Biomedical Engineering Reference
In-Depth Information
50
40
30
20
10
0
0
10
20
30
40
50
q
s
FIGURE 8.5
Velocity of substrate disappearance. Note that the reaction velocity is for
t
¼ 0, and
q
S
is the intial
quantity of substrate.
V
max
¼
50 and
K
M
¼
3
:
and after dividing both sides by
V
max
, we have
1
2
¼
q
S
q
S
þ
K
M
ð
Þ
Simplifying the previous equation gives
q
S
¼
K
M
V
¼
V
ma
2
:
Given the lack of computer simulation capability in the early 1900s, the quasi-steady-state
approximation gave an excellent and efficient solution to enzyme kinetics. However, with
the current computer power and the availability of stiff differential equation simulators, it
is far easier to simulate enzyme kinetics using the computer rather than solving a set of
algebraic equations.
when
EXAMPLE PROBLEM 8.2
Simulate the reaction given in Eq. 8.34 and compare with the quasi-steady-state approximation
for
q
S
,q
E
,q
ES
, and
q
P
:
Assume that
K
1
¼
8,
K
1
¼
0
:
01,
K
2
¼
5,
q
S
ð
0
Þ¼
1,
q
E
ð
0
Þ¼
0
:
08,
q
ES
ð
0
Þ¼
0,
and
q
P
ð
0
Þ¼
0
:
Solution
The SIMULINK model is shown in Figures 8.6 and 8.7, both executed using the
ode23tb
integrator. Because of the ease in solution, the quasi-steady-state approximation for
q
S
,q
E
,q
ES
,
and
q
P
is carried out using the differential equation for
q
S
, Eq. (8.41), and the algebraic equations,
Continued
