Reversible Mechanism with One Central Complex

AH enz5nnatic reactions are in principle reversible, in a sense that significant amounts of both substrates and products exist in the equilibrium mixture (Albeity, 1959 Cleland, 1970 Plowman, 1972). Therefore, it is evident that both Michaehs-Menten and Briggs-Haldane mechanisms are incomplete, and that allowance must be made for the reverse reaction  

The net rate of formation of product P is the difference between the forward and reverse reactions  

Substitution forXin this expression gives the rate law for reaction (3.20)  

This equation is the general reversible form of the Michaelis-Menten equation. If the enzymatic reaction is completely reversible, it can be started by mixing the substrate with the enzyme, or vice versa, by mixing the product with the enzyme. In the former case, P=o, and Eq. (3.27) reduces to the Michaelis-Menten equation in the forward direction  

In the latter case, A = o, and Eq. (3.27) reduces to the Michaelis-Menten equation in the reverse direction  

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Reversible Michaehs-Menten mechanisms provide us with another useful general relationships, the enzyme distribution equations. Since many enzymatic reactions are fully reversible, immediately after mixing the enzyme with the substrate, or vice versa, after mixing the substrate with the enzyme, the steady-state concentration of all forms of enzyme is established. In the reversible mechanism with one central complex, the enzyme is divided among two forms ... 

Now, we can cast the enzyme distribution equations in terms of all individual rate constants for both kinetic mechanisms. In the reversible mechanism with one central complex, the enzyme distribution equations are... 

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