Problems on enzyme reaction kinetics
1. Initial rates of enzyme-catalyzed reaction for various substrate concentrations are listed
below:
Rate
Substrate concentration
mol/(L min)x106
(mol/L)
177
0.0041
173
0.00095
125
0.00052
106
0.000103
80
0.000049
67
0.0000106
43
0.0000051
a)
b)
c)
Evaluate Vmax and Km by a Lineweaver-Burk plot.
Using the Eadie-Hofstee plot, evaluate Vmax and Km.
Plotting reaction rate and substrate concentration, find another estimate of Vmax and Km.
2. An enzyme with a Km of 1x10-3 M was assayed using an initial substrate concentration of
3x10-5 M. After 2 min, 5 percent of the substrate was converted. How much substrate will be
converted after 10, 30, and 60 min?
(Note: Solve using the integrated form of the Michaelis-Menton equation.)
3. Tyrosinase has a Km of 9.2 g/l. The reactant is -aminophenol. Acetone which acts as an
inhibitor, is present in the reaction mixture at a level of 1 g/l. The following data were obtained
in the presence of acetone. Is acetone competitive or uncompetitive? Explain? Calculate KI.
v (g/l-s)
0.909
0.658
0.493
0.400
0.333
0.289
0.227
[R] (g/l)
20
10
6.67
5
4
3.33
2.5
4. At very low reactant concentration, urea is hydrolysed as a first order reaction, where k is the
rate constant for the overall reaction. ESTIMATE the value of k for urease, given a Vmax of 4.6
moles-liter-1min-1 and a Km value of 2 x 10-6 M. What percentage of the urea is consumed each
second?
5. At 20oC, the rate of lactose hydrolysis with ß-galactosidase is 4.50 µmoles/min/mg. Determine
the rate of hydrolysis at 40oC. The activation energy (Ea) of ß-galactosidase is 11,534 cal/mole,
the Arrhenius constant (A) is 1.809 x 109 min-1 and R is 1.987 cal/moleK. Topt is >40oC.
6. Lactose intolerant people may be able to drink milk if the lactose level has been reduced. One
way to reduce or eliminate lactose is to treat the milk with lactase enzyme. Since lactase cannot
appear as a contaminant in the milk-product, the enzyme is immobilized by adsorption on
carboxy-methyl cellulose beads. The immobilized lactase beads are then loaded into a wellmixed reactor, and milk fed through the reactor on a continuous basis. Assume that the bead
loading is 10% of the total reactor operating volume, and that immobilization does not affect the
kinetic parameters for lactase. Determine the total reactor volume required to reduce lactose from
1 x 10-5 M in the fresh milk, to 9 x 10-6 M after a single pass through the reactor. The milk is fed
to the reactor at 0.5 L/min. Km and Vmax for lactase are 3.56 x 10-6 mole/L and 1.96 x 10-8
mole/Lmin respectively.