Growth_Contin_Culture_Mar_2010

Growth_Contin_Culture_Mar_2010 - GROWTH IN BATCH AND...

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Unformatted text preview: GROWTH IN BATCH AND CONTINUOUS CULTURES Bacterial Growth Kinetics •  Equation describing growth is very similar to that describing enzyme kinetics (Michaelis-Menten model of enzyme kinetics) V
=
 Vm
S
 Ks
+
S
 •  Good reason for this since growth is an enzyme mediated process. Therefore, the relationship between specific growth rate and substrate concentration can be described in a similar manner. 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 Monod
model
of
 growth
kine4cs
 µ

=

specific
growth
rate,
4me
‐1
 µm

=

maximum
specific
growth
rate,
4me‐1
 Ks

=

half
velocity
constant,
equals
the
substrate
 
concentra4on
at
which


µ = ½
µm

 S

=

essen4al
(limi4ng)
growth
substrate
 b

=

decay
rate
(negligible)
 Bacterial Growth Kinetics At
low
substrate
concentra4ons,
specific
growth
 rate
(µ)

is
a
func4on
of
S
conc.,
and
increases
 with
increasing
S
conc.

At
high
S
conc.,
µ
 reaches
a
saturated
value,
a
maximum
µ,
where
 increasing
S
conc.
has
no
further
effect.
 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 Ks
=
substrate
conc.
at
which
µ
=
½
µm
 
also
known
as
half
satura4on
constant
 µm
 µ
 Ks

 [S]
 Bacterial Growth Kinetics 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 µ
 [S]
 Bacterial Growth Kinetics 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 µ
 [S]
 Bacterial Growth Kinetics 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 µ
 [S]
 Bacterial Growth Kinetics 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 µm
 µm
 µ
 µm
 [S]
 Bacterial Growth Kinetics 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 • 
The
growth
kine4c
 µm
 µ
 parameters
for
each
 organism
is
different
and
 unique.


 • 
The
same
organism,
 however,
can
have
different
 growth
kine4cs
depending
 on
the
specific
condi4ons
of
 growth.

Different
 temperature,
different
C‐
 source,
different
N‐source
 can
alter
the
growth
 parameters.


 µm
 µm
 Ks
Ks
 Ks
 [S]
 Bacterial Growth Kinetics 


S








 µ
=
µm
 Ks
+
S
 ‐

b
 • 
The
growth
kine4c
 µm
 parameters
for
each
 organism
is
different
and
 unique.


 toluene
 µ
 p‐cresol
 µm
 µm
 benzene
 Ks
Ks
 Ks
 [S]
 • 
The
same
organism,
 however,
can
have
different
 growth
kine4cs
depending
 on
the
specific
condi4ons
of
 growth.

Different
 temperature,
different
C‐
 source,
different
N‐source
 can
alter
the
growth
 parameters.


 • 
e.g.
biodegrada4on
of
 toluene,
p‐cresol
or
 benzene
by
Burkholderia
 Bacterial Growth Kinetics • 
From
a
prac4cal
viewpoint,
however,
the
substrate
conc.,
or
how
fast
a
waste
is
being
 processed,
rather
than
how
fast
bacteria
are
growing
is
more
per4nent
informa4on.
 • 
We
can
write
this
model
in
more
useful
terms
and
we
can
describe
the
rela4onship
 between
growth
rate
and
substrate
u4liza4on
if
we
look
at
a
few
other
factors.
 Bacterial Growth Kinetics • 
From
a
prac4cal
viewpoint,
however,
the
substrate
conc.,
or
how
fast
a
waste
is
being
 processed,
rather
than
how
fast
bacteria
are
growing
is
more
per4nent
informa4on.
 • 
We
can
write
this
model
in
more
useful
terms
and
we
can
describe
the
rela4onship
 between
growth
rate
and
substrate
u4liza4on
if
we
look
at
a
few
other
factors.
 • 
Also,
we
can
use
more
measurable
terms
than
µ
and
µm.
 

1.




Y


=
 
dx/dt
 ‐dS/dt
 Y
=
yield






 conc.
cells
produced
 conc.
S
consumed
 Bacterial Growth Kinetics • 
From
a
prac4cal
viewpoint,
however,
the
substrate
conc.,
or
how
fast
a
waste
is
being
 processed,
rather
than
how
fast
bacteria
are
growing
is
more
per4nent
informa4on.
 • 
We
can
write
this
model
in
more
useful
terms
and
we
can
describe
the
rela4onship
 between
growth
rate
and
substrate
u4liza4on
if
we
look
at
a
few
other
factors.
 • 
Also,
we
can
use
more
measurable
terms
than
µ
and
µm.
 

1.




Y


=
 
dx/dt
 ‐dS/dt
 Y
=
yield






 • 
Rearrange
 2.
 ‐dS
 dx/dt


=


Y




 
dt
 ‐
bx
 • 
cell
growth
rate
is
a
constant
 frac4on
of
the
S
u4liza4on
rate
 conc.
cells
produced
 conc.
S
consumed
 x

=

conc.
ac4ve
organisms
(g /L)
 Y

=

yield
constant
(g/g)
 S

=

substrate
conc.
(g /L)
 b

=

decay
rate
(negligible)
 • 
Substrate
u4liza4on
rate
can
be
wriXen
as
 3.
 ‐dS
 





kS
 
dt
 =
 s
+
S
 x
 


K this
is
the
equivalent
of


 V
=
 where
 
k

=

maximum
substrate
 
 
 
u4liza4on
rate,
4me
‐1
 Vm
S
 Ks
+
S
 Bacterial Growth Kinetics • 
subs4tute
eq.
3
into
eq.
2
 





kS 4.
 dx/dt


=


Y




 
 x
 ‐
bx
 


Ks
+
S
 • 
rearrange
 
rate
of
cell
incr.
 
unit
cell
conc.
 





S
 5.
 dx/dt


=


Yk



K 
+
S
 ‐
b
 s 



x




 6.
 µ

=


µm
 


S








 ‐
b
 Ks
+
S
 µ =

 dx/dt



 



x




 • 
these
2
equa4ons
are
very
useful
for
describing
bacterial
growth
in
both
batch

 and
con4nuous
culture
systems.
 dx/dt


=


Yk






S
 ‐
b
 5.
 


Ks
+
S
 



x




 Bacterial Growth Kinetics 6.
 [S]
 Lag
phase
 


dx/dt

=

0
 µ

=


µm
 


S








 ‐
b
 Ks
+
S
 dx/dt


=


Yk






S
 ‐
b
 5.
 


Ks
+
S
 



x




 Bacterial Growth Kinetics 6.
 [S]
 Lag
phase
 


dx/dt

=

0
 Log
phase dx/dt
 

S


>>>
Ks,



then
















=

Yk




and




µ

=


µm
 



x
 µ

=


µm
 


S








 ‐
b
 Ks
+
S
 dx/dt


=


Yk






S
 ‐
b
 5.
 


Ks
+
S
 



x




 Bacterial Growth Kinetics 6.
 [S]
 Lag
phase
 


dx/dt

=

0
 dx/dt
 

S


>>>
Ks,



then
















=

Yk




and




µ

=


µm
 



x
 Sta4onary
phase
 





S
 dx/dt
 
growth

=

decay 



















=


0,













Yk

















=


b
 


Ks
+
S
 


x
 Log
phase µ

=


µm
 


S








 ‐
b
 Ks
+
S
 dx/dt


=


Yk






S
 ‐
b
 5.
 


Ks
+
S
 



x




 Bacterial Growth Kinetics 6.
 [S]
 Lag
phase
 


dx/dt

=

0
 dx/dt
 

S


>>>
Ks,



then
















=

Yk




and




µ

=


µm
 



x
 Sta4onary
phase
 





S
 dx/dt
 
growth

=

decay 



















=


0,













Yk

















=


b
 


Ks
+
S
 



x
 Log
phase Death
(decay) 
 dx/dt
 
S

=

0,























=


‐
b,










µ =


‐
b
 



x
 µ

=


µm
 


S








 ‐
b
 Ks
+
S
 dx/dt


=


Yk






S
 ‐
b
 5.
 


Ks
+
S
 



x




 Bacterial Growth Kinetics 6.
 µ

=


µm
 


S








 ‐
b
 Ks
+
S
 [S]
 Therefore: 
 
 
 
 
In
a
closed
batch
system,
what
this
clearly
shows
is
that
everything
is
 
changing,
cell
growth
rate,
cell
concentra4on,
substrate
concentra4on.

 
condi4ons
are
constantly
changing
by
the
ac4ons
of
the
growing
cells.
 In
contrast: 
We
can
describe
a
con4nuous
culturing
system
that
is
an
extremely
useful
 
 
 
tool
for
many
applica4ons,
such
as
waste
treatment,
industrial
 

 
 

















fermenta4ons,
microbial
ecology.
 Continuous flow (continuous culture) system (also known as a Chemostat) •  This is an experimental method that allows the operator (experimenter) to maintain a constant environment (as opposed to a changing environment). Hence, one can also control a constant rate of growth. •  In microbial ecology or microbial physiology, it is referred to as a chemostat, and used to generate steady state conditions for kinetic studies. This creates a constant environment so that cells are in a time invariant state of constant growth during the period of observation. F,

So
 x
 V
 F,

S
 F

=

flow
rate
 V

=

volume
 So

=

incoming
[S]
 S

=

outgoing
[S]
 x

=

cell
conc.
 D

=

F/V,


dilu4on
rate
 θ =

1/D
or
V/F,


deten4on
4me • 
Need
some
form
of
a
reactor
into
which
reactants
flow
at
a
steady
rate
and
from
 which
products
emerge.
 Continuous flow (continuous culture) system 
 F,

So
 x
 V
 S
 F,

S
 Continuous flow (continuous culture) system 
 Assump4ons:
 1.  completely
mixed
system
 2.  constant
flow
rate
 3.  constant
influent
So
 4.  instantaneous
u4liza4on
of
So
 
(vol.
of
So

<<<<

vol.
of
S)
 F,

So
 x
 V
 S
 F,

S
 Continuous flow (continuous culture) system 
 Assump4ons:
 1.  completely
mixed
system
 2.  constant
flow
rate
 3.  constant
influent
So
 4.  instantaneous
u4liza4on
of
So
 
(vol.
of
So

<<<<

vol.
of
S)
 F,

So
 x
 V
 S
 F,

S
 Organisms
adjust
growth
in
response

 to
So
resul4ng
in
a
steady
state
with
 the
following
characteris4cs:
 1.  constant
cell
concentra4on,

x
 2.  constant
growth
rate,

µ 3.  constant
substrate
concentra4on,

S
 Continuous flow (continuous culture) system 
 • Using
what
we
know
about
growth
based
on
the
Monod
model,
in
order
to
describe
 what
is
happening,
we
need
to
determine
2
things:
 
‐

cell
concentra4on,
and
 
‐

substrate
concentra4on

at
steady
state
 Continuous flow (continuous culture) system 
 • 
Using
what
we
know
about
growth
based
on
the
Monod
model,
in
order
to
describe
 what
is
happening,
we
need
to
determine
2
things:
 
‐

cell
concentra4on,
and
 
‐

substrate
concentra4on

at
steady
state
 • 
Change
in
organism
concentra4on
 
1.

in
the
vessel,
cell
growth
can
be
described
by
 
 
dx/dt

=

µx 
 dx/dt
 
this
is
consistent
with



















=


µ 



x
 
2.

cells
are
being
washed
out
(ouglow)
at
a
rate
described
as
 
 
‐
dx/dt

=

Dx
 
3.

the
net
rate
of
increase
of
cells
in
the
vessel
is

 
 
dx/dt

=

µx

‐

Dx
 
 
 
Thus,

if
µ

>

D,

cell
conc.
increases
 
 
 
4.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 






µ

<

D,

cell
conc.
decreases,
eventually
to
 
 
 






0
and
washout
occurs
 Continuous flow (continuous culture) system 
 
3.

the
net
rate
of
increase
of
cells
in
the
vessel
is

 
 
 
 
dx/dt

=

µx

‐

Dx
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Thus,

if
µ

>

D,

cell
conc.
increases
 
 






µ

<

D,

cell
conc.
decreases,
eventually
to
 
 
 
 






0
and
washout
occurs
 
4.

when
dx/dt

=

0,

cell
conc.
is
constant,

we
have
a
steady
state
in
which
the
conc.
 
 
 
 
 
 
of
cells
does
not
change
with
4me.
 
 
 
Then,


µ

=

D
 
the
specific
growth
rate

=

dilu4on
rate
 
 
 
This
is
a
very
important
rela4onship

and

a
very
convenient
rela4onship
since
D
 
is
one
of
the
few
parameters
that
you
(as
the
operator)
can
control.
 
 
So,
what
dilu4on
rate
makes
a
steady
state
possible?

What
is
the
value
of
D?
 Continuous flow (continuous culture) system 
 • 
Change
in
substrate
concentra4on
 
5.

the
net
rate
of
change
of
substrate
conc.

=

inflow

‐

ouglow

‐

consump4on
 x
 
 
dS/dt


=


DSo

‐

DS

‐








µ
 Y
 
dx/dt
 dx/dt

=

µx
 Y

=
 
6.

both
eq.
3
and
eq.
5
contain
µ
which
in
 ‐ds/dt
 
 
itself
is
a
func4on
of
S

 µ x
 


S








 ‐
dS/dt

=
 

Y
 µ

=


µm
 Ks
+
S
 
7.

(eq.
3)



dx/dt

=

µx

‐

Dx

 
 
 


S








 




dx/dt

=


x



µm
















‐

Dx

 Ks
+
S
 x
 
8.

(eq.
5)


dS/dt


=


(DSo

‐

DS)

‐











µm
 


S








 Ks
+
S
 Y
 Continuous flow (continuous culture) system 
 
9.

at
steady
state,
certain
values
of
x
and
S
exist
for
which

 
 
dx/dt

=

0



and



dS/dt

=

0
 
 
when
dx/dt

=

0,

solve
for
S

(eq.
7) 
 
S

=


Ks
 



D
 µm
‐

D
 
10.

when
dS/dt

=

0,

solve
for
x

(eq.
8)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


S








 =



D(S 

‐

S) 

 
 x
 


µm
























 o Ks
+
S
 
 
 Y
 
 
 
 
 
 
 
 
 
 
D
 
 
 
 

 
 
 
 
then 
x

=

Y
(So

‐

S)
 


 
So
at
steady
state
 


S








 
D

=

µ

=

µm
 K 
+
S
 s 
 

 Continuous flow (continuous culture) system 
 • 
Steady
state
concentra4on
of
cells
 
On
what
variable(s)
is(are)
the

 
steady
state
concentra4on
of
cells
 

dependent?
 • 
Steady
state
concentra4on
of
substrate
 On
what
variable(s)
is(are)
the

 steady
state
concentra4on
of
substrate
 dependent?

 x

=

Y
(So

‐

S)

 S

=


Ks
 



D
 µm
‐

D
 • 
Values
for
the
constants


Y,


Ks,


µm



are
needed
and
will
be
specific
to
the

 


organism,
substrate,
growth
condi4ons,
temperature,
etc.
 
‐
these
can
be
determined
separately
for
the
specific
condi4ons
in
batch
 



culture
 
dx/dt
 µm

=

Yk
 Y

=
 Ks

=

½
µm
 ‐ds/dt
 Continuous flow (continuous culture) system 
 x1



So1
 So1
 x2



So2
 x

=

Y
(So

‐

S)

 So2
 mg/L
 cells
(x)
 ____
 ____
 mg/L
 


S


 


S
 ____

 D
 Dm
 S

=


Ks
 



D
 µm
‐

D
 Dc
 • 
Cells,
x,
have
a
maximum
value
when
D

=

0

and
S

=

0,
a
situa4on
that
corresponds
 
to
the
final
stages
of
a
batch
culture.
 • 
As
D
increases,
S
also
increases;
eventually
cell
conc.,
x,
falls
and
at
a

 cri4cal
value
of
Dc,
washout
occurs,
then
resul4ng
in
S

=

So.
 • 
Dc
has
great
prac4cal
importance.

At
steady
state
when
D

=

µ,

 


So








 
Dc

=

µm



























,




since
So
>>>
Ks



,



Dc

~

µm

,



Thus
for
steady
state
condi4on
 Ks
+
So
 
 
 
 
 
 
 
 
 
 
 
 
growth
rate
must
be
less
than
 
 
 
 
 
 
 
 
 
 
 
 
µm
 Continuous flow (continuous culture) system 
 x1



(So1)
 So1
 x2



(So2)
 x

=

Y
(So

‐

S)

 So2
 mg/L
 cells
(x)
 ____
 ____
 mg/L
 


S


 ____

 D
 Dm
 S

=


Ks
 



D
 µm
‐

D
 Dc
 • 
Dc
has
great
prac4cal
importance.

At
steady
state
when
D

=

µ,

 


So








 
Dc

=

µm



























,




since
So
>>>
Ks



,



Dc

~

µm

,



Thus
for
steady
state
condi4on
 K 
+
S 
 
 
 
 s 
o 
 
 
 
 
 
 
 
growth
rate
must
be
less
than
 
 
 
 
 
 
 
 
 
 
 
 
µm
 • 
Note
that
at
any
D
<
Dc,
the
steady
state
conc.
of
S
is
independent
of
So,
and
dependent
 

only
on
D;
so
when
D
is
set,
S
finds
the
level
at
which
D
=
µ.
 Continuous flow (continuous culture) system 
 x1



(So1)
 So1
 x2


(So2)
 x

=

Y
(So

‐

S)

 So2
 mg/L
 cells
(x)
 ____
 ____
 mg/L
 


S


 ____

 D
 Dm
 S

=


Ks
 



D
 µm
‐

D
 Dc
 • 
Also
note
the
effect
of
So
on
x
;

at
any
give
D
<
Dc
,

x
is
dependent
on
So.

The
lower
 the
So
,
the
lower
the

x.
 • 
In
a
treatment
process,
you
want
to
op4mize
the
waste
or
S
removal,
but
increasing
 or
op4mizing
D
is
also
desired.

Dm

is
what
you
as
the
manager
set
depending
on
the
 criteria
for
outcome
(e.g.
90%
or
99%
removal?)
 Continuous flow (continuous culture) system In treatment processes:
 x1



(So1)
 So1
 mg/L
 So2
 


S


 ____

 x2



(So2)
 mg/L
 cells
(x)
 ____
 ____
 θc
 1/D

or

 θ
 • 
Consider
the
system
as
a
func4on
of
deten4on
4me, θ θ =

1/D

=

V/F

 • 
Applica4ons
include

waste
treatment,
where
the
deten4on
4me
(
θ
)
is
set
for
the
 removal
of
a
specific
frac4on
of
waste
(
S
).
 • 
Industrial
processes,
where
the
produc4on
of
vitamins,
ace4c
acid,
an4bio4cs
or
cell
 biomass,
e.g.
streptomycin,
bakers
yeast.
 Continuous flow (continuous culture) system A
 B
 µ D
 KsB






KsA
 [S]
 • 
In
environmental
studies,
a
con4nuous
flow
system
can
more
appropriately
simulate
 the
natural
environment;

a
very
dynamic
systems
with
constant
exchange
of
nutrients,
 substrate,
removal
of
metabolites,
removal
of
dead
cells.
 • 
One
important
condi4on
can
be
imposed
in
a
con4nuous
flow
system
that
cannot
occur
 in
a
batch
system.
 • 
Most
large
bodies
of
water
have

<<
10
mg/L
carbon.

How
do
you
find
and
grow
 organisms
that
effec4vely
use
low
S
conc.?
 Continuous flow (continuous culture) system A
 B
 µ D
 • 
Holger
Jannasch
did
this
classic
 experiment
using
a
chemostat
and
 reported
that

 


at
high
[S]


 
 


but
at
low
[S] 
A
>
B
 
B
>
A
 • 
In
batch
culture,
at
low
[S]
it
is
 rapidly
depleted
by
a
few
cells
 • 
By
selec4ng
or
sesng
D,
a
 completely
different
group
of
 organisms
can
be
favored
to
grow
 in
a
chemostat.
 KsB






KsA
 [S]
 • 
In
environmental
studies,
a
con4nuous
flow
system
can
more
appropriately
simulate
 the
natural
environment;

a
very
dynamic
systems
with
constant
exchange
of
nutrients,
 substrate,
removal
of
metabolites,
removal
of
dead
cells.
 • 
One
important
condi4on
can
be
imposed
in
a
con4nuous
flow
system
that
cannot
occur
 in
a
batch
system.
 • 
Most
large
bodies
of
water
have

<<
10
mg/L
carbon.

How
do
you
find
and
grow
 organisms
that
effec4vely
use
low
S
conc.?
 Con4nuous
culture

=

Chemostat
 Fig.
1.

Chemostat
design.

The
chemostat
was
maintained
at
a
constant
volume
 of
750
mL.

Samples
were
taken
through
a
sample
port
located
on
the
top
of
the
 reactor.
(John
J.
Scrivo.
2005)
 µm
 µm
 µm
 Ks
Ks
 Ks
 µm
 µ
 Ks

 [S]
 ...
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