Competitive Inhibition in a Drug Development Lab
In a pharmacology teaching lab, students measure the initial velocity of a dehydrogenase at several substrate concentrations. Without inhibitor, Vmax is 120 nmol/min and Km is 4.0 mM. In the presence of 10 µM compound X, Vmax remains 120 nmol/min but Km rises to 12.0 mM. Compound X is being developed as an oral drug; after a 100 mg dose, the free plasma concentration peaks at 8 µM and the substrate concentration in target tissue is approximately 4 mM. A colleague proposes that because the inhibition is competitive, higher doses will always overcome it in patients.
1. Identify the inhibition type and calculate Ki. Show the calculation and interpret the Ki relative to the free drug concentration.
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Vmax is unchanged (120 nmol/min) while Km rises from 4.0 to 12.0 mM; this is competitive inhibition. For competitive inhibition, Km_app = Km(1 + [I]/Ki). 12 = 4(1 + 10/Ki), so 3 = 1 + 10/Ki, 2 = 10/Ki, and Ki = 5 µM. At the 100 mg dose, free peak is 8 µM, about 1.6 × Ki. At [S] = 4 mM without inhibitor, v = Vmax[S]/(Km + [S]) = 120 × 4/(4 + 4) = 60 nmol/min. With 8 µM inhibitor, Km_app = 4(1 + 8/5) = 10.4 mM, so v = 120 × 4/(10.4 + 4) = 33.3 nmol/min, a 44% reduction. This indicates meaningful target engagement at the proposed dose.
2. Evaluate the colleague's claim that higher substrate will always overcome competitive inhibition in vivo. Use the data and the tissue substrate concentration to predict the effect of doubling the dose to 200 mg (free peak about 16 µM).
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The claim is false in vivo. In vitro, raising [S] toward infinity can overcome competitive inhibition, but in a patient the tissue substrate concentration is set by physiology, not by the investigator. Here [S] is about 4 mM, equal to Km, so the enzyme is not substrate-saturated. At 200 mg, free peak is about 16 µM; Km_app = 4(1 + 16/5) = 16.8 mM; v = 120 × 4/(16.8 + 4) = 23.1 nmol/min, a 62% reduction versus 60 nmol/min without inhibitor. Doubling the dose only modestly increases inhibition and may add off-target toxicity. Higher substrate cannot be assumed. A better development question is whether the in vivo substrate concentration can rise enough to reverse inhibition, or whether a noncompetitive inhibitor would be more robust; that requires tissue pharmacokinetics and target-engagement studies, not just enzyme kinetics.