Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors
Professional Reference Shelf
Example R9.62: Derive an Initial Rate Law for Alcohol Dehydrogenates
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 

(RE7.42.1) 



Solution  
Let E = ADH, S_{1} = CH_{3}CHO, S_{2} = NADH, = NAD^{+}, and P_{1} = CH_{3}CH_{2}OH. 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 

(RE7.42.2) 

Application of the PSSH to the holoenzyme (ES_{2}) and the apoenzyme 

allows one to solve for the concentrations of the cofactorenzyme complexes in terms of S_{2}, S_{2}^{*}, and E. 

(RE7.42.3) 
The total concentration of bound and unbound enzyme is 

(RE7.42.5) 

Substituting Equations (RE7.42.3) and (RE7.42.4) into Equation (RE7.42.5), the unbound enzyme concentration is 

(RE7.42.6) 

Setting (P_{1}) = 0, we obtain the initial rate law by combining Equations (RE7.42.2), (RE7.42.4), and (RE7.42.6): 

(RE7.42.7) 
