Question

In Michaelis-Menten's equation, if \( [S] = 15 K_m \), then the ratio \( \frac{V_0}{V_{\text{max}}} \) is _______. (Round off to three decimal places)

Hint:

In enzyme kinetics, it's essential to understand how changes in substrate concentration relative to ( K_m ) affect the rate of reaction, particularly in assessing enzyme efficiency and behavior under near-saturating conditions.

Answer 1

The Michaelis-Menten equation is given by: \[ V_0 = \frac{V_{\text{max}} [S]}{K_m + [S]} \]

where:

• \( V_0 \) is the initial velocity,
• \( V_{\text{max}} \) is the maximum velocity,
• \( [S] \) is the substrate concentration,
• \( K_m \) is the Michaelis constant.

Given Condition: \[ [S] = 15 K_m \] Step 1: Substituting the given condition into the equation. \[ V_0 = \frac{V_{\text{max}} \times 15 K_m}{K_m + 15 K_m} = \frac{V_{\text{max}} \times 15 K_m}{16 K_m} = \frac{15}{16} V_{\text{max}} \] Step 2: Calculating the ratio \( \frac{V_0}{V_{\text{max}}} \). \[ \frac{V_0}{V_{\text{max}}} = \frac{15}{16} \approx 0.9375 \] Conclusion:

Explanation: At a substrate concentration of \( 15 K_m \), the reaction velocity approaches but does not reach \( V_{\text{max}} \), calculated to be 0.9375. This closely matches the expected range provided (approximately 0.93 to 0.95).