Lecture 2: Advanced Growth Kinetics

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Lecture 2: Advanced Growth Kinetics
Lecture 2: Advanced Growth
Kinetics
Dr. AKM Shafiqul Islam
12/03/08
Kinetics of Balance Growth
• The net rate of cell mass growth rx is given by
the equation
rx  mx
Where
x = cell mass per unit culture volume
m = the specific growth rate of the cell
• Using this equation in the steady-state CSTR
material balance for cell mass gives
Dx f  D  m x
• The feed stream is normally sterile medium.
Therefore xf = 0 and Dxf=0.
• A cell population > 0 can be maintained if the
•
•
specific growth rate m is balanced by the
dilution rate
In this case, nonzero cell population can be
maintained if D=m
i.e., when the culture has adjusted so that its
specific growth rate is equal to the dilution
rate.
• Bacillus linens culture confirmed the indeterminate
nature of population level. After a steady continuous
operation at 6 h, two subsequent interruption of the
culture was observed.
• In this case, a portion of the
reactor contents consisting of
the cell plus medium was
removed and replaced by
medium alone
• Following each interruption, the system achieved a new
steady population of different size
• The are two types of media
– Synthetic media is one in which chemical
composition is well defined. e.g., minerals based
with necessary carbon, nitrogen and energy as
well as vitamins
– Complex media contain material of undefined
composition. e.g., mixed with unknown extract
chemicals. Complex media including beef broth,
blood infusion broth, corn-steep liquor, sewage.
• The general goal in making a medium is to
•
•
•
support good growth and/or high rate of
product synthesis
Should not supplied too much nutrient.
Excessive nutrient can inhibit or even poison
cell growth
If the cells grow too extensively, their
accumulated metabolic end will often disrupt
the normal biochemical processes of the cells
Therefore, the growth process are limited by
Monod Growth Kinetics
• If the concentration of one essential medium
constituent is varied while the concentrations of
all other medium components are kept constant,
the growth rate changes in a hyperbolic way
Monod Growth Kinetics
• A functional relationship between the specific growth
rate m and essential compound’s concentration was
proposed by Monod in 1942.
m
m max s
Ks  s
Here mmax is the maximum growth rate achieved and Ks
is a saturation constant, when s>>Ks and the
concentrations of all other essential nutrients are
unchanged.
Ks is that value of the limiting nutrient
•
concentration at which the specific growth rate
is half its maximum value.
It is the division between the lower
concentration range, where m is strongly
dependent on s. and the higher range where m
becomes independent of s.
• The Ks values for E. coli strains growing in
glucose- and tryptophan-limiting media are 0.22
x 10-4 M and 1.1 ng/ml, respectively
• The value of Ks is rather small. Thus s>>Ks and
the term s/(Ks + s) may be regarded simply as
an adequate description for calculating the
derivation of m and mmax as the concentration of
s become smaller
• The relation also suggests that the specific
growth rate is finite (m ≠ 0) for any finite
concentration of the rate limiting component
• When the population growth is related to
limiting nutrient as proposed by Monod, a
definite connections emerge among
reactor
– operating conditons
– microbial kinetics
– and stoichiometric parameters
• To show this we can write a mass balance on
•
limiting substrate which couples to the cell mass
balance since m depends on s
In the substrate balance we can write the yield
factor
YX / S
mass of cells formed

mass of substrate consumed
• The steady-state mass
1 balance on substrate is
then
Ds f  s  
YX / S
mx  0
• Putting the value of m
Ds f  s  
m max sx
YX / S s  K s 
0
• The corresponding cell mass balance is
 m max s


 D  x  Dx f  0
 Ks  s

• These two equation are called Monod chemostat
model equation
• For the common use of sterile feed (xf = 0), thus
the can be solved for x and s to yield
xsterilefeed
• and

DK s 

 YX / S  s f 
mmax  D 

xsterilefeed
DK s

m max  D

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