Biomedical Engineering Reference
In-Depth Information
K
S
i
,
μ
μ
=
μ
max
K
+
S
K
+
I
s
i
,
μ
(6)
where μ is specific growth rate; μ
max
is maximum specific growth rate; S is concentration of
the rating-limiting substrate; K
s
is concentration giving one-half of the maximum rate; I is
inhibitor concentration; K
i,μ
is inhibition coefficient of microbial growth.
In the absence of inhibitors (I=0), Equation 6 can be converted as follows:
S
s
+
μ
μ
=
0
max
K
S
(7)
Where μ
0
is specific growth rate under inhibitor-free condition.
Taking Equation 7 into consideration, then, the specific growth rate described in Equation
6 can be written as:
K
i
,
μ
μ
=
μ
0
K
+
I
i
,
μ
(8)
Equation 8 can be subsequently rearranged as:
μ
1
0
=
1+
I
μ
K
i
μ
,
(9)
In fact, a larger value of 1/K
i,μ
would indicate a greater inhibition degree. Similarly, in the
presence of inhibitors, the specific COD removal rate can be expressed as:
q
1
=
1+
I
0
q
K
i
,
q
(10)
where q
0
is specific COD removal rate under inhibitor-free condition. It is clear that the term
1/K
i,q
is a indicator of the inhibition degree on the substrate removal.
Saini et al. [86] used the model organism
Shewanella oneidensis
MR-1 to study the effect
of both excess substrate (pyruvate) and chemical uncoupler (TCS) addition on cell growth
simultaneously and proposed the following empirical expression:
1
1
1
S
X
1
C
X
=
+
×
+
×
0
0
u
Y
(
Y
)
(
Y
)
S
X
+
K
(
Y
)
C
X
+
K
obs
obs
max
w
min
0
0
S
X
wu
min
u
u
X
(11)
where (Y
obs
)
max
is observed growth yield under substrate-limited conditions; (Y
w
)
min
is
minimal energy spilling related growth yield; (Y
wu
)
min
is minimal energy spilling related
