Multisubstrate enzymatic reactions

For multisubstrate enzymatic reactions, the rate equation can be expressed with respect to each substrate as an m function, where n and m are the highest order of the substrate for the numerator and denominator terms respectively (Bardsley and Childs, 1975). Thus the forward rate equation for the random bi bi derived according to the quasi-equilibrium assumption is a 1 1 function in both A and B (i.e., first order in both A and B). However, the rate equation for the random bi bi based on the steady-state assumption yields a 2 2 function (i.e., second order in both A and B). The 2 2 function rate equation results in nonlinear kinetics that should be differentiated from other nonlinear kinetics such as allosteric/cooperative kinetics (Chapter 6, Bardsley and Waight, 1978) and formation of the abortive substrate complex (Dalziel and Dickinson, 1966 Tsai, 1978). 

The most common enzymatic reactions are those with two or more substrates and as many products. But many of the simpler single-substrate schemes are valuable for the development of kinetic ideas concerning effects of pH, temperature, etc., on enzyme reaction rates. Although the mechanisms of multisubstrate reactions are complicated, their kinetics can often be described by an equation of the form ... 

Vrzheshch PV, Varfolomeev SD. Steady-state kinetics of multisubstrate enzymatic reactions - inactivation of the enzyme in the course of reaction. Biochemistry (Moscow) 1985 50 125-32. 

This book starts with a review of the tools and techniques used in kinetic analysis, followed by a short chapter entitled How Do Enzymes Work , embodying the philosophy of the book. Characterization of enzyme activity reversible and irreversible inhibition pH effects on enzyme activity multisubstrate, immobilized, interfadal, and allosteric enzyme kinetics transient phases of enzymatic reactions and enzyme... 

The reduction in enzymatic activity that results from the formation of nonproductive enzyme complexes at high substrate concentration. The most straightforward explanation for substrate inhibition is that a second set of lower affinity binding sites exists for a substrate, and occupancy of these sites ties up the enzyme in nonproductive or catalytically inefficient forms. Other explanations include (a) the removal of an essential active site metal ion or other cofactor from the enzyme by high concentrations of substrate, (b) an excess of unchelated substrate (such as ATP" , relative to the metal ion-substrate complex (such as CaATP or MgATP ) which is the true substrate and (c) the binding of a second molecule of substrate at a subsite of the normally occupied substrate binding pocket, such that neither substrate molecule can attain the catalytically active conformation". For multisubstrate enzymes, nonproductive dead-end complexes can also result in substrate inhibition in the presence of one of the reaction... 

One can probably guess that in relation to reality, the reaction examples of the illustration or of equation (3-73) are much simplified. Many enzymes of known function catalyze reactions involving more than one substrate. The mechanisms can be quite complex, however, the rate laws do generally follow the form of equation (3-73) if the composition of only one substrate is varied at one time. A good discussion of such multisubstrate enzyme-catalyzed reactions is given by Plowman [K.M. Plowman, Enzyme Kinetics, McGraw-Hill Book Co., New York, NY, (1972)]. There is a strong family resemblance between these enzymatic sequences and those encountered in the detailed collision theory of Benson and Axworthy in Chapter 1. 

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