Question

1. The hydration of carbon dioxide CO₂ in red blood cells takes place due to an enzyme catalytic process, where bicarbonate ions are formed:

CO₂(g) + H₂O(l) ® HCO₃^¯ (aq) + H⁺(aq)

At the enzyme concentration of [E]₀ = 2.3´10^-6 mol/L, the following kinetic data for initial reaction rate vs. initial concentration of carbon dioxide were obtained:

[CO2], mol/L	1.25	2.50	5.00	20.00
Rate, (mol/L)s-1	2.78´10-2	5.01´10-2	8.32´10-2	1.67´10-1

Determine the Michaelis constant and the turnover number of the catalytic process.

2. The enzyme a-chymotrypsin is secreted in the pancreas of mammals and cleaves peptide bonds made between certain amino acids. Several solutions containing the small peptide N-glutaryl-1-phenylalanine-p-nitroanilide (a substrate) at different concentrations were prepared and the same amount of a-chymotrypsin was added to each one. The following data were obtained on the initial rates of the formation of product:

[S]0, mol/L	0.334	0.450	0.667	1.00	1.33	1.67
Rate, (mol/L)s-1	0.152	0.201	0.269	0.417	0.505	0.667

Determine the maximum reaction rate and the Michaelis constant for the enzyme reaction.

Answer 1

1.

The plot of 1/ rate vs 1/ [CO2] is as shown

Rate CO21/[rate] 1/[CO2] 0.0278 0.0501 0.0832 0.167 40 35.971223 19.9600798 0.4 12.0192308 0.2 5.988023950.05 0.8 35 2.5 30 y 39.95x + 4 20 25 1/rate 20 Slope Intercept 4.000048 39.95749 15 10 0.2 0.4 0.6 0.8 1/[co2]

Y intercept $= \dfrac {1}{V_{max}}= 4$

Hence, the maximum reaction rate

$V_{max}= \dfrac {1}{4}= 0.25 \; (mol/L)s^{-1}$

Slope $= \dfrac {K_M}{V_{max}}$

$39.96= \dfrac {K_M}{0.25 \: (mol/L)s^{-1}}$

Hence, the Michaelis constant

$K_{cat} = \dfrac {V_{max}}{[E]_0}= \dfrac {0.25 \: (mol/L)s^{-1}}{2.3 \times 10^{-6 } \: mol/L}$