The kinetics of enzyme systems involving activation of zymogens

A general model of zymogen activation is proposed and explicit kinetic equations for the time courses of the various species and products involved are given. These equations are valid for the whole course of the reaction and therefore for both the transient phase and the steady state. This model is sufficiently general to include mechanisms possessing one or more steps of zymogen activation besides possible steps of inhibition (reversible or irreversible) or inactivation.     

Prostaglandin H synthetase as a multisubstrate enzyme. Fluorimetric study of enzyme kinetics

The kinetics of a multisubstrate enzymatic reaction catalyzed by prostaglandin H synthase (PGH-synthase, EC 1.14.99.1) was studied, using homovanillic acid, a new electron donor for the given system. Homovanillic acid was shown to be a participant in a reaction with arachidonic acid/O2 stoichiometric ratios and is oxidized to a readily fluorescing product with an absorbance maximum (excitation) at 315 nm and fluorescence maximum at 425 nm. This allows for determination of the rate of enzymatic reaction with the sensitivity exceeding by one order of magnitude that of polarographic or spectrophotometric assays. Using fluorescent techniques, the dependence of the rate of PGH-synthase reaction on substrate (arachidonic acid, O2 and homovanillic acid) concentrations was studied, and the corresponding Km values were determined. The effect of Tween-20 and Lubrol PX concentrations on the reaction rate were examined. It was shown that with a decrease in the surfactant concentration the reaction rate increases.     

Applications of graph theory to enzyme kinetics and protein folding kinetics. Steady and non-steady-state systems

Graphic methods have proved to be very useful in enzyme kinetics, as reflected in both raising the efficiency of performing calculations and aiding in the analysis of catalytic mechanisms. The kinetic relations among protein folding states are very similar to those between enzyme-catalyzed species. Therefore, it should be equally useful to provide a visually intuitive relation between kinetic calculations and folding mechanisms for protein folding kinetics, as manifested by the graphic rules in enzyme kinetics. It can actually be anticipated that, due to increasing interest in protein folding, the graphic method will become an important tool in folding kinetics as well. Based on the recent progress made in graphic methods of enzyme kinetics, in this review four graphic rules are summarized, which can be used to deal with protein folding systems as well as enzyme-catalyzed systems. Rules 1-3 are established for deriving the kinetic equations for steady-state processes and Rule 4 for those in the case of non-steady-state processes. In comparison with conventional graphic methods, which can only be applied to a steady-state system, the current rules have the following advantages: (1) Complicated and tedious calculations can be greatly simplified. (2) A lot of wasted labor can be turned away. (3) Final results can be double-checked by a formula provided in each of the graphic rules. (4) Transient kinetic systems can also be treated. The mathematical proof of Rules 1-4 is given in appendices A-D, respectively.     

The origins of enzyme kinetics

The equation commonly called the Michaelis–Menten equation is sometimes attributed to other authors. However, although Victor Henri had derived the equation from the correct mechanism, and Adrian Brown before him had proposed the idea of enzyme saturation, it was Leonor Michaelis and Maud Menten who showed that this mechanism could also be deduced on the basis of an experimental approach that paid proper attention to pH and spontaneous changes in the product after formation in the enzyme-catalysed reaction. By using initial rates of reaction they avoided the complications due to substrate depletion, product accumulation and progressive inactivation of the enzyme that had made attempts to analyse complete time courses very difficult. Their methodology has remained the standard approach to steady-state enzyme kinetics ever since.     

The kinetics of enzyme inactivation

The course of hydrolysis of β-glycerophosphate catalyzed by a group of different enzyme extracts, both with and without the addition of Mg, with and without preincubation of the enzyme, has been studied and the results discussed on the basis of a mathematical analysis. In all the extracts, it appears that two distinct and independently acting constituent enzymes—or perhaps “principles” of the same enzyme—are present, one acting much more rapidly but also more rapidly inactivated than the other. Storage in the refrigerator changes markedly the behavior of both constituents, though in different ways. There is evidence that in some cases an enzyme is limited in its hydrolytic “capacity” in the sense that after an enzyme molecule has decomposed a definite number of substrate molecules, it thereafter becomes entirely passive. Further, there is evidence, in the case of one extract, that the roles of catalytically more and less active constituents in the absence of Mg are reversed in its presence. Finally, a damped periodicity is found which indicates the presence of two factors of an unknown sort which influence and are influenced by the inactivation of the enzyme.     

The computation of hyperbolic dependences in enzyme kinetics.

A computer program aimed at analysing results following Michaelis-Menten kinetics can be used unmodified in the treatment of other kinetic results provided that the kinetic equations in these cases can be written in the form of the Michaelis-Menten equation. A list is presented of the parameters to be set instead of substrate concentration and reaction rate, and of constants replacing Km and V, if such a program is applied in analysing enzyme inhibitions, activations and pH-dependences.     

Steady state enzyme kinetics for systems with three enzyme-binding species

The steady state enzyme kinetics of those systems are discussed, which involve three species binding to enzymes. Two specific systems are considered. In one system, all three species bind only once to the enzyme. In the other system, two species bind once and one binds twice to the enzyme. The species are labeled S, A and B. The general case is considered, in which all possible complexes involving enzyme E and species S generate product P. Species A and B may become co-substrates, activators or inhibitors. The steady state enzyme kinetic equations for the general case for both systems are presented. These equations are further discussed for a number of special cases, which may be of interest to enzymologists and others using enzymes.     

Staphylococcal L-asparaginase: enzyme kinetics.

The ph optimum of purified staphylococcal L-asparaginase (EC 3.5.1.1) was found to be between 8.6 and 8.8. The temperature optimum was 30 degrees-32 degrees C and the highest reaction rate occurred at 30 degrees C. The KM of the enzyme calculated from Lineweaver-Burk plot was 3.71 x 10(-2) M. Besides L-asparaginase, the substrate specificity of enzyme was restricted to N-alpha-acetyl-L-asparagine. D-asparagine, L-aspartic acid and D-glutamic acid were competitive inhibitors. Hg2+ and Cu2+ cations strongly inhibited the enzyme while Na+ and K+ cations strongly stimulated activity. Two SH-groups could be detected after enzyme denaturation with guanidine.     

A general solution for the steady-state kinetics of immobilized enzyme systems

A power series solution is presented which describes the steady-state concentration profiles for substrate and product molecules in immobilized enzyme systems. Diffusional effects and product inhibition are incorporated into this model. The kinetic consequences of diffusion limitation and product inhibition for immobilized enzymes are discussed and are compared to kinetic behavior characteristic of other types of effects, such as substrate inhibition and substrate activation.     

Evolution of complex probability distributions in enzyme cascades

Unusual probability distribution profiles, including transient multi-peak distributions, have been observed in computer simulations of cell signaling dynamics. The emergence of these complex distributions cannot be explained using either deterministic chemical kinetics or simple Gaussian noise approximation. To develop physical insights into the origin of complex distributions in stochastic cell signaling, we compared our approximate analytical solutions of signaling dynamics with the exact numerical simulations. Our results are based on studying signaling in 2-step and 3-step enzyme amplification cascades that are among the most common building blocks of cellular protein signaling networks. We have found that while the multi-peak distributions are typically transient, and eventually evolve into single peak distributions, in certain cases these distributions may be stable in the limit of long times. We also have shown that introducing positive feedback loops results in diminution of the probability distribution complexity.     

High pressure enzyme kinetics of dextransucrase.

The pressure dependence of enzymatic dextran formation has been observed up to 1000 at for several substrate concentrations. First order denaturation effects could be separated from the thermodynamic effects, which lead to a volume of 30.4 to 44.0 ccm per mole for the formation and -13.6ccm per mole for the activation of the enzyme-substrate complex. Denaturation depends on the substrate concentration. This leads to the conslusion that only the free enzyme is denatured, wheras the ES complex is stable.