Linear Formalism Enzyme kinetics

Investigations with the graphs of non-linear mechanisms had been stimulated by an actual problem of chemical kinetics to examine a complex dynamic behaviour. This problem was formulated as follows for what mechanisms or, for a given mechanism, in what region of the parameters can a multiplicity of steady-states and self-oscillations of the reaction rates be observed Neither of the above formalisms (of both enzyme kinetics and the steady-state reaction theory) could answer this question. Hence it was necessary to construct a mainly new formalism using bipartite graphs. It was this formalism that was elaborated in the 1970s. 

Many of the subsequent developments in enzyme kinetics share the same basic postulates of Michaelis-Menten kinetics. Although the mechanisms and equations may be different in detail, they all lead to rate laws that are linear functions of enzyme concentration and rational functions of the reactant and modifier concentrations. Hence, all these developments are based upon the same underlying formalism, which I shall refer to as the Michaelis-Menten Formalism. 

As has already been shown, graph theory methods were first used in chemical kinetics by King and Altman who applied them to linear enzyme mechanisms [1] to derive steady-state kinetic equations. Vol kenshtein and Gol dshtein in their studies during the 1960s [2 1] also elaborated a new formalism for the derivation of steady-state kinetic equations based on graph theory methods ("Mason s rule , etc.). 

The Michaelis-Menten Formalism did not anticipate the type of enzyme-enzyme organization described above. One of its fundamental assumptions has been that complexes do not occur between different forms of an enzyme or between different enzymes (Segal, 1959 Webb, 1963 Cleland, 1970 Segel, 1975 Wong, 1975). From the derivation of the classical Michaelis-Menten rate law, it can be seen that such complexes must be excluded or they will destroy the linear structure of the kinetic equations. 

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