enzyme and enzyme kinetics
DESCRIPTION
enzyme and enzyme kineticsTRANSCRIPT
AUSTRIA, BABYLYN C. ChE - 5201
11 – 93498 BIOCHEMICAL ENGINEERING
PROBLEMS IN ENZYME KINETICS
PROBLEM #1:
Relation between Reaction Velocity and Substrate Concentration: Michaelis-
Menten Equation
a) At what substrate concentration will an enzyme with 𝑘𝑐𝑎𝑡 of 30 s-1 and a 𝐾𝑚 of
0.005 show one-quarter of its maximum rate?
b) Determine the fraction of 𝑉𝑚𝑎𝑥 that would occur at the following substrate
concentrations:[𝑆] =1
2𝐾𝑚, 2𝐾𝑚, and 10𝐾𝑚.
Answers:
a) Since 𝑉𝑜 =𝑉𝑚𝑎𝑥[𝑆]
𝐾𝑚+[𝑆] and 𝑉𝑜 = 0.25(30 𝑠−1), = 7.5𝑠−1, we can substitute into the
Michaelis-Menten equation to give
𝑉𝑜 =𝑉𝑚𝑎𝑥[𝑆]
𝐾𝑚 + [𝑆]
7.5 𝑠−1 =30 𝑠−1[𝑆]
5𝑚𝑀 + [𝑆]
[𝑆] = 1.7 𝑚𝑀 = 1.7 𝑥 10−3 𝑀
b) We can arrange the Michaelis-Menten equation into the form
𝑉𝑜
𝑉𝑚𝑎𝑥=
[𝑆]
𝐾𝑚 + [𝑆]
Substituting [𝑆] =1
2𝐾𝑚 into this equation gives
𝑉𝑜
𝑉𝑚𝑎𝑥= 0.33
Substituting [𝑆] = 2𝐾𝑚 into this equation gives 𝑉𝑜
𝑉𝑚𝑎𝑥= 0.67
Substituting [𝑆] = 10𝐾𝑚 into this equation gives 𝑉𝑜
𝑉𝑚𝑎𝑥= 0.91
PROBLEM #2:
Properties of an Enzyme of Prostaglandin Synthesis
Prostaglandins are a class of eicosanoids, fatty acid derivatives with a variety of
extremely potent actions on vertebrate tissues. Prostaglandins are responsible for
producing fever and inflammation and its associated pain. They are derived from the 20-
carbon fatty acid arachidonic acid in reaction catalyzed by the enzyme prostaglandin
endoperoxide synthase. This enzyme, a cyclooxygenase, uses oxygen to convert
arachidonic acid to PGG2, the immediate precursor of many different prostaglandins.
a) The kinetic data given below are for the reaction catalyzed by prostaglandin
endoperoxide synthase. Focusing here on the two columns, determine the
𝑉𝑚𝑎𝑥 and 𝐾𝑚 of the enzyme.
Arachidonic
Acid (mM)
Rate of Formation of PGG2
(mW/min)
Rate of Formation of PGG2
with 10 mg/mL ibuprofen
(mW/min)
0.5 23.5 16.67
1.0 32.2 25.25
1.5 36.9 30.49
2.5 41.8 37.04
3.5 44.0 38.91
b) Ibuprofen is an inhibitor of prostaglandin endoperoxide synthase. By inhibiting the
synthesis of prostaglandins, ibuprofen reduces inflammation and pain. Using the
data in the first and third columns of the table, determine the type of inhibition that
ibuprofen exerts on the prostaglandin endoperoxide synthase.
Answers:
a) Calculate the reciprocal values for the data, as in parentheses below, and prepare
a double-reciprocal plot to determine the kinetic parameters.
[S] (mM) (1/[S]
(mM-1))
𝑽𝒐 (mM/min)
(𝟏/𝑽𝒐 (min/mW))
𝑽𝒐 with 10 mg/mL
ibuprofen(mM/min)
(𝟏/𝑽𝒐 (min/mW))
0.5 (2.0) 23.5 (0.043) 16.67 (0.06)
1.0 (1.0) 32.2 (0.0321) 25.25 (0.0396)
1.5 (0.67) 36.9 (0.027) 30.49 (0.0328)
2.5 (0.4) 41.8 (0.024) 37.04 (0.027)
3.5 (0.27) 44.0 (0.023) 38.91 (0.0257)
From the graph,
𝑉𝑚𝑎𝑥 = 51.55 mM/min
𝐾𝑚 = 0.598 mM
Solving for 𝑉𝑚𝑎𝑥 and 𝐾𝑚 using linear regression:
1
𝑉=
𝐾𝑚
𝑉𝑚𝑎𝑥(
1
𝑆) +
1
𝑉𝑚𝑎𝑥
𝑦 = 𝑚𝑥 + 𝑏
where =1
𝑣 , 𝑥 =
1
𝑆 , and 𝑚 =
𝐾𝑚
𝑉𝑚𝑎𝑥
Using the linear regression, the following values are obtained:
A = b = 0.019371
B = m = 0.011604
Substituting the values of b and m to solve for 𝑉𝑚𝑎𝑥 and 𝐾𝑚:
𝐴 =1
𝑉𝑚𝑎𝑥
0.019371 = 1
𝑉𝑚𝑎𝑥
𝑉𝑚𝑎𝑥 = 51.6245 mM/min
and, 𝑚 =𝐾𝑚
𝑉𝑚𝑎𝑥
0.011604 =𝐾𝑚
51.6245
𝐾𝑚 = 0.59907 𝑚𝑀
b) Ibuprofen acts as a competitive inhibitor. The double reciprocal plot (with inhibitor)
shows that, in the presence of ibuprofen, the 𝑉𝑚𝑎𝑥 of the reaction is unchanged
(the intercept on the the 1/𝑉𝑜 axis is the same) and 𝐾𝑚 is increased (1/𝐾𝑚 is closer
to the origin).
PROBLEM #3:
Determination of 𝑲𝒎
An enzyme is discovered that catalyzes the chemical reaction
SAD HAPPY
A team of motivated researchers set out to study the enzyme, which they call
happyase. They find that the 𝑘𝑐𝑎𝑡 for happyase is 600𝑠−1. They carry out several
experiments.
When [𝐸𝑡] = 20 𝑛𝑀 and [𝑆𝐴𝐷] = 40 µ𝑀, the reaction velocity, 𝑉𝑂, is 9.6 µMs-1.
Calculate 𝐾𝑀 for the substrate SAD.
Answer:
We know 𝑘𝑐𝑎𝑡, [𝐸𝑡], [𝑆], and [𝑉𝑂]. We want to solve for 𝐾𝑀. Substituting the
known values allows us to solve for 𝐾𝑀.
𝑉𝑂 =𝑘𝑐𝑎𝑡[𝐸𝑡][𝑆]
𝐾𝑚 + [𝑆]
9.6 µ𝑀𝑠−1 =(600𝑠−1)(0.020µ𝑀)(40µ𝑀)
𝐾𝑚 + 40µ𝑀
9.6 µ𝑀𝑠−1 =480µ𝑀2𝑠−1
𝐾𝑚 + 40µ𝑀
Solving for 𝐾𝑚 gives,
𝐾𝑚 = 10µ𝑀
Reference:
CourseSmart International E-Book for Principles of Biochemistry
by David L. Nelson, Michael M. Cox