Schematic methods for probabilistic enzyme kinetics.

The theory of steady-state enzyme processes which avoids using the mass action law of chemical kinetics and consistently describes catalytic mechanisms by probabilistic concepts has recently been proposed (Mazur, 1991, J. theor. Biol. 148, 229-242). To facilitate the analysis of complex reaction graphs by this theory the possibility of constructing schematic rules similar to those used in classical kinetics is studied. It is found that due to the similarity of algebraic procedures the popular method of King & Altman can be applied in probabilistic kinetics in addition to the earlier proposed rule based on enumeration of cycles of the reaction graph. This similarity also allows one to adapt many other shortcut methods of classical kinetics for probabilistic reaction graphs. The paper considers separately the possibility of transforming reaction mechanisms so that the initial graph is replaced by a simpler but equivalent one. It is shown that there are few cases when a group of states can be replaced by one united state, with earlier known rules such as the rule of Cha for equilibrium stages being particular cases of a more general procedure. In addition a novel method is proposed which performs step-by-step reduction of any reaction graph. All the new methods can be adapted for traditional kinetics as well. The results obtained demonstrate that many schematic rules of classical kinetics are of probabilistic origin.     

A novel thermodynamic relationship based on Kramers Theory for studying enzyme kinetics under high viscosity

In most studies of enzyme kinetics it has been found sufficient to use the classical Transition State Theory (TST) of Eyring and others. This theory was based on the solvent being an ideal dilute substance treated as a heat bath. However, enzymes found in organisms adapted to very low (psychrophiles) and very high (thermophiles) temperatures are also subjected to variable solute concentrations and viscosities. Therefore, the TST may not always be applicable to enzyme reactions carried out in various solvents with viscosities ranging from moderate to very high. There have been numerous advances in the theory of chemical reactions in realistic non-ideal solvents such as Kramers Theory. In this paper we wish to propose a modified thermodynamic equation, which have contributions from kcat, Km and the viscosity of the medium in which the enzyme reaction is occurring. These could be very useful for determining the thermodynamics of enzymes catalyzing reactions at temperature extremes in the presence of substrate solutions of different compositions and viscosities.     

An NMR method for studying the kinetics of metal exchange in biomolecular systems

The kinetics of lanthanide (III) exchange for calcium(II) in the C-terminal EF-hand of the protein calbindin D_9khave been studied by one-dimensional (1D) stopped-flow NMR. By choosing a paramagnetic lanthanide (Ce³⁺), kinetics in the sub-second range can be easily measured. This is made possible by the fact that (i) the kinetic behaviour of hyperfine shifted signals can be monitored in 1D NMR and (ii) fast repetition rates can be employed because these hyperfine shifted signals relax fast. It is found that the Ce³⁺-Ca²⁺exchange process indeed takes place on a sub-second timescale and can be easily monitored with this technique. As the rate of calcium-cerium substitution was found not to depend on the presence of excess calcium in solution, the kinetics of the process were interpreted in terms of a bimolecular associative mechanism, and the rate constants extracted. Interestingly, the dissociative mechanism involving the apoform of the protein, which is generally assumed for metal ion exchange at protein binding sites, was not in agreement with our data.     

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.     

An immunocytochemical method for studying the kinetics of osteoclast nuclei on intact mouse parietal bone

Summary An immunocytochemical method using an antibody against 5-bromo-2-deoxyuridine has been applied to the study of the kinetics of osteoclast nuclei on intact mouse parietal bones. Osteoclasts containing tartrate-resistant acid phosphatase show nuclei that are positive for the thymidine analogue within 24 hours of injection into four-day old mice. Labelled osteoclast nuclei decline in number with a half-life of 1.3 days, compatible with a random mechanism of cell death rather than a fixed lifespan. This is shorter than has previously been reported and the possible reasons for this are suggested. The main advantages compared with autoradiography are the shortened processing time and the large number of osteoclasts that can be examined per parietal bone.     

Microcomputer tools for steady-state enzyme kinetics

Three programs useful for the investigation of steady–statekinetics have been developed. Two provide the solution to thesteady–state rate equation; the first of these is a straightforwardimplementation of the rules developed by Chou. The second isa very efficient procedure for evaluating King–Altmandiagrams and can be used for quite large mechanisms. The thirdprogram provides the numeric solution for a specific mechanismand set of initial conditions; it is well suited to extremelylarge models. Received on April 1, 1985; accepted on April 19, 1985     

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.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.