Question

Kcat =30.0 s-1

Km= 0.005 M

Operating at 1/4 Vmax

What is [S] ?

The solutions manuel doesn't explain the problem well. Whete does the 0.33 km come from?

For part 2 : Plug in [S]= 1/2 Km, 2 Km, and 10 Km

Where does the 1.5 Km come from?

Answer (a) Here we want to find the value of [S] when Vo = 0.25 V max. The Michaelis-Menten equation is V = Vmax[S]/(Km + [SD so V = Vmax when (SVK + (SD) = 0.25; or [S] = 0.33K = 0.33(0.0050 M) = 1.7 x 10-3 M (b) The Michaelis-Menten equation can be rearranged to V/V max = (S)/(Km + (SD) Substituting (S) = Km into the equation gives V/V max = 0.5 km/1.5K = 0.33 Similarly, substituting (S) = 2K gives Vo/V max = 0.67 And substituting (S) = 10Km gives V/Vmax = 0.91

Answer 1

Solution:

Part A)

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

1/4 Vmax = Vmax [S] / Km + [S]

0.25 = [S] / Km + [S]

Multiply by 4, we get,

1 = 4 [S] / Km + [S]

4 [S] = Km + [S]

3 [S] = Km

[S] = Km / 3 = 0.33 Km

[S] = 0.33 x 0.0050 M

[S] = 1.7 x 10^-3 M

Part B)

Vo/Vmax = [S] / (Km + [S] )

Substituting [S] = 1/2 Km = 0.5 Km

Vo/Vmax = Km / ( Km + 0.5 Km) = Km / 1.5 Km

Thus,

Vo/Vmax = Km / 1.5 Km = 0.33