Question

For an enzyme following Michaelis-Menten kinetics, when \([S]=K_M\) then, the velocity v is 
([S] is substrate concentration, \(K_M\) is Michaelis constant, \(V_{max}\) is maximal velocity)

• A. \([S] \times V_{max}\)
• B. \(0.75\times V_{max}\)
• C. \(0.5\times V_{max}\)
• D. \(K_M\times V_{max}\)

Answer 1

The Correct Option is C

To determine the velocity \( v \) when the substrate concentration \([S]\) is equal to the Michaelis constant \( K_M \) for an enzyme following Michaelis-Menten kinetics, we use the Michaelis-Menten equation:

\(v = \frac{V_{max} \cdot [S]}{K_M + [S]}\)

Given that \([S] = K_M\), we substitute into the equation:

\(v = \frac{V_{max} \cdot K_M}{K_M + K_M}\)

Simplify the equation:

\(v = \frac{V_{max} \cdot K_M}{2K_M}\)

Cancel \( K_M \) from the numerator and the denominator:

\(v = \frac{V_{max}}{2}\)

Thus, when \([S] = K_M\), the velocity \( v \) is:

\(v = 0.5 \times V_{max}\)

The correct answer is \(0.5\times V_{max}\)