Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Loss of enzyme activity during turnover of the Bacillus cereus β-lactamase catalysed hydrolysis of β-lactams due to loss of zinc ion

Metallo-beta-lactamases are zinc-ion-dependent and are known to exist either as mononuclear or as dinuclear enzymes. The kinetics and mechanism of hydrolysis of the native zinc Bacillus cereus metallo-beta-lactamase (BcII) have been investigated under pre-steady-state conditions at different pHs and zinc-ion concentrations. Biphasic kinetics are observed for the hydrolysis of cefuroxime and benzylpenicillin with submicromolar concentrations of enzyme and zinc. The initial burst of product formation far exceeds the concentration of enzyme and the subsequent slower rate of hydrolysis is attributed to a branched kinetic pathway. The pH and metal-ion dependence of the microscopic rate constants of this branching were determined, from which it is concluded that two enzyme species with different metal-to-enzyme stoichiometries are formed during catalytic turnover. The dizinc enzyme is responsible for the fast route but during the catalytic cycle it slowly loses the less tightly bound zinc ion via the branching route to give an inactive monozinc enzyme; the latter is only catalytic following the uptake of a second zinc ion. The rate constant for product formation from the dinuclear enzyme and the branching rate constant show a sigmoidal dependence on pH indicative of important ionizing groups with pK (a)s of 9.0 +/- 0.1 and 8.2 +/- 0.1, respectively. The rate constant for the regeneration of enzyme activity depends on zinc-ion concentration. This unusual behaviour is attributed to an intrinsic property of metallo hydrolytic enzymes that depend on a metal bound water both as a ligand for the second metal ion and as the nucleophile which is consumed during hydrolysis of the substrate and so has to be replaced to maintain the catalytic cycle.     

Asymmetry and free energy transduction in biology

This paper is an extension of our earlier theoretical studies on the relationship between kinetic asymmetry and free-energy transductions in biological systems induced by external fluctuations. In the first part of the paper, the asymmetry conditions necessary for external-noise-induced free-energy transductions to occur are derived for a special cyclic, four-state model in which only one reaction step is perturbed by the fluctuations. The results can be used to explain the earlier findings that asymmetry in rate constants was not required in the uphill transport of ligands induced by externally fluctuating the ligand concentrations. In the second part of the paper, the coupling between two enzyme systems through direct enzyme-enzyme inter-actions is studied. The existence of kinetic asymmetry in both the driving and the driven enzyme systems is found necessary for coupling and free-energy transductions to occur.     

Fluxes,first passage times,and the reduction of Hill diagrams

The steady-state flux resulting from the coupling of two multistate systems is considered. The dynamics of these systems are described (a) as diffusion along a continuous one-dimensional free-energy profile specified by a conformational coordinate or (b) in terms of transitions between a discrete but arbitrary number of substates. If these multistate systems are connected in a simple way, it is shown that the steady-state flux can be obtained analytically. For both the continuous and discrete cases, the exact flux is shown to be identical to that calculated from a simple kinetic scheme involving only four states, if the effective rate constants of this reduced scheme are appropriately defined in terms of the mean first passage times for moving between various points along the multistate cycles. These results clarify and quantify the manner in which the internal conformational dynamics of two multistate systems influences the steady-state flux.     

Generalized microscopic reversibility, kinetic co-operativity of enzymes and evolution.

Generalized microscopic reversibility implies that the apparent rate of any catalytic process in a complex mechanism is paralleled by substrate desorption in such a way that this ratio is held constant within the reaction mechanism [Whitehead (1976) Biochem. J. 159, 449--456]. The physical and evolutionary significances of this concept, for both polymeric and monomeric enzymes, are discussed. For polymeric enzymes, generalized microscopic reversibility of necessity occurs if, within the same reaction sequence, the substrate stabilizes one type of conformation of the active site only. Generalized microscopic reversibility suppresses the kinetic co-operativity of the slow transition model [Ainslie, Shill & Neet (1972) J. Biol. Chem. 247, 7088--7096]. This situation is obtained if the free-energy difference between the corresponding transition states of the two enzyme forms is held constant along the reaction co-ordinate. This situation implies that the 'extra costs' of energy (required to pass each energy barrier) that are not covered by the corresponding binding energies of the transition states vary in a similar way along the two reaction co-ordinates. The regulatory behaviour of monomeric enzymes is discussed in the light of the concept of 'catalytic perfection' proposed by Albery & Knowles [(1976) Biochemistry 15, 5631--5640]. These authors claim that an enzyme will be catalytically 'perfect' when its catalytic efficiency is maximum. If this situation occurs for a monomeric enzyme obeying either the slow transition or the mnemonical model, it can be shown that the kinetic co-operativity disappears. In other words, kinetic co-operativity of a monomeric enzyme is 'paid for' at the expense of catalytic efficiency, and the monomeric enzyme cannot be simultaneously co-operative and catalytically very efficient. This is precisely what has been found experimentally in a number of cases.     

Catalytic efficiency, kinetic co-operativity of oligomeric enzymes and evolution

The catalytic performance of an enzyme, whether it is monomeric or oligomeric, depends on extra costs of energy in passing from the initial ground state to the various transition states, along the reaction co-ordinate. The improvement, during evolution, of the catalytic performance of individual subunits implies that three structural requirements are met in the course of an enzyme reaction: the unstrained enzyme subunits exist in the ground states under two conformations, one corresponding to the non-liganded state and the other to the liganded state; the inter-subunit strain is relieved in the various transition states; the subunits bound to the various transition states S not equal to, X not equal to and P not equal to have the same conformation. These structural requirements are precisely those which have been used to derive structural rate equations for polymeric enzymes. When subunits are loosely coupled, their arrangement controls the various rate constants, but not the extra costs of energy required to reach the various transition states. Moreover, one cannot expect the rate curve to display any sigmoidicity under these conditions. If subunits are tightly coupled and if the strained non-liganded and half-liganded states are destabilized with respect to the corresponding unstrained states, that is if they contain more conformational energy, the oligomeric enzyme is more catalytically efficient than the ideally isolated subunits. Moreover, if the available conformational energy of the half-liganded state is more than twice that of the non-liganded state, kinetic co-operativity is positive and the rate curve is sigmoidal. It is therefore the extent of inter-subunit strain in the half-liganded state which controls the appearance of sigmoidal kinetic behaviour. If subunits are tightly coupled but if inter-subunit strain is relieved in both the non-liganded and fully-liganded states, the half-liganded state controls both the catalytic efficiency of the enzyme and the sigmoidicity of the rate curve. Sigmoidicity and high catalytic efficiency are to be observed when this half-liganded state is destabilized relative to the corresponding unstrained state.(ABSTRACT TRUNCATED AT 400 WORDS)     

Unmasking tandem site interaction in human acetylcholinesterase. Substrate activation with a cationic acetanilide substrate

Acetylcholinesterase (AChE) contains a narrow and deep active site gorge with two sites of ligand binding, an acylation site (or A-site) at the base of the gorge, and a peripheral site (or P-site) near the gorge entrance. The P-site contributes to catalytic efficiency by transiently binding substrates on their way to the acylation site, where a short-lived acyl enzyme intermediate is produced. A conformational interaction between the A- and P-sites has recently been found to modulate ligand affinities. We now demonstrate that this interaction is of functional importance by showing that the acetylation rate constant of a substrate bound to the A-site is increased by a factor a when a second molecule of substrate binds to the P-site. This demonstration became feasible through the introduction of a new acetanilide substrate analogue of acetylcholine, 3-(acetamido)-N,N,N-trimethylanilinium (ATMA), for which a = 4. This substrate has a low acetylation rate constant and equilibrates with the catalytic site, allowing a tractable algebraic solution to the rate equation for substrate hydrolysis. ATMA affinities for the A- and P-sites deduced from the kinetic analysis were confirmed by fluorescence titration with thioflavin T as a reporter ligand. Values of a >1 give rise to a hydrolysis profile called substrate activation, and the AChE site-specific mutant W86F, and to a lesser extent wild-type human AChE itself, showed substrate activation with acetylthiocholine as the substrate. Substrate activation was incorporated into a previous catalytic scheme for AChE in which a bound P-site ligand can also block product dissociation from the A-site, and two additional features of the AChE catalytic pathway were revealed. First, the ability of a bound P-site ligand to increase the substrate acetylation rate constant varied with the structure of the ligand: thioflavin T accelerated ATMA acetylation by a factor a(2) of 1.3, while propidium failed to accelerate. Second, catalytic rate constants in the initial intermediate formed during acylation (EAP, where EA is the acyl enzyme and P is the alcohol leaving group cleaved from the ester substrate) may be constrained such that the leaving group P must dissociate before hydrolytic deacylation can occur.     

The catalytic power of enzymes: conformational selection or transition state stabilization?

The mechanism by which enzymes produce enormous rate enhancements in the reactions they catalyze remains unknown. Two viewpoints, selection of ground state conformations and stabilization of the transition state, are present in the literature in apparent opposition. To provide more insight into current discussion about enzyme efficiency, a two-state model of enzyme catalysis was developed. The model was designed to include both the pre-chemical (ground state conformations) and the chemical (transition state) components of the process for the substrate both in water and in the enzyme. Although the model is of general applicability, the chorismate to prephenate reaction catalyzed by chorismate mutase was chosen for illustrative purposes. The resulting kinetic equations show that the catalytic power of enzymes, quantified as the k(cat)/k(uncat) ratio, is the product of two terms: one including the equilibrium constants for the substrate conformational states and the other including the rate constants for the uncatalyzed and catalyzed chemical reactions. The model shows that these components are not mutually exclusive and can be simultaneously present in an enzymic system, being their relative contribution a property of the enzyme. The developed mathematical expressions reveal that the conformational and reaction components of the process perform differently for the translation of molecular efficiency (changes in energy levels) into observed enzymic efficiency (changes in k(cat)), being, in general, more productive the component involving the transition state.     

A new paradigm for DNA polymerase specificity

We show that T7 DNA polymerase exists in three distinct structural states, as reported by a conformationally sensitive fluorophore attached to the recognition (fingers) domain. The conformational change induced by a correct nucleotide commits the substrate to the forward reaction, and the slow reversal of the conformational change eliminates the rate of the chemistry step from any contribution toward enzyme specificity. Discrimination against mismatches is enhanced by the rapid release of mismatched nucleotides from the ternary E.DNA.deoxynucleoside triphosphate complex and by the use of substrate-binding energy to actively misalign catalytic residues to reduce the rate of misincorporation. Our refined model for enzyme selectivity extends traditional thermodynamic formalism by including substrate-induced structural alignment or misalignment of catalytic residues as a third dimension on the free-energy profile and by including the rate of substrate dissociation as a key kinetic parameter.     

Kinetic studies on beta-site amyloid precursor protein-cleaving enzyme (BACE). Confirmation of an iso mechanism

The steady-state kinetic mechanism of beta-amyloid precursor protein-cleaving enzyme (BACE)-catalyzed proteolytic cleavage was evaluated using product and statine- (Stat(V)) or hydroxyethylene-containing (OM99-2) peptide inhibition data, solvent kinetic isotope effects, and proton NMR spectroscopy. The noncompetitive inhibition pattern observed for both cleavage products, together with the independence of Stat(V) inhibition on substrate concentration, suggests a uni-bi-iso kinetic mechanism. According to this mechanism, the enzyme undergoes multiple conformation changes during the catalytic cycle. If any of these steps are rate-limiting to turnover, an enzyme form preceding the rate-limiting conformational change should accumulate. An insignificant solvent kinetic isotope effect (SKIE) on k(cat)/K(m), a large inverse solvent kinetic isotope effect on k(cat), and the absence of any SKIE on the inhibition onset by Stat(V) during catalysis together indicate that the rate-limiting iso-step occurs after formation of a tetrahedral intermediate. A moderately short and strong hydrogen bond (at delta 13.0 ppm and phi of 0.6) has been observed by NMR spectroscopy in the enzyme-hydroxyethylene peptide (OM99-2) complex that presumably mimics the tetrahedral intermediate of catalysis. Collapse of this intermediate, involving multiple steps and interconversion of enzyme forms, has been suggested to impose a rate limitation, which is manifested in a significant SKIE on k(cat). Multiple enzyme forms and their distribution during catalysis were evaluated by measuring the SKIE on the noncompetitive (mixed) inhibition constants for the C-terminal reaction product. Large, normal SKIE values were observed for these inhibition constants, suggesting that both kinetic and thermodynamic components contribute to the K(ii) and K(is) expressions, as has been suggested for other iso-mechanism featuring enzymes. We propose that a conformational change related to the reprotonation of aspartates during or after the bond-breaking event is the rate-limiting segment in the catalytic reaction of beta-amyloid precursor protein-cleaving enzyme, and ligands binding to other than the ground-state forms of the enzyme might provide inhibitors of greater pharmacological relevance.     

Tyrosine phenol-lyase and tryptophan indole-lyase encapsulated in wet nanoporous silica gels: Selective stabilization of tertiary conformations

The pyridoxal 5'-phosphate-dependent enzymes tyrosine phenol-lyase and tryptophan indole-lyase were encapsulated in wet nanoporous silica gels, a powerful method to selectively stabilize tertiary and quaternary protein conformations and to develop bioreactors and biosensors. A comparison of the enzyme reactivity in silica gels and in solution was carried out by determining equilibrium and kinetic parameters, exploiting the distinct spectral properties of catalytic intermediates and reaction products. The encapsulated enzymes exhibit altered distributions of ketoenamine and enolimine tautomers, increased values of inhibitors dissociation constants, slow attaining of steady-state in the presence of substrate and substrate analogs, modified steady-state distribution of catalytic intermediates, and a sixfold-eightfold decrease of specific activities. This behavior can be rationalized by a reduced conformational flexibility for the encapsulated enzymes and a selective stabilization of either the open (inactive) or the closed (active) form of the enzymes. Despite very similar structures and catalytic mechanisms, the influence of encapsulation is more pronounced for tyrosine phenol-lyase than tryptophan indole-lyase. This finding indicates that subtle structural and dynamic differences can lead to distinct interactions of the protein with the gel matrix.     

Conformational isomerism can limit antibody catalysis

Ligand binding to enzymes and antibodies is often accompanied by protein conformational changes. Although such structural adjustments may be conducive to enzyme catalysis, much less is known about their effect on reactions promoted by engineered catalytic antibodies. Crystallographic and pre-steady state kinetic analyses of antibody 34E4, which efficiently promotes the conversion of benzisoxazoles to salicylonitriles, show that the resting catalyst adopts two interconverting active-site conformations, only one of which is competent to bind substrate. In the predominant isomer, the indole side chain of Trp(L91) occupies the binding site and blocks ligand access. Slow conformational isomerization of this residue, on the same time scale as catalytic turnover, creates a deep and narrow binding site that can accommodate substrate and promote proton transfer using Glu(H50) as a carboxylate base. Although 34E4 is among the best catalysts for the deprotonation of benzisoxazoles, its efficiency appears to be significantly limited by this conformational plasticity of its active site. Future efforts to improve this antibody might profitably focus on stabilizing the active conformation of the catalyst. Analogous strategies may also be relevant to other engineered proteins that are limited by an unfavorable conformational pre-equilibrium.     

Important subunit interactions in the chloroplast ATP synthase

General structural features of the chloroplast ATP synthase are summarized highlighting differences between the chloroplast enzyme and other ATP synthases. Much of the review is focused on the important interactions between the epsilon and gamma subunits of the chloroplast coupling factor 1 (CF(1)) which are involved in regulating the ATP hydrolytic activity of the enzyme and also in transferring energy from the membrane segment, chloroplast coupling factor 0 (CF(0)), to the catalytic sites on CF(1). A simple model is presented which summarizes properties of three known states of activation of the membrane-bound form of CF(1). The three states can be explained in terms of three different bound conformational states of the epsilon subunit. One of the three states, the fully active state, is only found in the membrane-bound form of CF(1). The lack of this state in the isolated form of CF(1), together with the confirmed presence of permanent asymmetry among the alpha, beta and gamma subunits of isolated CF(1), indicate that ATP hydrolysis by isolated CF(1) may involve only two of the three potential catalytic sites on the enzyme. Thus isolated CF(1) may be different from other F(1) enzymes in that it only operates on 'two cylinders' whereby the gamma subunit does not rotate through a full 360 degrees during the catalytic cycle. On the membrane in the presence of a light-induced proton gradient the enzyme assumes a conformation which may involve all three catalytic sites and a full 360 degrees rotation of gamma during catalysis.     

Conformational equilibrium of an enzyme catalytic site in the allosteric transition.

The dynamic equilibrium of a catalytic site between active and inactive conformations, the missing link between the structure and function of allosteric enzymes, was identified using protein engineering and NMR techniques. Kinetic analyses of the wild-type and three mutants of Thermus L-lactate dehydrogenase established that the allosteric property of the enzyme is associated with a concerted transition between the high-affinity (R) and low-affinity (T) states. By introducing mutations, we prepared an enzyme in which the R and T states were balanced. The conformation of the enzyme-bound coenzyme, NAD+, which interacts directly with the substrate, was analyzed using NMR spectroscopy. NAD+ bound to the mutant enzyme was in a conformational mixture of the active and inactive forms, while NAD+ took on predominantly one of the two forms when it was bound to the other enzymes we had analyzed. We interpret this to mean that the catalytic site is in equilibrium between the two conformations. The ratio of the conformers of each enzyme agreed with the [T]/[R] ratio as determined by kinetic analyses. Therefore, it is the identified conformational equilibrium of the catalytic site that governs the allosteric regulation of the enzyme activity.     

Kinetics and thermodynamics of ligand binding by cytochrome P450 3A4

Cytochrome P450 (P450) 3A4, the major catalyst involved in human drug oxidation, displays substrate- and reaction-dependent homotropic and heterotropic cooperative behavior. Although several models have been proposed, these mainly rely on steady-state kinetics and do not provide information on the contribution of the individual steps of P450 catalytic cycle to the observed cooperativity. In this work, we focused on the kinetics of substrate binding, and the fluorescent properties of bromocriptine and alpha-naphthoflavone allowed analysis of an initial ligand-P450 3A4 interaction that does not cause a perturbation of the heme spectrum. The binding stoichiometry for bromocriptine was determined to be unity using isothermal titration calorimetry and equilibrium dialysis methods, suggesting that the ligand bound to the peripheral site during the initial encounter dissociates subsequently. A three-step substrate binding model is proposed, based on absorbance and fluorescence stopped-flow kinetic data and equilibrium binding data obtained with bromocriptine, and evaluated using kinetic modeling. The results are consistent with the substrate molecule binding at a site peripheral to the active site and subsequently moving toward the active site to bind to the heme and resulting in a low to high spin iron shift. The last step is attributed to a conformational change in the enzyme active site. The later steps of binding were shown to have rate constants comparable with the subsequent steps of the catalytic cycle. The P450 3A4 binding process is more complex than a two-state system, and the overlap of rates of some of the events with subsequent steps is proposed to underlie the observed cooperativity.     

Substitution at residue 214 of human thymidylate synthase alters nucleotide binding and isomerization of ligand-protein complexes

Based on crystal structures of bacterial thymidylate synthases (TS), a glutamine corresponding to residue 214 in human TS (hTS) is located in a region that is postulated to be critical for conformational changes that occur upon ligand binding. Previous steady-state kinetic studies indicated that replacement of glutamine at position 214 (Gln214) of hTS by other residues results in a decrease in nucleotide binding and catalysis, with only minor effects on folate binding (D. J. Steadman et al. (1998) Biochemistry 37, 7089-7095). The data suggested that Gln214 maintains the enzyme in a conformation that facilitates nucleotide binding. In the present study, transient-state kinetic analysis was utilized to determine rate constants that govern specific steps along the catalytic pathway of hTS, which provides the first detailed kinetic mechanism for hTS. Analysis of the reaction mechanisms of mutant TSs revealed that substitution at position 214 significantly affects nucleotide binding and the rate of chemical conversion of bound substrates to products, which is consistent with the results of steady-state kinetic analysis. Furthermore, it is shown that substitution at position 214 affects the rate of isomerization, presumably from an open to a closed form of the enzyme-substrate complex. Although the affinity of the initial binding of CH2H4folate is not substantially affected, Kiso, the ratio of the forward rate of isomerization (kiso) to the reverse rate of isomerization (kr, iso), is 2-6-fold lower for the mutants at position 214 compared to Q214, with the greatest effects on kiso. In addition, the binding of the folate analogue, CB3717, to dUMP binary complexes of mutant enzymes was characterized by a slow isomerization phase that was not detected in binding studies utilizing wild-type hTS. The data are consistent with the hypothesis that Gln214 is located at a structurally critical region of the enzyme.