Diagnostics of rapid equilibrium systems

In rapid equilibrium systems, the Haldane relationship can be obtained directly from rate equations. In equilibrium, the rate equation for the Rapid Equilibrium Ordered Bi Bi system (Eq. (8.12)), becomes 

for the Rapid Equilibrium Ordered Bi Bi system, the Haldane relationship is 

The Haldane relationship is identical for all rapid equilibrium random systems (Haldane, 1930 Cleland, 1982). Thus, from Eq. (8.37), one also obtains 

The derivation of velocity equations for the rapid equilibrium systems is very simple indeed, as already pointed out in Chapter 4 (Section 4.1), because all forms of enzyme are in a rapid equilibrium with each other and the slowest process is the chemical reaction between the central complexes. 

In the general case, the Rapid Equilibrium Random Bi Bi system with both dead-end complexes ElAP and EBQ (Reaction (8.35)), the denominator of the rate equation has nine terms, each for one form of enzyme the unity represents the free enzyme (Eq. (8.37)). From the general rate Eq. (8.37), one can write down directly the rate equations for all other possible combinations of the Rapid Equilibrium Random Bi Bi system. 

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