Before considering the possibility of going directly from the apoenzyme to the holoenzyme, assume that the rate of dissociation of the complex (ADHNAD⁺),

is irreversible, and show that the initial rate law for ethanol in the enzyme cofactor reaction sequence discussed earlier is of the form

(RE7.4-2.1)

Let E = ADH, S₁ = CH₃CHO, S₂ = NADH, = NAD⁺, and P₁ = CH₃CH₂OH. Then

By adding the rate law for the rate of formation of ethanol (P ₁),

to the equation for(below), we see that the rate law for ethanol can be written as

(RE7.4-2.2)

Application of the PSSH to the holoenzyme (ES₂) and the apoenzyme
(E)

allows one to solve for the concentrations of the cofactor-enzyme complexes in terms of S₂, S₂^*, and E.

(RE7.4-2.3)



(RE7.4-2.4)

The total concentration of bound and unbound enzyme is

(RE7.4-2.5)

Substituting Equations (RE7.4-2.3) and (RE7.4-2.4) into Equation (RE7.4-2.5), the unbound enzyme concentration is

(RE7.4-2.6)

Setting (P₁) = 0, we obtain the initial rate law by combining Equations (RE7.4-2.2), (RE7.4-2.4), and (RE7.4-2.6):

(RE7.4-2.7)