King-Altman procedure

By using the King-Altman procedure, derive the steady-state rate equation for the following enzyme mechanism ... 

Comparison of Different Steady-State Methods. For relatively simple mechanisms, all the diagrammatic and systematic procedures illustrated in the foregoing sections are quite convenient. The King-Altman method is best suited for single-loop mechanisms, but becomes laborious for more complex cases with five or more enzyme forms because of the work involved in the calculation and drawing of valid patterns. With multiloop reaction schemes involving four to five enzyme species, the systematic approach requires the least effort, especially... 

In Chapter 3 (Section 3.4), we have derived the rate law for the reversible Michaelis-Menten mechanism with two central complexes (Reaction (3.31)) with the aid of the steady-state roximation. We shall proceed now with the derivation of the same rate law with the aid of the King-Altman method. In order to apply the King-Altman method efficiently to a specific mechanism, a rigorous procedure must be strictly followed (Fromm, 1975 Wong, 1975 Punch Allison, 2000). 

A comparison of the derivation procedure for Eq. (3.36) described in Chapter 3 (Section 3.4) with the derivation procedure of the King-Altman method, clearly shows the advantage of the latter method. With increased complexity of mechanisms, the advantage of the King-Altman method increases dramatically. 

Cha (1968) has described a method for analyzing mechanisms that contain steps in equilibrium that is much simpler than the complete King-Altman andysis because each group of enzyme forms at equilibrium can be treated as a single species. Thus, the method of Cha provides for a condensation of King-Altman patterns and shortens considerably the procedure of derivatioa... 

Equations for the initial rate of isotope exchange in Ping Pong mechanisms may be derived by one of the methods described in Chapter 4 the usual procedure will be to apply the King-Altman method or the net rate constant method (Cleland, 1975) (Table 4). 

The Systematic Approach. The systematic approach for deriving rate equations was first devised by Fromm based on certain concepts advanced by Volkenstein and Goldstein. Its underlying principles, however, are more akin to the graphic method of King and Altman. The procedure to be described here is a modified method that includes the contributions from the aforementioned workers and from Wong and Hanes. ... 

A useful procedure for deriving steady-state rate expressions for enzyme-catalyzed reactions . Although not as commonly used as the King and Altman method, it is far more convenient (and less error-prone) when attempting to obtain expressions for complicated reaction schemes. One of its values is that the approach is very systematic and straightforward. The systematic nature of the procedure can be illustrated by the derivation of the steady-state ordered Bi Bi reaction. 

In principle, the steady-state rate expression for any enzyme with any number of reactants can be derived using the methods of the previous section. In practice, the procedure is very laborious, so use is made of an algorithmic method, introduced by King and Altman in 1956 it is not applicable to (1) nonenzymatic reactions (each reactant concentration must be S>[E]0), (2) mixtures of enzymes, or (3) reactions with nonenzymatic steps. However, these are not severe restrictions. It is applied as follows ... 

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