Kinetic analysis of modification reactions at comparable enzyme and modifier concentrations

Kinetics of the enzyme titration process by reversible modifiers

The effect of reversible modifiers on the initial rate of enzyme catalysed reactions has been investigated in a quasi-equilibrium approximation using the general modifier mechanism of Botts and Morales. It has been shown that, when investigating the dependence of the initial rate on the modifier concentration at a fixed substrate concentration, the kinetics of enzyme titration by reversible modifiers can generally be described using two kinetic constants. Just as the dependence of the initial rate on the substrate concentration (at a fixed modifier concentration) is described using two kinetic constants: the Michaelis constant Km and the limiting rate Vm. Only one constant M50 is needed to describe the kinetics of linear inhibition, and in the case of nonlinear inhibition and activation, along with M50 the constant QM is also needed. Knowing the values of the constants M50 and QM, it is possible to unambiguously determine the modification efficiency, that is, to calculate how many times the initial rate of the enzyme catalysed reaction will change when a certain modifier concentration is added to the incubation medium. The properties of these fundamental constants have been analysed in detail and the dependence of these constants on other parameters of the Botts-Morales model have been shown. Equations describing the dependence of relative reaction rates on the modifier concentration using these kinetic constants are presented. Various ways of linearising these equations for calculating the kinetic constants M50 and QM from experimental data are also presented.

Kinetic behavior of the general modifier mechanism of Botts and Morales with non-equilibrium binding

In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady states and non-equilibrium steady states (NESS). Enlightened by the non-equilibrium theory of Markov chains, we introduce the net flux into discussion and acquire an expression of the rate of product formation in NESS, which has clear biophysical significance. Up till now, it is a general belief that being an activator or an inhibitor is an intrinsic property of the modifier. However, we reveal that this traditional point of view is based on the equilibrium assumption. A modifier may no longer be an overall activator or inhibitor when the reaction system is not in equilibrium. Based on the regulation of enzyme activity by the modifier concentration, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bell-shaped behavior, and switching behavior, respectively. We show that the switching phenomenon, in which a modifier may convert between an activator and an inhibitor when the modifier concentration varies, occurs only in NESS. Effects of drugs on the Pgp ATPase activity, where drugs may convert from activators to inhibitors with the increase of the drug concentration, are taken as a typical example to demonstrate the occurrence of the switching phenomenon.

The kinetic model and simulation of blood coagulation—the kinetic influence of activated protein C

The paper described a limited part of the coagulation pathway, and in particular the inhibitory effects of activated protein C in the context of thrombin production. This is a computational modeling study with various assumption made of kinetic rates laws and their summation. The level of complexity and assumed parameters makes conclusions uncertain. However, an interesting outcome is that kinetic reaction rates may show oscillation behavior under particular, high levels of protein C feedback inhibition. The model would defy quantitative practical use, but could have predictive value as a qualitative descriptor of coagulation.

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).

A novel method for determining kinetic parameters of dissociating enzyme systems

The theoretical analysis has been presented for the kinetics of dissociating-associating enzyme-catalyzed reactions. On the basis of the kinetic equation of substrate reaction, a general procedure is developed for determining the kinetic constants of dissociating-associating enzyme reactions. By analyzing the experimental data of initial velocity and steady-state velocity as functions of enzyme and substrate concentration, all unknown kinetic parameters can be determined from several simple, sequential calculations. This method is simple and rigorous, and the required experiments may also not be difficult for most dissociating enzyme systems. Therefore, the present method should be a useful addition to the available methods for studying subunit dissociation of enzymes. In comparison to other physical methods, the advantage of this method is not only its usefulness in the study of self-associating reactions at very low protein concentration but its convenience in the study of substrate effects on subunit-subunit interactions.

A simple method for determining kinetic constants of complexing inactivation at identical enzyme and inhibitor concentrations

The kinetics of complexing inactivation at identical enzyme and inhibitor concentrations were analyzed and the equations of product generation were derived when the free enzyme concentration is great, larger or smaller than the dissociation constant of inhibitor, K(I). The kinetic constants can be obtained by fitting the derived equations to the progress curve. Numerical examples show that this method is valid and gives satisfactory results.