Steady-state kinetics Briggs-Haldane approach

Briggs-Haldane approach (Briggs and Haldane, 1925) The change of the intermediate concentration with respect to time is assumed to be negligible, that is, d(CES)/dt = 0. This is also known as the pseudo-steady-state (or quasi-steady-state I assumption in chemical kinetics and is often used in developing rate expressions in homogeneous catalytic reactions. 

In this section, we shall begin to see how the Briggs-Haldane steady state approach can be enlarged to derive steady state kinetics equations appropriate to more complex kinetic schemes. In doing this, there will be some pleasant surprises in that the form of these new steady state kinetic equations will follow the form of Michaelis-Menten equation (8.8) with a few adaptations not unlike those seen in the Uni Uni steady state kinetic scheme adapted to fit the presence of inhibitors (see Section 8.2.4). 

The next level of complexity is to review the situation of a single-substrate biocatalyst with a single catalytic site that is responsible for more than one product-forming/release step (a multiple-product situation). This scenario will be analysed by means of the Briggs-Haldane steady state approach with reference to the indicated Uni Bi kinetic scheme, where Uni refers to one substrate and Bi to the evolution of two products. Irreversibility is also assumed (Scheme 8.7). By analogy with the previous treatments above, we may derive two equations ... 

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. 

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