Question

The Michaelis-Menten equation is an expression of the relationship between the initial velocity,V0, of an enzymatic reaction and substrate concentration, [S]. There are three conditions that are useful for simplifying the Michaelis-Menten equation to an expression from which the effect of [S] on the rate can be more readily determined. Match the condition (e.g. [S] = Km) with the statement(s) that describe it:
1. Doubling [S] will almost double the rate.
2. Half of the active sites are occupied by substrate.
3. About 90% of the active sites are occupied by substrate.
4. Doubling [S] will have little effect on the rate.
5. Less than 10% of the active sites are occupied by substrate.
6. This condition will result in the highest rate.

Answer 1

Answer:

Option 2, Half of the active sites are occupied by substrate

Explanation:

Michaelis-Menten expression for enzyme catalysed equation is as follows:

$V_0=\frac{V_{max\ [S]}}{k_M+[S]}$

Here, $K_m$ is Michaelis-Menten constant and [S] is substrate concentration.

When [S]=Km

Rearrange the above equation as follows:

$V_0=\frac{V_{max}[S]}{k_M+[S]}\\V_0=\frac{V_{max}[S]}{[S]+[S]}\\V_0=\frac{V_{max}[S]}{2[S\\]}\\V_0=\frac{V_{max}}{2}$

when [S]=Km, the rate of enzyme catalysed reaction becomes half of the maximum rate, that means half of the active sites are occupied by substrate.

Therefore, the correct option is option 2.