Biochemical Reactions and Enzyme Kinetics - Introduction to Biomedical Engineering - page 506

9. For the reaction given in Eq. (8.25) and with q A ð 0 Þ¼ 10, q B ð 0 Þ¼ 10, q P ð 0 Þ¼ 0, K 1 ¼ 0 : 5, K 1 ¼

0 : 3, a ¼ 3, and b ¼ 2, simulate the solution for q P :

10. For the reaction given in Eq. (8.27) and with q A ð 0 Þ¼ 15, q B ð 0 Þ¼ 0, q P ð 0 Þ¼ 0, K 1 ¼ 8, and K 2 ¼

3, solve and simulate the solution for q A , q B and q P : Compare these results with the quasi-

steady-state solutions.
11. For the reaction given in Eq. (8.27) and with

q A ð 0 Þ¼ 25, q B ð 0 Þ¼ 0, q P ð 0 Þ¼ 0, K 1 ¼ 2, and K 2 ¼

10, solve and simulate the solution for q A , q B and q P : Compare these results with the quasi-

steady-state solutions.
12. For the reaction given in Eq. (8.27) and with

q A ð 0 Þ¼ 10, q B ð 0 Þ¼ 0, q P ð 0 Þ¼ 0, K 1 ¼ 5, and K 2 ¼

20, solve and simulate the solution for q A , q B and q P : Compare these results with the quasi-

steady-state solutions.
13. Generate the solutions for Figures 8.3 and 8.4.
14. Simulate the reaction given in Eq. (8.33) and compare with the quasi-steady-state approximation
for q S , q E , q ES and q P : Assume that K 1 ¼ 5, K 1 ¼ 0 : 3, K 2 ¼ 1, q S ð 0 Þ¼ 9, q E ð 0 Þ¼ 0 : 01, q ES ð 0 Þ¼ 0,

:
15. Simulate the reaction given in Eq. (8.33) and compare with the quasi-steady-state approximation
for

and q P ð 0 Þ¼ 0

q S , q E , q ES and q P : Assume that K 1 ¼ 1, K 1 ¼ 0 : 1, K 2 ¼ 5,

:
16. Simulate the reaction given in Eq. (8.33) and compare with the quasi-steady-state approximation
for

q S ð 0 Þ¼ 20, q E ð 0 Þ¼ 0 : 008, q ES ð 0 Þ¼ 0, and q P ð 0 Þ¼ 0

q S ,

q E , q ES and q P : Assume that K 1 ¼ 10, K 1 ¼ 1, K 2 ¼ 3, q S ð 0 Þ¼ 30, q E ð 0 Þ¼ 1, q ES ð 0 Þ¼ 0,

:
17. Given the model in Eq. (8.51) and with

and q P ð 0 Þ¼ 0

q S ð 0 Þ¼ 10, V max ¼ 25, K M ¼ 5, and f ð t Þ¼ 5d ð t 1 Þ ,

q S :
18. Given the model in Eq. (8.51) and with

simulate the solution for

q S ð 0 Þ¼ 50, V ¼ 5, K M ¼ 1, and f ð t Þ¼ u ð t Þ u ð t 1 Þ ,

max

q S :
19. Given the model in Eq. (8.51) and with

simulate the solution for

e t , q S ð 0 Þ¼ 25, V max ¼ 10, K M ¼ 3, and f ð t Þ¼ 5

q S :
20. Given the model in Eq. (8.51) and with

simulate the solution for

q S ð 0 Þ¼ 10, V max ¼ 25, K M ¼ 5, and f ð t Þ¼ 5dð t 1 Þ ,

q S :
21. Simulate the model in Eq. (8.66) given that

simulate the solution for

K 12 ¼ 3, K 21 ¼ 1, V max ¼ 10, K M ¼ 1, K 10 ¼ 0,

and K 20 ¼ 0 : 02 : The inputs are f 1 ð t Þ¼ 4dð t Þ and f 2 ð t Þ¼ 0 : The initial conditions are zero.

22. Simulate the model in Eq. (8.66) given that K 12 ¼ 3, K 21 ¼ 2, V max ¼ 20, K M ¼ 2, K 10 ¼ 0,

and K 20 ð 0 Þ¼ 0 : The inputs are f 1 ð t Þ¼ 4 ð u ð t Þ u ð t 10 Þ Þ and f 2 ð t Þ¼ 3 ð u ð t 1 Þ u ð t 6 Þ Þ: The

initial conditions are zero.
23. Simulate the model in Eq. (8.67) given that K 12 ¼ 0 : 25, K 21 ¼ 3, V max ¼ 30, K M ¼ 5, K 10 ¼ 0,

and K 20 ð 0 Þ¼ 0 : 2 : The inputs are f 1 ð t Þ¼ 2 u ð t Þ and f 2 ð t Þ¼ 3 u ð t Þ: The initial conditions are zero.

24. Simulate the model in Eq. (8.67) given that K 12 ¼ 2, K 21 ¼ 3, V max ¼ 40, K M ¼ 8, K 10 ¼ 0,

e :03 t u ð t Þ: and K 20 ð 0 Þ¼ 0 : 2 : The inputs are f 1 ð t Þ¼ 5 u ð t Þ and f 2 ð t Þ¼ 3 The initial conditions are

zero.
25. Simulate the model in Eq. (8.67) given that K 12 ¼ 3, K 21 ¼ 2, V max ¼ 10, K M ¼ 0 : 8, K 10 ¼ 0 : 1,

K 20 ð

0 Þ¼ 0 : 3 : The inputs are

f 1 ð t Þ¼

4

u ð t Þ

and

f 2 ð t Þ¼

0 : The initial conditions are zero.

and