The data in Table 1 were obtained from a kinetic study of an enzymatic reaction. The substrate S (with a concentration s) was converted, using an enzyme, to a product in 4 different experimental runs. The initial conditions of each experiment (initial substrate and enzyme concentrations, temperature, pH,...) were the same in each experiment except for the concentration of the inhibitor (i) which was different in each run (see the Table below). Assume that the inhibitor concentration remained constant during each run (i.e. i was not a function of time)
· Determine the type of inhibition;
· Calculate the values of the following kinetic constants: Km, vmax, Ki using three different methods, the choice is yours;
· If there is a difference between the values of each of the constants, calculated by different methods, propose the possible reasons. Which method is most precise and why? Justify.
Table 1. Change of substrate concentration (s) with time (t) with different inhibitor concentrations (i)
|
i=1mM/L
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i=5 mM/L
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i=15 mM/L
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i=35 mM/L
|
|
s, mM/L
|
time, h
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s, mM/L
|
time, h
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s, mM/L
|
time, h
|
s, mM/L
|
time, h
|
|
20.02
|
0
|
19.91
|
0
|
19.92
|
0
|
19.98
|
0
|
|
18.95
|
0.06
|
18.90
|
0.07
|
18.96
|
0.11
|
18.96
|
0.19
|
|
17.79
|
0.11
|
18.15
|
0.14
|
18.05
|
0.22
|
17.96
|
0.38
|
|
17.00
|
0.17
|
17.00
|
0.21
|
17.07
|
0.33
|
16.98
|
0.57
|
|
16.12
|
0.23
|
15.99
|
0.29
|
16.02
|
0.45
|
16.01
|
0.77
|
|
14.97
|
0.28
|
15.08
|
0.36
|
15.05
|
0.56
|
14.96
|
0.96
|
|
13.96
|
0.34
|
14.09
|
0.43
|
13.96
|
0.67
|
13.90
|
1.15
|
|
13.01
|
0.40
|
12.91
|
0.51
|
12.96
|
0.79
|
13.04
|
1.35
|
|
12.10
|
0.46
|
11.98
|
0.59
|
11.88
|
0.91
|
11.95
|
1.55
|
|
11.07
|
0.52
|
11.08
|
0.66
|
10.98
|
1.02
|
10.99
|
1.74
|
|
10.11
|
0.59
|
9.90
|
0.74
|
9.87
|
1.14
|
10.02
|
1.94
|
|
8.95
|
0.65
|
9.01
|
0.83
|
9.02
|
1.27
|
8.98
|
2.15
|
|
7.99
|
0.72
|
8.02
|
0.91
|
8.02
|
1.39
|
7.98
|
2.35
|
|
6.93
|
0.80
|
6.96
|
1.00
|
7.02
|
1.52
|
7.05
|
2.56
|
|
5.99
|
0.87
|
6.04
|
1.09
|
6.01
|
1.65
|
5.95
|
2.77
|
|
5.03
|
0.96
|
5.02
|
1.19
|
4.95
|
1.79
|
5.02
|
2.99
|
|
4.04
|
1.05
|
4.01
|
1.30
|
3.97
|
1.94
|
3.99
|
3.22
|
|
3.02
|
1.16
|
2.99
|
1.43
|
2.98
|
2.11
|
3.01
|
3.47
|
|
2.01
|
1.31
|
1.99
|
1.59
|
1.99
|
2.31
|
2.02
|
3.75
|
|
1.01
|
1.55
|
0.99
|
1.85
|
1.00
|
2.61
|
1.00
|
4.13
|
|
|
|
|
|
|
|
|
|