# 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 Ds f s YX / S mx 0 • Putting the value of m Ds 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