Lora´nd Eo¨tvo¨s University, Pa´zma´ny Pe´ter st. 2, H-1117 Budapest, Hungary
Abstract An overview is given on experimental and theoretical methods applied to the study of enzyme mechanisms. While experiments provide more or less precise data on realistic systems, the obtained information often overlap and a mixture of observations has to be resolved in order to appropriately understand enzymatic processes at the molecular level. On the other hand, computations to be done on adequate models reflecting all important properties of the system, may not provide results that are accurate enough to be compared with experiments. It is stressed that in a computational study the level of sophistication of the model and the method applied to it should be about the same in order to obtain sound results. A case study, the catalytic mechanism of serine proteases, is discussed in detail calling attention to the problems where the interplay between computations and experimental studies was necessary to understand mechanistic details. It is computational chemistry that lead to the discovery of the crucial role of the protein electrostatic field in the acceleration of the enzyme reaction as well as protonation state of the side chains of the active site. We stress that computational studies are especially important in the right interpretation of experimental observations and should replace speculations based on textbook chemistry. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Enzyme mechanism; Mechanistic studies; Serine proteases
1. Introduction The spectacular development of experimental and computational techniques in the last few decades allowed to perform detailed studies on enzyme mechanisms [1,2]. Combination of enzyme kinetics, genetic engineering, protein crystallography, nuclear magnetic resonance spectroscopy, kinetic isotope effects as well as computer modelling provides a powerful arsenal that can be applied to study even subtle details of complicated enzymatic processes. It is important to notice that there is no single method, be it experimental or computational, that provides full and precise information both on structural and kinetic * Tel.: ⫹ 36-1-209-0555; fax: ⫹ 36-1-209-0602. E-mail address: [email protected] (G. Na´ray-Szabo´).
aspects of enzyme action. Thus, the multidisciplinary approach is imperative, a successful research group should include both experimentalists and theorists who are skilled in several techniques complementing each other. In this paper we present an overview on the most important methods for the study of enzyme reactions that should be, and are in fact often, combined in mechanistic studies. A separate section will be devoted to the construction of models that is prerequisite for any structural consideration, especially computational studies. It has to be stressed that model and method should be at about the same level of sophistication in a specific study in order to be able to draw sound conclusions. A rough model, even if combined with the most advanced calculation, cannot provide relevant results while even the most precise
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model may be misleading if the applied computational method is inaccurate. In the last section we present a case study, serine proteases, for which there is probably the largest amount of structural and mechanistic information available. Special attention will be paid to computational studies, especially if they complete results obtained by various experimental techniques that alone are not sufficient to answer some specific questions, e.g. relative stability of protonation states or structure and charge distribution of the transitionstate complex. 2. Models Prerequisite for a mechanistic study on an enzymatic process is a three-dimensional (3D) model of the group of atoms participating in the reaction. In general, enzyme active sites consist of more atoms than the bare substrate and the reacting functional group. Other components, like adjacent side chains, prosthetic group, water molecules and metal ions, even the protein environment and the surrounding biophase, have to be considered in a precise model. In general, this model can be constructed on the basis of experiment though there are some cases where computational methods are also applicable. We discuss the most important methods below. 2.1. Protein crystallography [3] Though proteins are high molecular weight, mobile macromolecules, it is possible to position them in a 3D periodic lattice with great precision, they frequently form regular crystals. In contrast to small molecules, unit cells of many proteins contain 30– 80% (by volume) of water as solvent, which means that there are few contacts between protein molecules, the crystals are stabilised by a few hydrogen bonds and van der Waals contacts. The high proportion of solvent means that the crystal environment is similar to the natural one, thus proteins in crystals are often functional. Growing of crystals is even nowadays more of an art than an established technique; there are dozens of factors, like protein purity, buffer type, pH, temperature, ionic strength or the presence of organic solvents, that strongly influence the success. Once we have appropriate crystals, it is possible to
collect many thousands of X-ray reflections allowing to determine the electron density. In order to do that the so-called phase problem has to be solved which means that not only the directly detectable intensities but also the phases of the reflections have to be known for the evaluation. The isomorphous replacement method may provide a solution when heavy metal ions are introduced into the crystal without changing its structure and the differences in the intensities contain information about the phases. Thus, the electron density map can be obtained which allows to fit a relatively rough model yielding the approximate location of protein atoms. Afterwards atomic positions have to be refined by sophisticated computational methods, making use of standard models of protein backbone and side chains, even molecular dynamics calculations. Finally, a quite precise geometric model of the protein structure is available with an estimated error of 30 pm for the positions of well-defined rigid atoms. While protein crystallography provides reliable positions for heavier atoms, in most of the cases hydrogen atoms cannot be seen because of the small electron density around them. This makes the study of protonation states of side chains, prosthetic groups and substrate very difficult. The problem can be surmounted by the neutron diffraction technique which, however, needs high-intensity neutron beams and these can be obtained only from nuclear reactors. Thus, the method is available only for a limited number of laboratories. A further problem may arise in case of disorder because the electronic density near disordered atomic positions is lower and more spread out which makes evaluation more difficult, sometimes impossible. On the other hand, some of the tightly bound water molecules around the protein can be located that may provide essential information on the enzymatic mechanism. It has to be borne in mind that X-ray crystallography does not allow study of energetic aspects and is essentially limited to static models. 2.2. Nuclear magnetic resonance spectroscopy [4] Complementary to protein crystallography in the experimental derivation of reliable enzyme models is nuclear magnetic resonance (NMR) spectroscopy. NMR measurements are carried out in solution under
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potentially physiological conditions, thus crystallisation is not a problem. On the other hand, strongly aggregated systems are not amenable to study by NMR. Spectra contain structural information through chemical shifts which are sensitive to the local environment, spin–spin coupling constants which are sensitive to dihedral angles and relaxation (Nuclear Overhauser Effect, NOE) which is sensitive to the positions of nearby spins (proton–proton distances). These data provide information that can be converted to 3D structures. In order to determine the structure a protein solution in the range of mM concentration has to be prepared first, then the NMR data can be recorded. This is followed by spectral analysis to yield NMR parameters and subsequently sequence-specific resonance assignments that provided earlier the major hurdle in interpretation. Fortunately, over the past decade spectacular progress has been made through the introduction of multidimensional NMR techniques and advances in spectrometer hardware. The conformational constraints needed as input have to be collected, then the structure can be calculated and refined from these data. In practice these steps are linked and one goes through repeated cycles of data analysis and structure determination. Once sequential resonance assignments have been obtained cross-peaks can be assigned, too, especially those involving residues far apart in the sequence and therefore provide information about the polypeptide fold. With the assignment in hand, a large number of interproton distance restraints can be derived which provide the necessary information to determine the 3D structure of the protein. To do this a number of computational methods can be employed such as distance geometry, minimisation of torsion angles with a variable target function, restrained molecular dynamics and simulated annealing [5]. While X-ray diffraction may yield structures even for quite large systems, like viruses, de novo structure determination with the NMR method is practicable for proteins with a molecular weight of at most 20 kD. New techniques applying 13C and 15N isotope labelling allow to study larger systems, even beyond 100 kD. A further complementary feature of the NMR method is that it provides information on protein dynamics. The precision with which the majority of structures has been determined is around
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100 pm for backbone atoms and 200 pm for all atoms. This limit can be reduced in some cases to 30 pm for backbone atoms and 50 pm for all atoms.
2.3. Homology modelling [6] In the absence of definitive information about the geometric parameters of the 3D model of a protein by X-ray diffraction or NMR spectroscopy prediction is often possible on the basis of the amino-acid sequence alone by detecting similarities between the new structure and the previously solved ones. There are several dozens of thousand sequences available in a database, many of which can be clustered into homologous families. If at least one structure within a family with at least 30% sequence homology is available, modelling of the others becomes a realistic possibility. The main steps of modelling are as follows. A sequence alignment between the protein to be modelled and a protein of known structure has to be established. Obviously, the higher the percentage identity observed in this alignment, and the lower the number of insertions and deletions, the easier the modelling and the better the final result will be. Based on this alignment a backbone has to be generated which is normally the backbone of the most homologous structure. Afterwards side chains have to be placed in the model, normally the side chains of the conserved residues will not be altered. During this process the major problem is that many residues have multiple favourable side chain conformations that may lead to steric conflict which should be avoided by applying Monte Carlo procedures or other algorithms. If the protein to be modelled has insertions or deletions with respect to the known structure, loops have to be re-modelled, or modelled ab initio. Database searches for loops with similar anchoring points in the structure are often used to build these loops, but energy based ab initio modelling techniques can be employed, too. After constructing the initial rough model, it needs to be optimised by some energy minimisation or molecular dynamics technique. Generally, a comparison of the predicted and observed structures shows an average rms superposition error of 100 pm for backbone atoms and 200 pm for all atoms including side chains.
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3. Methods
3.2. Site-directed mutagenesis [7]
3.1. Enzyme kinetics
The best method for altering the covalent structure of a protein for structure–function studies is by mutagenesis of the gene coding for it. In this way, any amino acid of the protein primary structure can be replaced by another one, they can be also deleted or inserted, either individually or collectively. This approach requires that there be available a gene coding for the protein and an expression system for producing the protein from the gene. The technology for cloning and producing the genes became standard by now. The basic principles of oligonucleotide-directed mutagenesis may be summarised as follows. The DNA of interest is cloned into the double-stranded form of a single-stranded bacteriophage, then the DNA carrying the insert is transfected into a bacterial cell line that amplifies it. These single-stranded copies are packaged into phage and excreted from the cell. A mismatch primer, a short oligonucleotide, is used to introduce the desired mutation. The primer is complementary to the target sequence except for the mutated position. The single-stranded recombinant DNA is annealed to the mutated primer, then the primerannealed template is converted to a double-stranded closed circular DNA through the action of a suitable polymerase in the presence of the four deoxynucleoside triphosphates and a ligase. On transfection into a suitable cell line, the desired mutant can be obtained. Site-directed mutagenesis allows to study the specific role of single amino-acid residues or a group of them in the enzymatic process. A point mutation, leading to drastic changes in the catalytic rate, indicates the participation of the corresponding aminoacid residue in the process. Thus, the active site residues can be identified even in the absence of the full 3D structure and an approximate model can be constructed for computational studies.
Kinetic parameters, derived from rate equations which are based on mathematical treatment of enzyme-catalysed reactions, are most important for the characterisation of their mechanism. The exceptionally high rate of enzyme reactions makes it easy to study their kinetic properties. It is the Michaelis–Menten theory that accounts for the kinetic behaviour of very many, but not all, enzymes. The critical feature of this model is that a specific enzyme–substrate complex is a necessary intermediate in catalysis. Two basic reactions are involved in the formation and breakdown of the enzyme–substrate complex: E ⫹ S $ ES and ES $ E ⫹ P with forward and backward reaction rates of k1 and k⫺1 and k2 and k⫺2, respectively. Here E, S, ES and P stand for the enzyme, substrate, enzyme–substrate complex and product, respectively. If we define KM as k2 ⫹ k⫺1 =k1 and Vmax as k2[Et] and derive a double reciprocal plot from the measured rate versus substrate concentration relationship (the Lineweaver–Burk equation) this yields a straight line with slope KM =k2 Et and y-intercept 1/k2[Et]. Here Vmax is the rate when all available E is present in the form of ES. Since the slope and intercept can be readily obtained from the graph, k2 (hereinafter called kcat) and KM can be accurately determined. KM is that concentration of substrate at which half the active sites of the enzyme are filled. It represents the strength of binding or affinity of the substrate for the enzyme. Tightly bound substrates have a low KM e.g. in the mM region and loosely bound substrates have a high KM e.g. in the mM region. The maximal rate, Vmax reveals the turnover number of an enzyme i.e. the number of substrate molecules being catalysed per second. This varies considerably from 10 in the case of lysozyme to 600,000 in the case of carbonic anhydrase. The binding energy of a substrate in the Michaelis-complex and the activation energy of the overall enzymatic reaction are proportional to log KM and log kcat =KM ; respectively. These values can be compared to computationally derived energy quantities, substrate binding energy and activation energy.
3.3. Quantum mechanics Most enzymatic processes involve fission or formation of covalent bonds, therefore high-level quantum mechanical calculations are needed to obtain reliable activation energies that can be compared to data from kinetic measurements. In case of metalloenzymes the
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spin distribution and other properties, characterising free radicals, are also of interest and these can only be calculated using a quantum mechanical method. Present-day computer hardware and software allows to perform both conventional ab initio molecular orbital [8] and density functional [9] calculations on quite large active-site models with up to 200 non-hydrogen atoms. This limit can be extended in case of semi-empirical methods to 600 [10], while recent fast multipole techniques allow to treat systems with as many as 2000 atoms or more [11]. Gradually, geometry optimisation becomes the rate-limiting step of calculations, therefore robust methods are under development [12]. In order to achieve the sufficient accuracy for the calculation of reaction paths electron correlation has to be considered that reduces the size of the applicable model. However, density functional theory seems to overcome this problem and may provide reliable activation energies also for realistic activesite models. Owing to the careful parameterisation of recent semi-empirical methods, these are also acceptable [13]. Active-site models alone, be they quite large, are not complete since they do not consider the distant enzyme environment and the biophase being often of utmost importance in the precise description of an enzymatic process. This is in most cases localised to the active site, which should be treated quantum mechanically, while the surroundings may be described by a simpler quantum mechanical or a molecular orbital method. This is the basis of combined QM/QM [14–16] and QM/MM [17,18] methods that allow to treat the enzyme as a whole. QM/MM methods make possible to treat dynamic aspects of enzyme reactions, too, which may become especially important if, e.g. NMR experiments have to be interpreted. The most precise calculations on enzyme dynamics can be performed with the Carr–Parinello method [19,20] where atoms move classically over a potential energy surface that is calculated by quantum mechanics. The method is very precise, but needs enormous computer times therefore its application to larger systems, like enzymes, is limited to supercomputers.
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3.4. Molecular dynamics [21] Since enzymes are dynamic systems fluctuating quite intensively under physiological conditions, efficient methods are needed to describe this aspect of their action. In a molecular dynamics simulation atoms move according to the laws of classical mechanics, and Newton’s equations of motion have to be integrated over time for the molecular system. Here the potential energy is needed that can be best obtained from some classical force field breaking down the total energy into bond stretching, bending, torsion, and non-bonded (van der Waals and electrostatic) contributions, as well as cross terms. Owing to the mathematical simplicity of the force field and the available effective integration techniques, enzymes with up to 50 kD molecular weight can be fully simulated by molecular dynamics. For smaller proteins, some thousands of water molecules, as well as counter-ions can also be explicitly treated allowing the more appropriate simulation of the biophase. Conventional molecular dynamics calculations have been used to study many aspects of enzyme structure and function at the picosecond time scale, like atomic fluctuations and their correlation with X-ray diffraction and NMR results, the thermodynamics of ligand binding, dynamic aspects of catalysis, conformational transitions and hydrogen exchange reactions. Since application of classical force fields to bond breaking and formation processes is problematic enzymatic reaction paths cannot be treated by ground-state molecular dynamics. Possible ways to do this are the Free Energy Perturbation method [22] and the Car–Parrinello method, the latter has been applied recently to the study of the mononuclear copper enzyme, galactose oxidase [23]. 3.5. Electrostatic calculations [24] There are several enzymatic processes where the time-consuming and complicated quantum mechanical or molecular dynamics methods do not have to be applied. Shift of protonation equilibrium states inside proteins, energetic aspects of ligand binding involving charge–charge interactions or hydrogen bonds, as well as effects of point mutations on reaction rates can be accurately predicted by classical electrostatics alone. While there are several methods available for
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Fig. 1. Schematic diagram of the rate-limiting acylation step in the hydrolysis of the peptide bond by subtilisin. E.S, Michaelis complex; E.S ‡, transition-state complex; E-Ac, acyl-enzyme.
the calculation of protein electrostatic potentials and interaction energies, we mention here only the most popular linearised Poisson–Boltzmann method [25] which is based on the Poisson equation relating the spatial variation of the protein electrostatic potential to the charge density and dielectric constant. It is possible to account for ionic strength effects of the biophase which is an essential improvement over gas-phase models. Numerical solution of the Poisson–Boltzmann equation is quite complicated since they are non-linear, 3D partial differential equations thus finite difference methods should be used. The commercial software DelPhi, developed for largescale applications, makes use of this procedure [26].
4. A case study: serine proteases Serine proteases are probably the most studied enzymes to date (for a review, see Ref. [27]). They are members of a large family of homologous proteins which require a serine side chain for reaction, which forms a so-called catalytic triad with spatially closely located histidine and aspartate side chains. These enzymes catalyse the hydrolysis of ester or amide substrates through an acyl-enzyme intermediate, in which the hydroxyl group of the active serine side chain is acylated by the substrate. The reaction involves proton transfer from the serine to the catalytic histidine side chain, an attack of the serine oxygen
Fig. 2. Space-filling representation of the catalytic triad of subtilisin with substrate. Large grey spheres, oxygen; small grey spheres, hydrogen; white spheres, nitrogen; light grey spheres, carbon. Note the hydrogen bond between the oxyanion and the amino group of Asn-155 (left), the Ser-221 (center) and His-64 side chains (right). Co-ordinates are from Protein Data Bank [32].
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on the carbonyl carbon of the substrate and the formation of a high-energy tetrahedral intermediate. This will break down then the leaving group accepts the proton from the histidine and an acyl enzyme is formed which is then hydrolysed via the reverse route. The mechanism is depicted in Fig. 1. It is interesting to follow, how details of the mechanism were gradually elucidated first by kinetic, X-ray diffraction and NMR spectroscopic, then by computational methods. Experimental methods have been completed by speculations based on chemical evidence that has been drawn from solution experiments on small model molecules. In spite of the wide applicability of such evidences in classical organic chemistry, these were not necessarily valid in the protein. For example, the pKa values of amino-acid residues participating in the reaction may differ strongly from those of the corresponding free amino acids in aqueous solution. The best way to detect and rationalise these changes is to do computations on an adequate model. The amino-acid sequence of the zymogen precursor of bovine a-chymotrypsin has been determined in 1964 [28], then the tertiary structure became available through X-ray diffraction studies [29]. While it has been known earlier that the enzymatic reaction makes use of an active serine side chain, the essential role of the nearby histidine was discovered only later [30]. A reaction mechanism was proposed by Wang and Parker suggesting that it is an alkoxide ion of the active serine that attacks the substrate [31]. Blow and co-workers refined this mechanism suggesting that the Ser, nearby His and Asp side chains form a catalytic triad (see Fig. 2) and a “charge-relay” mechanism will conduct electrons from the buried carboxyl group to hydrogen bonds in the surface. Accordingly, the active serine donates its proton to NE2 of His which, in turn, donates its proton from ND1 to the buried aspartate. The peptide bond will then be cleaved upon attack by the alkoxide and an acylenzyme forms where Asp donates its proton back to ND1 of His, which protonates the leaving group from its NE2 atom. Though the charge-relay mechanism has been questioned quite early by Polga´r and Bender on the basis of kinetic studies stating that the buried aspartate remains charged during the catalytic process [33], it was very popular in the 1970s and early 1980s. 13C
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NMR [34] and infrared spectroscopy [35] assigned high and low pK values to the protonation of Asp102 and His-57, respectively, indicating that the Asp side chain is protonated. Early molecular orbital calculations using semi-empirical methods showed that the proton transfer occurs from His to Asp-102 when Ser donates its proton to the former [36–41]. It seemed that theory and experiment correspond to each other, the enzyme mechanism is well established. The situation changed in the 1980s and it has been recognised gradually that the following points have not been considered to be essential. (i) Protons cannot be seen in X-ray diffraction experiments, which may provide only an indirect answer to the question, where is the proton located between Asp and His? (ii) Signals in NMR spectra are difficult to assign because of the large number of magnetically active nuclei and the influence of the macromolecular environment. (iii) Quantum mechanical methods in the seventies were not reliable enough to provide accurate relative energies of various protonation states. (iv) It is not sufficient to do quantum mechanical calculations, despite being quite precise, on models of limited size. Johannin and Kellersohn were the first who recognised the importance of the protein electrostatic field on the catalytic His·· ·Asp protonation state, their calculated field suggested that the ion pair is favoured in a-chymotrypsin [42]. This suggestion was supported later by a calculation on the full protein model [43] and confirmed by refined calculations that properly represented the protein dielectric [44,45]. Molecular orbital calculations on large models of the active site also provided evidence for the formation of the ion pair [46,47]. On the basis of refined NMR spectroscopic experiments Bachovchin and Roberts concluded that the buried aspartate remains charged during the catalytic process [48]. The strongest argument was provided by Kossiakoff and Spencer [49] who detected the Asp ⫺ –HisH ⫹ couple in monoisopropyl phosphoryl trypsin, a model of the transition-state complex, by neutron diffraction. Since this method is able to locate hydrogen positions, the final answer to the problem of protonation state has been given. However, some still argued that this model is valid only for the ground state, but not necessarily for the transition state, where the charge relay mechanism may still work [50,51].
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Fig. 3. Three-dimensional model of the complex between protease B and its substrate. Hydrogen bonds are indicated by dashed lines.
Furthermore, it was not clear, what is the role, if any, of the buried aspartate in catalysis. Important information has been provided by sitedirected mutagenesis, where Asp-102 of trypsin was replaced by an isosteric but uncharged Asn residue [52,53] and Asp-32 of subtilisin by Ala [54]. In both point mutants the activity decreases by about four orders of magnitude, while the geometric structure remains almost exactly the same as in the wild-type enzyme. This means that the role of the buried aspartate is to stabilise the transition-state complex by electrostatic interaction which leads to rate acceleration. Early molecular orbital calculations already predicted this role, however, the energy effect was severely overestimated because the influence of water solvent around the protein was not considered in the models applied [55–57]. The rate decrease could be quantitatively reproduced by a computational study and the success of the applied method allowed to rule out the double proton transfer mechan-
ism as a possible route for the catalytic reaction [58]. This study provided also very strong argument for the nature of the driving force of the catalytic reaction, which is the electrostatic stabilisation of the polar transition-state complex by the protein environment. The electrostatic effect, also proved to be important by point mutation studies on subtilisin BPN 0 [59], seems to effective in a number of catalytic reactions, be they homogeneous, heterogeneous or enzymatic [60]. The last important question to be answered was related to the rate-limiting step. Kinetic studies indicate that while formation of the acyl-enzyme is slower, thus rate-limiting, for amide substrates, its breakdown becomes slower for ester substrates. Kollman and co-workers [61,62] performed gas-phase semi-empirical calculations on a model of the active site and completed them by molecular mechanics and molecular dynamics calculations on the full enzyme. They state that using the gas-phase active site model implies formation of the first tetrahedral intermediate
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Fig. 4. Electrostatic complementarity between the active site of protease B and its substrate. Dark and light regions on the van der Waals envelope represent negative and positive electrostatic potentials, respectively.
as the rate-limiting step for both amide and ester substrates. However, molecular dynamics calculations provide evidence that protein fluctuations favour deacylation as the rate limiting step for ester substrates in agreement with kinetic studies. This again calls the attention to the crucial role of the model applied, rigid models could not reproduce experimental findings in this case. Combination of experimental and theoretical methods is also important in the study of enzyme–ligand interactions. In case of serine proteases specificity has been extensively studied by site-directed mutagenesis, X-ray diffraction and computational methods. Gra´f and co-workers [63,64] tested the role of Asp-189, buried in the base of the substrate-binding pocket, in determining the specificity of trypsin toward basic substrates. Applying site-directed mutagenesis they
replaced this residue by lysine in the hope that charge specificity will change to the opposite. Surprisingly, they found that, though the mutant does not display catalytic activity toward arginyl and lysyl substrates, there is no specificity change toward aspartyl or glutamyl substrates. Computer modelling studies dissolved this controversy: the extended Lys side chain is most probably directed outside the substrate-binding pocket in the mutant therefore cannot favourably interact with acidic substrates. Electrostatic calculations provided simple relations explaining activity changes of various substrates on point mutants of trypsin and subtilisin [65,66]. In the Asp/Ser-189 mutant it was found that the enzyme–substrate interaction free energy is larger for charged–charged (monopole–monopole) and polar–polar (dipole–dipole) pairs of side chains than
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for charged–polar (monopole–dipole) ones [65,66]. This is in contrast to the situation in the gas phase, but could be interpreted on the basis of hydrophobic complementarity. The similis simili gaudet principle states that molecular regions, characterised by similar values of the hydration ability (e.g. the gradient of the electrostatic potential) tend to associate stronger than dissimilar ones [67]. On the basis of the quantitative measure of hydration ability it was possible to derive a simple quantitative structure-specificity relationship for subtilisin point mutants [68]. An interplay between theory and experiment allowed to explain ligand binding characteristics of oligopeptidase B, an enzyme belonging to a recently discovered new family of serine proteases [69]. We applied homology modelling to determine the structure on the basis of prolyl oligopeptidase for which 3D co-ordinates are already available [70,71]. The model allows to dock substrates in the binding pocket and to construct the enzyme–substrate complex (cf. Fig. 3). Electrostatic complementarity gave an explanation why the doubly charged Z–Arg–Arg (Z benzyloximino-carbonyl) is a better substrate than the monobasic Z–Arg [72] (cf. Fig. 4). The larger negative potential in the active site binds the more positive dibasic substrate better than the monobasic one. Furthermore, molecular basis of the experimentally observed selectivity of oligopeptidase B towards processing at dibasic sites can also be interpreted in terms of electrostatic potentials. We found that the overall binding site of oligopeptidase B is more negative than the binding site of prolyl oligopeptidase, which is in accordance with the increased activity of the former against basic substrates. Considering the amino-acid composition of the binding site of oligopeptidase B and prolyl oligopeptidase the more negative character of the binding site of the latter can be rationalised in terms of some mutations from nonpolar to polar or acidic amino acid residues in OpB with respect to PEP.
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