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		Example CD7-3 Derive a Rate Law For Competitive Inhibition
		Show that the rate law for the mechanism in Equation (CD7-10) involving competitive inhibition, is
			(CD7-11)
		where I is the inhibitor concentration and rp is the rate of formation of product P. [Hint: Apply the pseudo-steady-state hypothesis to (ES) and (IE).]
		Solution
		The rate of formation of product P corresponding to the last step in this reaction sequence is
			(CDE7-3.1)
		The uncomplexed or free enzyme concentration is
			(CDE7-3.2)
		Using the pseudo-steady-state approximation for the enzyme-substrate complex yields

(CDE7-3.3)

(CDE7-3.4)

 

		Dividing Equation by k1(S) and Equation (CDE7-3.4) by k3(I) and rearranging each, we obtain
			(CDE7-3.5) (CDE7-3.6)
		Subtracting Equation (CDE7-3.5) from (CDE7-3.6) and solving for EI, we find that
			(CDE7-3.7)
		After substituting Equation (CDE7-3.7) into (CDE7-3.5) to solve for ES,
			(CDE7-3.8)
		we substitute for ES in Equation (CDE7-3.1) to obtain the rate law for the inhibition of the competitive type:
			(CD7-11)
		WHERE
		Letting= Km(1 + I/K i), we see that the effect of a competitive inhibitor is to increase the apparent Michaelis constant,.