1. Lecture 2: Advanced Growth Kinetics
Dr. AKM Shafiqul Islam
12/03/08

2. Kinetics of Balance Growth
The net rate of cell mass growth rx is given by the equation
Where
x = cell mass per unit culture volume
m = the specific growth rate of the cell

3. Using this equation in the steady-state CSTR material balance for cell mass gives
The feed stream is normally sterile medium. Therefore xf = 0 and Dxf=0.

4. 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.

5. 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

6. 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.

7. 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 limiting the amount of nutrient in the medium

8. 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

9. Monod Growth Kinetics
A functional relationship between the specific growth rate m and essential compound’s concentration was proposed by Monod in 1942.
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.

10. 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.

11. 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

12. The value of Ks is rather small
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

13. 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

14. 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
The steady-state mass balance on substrate is then

15. Putting the value of m
The corresponding cell mass balance is
These two equation are called Monod chemostat model equation

16. For the common use of sterile feed (xf = 0), thus the can be solved for x and s to yield