The Michaelis–Menten equation is an expression of the relationship between the initial velocity 0 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 or statements 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.

(2) Half of the active sites are occupied by substrate.

Explanation:

The Michaelis–Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction.  It is an expression of the relationship between the initial velocity V₀ of an enzymatic reaction, the maximum velocity Vmax, and substrate concentration [S] which are all related through the Michaelis constant, Km.

Mathematically, the Michaelis–Menten equation is given as:

V₀ = Vmax[S]/Km + [S]

A special relationship exists between the Michaelis constant and substrate concentration when the enzyme is operating at half its maximum velocity, i.e. at V₀ = Vmax/2

substituting, Vmax/2 = V₀ in the Michaelis–Menten equation

Vmax/2 = Vmax[S]/Km + [S]

dividing through with Vmax

1/2 = [S]/Km + [S]

2[S] = Km + [S]

2[S] - [S] = Km

[S] = Km

Therefore, when the enzyme is operating at half its maximum velocity, i.e. when half of the active sites are occupied by substrate, [S] = Km

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