Transcript lecture notes-growth kinetics-web

Cells Growth in Continuous Culture
Ideal Chemostat
When qp=0, kd ≈0, X0=0, Monod equation is applied,
at steady state, the dilution rate that maximizes cell mass
Productivity (DX) is obtained by
d ( DX )
dD
DX  DY
M
X /S
(S 0 
D opt   m (1 
X opt  Y
M
X /S
 0  D opt
KsD
m  D
Ks
K s  S0
(S0 
)
)
K s (K s  S0 )  K s )
Intrinsic coefficient
Cells Growth in Continuous Culture
Ideal Chemostat
When endogenous metabolism (kd > 0) is considered,
Cell mass balance yields
FX 0  FX  V R  g X  V R k d X  V R
DX 0  (  g  k d  D ) X 
At steady state,
D   g  k d   net
or
 g  D  kd
dX
dt
dX
dt
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0) is considered
substrate mass balance yields (qp=0)
1
FS 0  FS  V R  g X
M
 VR q p X
Y
At steady state,
1
Yp/s
 VR
dS
dt
X / S
D (S0  S ) 
g X
M
Y
X /S
Since  g  D  k d
then
1
D (S0  S ) 
M
Y
X /S
(D  kd ) X  0
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp=0) is considered
To determine the intrinsic yield through the apparent yield
1
D (S0  S ) 
(D  kd ) X  0
M
Y
X /S
Re-arranging the above equation yields
D(
S0  S
1
)
X
M
(D  kd )  0
Y
X /S
1
D(
AP
D
)
Y
M
Y
X /S
where Y
X /S

M
0
Y
X /S
AP
kd

X /S
X  X0
X

at X 0  0
S0  S
S0  S
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp=0) is considered
1
AP
1

Y
M
Y
X /S
1
AP
Y
kd

M
Y
X /S
X /S
1


M
ms
D
Y
X /S
D
X /S
kd
where m s 
M
is the maintenanc e coefficien t based on
Y
X /S
external substrate S.
It is defined by the specific
m
( dS / dt ) m
X
(1/time);
rate of substare uptake for cellular maintenanc e
kd
ms 
Y
M
X /S
(

dX
dX
)m
(
)m
( dS / dt ) m
1
Xdt
dt


M
X YM
X
Y
X /S
X /S
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp=0) is considered
1
1

AP
Y
D
Y
X /S
Y

M
ms
X /S
M
and m s can be obtained from chemostat experiemnt s
X /S
X
AP
AP
by plotting 1/ Y
(Y

) against 1/D.
X /S
X /S
S0  S
Then k d can be obtained from
kd
ms 
M
Y
X /S
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp=0) is considered
To find out the relationship of D, S and X,
Cell mass balance
Substrate mass balance
 g  D  kd
D (S0  S ) 
g X
M
Y
X /S
X Y
M
D
(S0  S )
X /S
D  kd
from Monod equation :  g 
 mS
Ks  S
Ks ( D  k d )
S 
m  D  kd
 S 
Ks  g
m   g
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp=0) is considered
Equation summary
 net   g  k d 
Ks  S
M
D
(S0  S )
X /S
D  kd
Productivities: DP, DX
1
AP
Y
1

M
Y
X /S
 kd
Ks ( D  k d )
S 
m  D  kd
 g  D  kd ;
X Y
mS
X /S

ms
D
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp > 0) is considered
The mass balance on product formation
V
R
q p X  FP  V
dP
R

dt
:
q p X  DP 
dP
dt
at steady state, DP  q p X
The
substrate
mass
balance :
1
FS 0  FS  V R  g X
M
1
 VR kd X
Y
M
Y
X /S
at steady
 VR q p X
1
Yp/s
 VR
X /S
state
1
D (S0  S ) 
M
Y
X /S
(D  kd ) X 
1
Yp/s
q p X , where  g  D  k d
dS
dt
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp > 0) is considered
Then S and
X Y
X can
be expressed
M
(S  S )
X /S 0
D
M
D  kd  q p
from Monod equation :  g 
 mS
Ks  S
 g  D  kd
S 
as :
Ks ( D  k d )
m  D  kd
YX
/S
Yp / s
 S 
Ks  g
m   g
Cells Growth in Continuous Culture
Ideal Chemostat
Endogenous metabolism (kd > 0, qp > 0) is considered
Equation summary:
X Y
DP  q p X
M
(S  S )
X /S 0
D
M
D  kd  q p
 g  D  kd
Ks ( D  k d )
S 
m  D  kd
Productivities: DP, DX
YX
/S
Yp / s
Summary of Growth Kinetics
- Autocatalytic reaction: The rate of growth is directly related
to cell concentration
Net specific growth rate (1/time):
 net 
1 dX
X
dt
 net   g  k d
- Cell concentration determination
- Growth patterns and kinetics in batch culture
- lag phase
X
 μ net t ,  d
- logrithmic or exponential growth phase: ln
X0
- deceleration phase
- stationary phase: endogenous metabolism dX   k d X
dt
- death phase
Summary of Growth Kinetics
- Effect of factors:
- Dissolved oxygen:
oxygen consumptio n rate :
g X
YX / O
2
oxygen tra nsfer rate : k L a ( C *  C )
- Temperature, pH, ionic strength, substrate
concentration.
- Heat evolution:
H s
Y
X /S
 H c 
1
Y
H
Summary of Growth Kinetics
- Monod equation:
g 
m S
KS  S
-Cell growth in continuous culture:
qp=0, kd ≈0, X0=0, Monod equation is applied:
g  D 
X Y
M
X /S
Productivity: DX
m S
S 
KS  S
(S0  S )
X Y
X /S
D opt   m (1 
X opt  Y
M
M
X /S
S
D
m  D
(S0  S )  Y
Ks
K s  S0
(S0 
K
M
X /S
(S0 
)
K s (K s  S0 )  K s )
KsD
m  D
)
Summary of Growth Kinetics
-Cell growth in continuous culture:
qp=0, kd >0, X0=0, Monod equation is applied:
 net   g  k d 
Ks  S
M
D
(S0  S )
X /S
D  kd
Productivities: DP, DX
1
AP
Y
1

M
Y
X /S
 kd
Ks ( D  k d )
S 
m  D  kd
 g  D  kd ;
X Y
mS
X /S

ms
D
Summary of Growth Kinetics
-Cell growth in continuous culture:
qp>0, kd >0, X0=0, Monod equation is applied:
DP  q p X
X Y
M
(S  S )
X /S 0
D
M
D  kd  q p
 g  D  kd
Ks ( D  k d )
S 
m  D  kd
Productivities: DP, DX
YX
/S
Yp / s