Calculate the Km of an enzyme using Michaelis-Menten kinetics if the forward rate constant for ES formation is 4.3 x 10⁶ M^-1s^-1, the reverse rate constant for ES dissociation into E + S is 2.4 x 10² s^-1, and the forward rate constant for ES dissociation into E + P is 1.2 x 10 ³ s^-1.

• A. 3.35 x 10^-4 M^-1.
• B. 3.58 x 10³ M.
• C. 3.85 x 10³ M^-1.
• D. 3.35 x 10^-4 M.

Answer: (D)

Verified step by step guidance

1. Understand that Km, the Michaelis constant, is a measure of the substrate concentration at which the reaction rate is half of its maximum value. It is calculated using the rate constants of the enzyme-catalyzed reaction.
2. The formula to calculate Km using the rate constants is: \( K_m = \frac{k_{-1} + k_{2}}{k_{1}} \), where \( k_{1} \) is the forward rate constant for ES formation, \( k_{-1} \) is the reverse rate constant for ES dissociation into E + S, and \( k_{2} \) is the forward rate constant for ES dissociation into E + P.
3. Substitute the given values into the formula: \( k_{1} = 4.3 \times 10^{6} \text{ M}^{-1}\text{s}^{-1} \), \( k_{-1} = 2.4 \times 10^{2} \text{ s}^{-1} \), and \( k_{2} = 1.2 \times 10^{3} \text{ s}^{-1} \).
4. Calculate the numerator of the Km formula: \( k_{-1} + k_{2} = 2.4 \times 10^{2} + 1.2 \times 10^{3} \).
5. Divide the result from the previous step by \( k_{1} \) to find Km: \( K_m = \frac{2.4 \times 10^{2} + 1.2 \times 10^{3}}{4.3 \times 10^{6}} \).