Enzyme Briggs-Haldane approach

This expression by Briggs-Haldane is similar to Equation 3.28, obtained by the Michaelis-Menten approach, except that Km is equal to (k 1+k2)/k1. These two approaches become identical, if k 1 k2, which is the case of most enzyme reactions. 

Perusal of the physicochemical chapters of textbooks on physiology and biochemistry, published up to the 1950s, reveals an overwhelming concern with the analysis of equilibria. This interest in the presentation of detailed and useful accounts of ionic processes and the energy balance of metabolic pathways left little space for attention to rate processes. Briggs Haldane (1925) introduced the steady state treatment of simple enzyme reactions, as opposed to the earlier, unrealistic, equilibrium approach (see section 3.3). Since then, and especially from the 1950s onwards, there has been more appreciation of the fact that cellular processes are in a constant state of flux or are in a steady state. Individual reactions may be at or near equilibrium, but for the cell as a whole equilibrium is death. 

The derivation mathematics are detailed in many publications dealing with enzyme kinetics. The Michaelis-Menten constant is, however, due to the individual approximation used, not always the same. The simplest values result from the implementation of the equilibrium approximation in which represents the inverse equilibrium constant (eqn (4.2(a))). A more common method is the steady-state approach for which Briggs and Haldane assumed that a steady state would be reached in which the concentration of the intermediate was constant (eqn (4.2(b))). The last important approach, which should be mentioned, is the assumption of an irreversible formation of the substrate complex [k--y = 0) (eqn (4.2(c))), which is of course very unlikely. In real enzyme reactions and even in modelled oxo-transfer reactions, this seems not to be the case. 

One may postulate isomerisations of EA preceding the release of products, but the basic point is that a specific, stoichiometric enzyme-substrate complex is formed. This fact is now so totally taken for granted by biochemists that it is easy to forget that its establishment was the first major milestone in enzyme kinetics. The analysis of Scheme 1 by Brown [1] and Henri [2] and subsequently by Michaelis and Men ten [3] and Briggs and Haldane [4] provided an explanation of the previously puzzling observation that the rate of a typical enzyme reaction plotted as a function of substrate concentration increases asymptotically to a maximum (Fig. 1). In Scheme 1 the overall rate of the catalysed reaction, i.e. of product formation, is proportional to [EA]/([E]-h [EA]), the fraction of the total enzyme present as the productive complex EA at low substrate concentration this fraction is proportional to [A], whereas at high substrate concentration the fraction approaches 1, and the rate is then limited only by the rate constant for conversion of EA to E + products. 

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