For which one of the following enzyme activity plots, will the K$_m$ of the enzyme for substrate ‘S' be 20? [S] indicates substrate concentration.
Show Hint
To quickly find $K_m$ from a Michaelis-Menten plot:
1. Look at the flat top value ($V_{max}$).
2. Cut it in half.
3. Go horizontally from that half-value on the y-axis to the curve, and then look straight down to read the concentration on the x-axis.
Step 1: Understanding the Concept:
The Michaelis constant ($K_{m}$) is the substrate concentration $[S]$ at which the reaction velocity ($V$) is exactly half of the maximum velocity ($V_{max}$). Key Formula or Approach:
Identify $V_{max}$ from the plateau of the curves and then find the corresponding $[S]$ for $V = V_{max}/2$. Step 2: Detailed Explanation:
$\bullet$ In all four provided plots, the horizontal dashed line representing $V_{max}$ is at $V = 16$.
$\bullet$ Therefore, $V_{max}/2 = 16 / 2 = 8$.
$\bullet$ We need to find the plot where the curve crosses $V = 8$ at the point where the x-axis value $[S] = 20$.
$\bullet$ Plot (a): At $[S] = 20$, the velocity $V$ is exactly 8. This satisfies $K_{m} = 20$.
$\bullet$ Plot (b): At $[S] = 20$, $V$ is around 4. The velocity 8 is reached at $[S] = 40$. Thus $K_{m} = 40$.
$\bullet$ Plot (c): At $[S] = 20$, the velocity is already near 16. $V = 8$ is reached at a much lower concentration (approx $[S] = 5$).
$\bullet$ Plot (d): The curve is sigmoidal and doesn't reach $V = 8$ until well past $[S] = 20$. Step 3: Final Answer:
Only Plot (a) shows $V_{max}/2$ at $[S] = 20$.
This corresponds to option (A).
