Rapid Equilibrium Ordered bisubstrate mechanism

This rate equation is identical to that for a rapid equilibrium ordered addition bisubstrate mechanism (/.c., a scheme where substrate A rapidly binds prior to the addition of the second substrate B). Huang has presented the theoretical basis for mechanisms giving rise to... 

The intersecting pattern for an Ordered bisubstrate mechanism in Fig. 1 (left) will also be obtained with a Rapid Equilibrium bisubstrate mechanism in each case, an intersecting point may be above, below, or on the axis. 

The Rapid Equilibrium Ordered Bi Bi system (Section 8.2) is a limiting case of the more realistic Steady-State Ordered Bi Bi system (Section 9.2). In bisubstrate mechanisms, the two approaches yield different velocity equations. As described... 

In an ordered bisubstrate mechanism one must vary the second substrate, B, and determine V/JSTb, regardless of whether the label is in A or B, since ly AwiU not show an isotope effect. For a random mechanism one must vary both A and B, since one may see different isotope effects on VfK and V/Aa, a distinction that may help to characterize the mechanism. The effects onV/K and V/Aa shouldbe different when one or both substrates are sticky, that is, dissociate more slowly from the enzyme than they react to give products. The substrate with the lower V7A is the sticky one. Larger effects on Vthan on either V7A show that both substrates are sticky smaller ones show that a slow step follows release of the first product. A rapid equilibrium random mechanism will show equal isotope effects on V, V/Ab, and F/Aa, aU larger than unity. 

This example clearly shows that completely randomized steady-state bisubstrate reactions wiU produce extremely complex rate equations which are, in most cases, unmanageable and almost useless for practical purposes. Thus, for example, the rate equation for an Ordered Bi Bi mechanism has 12 terms in the denominator (compare Eq. (9.8)). A completely Random Bi Bi mechanism yields an even more comphcated rate equation with 37 new terms in the denominator. Eor this reason, and in such cases, we shah usuahy revert to simplifying assumptions, usually introducing the rapid equilibrium segments in the mechanism in order to reduce the rate equations to manageable forms. 

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