Equations for progress curves of some kinetic models of enzyme-single substrate-single slow binding modifier system

On a nonelementary progress curve equation and its application in enzyme kinetics

The analytical equation describing progress curves of an enzyme catalyzed reaction acting upon the Michaelis-Menten mechanism has been known for the case in which only the free enzyme incurs a loss of its activity, either spontaneously or as a result of an irreversible inhibitor action. The solution of differential equations which defines the rates of enzyme inactivation and substrate utilization is expressed by a nonelementary function in equation of an implicit type that precludes direct calculation of the extent of reaction at any time. Previously, the implicit equations have been rearranged to the alternative formulas and solved by the Newton-Raphson method, but this procedure may fail when used upon the presented equation. For this reason the other root-finding numerical method was applied, and the enzyme kinetic parameters of such numerically solved implicit equation for the reaction mechanism of irreversibly inhibited acetylcholinesterase were fitted to the experimental data by a nonlinear regression computer program.

Acceleration of Drosophila melanogaster acetylcholinesterase methanesulfonylation: peripheral ligand D-tubocurarine enhances the affinity for small methanesulfonylfluoride

D-Tubocurarine, a reversible peripheral inhibitor of cholinesterases accelerates methanesulfonylation of Drosophila melanogaster wild type and W359L mutant. The kinetic evaluation of the process was performed in a step-by-step analysis. The second order overall sulfonylation rate constants, determined from classical residual activity measurements, were used in the subsequent analysis of progress curves. The latter were obtained by measuring the hydrolysis of acetylthiocholine in a complex reaction system of enzyme, substrate, irreversible and reversible inhibitor. The underlying kinetic mechanisms, from such a complex data, could only be untangled by targeted inspection and successive incorporation of reaction steps for which experimental evidence existed. The study showed that the peripheral ligand D-tubocurarine, by binding at the entrance into the active site of the two investigated enzymes (Golicnik et al., Biochemistry 40 (2001) 1214), enhances the affinity for small methanesulfonylfluoride, rather to speeding up the formation of a stable covalent enzyme-inhibitor complex. The specific arrangements at the rim of the active site of each individual enzyme dictate the actual events which can be detected by kinetic means.

Kinetics of the inhibition of proteinase 3 by elafin

Excessive proteolytic activity of proteinase 3 (Pr3) has been suggested to be a factor contributing to the pathogenesis of emphysema and other inflammatory disorders. We report here on the kinetics of inhibition of Pr3 by one of its major endogenous inhibitors, the 6-kD inhibitory domain of elafin. The results are consistent with a reaction mechanism in which a single elafin molecule binds a single Pr3 molecule to form a fully reversible complex. The association and dissociation rate constants, and the inhibition constant were measured to be 4.0 x 10(6) M(-1) s(-1), 1.7 x 10(-3) s(-1), and 4.2 x 10(-10) M, respectively. Triton X-100 and dimethyl sulfoxide, which are frequently added in assay mixtures for enzymatic analysis of Pr3 activity, significantly reduced the association rate. A fraction of the total neutrophil content of Pr3 has been reported to be bound to the surface of the plasma membrane of activated and nonactivated neutrophils. In this study, we also measured the reaction rate constants of elafin with Pr3 that had been previously allowed to associate with phospholipid bilayer vesicles. Binding to the model membranes slowed down the association rate to 3.3 x 10(5) M(-1) s(-1), but the membrane-bound Pr3 and elafin formed a more stable complex, with a dissociation rate constant of 9.1 x 10(-4) s(-1). Based on the kinetic parameters determined here and the estimated elafin concentrations in vivo, it may be concluded that elafin plays a limited role in the regulation of proteolytic activity of Pr3 in lung secretions.

Inhibition of Drosophila acetylcholinesterase by 7-(methylethoxyphosphinyloxy)1-methyl-quinolinium iodide

The kinetic behaviour of Drosophila melanogaster acetylcholinesterase toward its substrate shows, in comparison with classic Michaelis-Menten kinetics, an apparent homotropic cooperative double activation-inhibition pattern. In order to construct an appropriate kinetic model and obtain further information on the mechanism of the catalytic action of this enzyme, the hydrolysis of acetylthiocholine in the absence and presence of different concentrations of synthetic quaternary methylphosphonate, 7-(methylethoxyphosphinyloxy)1-methyl-quinolinium iodide (MEPQ), was followed on a stopped-flow apparatus. The reaction at low substrate concentrations was followed until the change of the absorbance became negligible and at high concentrations only initial parts were recorded. A simultaneous analysis of the progress curves using numerical integration showed that the powerful organophosphonate inhibitor binds and compete with the substrate for the same binding sites. The results are also in accordance with the hypothesis that virtually every substrate or quasi-substrate molecule that enters into the gorge of active site is hydrolysed.