Exercise 10.2 The hydration of CO2 is catalyzed by the enzyme carbonic anhydrase

Question

Exercise 10.2 The hydration of CO2 is catalyzed by the enzyme carbonic anhydrase. The steady-state kinetics of the forward (hydration) and reverse (dehydration) reactions at pH 7.1, 0.5 C, and 2 mM phosphate buffer was studied using bovine carbonic anhydrase (H. DeVoe and G. B. Kistiakowsky, 1961, J. Am. Chem. Soc. 83:274). Some typical results for an anzyme concentration of 2.3 nM are Hydration Dehydration 36 X 103 20 X103 12 X 103 6×103 95 X103 45 X 103 29 X 103 24 X 103 1.25 2.5 10 20 15 Plot the data in an appopriate way and determine Part A the Michaelis constant KM for the decomposition of the enzyme-substrate complex to form product for the hydration reaction Express your answer using two significant figures. K1.1.10 mM Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B

Explanation / Answer

Part A:

For the hydration of H2CO3 (i.e. S), the data can be tabulated as shown below.

The equation for the Line-Weaver Burke plot can be written as shown below.

1/v0 = 40*1/[S]0 + 4

By comparing the above equation with the 1/v0 = (KM/vmax)*1/[S]0 + 1/vmax, you will get

1/vmax = 4 mM-1 s and KM/vmax = 40

i.e. KM*4 = 40

i.e. KM = 10 mM

Part B:

Formula: k2 = vmax/[E]0, where [E]0 is the initial concentration of enzyme

Here, vmax = 1/4 mM s-1 and [E]0 = 2.3 nM

i.e, k2 = (1/4) mM s-1 / 2.3*10-6 mM (since 1nM = 10-6 mM)

i.e. k2 = 1.087*105 s-1

Part C:

For the dehydration of HCO3- (i.e. S), the data can be tabulated as shown below.

The equation for the Line-Weaver Burke plot can be written as shown below.

1/v0 = 164.4*1/[S]0 + 12.6

By comparing the above equation with the 1/v0 = (KM/vmax)*1/[S]0 + 1/vmax, you will get

1/vmax = 12.6 mM-1 s and KM/vmax = 164.4

i.e. KM*12.6 = 164.4

i.e. KM ~ 13 mM

Part D:

Formula: k2 = vmax/[E]0, where [E]0 is the initial concentration of enzyme

Here, vmax = 1/12.6 mM s-1 and [E]0 = 2.3 nM

i.e, k2 = (1/12.6) mM s-1 / 2.3*10-6 mM (since 1nM = 10-6 mM)

i.e. k2 = 3.445*104 s-1

S. No. 1/[S]0 (in mM-1) 1/v0 (in mM-1 s) 1 1/1.25 = 0.8 36 2 1/2.5 = 0.4 20 3 1/5 = 0.2 12 4 1/20 = 0.05 6

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