Question

Consider an enzyme that follows simple Michaelis-Menten kinetics, and has a $ 𝐾_𝑀 of 5 µ𝑀$. The initial velocity of the reaction will be 10% of the maximum velocity at a substrate concentration of µ𝑀 (rounded off to two decimal places).

Answer 1

Correct Answer: 0.54

For Michaelis-Menten kinetics, the initial velocity (\(v_0\)) at 10 is \( v_0 = 0.1 \cdot V_{\text{max}}\). The formula for the reaction velocity is:

\( v_0 = \frac{V_{\text{max}}[S]}{K_M + [S]}. \)

Setting \(v_0 = 0.1 V_{\text{max}}\) and solving for \([S]\):

\( 0.1 = \frac{[S]}{K_M + [S]}. \)

Substitute \(K_M = 5\):

\( 0.1 = \frac{[S]}{5 + [S]}, \)

\( 0.1(5 + [S]) = [S], \)

\( 0.5 + 0.1[S] = [S], \)

\( 0.5 = 0.9[S], \)

\( [S] = \frac{0.5}{0.9} = 0.556 \mu \text{M}. \)