Biomedical Engineering Reference
In-Depth Information
From the table, we find that the maximum specific growth rate,
m
max
¼
0
:
088
=
h
.
D
X
DS
¼
20
:
9
1
:
0
(b) Y
X
=S
¼
3
¼
0
:
400
50
:
0
0
:
(c)
X
max
¼
l
(d)
For each increase in generation, cell biomass doubles. That is, X
X
0
þ
Y
X
=S
S
0
¼
1
:
0
þ
0
:
4
ð
150
Þ¼
61
:
0
g cells
=
2
n
or
=
X
0
¼
n
¼
ln
ð
X
=
X
0
Þ=
ln
2
, Therefore,
ln
ðX=X
0
Þ
ln2
ln
ð
61
:
0
=
1
:
0
Þ
n ¼
¼
¼
5
:
93
ln2
There are 6
þ
1
¼
7 generations of cells in the final culture.
11.4. APPROXIMATE GROWTH KINETICS
AND MONOD EQUATION
In Chapter 8, we have learned that enzymatic reactions in general are governed by
Michaelis
e
Menten kinetics or its variations. This same type of kinetic equation is also
evident in the DNA and RNA replication and manipulations as one can infer from Chapter
10. In Chapter 10, we also learned that cell metabolism involves numerous groups, path-
ways, and reaction steps. Each reaction step along the metabolic pathway is an enzymatic
reaction. Quantifying cell growth with all the governing parameters following all the
genetic steps and metabolic pathways would make the computation tedious if not impos-
sible. To the least, determining all the parameters would be very difficult. Therefore,
some simplification of the kinetics is necessary in quantifying cell growth and thus bio-
reactions in general.
To begin with, let us examine a simple metabolic pathway as shown in
Fig. 11.3
. Substrate
is uptaken into the cell and then converted into two products: P
1
and P
2
after a few interme-
diate steps. We assume that P
1
is an extracellular product, while P
2
is an intracellular product.
The stoichiometries along the pathway illustrated in
Fig. 11.3
can be written as:
k
1
k
1
c
M
1
$
E
1
S þ
E
1
%
S$
E
1
/
(11.15a)
k
1
k
2
k
2
E
2
þ
M
1
$
E
1
%
M
1
$
E
2
þ
E
1
(11.15b)
k
2
c
M
2
$
E
2
M
1
$
E
2
/
(11.15c)
k
3
M
2
$
E
2
þ
E
3
%
M
2
$
E
3
þ
E
2
(11.15d)
k
3
k
3
c
M
3
$
E
3
M
2
$
E
3
/
(11.15e)
Search WWH ::
Custom Search