An alternative method for determining inhibition rate constants by following the substrate reaction

Quantifying the inactivation rate constants for the molecular species comprising the catalytic cycle of Leuconostoc mesenteroides glucose 6-phosphate dehydrogenase

When an unstable enzyme is incubated with its substrate(s), catalysis may cease before chemical equilibrium is attained. The residual substrate concentrations depend on their initial concentrations, the initial enzymic activity, and the inactivation rate constants for each molecular species that comprise the catalytic cycle. The underlying theory has been elaborated previously for single-substrate reactions and here it is extended to bi-substrate reactions. The theory is illustrated by application to glucose 6-phosphate dehydrogenase, which is unstable when exposed to a low concentration of sodium dodecyl sulphate. It is shown that the ternary complex containing both substrates is resistant to inactivation while each of the remaining complexes undergoes first-order decay. Rate constants for the inactivation of each complex are calculated.

The mechanism of p21-activated kinase 2 autoactivation

The p21-activated kinases (PAKs) play an important role in diverse cellular processes. PAK2 is activated by autophosphorylation upon binding of small G proteins such as Cdc42 and Rac in the GTP-bound state. However, the mechanism of PAK2 autophosphorylation in vitro is unclear. In the present study, the kinetic theory of the substrate reaction during modification of enzyme activity has been applied to a study of the autoactivation of PAK2. On the basis of the kinetic equation of the substrate reaction during the autophosphorylation of PAK2, the activation rate constants for the free enzyme and enzyme-substrate complex have been determined. The results indicate that 1) in the presence of Cdc42, PAK2 autophosphorylation is a bipartite mechanism, with the regulatory domain autophosphorylated at multiple residues, whereas activation coincides with autophosphorylation of the catalytic domain at Thr-402; 2) the autophosphorylation reactions in regulatory domain are either a nonlimiting step or not required for activation of enzyme; 3) the autophosphorylation at site Thr-402 on the catalytic domain occurs by an intermolecular mechanism and is required for phosphorylation of exogenous substrates examined; 4) binding of the exogenous protein/peptide substrates at the active site of PAK2 has little or no effect on the autoactivation of PAK2, suggesting that multiple regions of PAK2 are involved in the enzyme-substrate recognition. The present method also provides a novel approach for studying autophosphorylation reactions. Since the experimental conditions used resemble more closely the in vivo situation where the substrate is constantly being turned over while the enzyme is being modified, this new method would be particularly useful when the regulatory mechanisms of the reversible phosphorylation reaction toward certain enzymes are being assessed.

Kinetic analysis of the general modifier mechanism of Botts and Morales involving a suicide substrate

Suicide substrates are widely used in enzymology for studying enzyme mechanisms and designing potential drugs. The presence of a reversible modifier decreases or increases the rate of substrate-induced inactivation, with evident physiological and experimental consequences. To date, only the action of a competitive or uncompetitive inhibitor of an enzyme system involving suicide substrate has been reported. In this paper, we analyse the kinetics of enzyme-catalysed reactions which evolve in accordance with the general modifier mechanisms of Botts and Morales in which enzyme inactivation is induced by suicide substrate. Rapid equilibrium of all of the reversible reaction steps involved is assumed and the time course equations for the residual enzyme activity, the inactive enzyme forms and the reaction product are derived. Partition ratios giving the relative weight of the product and inactive enzyme concentrations, and the relative contribution to the product formation of each of the unmodified and modified catalytic routes, are studied. New indices pointing to the conditions under which the modifier acts as inhibitor or as activator are suggested. The goodness of the analytical solutions is tested by comparison with the simulated curves obtained by numerical integration. An experimental design and kinetic data analysis to evaluate the kinetic parameters from the time progress curves of the product are proposed. From these results, those corresponding to several reaction mechanisms involving both a suicide substrate and a modifier, and which can be regarded as particular cases of the general case analysed here, can be directly and easily derived.

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible, uncompetitive inhibitor

We present a general kinetic analysis of enzyme catalyzed reactions evolving according to a Michaelis-Menten mechanism, in which an uncompetitive, reversible inhibitor acts. Simultaneously, enzyme inactivation is induced by an unstable suicide substrate, i.e. it is a Michaelis-Menten mechanism with double inhibition: one originating from the substrate and another originating from the reversible inhibitor. Rapid equilibrium of the reversible reaction steps involved is assumed and the time course equations for the reaction product have been derived under the assumption of limiting enzyme. The goodness of the analytical solutions has been tested by comparison with simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested.

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.

Use of a windows program for simulation of the progress curves of reactants and intermediates involved in enzyme-catalyzed reactions

A program that performs simulation of the kinetics of enzyme-catalyzed reactions with up to 32 species is described. The program is written in C++ for MS Windows 95/98/NT and uses a simple text file to define the kinetic model. The use of the program is illustrated with some examples. WES is available free of charge on request from the authors (e-mail: fgarcia@iele-ab.uclm.es).

Comparison of conformational changes and inactivation of soybean lipoxygenase-1 during urea denaturation

The unfolding and inactivation of soybean lipoxygenase-1 during urea denaturation has been compared. Equilibrium study indicates that inactivation of the enzyme occurs at low urea concentrations before significant conformational change of the molecule as a whole. In the presence of 6.0 M urea, the unfolding of soybean lipoxygenase-1, as monitored by fluorescence intensity, is a triphasic process, while the inactivation of the enzyme shows single-phase kinetics. The rate constant of inactivation is consistent with that of the fast conformational change of the enzyme. The results suggest that active sites of lipoxygenase-1 containing iron cofactor are situated in a limited region of the enzyme molecule that is more fragile to denaturants than the protein as a whole. The kinetic theory of substrate reactions catalyzed by unstable enzymes (Duggleby (1986) J. Theor. Biol. 123, 67-80) has been applied to study the effect of substrate on enzyme inactivation. On the basis of the kinetic equation of substrate reaction in the presence of urea, inactivation rate constants for the free enzyme and enzyme-substrate complex have been determined. The substrate, linoleic acid, has no effect on inactivation of the ferric form of lipoxygenase-1.

The inactivation kinetics of papain by guanidine hydrochloride: a re-analysis

The kinetic theory of the substrate reaction during modification of enzyme activity has been applied to study the inactivation kinetics of enzymes by denaturant. However, an important problem related to the determination of the inactivation rate constants has not been considered in a previous publication (Xiao, et al., Biochim. Biophys. Acta, 1164 (1993) 54-60). In most denaturation experiments, the high concentrations of denaturants may greatly affect the kinetic behavior of the system to preclude the use of the kinetic parameters determined in the absence of denaturant. In the present study, the kinetic equation of substrate reaction in presence of denaturant has been derived. A re-examination of the effect of high concentrations of guanidine hydrochloride on the inactivation of papain, taking into consideration the effect of high concentrations of guanidine hydrochloride on the Michaelis constant, showed that, for papain, the substrate gives no protection on its inactivation. It is the purpose of the present communication to stress the importance of observing the effect of the denaturant on the kinetic parameters for kinetic analysis of enzyme inactivation by denaturants generally.

Kinetics of enzyme systems with unstable suicide substrates

This paper deals with kinetic studies of enzyme reaction mechanisms with enzyme inactivation induced by an unstable suicide substrate. An initial steady-state of the catalytic route is assumed and the time course equations for the total active enzyme forms and the reaction product have been derived. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters is suggested and the time course equations of an important reaction mechanisms involving a stable suicide substrate and which can be regarded as particular case of that under study has also been derived from the corresponding equations. The simplicity of our method allows its systematic application to more complex mechanisms.

Inactivation kinetics of the reduced spinach chloroplast fructose-1,6-bisphosphatase by subtilisin

The course of inactivation of the reduced spinach chloroplast fructose-1,6-bisphosphatase by digestion with subtilisin has been followed by the progress curve method [Tsou, C. L. (1988) Adv. Enzymol. 61, 381-436] and found to follow first-order kinetics. On the basis of the hydrolysis of the substrate, fructose 1,6-bisphosphate, at different concentrations during proteolysis by subtilisin, the first-order inactivation rate constants for the free enzyme and the enzyme-substrate complex can both be determined. The ratio between the inactivation rate constants for the free enzyme and the enzyme-substrate complex indicates strong protection against subtilisin proteolysis by the substrate. It is proposed that the above ratio can be used as a quantitative measure of substrate protection for enzyme inactivation generally. As it has been found that the site of proteolysis is located in a loop region near the N-terminus and well away from the active site, the substrate protection indicates a conformation change of the enzyme away from the substrate binding site.

Kinetics of inactivation of bovine pancreatic ribonuclease A by bromopyruvic acid

The kinetic theory of substrate reaction during the modification of enzyme activity [Duggleby (1986) J. Theor. Biol. 123, 67-80; Wang and Tsou (1990) J. Theor. Biol. 142, 531-549] has been applied to a study of the inactivation kinetics of ribonuclease A by bromopyruvic acid. The results show that irreversible inhibition belongs to a non-competitive complexing type inhibition. On the basis of the kinetic equation of substrate reaction in the presence of the inhibitor, all microscopic kinetic constants for the free enzyme, the enzyme-substrate complex and the enzyme-product complex have been determined. The non-competitive inhibition type indicates that neither the substrate nor the product affects the binding of bromopyruvic acid to the enzyme and that the ionization state of His-119 may be the same in both the enzyme-substrate and the enzyme-product complexes.

Kinetics of inactivation of aminoacylase by 2-chloromercuri-4-nitrophenol: a new type of complexing inhibitor

The kinetic theory of the substrate reaction during modification of enzyme activity previously described [Tsou (1988) Adv. Enzymol. 61, 381-436] has been applied to a study of the inactivation kinetics of aminoacylase by 2-chloromercuri-4-nitrophenol (MNP). The results indicate that the mechanism of reaction between MNP and aminoacylase is a special type of irreversible inhibition. The main features of this type of inhibitor are as follows: (i) the reaction kinetics of inhibitor with enzyme is a single exponential process; (ii) inhibition shows a noncompetitive, complexing behavior; (iii) the first inhibitor-enzyme complex, EI, still has some enzyme activity, and hence the plot of [P]infinity versus the reciprocal of inhibitor concentration gives a straight line with a positive intercept at the ordinate. On the basis of the kinetic equation of substrate reaction in the presence of the inhibitor, a plotting method has been developed for determining the inhibition kinetic constants. As an example, all reaction kinetic constants of aminoacylase with 2-chloromercuri-4-nitrophenol have been determined. The results of the present study suggest that the essential thiol group at the active site of aminoacylase may have a significant effect on the catalytic step but is not involved in substrate binding.