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

The Michaelis-Menten equation relates the initial velocity of an enzymatic reaction to substrate concentration. Conditions involving the ratio of substrate concentration to the Michaelis constant (Km) can simplify the interpretation of the equation. These conditions include [S] = Km (half active sites occupied), [S] << Km (less than 10% occupancy increases rate significantly), and [S] >> Km (90% occupancy, further increases in [S] have little effect on the rate).

Step-by-step explanation:

Understanding the Michaelis-Menten Equation in Relation to Substrate Concentration:

The Michaelis-Menten equation describes the relationship between the initial velocity (V0) of an enzymatic reaction and the substrate concentration ([S]). The equation is represented by V = Vmax[S] / (Km + [S]), where Vmax is the maximum initial reaction velocity and Km is the Michaelis constant—a measure of the affinity between an enzyme and its substrate.

Under specific conditions that involve substrate concentration ([S]) relative to the Michaelis constant (Km), we can simplify the Michaelis-Menten equation to infer the effect of [S] on the reaction rate:

• When [S] = Km, it leads to the condition where V = 1/2Vmax. This implies that half of the active sites are occupied by substrate, corresponding to statement 2.
• When [S] << Km, a small increase in [S] will significantly increase the reaction rate, since less than 10% of the active sites are occupied. This matches with statement 5 and indicates that doubling [S] will almost double the rate, in line with statement 1.
• Conversely, when [S] >> Km, the enzyme active sites are nearly all occupied, leading to approximately 90% saturation. At this stage, further increases in [S] will have little effect on the rate (statement 4), as the reaction approaches Vmax and is thus running at the highest rate possible, linking to statement 6.

Through the Michaelis-Menten equation, we are able to determine the efficiency and binding affinity of an enzyme based on its Km value. A lower Km indicates stronger affinity, whereas a higher Km suggests weaker affinity.