Question

In Michaelis-Menten kinetics what value of [S], as a fraction of $K_{m}$, is required to obtain a velocity equal to 80% $V_{max}$?

• A. $2 K_{m}$
• B. $4 K_{m}$
• C. 0.8 $K_{m}$
• D. $K_{m}$

Hint:

Quick ratio: For $v = \frac{n}{m} V_{max}$, $[S] = \frac{n}{m-n} K_{m}$. Here: $80% = 4/5$, so $[S] = \frac{4}{5-4} K_{m} = 4 K_{m}$.

Answer 1

The Correct Option is B

Step 1: Concept
The Michaelis-Menten equation is $v = \frac{V_{max}[S]}{K_{m} + [S]}$.

Step 2: Meaning
We are given $v = 0.8 V_{max}$. We need to find $[S]$ in terms of $K_{m}$.

Step 3: Analysis
Substitute the values:
$0.8 V_{max} = \frac{V_{max}[S]}{K_{m} + [S]}$
$0.8 = \frac{[S]}{K_{m} + [S]}$
$0.8(K_{m} + [S]) = [S]$
$0.8 K_{m} + 0.8[S] = [S]$
$0.8 K_{m} = 0.2[S]$
$[S] = \frac{0.8}{0.2} K_{m} = 4 K_{m}$.

Step 4: Conclusion
To reach 80% of maximum velocity, the substrate concentration must be 4 times the $K_{m}$. Final Answer: (B)