Rate Equations in Coefficient Form

Let us compare the rate laws for the two reversible Michaelis-Menten mechanisms ((3.20) and (3.31)), that is, Eq. (3.24) with Eq. (3.36). We can rewrite both equations in a more general form, using the kinetic coefficients in a manner of Cleland (1963)  

The use of coefficients may be of only marginal help in making Eqs. (3.24) and (3.36) less formidable however, this nomenclature is of immense help in more complex cases, particularly with multisubstrate reactions. 

one can see that, in both cases, the catalytic constants can be cast in a more general form  

Relationships similar to Eqs. (3.44)-(3.48) are applicable not only to mechanisms (3.20) and (3.31) but also to any other monosubstrate or multisubstrate mechanism. Therefore, with the help of coefficients from an appropriate rate law, one can write the equations for aU Idnetic constants in terms of rate constants for almost any kinetic mechanism. 

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