Many drugs function by acting as inhibitors of particular enzyme reactions.

Many drugs function by acting as inhibitors of particular enzyme reactions. If an enzyme’s Vmax is 15 units/min/mg protein, with a Km of 1.25 µM in the absence of inhibitor, but in the presence of 5 µM inhibitor the Vmax is 6 units/min/mg protein, with the same Km, what is the velocity of the reaction in the presence of 5 µM inhibitor at a substrate concentration of 2.50 µM? (A) 2 units/min/mg protein (B) 4 units/min/mg protein (C) 6 units/min/mg protein (D) 8 units/min/mg protein (E) 10 units/min/mg protein

The Correct Answer and Explanation is:

To solve this problem, we use the Michaelis-Menten equation: v=Vmax⁡[S]Km+[S]v = \frac{V_{\max} [S]}{K_m + [S]}

Where:

• vv is the reaction velocity,
• Vmax⁡V_{\max} is the maximum velocity,
• [S][S] is the substrate concentration,
• KmK_m is the Michaelis constant.

Given:

• In the presence of inhibitor:
  • Vmax⁡=6V_{\max} = 6 units/min/mg protein
  • Km=1.25 μMK_m = 1.25 \, \mu M
• Substrate concentration, [S]=2.50 μM[S] = 2.50 \, \mu M

Step-by-step Calculation:

v=6×2.501.25+2.50=153.75=4 units/min/mg proteinv = \frac{6 \times 2.50}{1.25 + 2.50} = \frac{15}{3.75} = 4 \, \text{units/min/mg protein}

Correct Answer:

(B) 4 units/min/mg protein

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Explanation

Many drugs inhibit enzymes to regulate biochemical pathways. These inhibitors can be classified by their effects on enzyme kinetics, especially on two key parameters: Vmax⁡V_{\max} and KmK_m.

The Michaelis-Menten equation models how reaction rate depends on substrate concentration. In this problem, the enzyme exhibits a Vmax⁡V_{\max} of 15 units/min/mg protein and a KmK_m of 1.25 µM under normal conditions. When 5 µM of an inhibitor is added, the Vmax⁡V_{\max} drops to 6 units/min/mg protein, but KmK_m remains unchanged.

A constant KmK_m indicates that the affinity of the enzyme for the substrate is unaffected. This suggests the inhibitor is likely non-competitive, binding to an allosteric site rather than the active site. Non-competitive inhibitors reduce the overall number of functional enzymes, lowering Vmax⁡V_{\max}, but not altering substrate binding (KmK_m).

To calculate the reaction rate at a substrate concentration of 2.50 µM, we apply the Michaelis-Menten equation using the inhibited Vmax⁡V_{\max} (6 units/min/mg protein) and the unchanged KmK_m (1.25 µM). The result: v=6×2.51.25+2.5=153.75=4 units/min/mg proteinv = \frac{6 \times 2.5}{1.25 + 2.5} = \frac{15}{3.75} = 4 \, \text{units/min/mg protein}

Thus, the reaction velocity under these inhibited conditions is 4 units/min/mg protein, matching choice (B).

This analysis highlights how enzyme inhibitors affect reaction kinetics and how mathematical modeling helps understand drug actions at the molecular level.