Quasi-Equilibrium Treatment of Random Reactions

The steady-state kinetic treatment of random reactions is complex and gives rise to rate equations of higher order in substrate and product terms. For kinetic treatment of random reactions that display the Michaelis-Menten (i.e. hyperbolic velocity-substrate relationship) or linear (linearly transformed kinetic plots) kinetic behavior, the quasi-equilibrium assumption is commonly made to analyze enzyme kinetic data. 

Write the initial velocity expression v = k[EAB] - k [EPQ] where the interconversion between the ternary complexes is associated with the rate constants, k and k in the forward and reverse directions respectively. 

The random addition of substrates, A and B forms binary (EA and EB) and ternary (EAB) complexes. The two ternary complexes, EAB and EPQ interconvert with the rate constant of k and k. The release of products, P and Q also proceeds in a random manner via binary complexes (EP and EQ). K s are dissociation constants where K,Kab = KbKb. and KpKp, = K,K, . 

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