A sample Problem on Biochemical Engineering

GROUP 1

Andrada, Filmar T. Dulliyao, Van Vesper J. Cauilan, Kaicee Lapuebla, Jeremy C.  Necesito, Miko Paul B.

2.5 Eadie (1942) measured the initial reaction rate of hydrolysis of acetylcholme (substrate) by dog serum (source of enzyme) and obtained the following data: Substrate Concentration (mol/L) Initial Reaction Rate (mol/L) 0.0032 0.111 0.0049 0.148 0.0062 0.143 0.0080 0.166 0.0095 0.200 Evaluate the Michaelis-Menten kinetic parameters by employing a)  b) c) d)

The Langmuir plot; The Lineweaver-Burk plot; The Eadie-Hofstee plot; and  Non-linear regression procedure

Solution: a) Employing the Langmuir plot x (Cs) 0.0032 0.0049 0.0062 0.008 0.0095

y (r) 0.028829 0.033108 0.043357 0.048193 0.0475

Langmuir Plot 0.06

0.04      r         /

     s

       C

r max

1 

y = 3.3133x + 0.0191 R² = 0.8837

0.05

0.03 0.02

slope 0.01

K m



y

r max max  K m 



intercept r max  0.301814 0.005765

0 0

0.002

0.004

0.006

Cs

1

0.008

0.01

 b) Lineweaver-Burk Plot x (1/Cs) 312.5 204.0816 161.2903

y (1/r) 9.009009 6.756757 6.993007

10

125 105.2632

6.024096 5

7

Lineweaver-Burk Plot

6

K m



y



3

intercept

2 1

slope r max 

r max  K m 

5 4

1 

R² = 0.9146

8

     r         /        1

r max

y = 0.0172x + 3.6342

9

0 0

0.275164 0.004733

50

100

150

200

250

300

350

1/Cs

c) Eadie-Hofstee Plot x (r/Cs) 34.6875 30.20408 23.06452 20.75 21.05263

y (r) 0.111 0.148 0.143 0.166 0.2

Eadie-Hofstee Plot 0.25 0.2 0.15 y = -0.0043x + 0.2645 R² = 0.6584

     r

r max



y intercept

K m

 

r max  K m 



slope 0.2645 0.0043

0.1 0.05 0 0

5

10

15

20

r/Cs

2

25

30

35

40

2.19 The initial rate of reaction for the enzyme cleavage of deoxyguanosine triphosphate was measured as a function of initial substrate concentration as follows: Substrate Concentration (μmol/L) Initial Reaction Rate (μmol/L) 6.7 0.30 3.5 0.25 1.7 0.16 a) Calculate the Michaelis-Menten constants of the above reaction.

Solution: In finding the Michaelis-Menten constants, we first determine the highest coefficient of R  by plotting the three different graphs namely Langmuir, Lineweaver-Burk, and Eadie-Hofstee plot. Cs 6.7 3.5 1.7

r 0.3 0.25 0.16

1. Langmuir Plot Cs 6.7 3.5 1.7

Cs/r 22.33333 14 10.625

Langmuir Plot 30 y = 2.3722x + 6.2429 R² = 0.9937

20

     r         /

     s

       C

10 0

R 2=0.9937

0

2

4

6

8

Cs

2. Lineweaver-Burk Plot 1/Cs  0.149254 0.285714 0.588235

1/r 3.333333 4 6.25

Lineweaver-Burk Plot 8 y = 6.7758x + 2.2168 R² = 0.9922

6      r         /        1

4 2

R 2=0.9922

0 0

0.1

0.2

0.3

0.4

1/Cs

3

0.5

0.6

0.7

3. Eadie-Hofstee Plot r/Cs 0.044776 0.071429 0.094118

r 0.3 0.25 0.16

Eadie-Hofstee Plot 0.4 0.3      r

R 2=0.9566

0.2

y = -2.8096x + 0.4336 R² = 0.9566

0.1 0 0

0.02

0.04

0.06

0.08

0.1

r/Cs

Among the above graphs, the Langmuir plot displayed the best fit of our data. Using the Langmuir plot to solve the problem, the equation below shall be used: r max

K m



y

r max  K m 



1 

slope

intercept r max  0.42155 2.631692

The Michaelis-Menten constant (K m) is equal to 2.631692.

4