Briggs-Haldane steady state approach

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 ... 

Today, this synonym is used for the more common steady-state approach by Briggs and Haldane (see [17]). 

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. 

Briggs- Haldane Approach In this approach, the concentration of the intermediate is assumed to attain a steady-state value shortly after the start of a reaction (steady state approximation) that is, the change of with time becomes nearly zero [3]. 

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 the second approach, formulated by Briggs and Haldane, the formation of the complex A-E does not necessarily reach equilibrium, but its concentration is eliminated by applying the pseudo steady state approximation... 

Michaelis and Menten derived their rate law in 1913 in a more restrictive way. by assuming a rapid equilibrium. The approach we take is a generalization using the steady-state approximation made by Briggs and Haldane in 1925. 

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. 

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