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The Effects of Cooperativity and Growth Yield Variation on the Kinetics of Nitrogen or Phosphate Limited Growth of Chlorella in a Chemostat Culture
Abstract
Accounting for a cooperativity effect in substrate uptake by a microbial culture leads to a Hill type of equation for the specific rate of substrate uptake (Q), that is,
where S is substrate concentration, n is the Hill number and K
sh is a constant. For substrates such as N or P, which are conserved in the biomass, the substrate content of the biomass (α) will vary according to the relation
where α
0 is the minimum substrate content of the biomass, occurring when S → 0, and α
m is the maximum substrate content of the biomass, occurring when the biomass is saturated with substrate. The specific growth rate is given by
where L is a constant given by α 0/α m. If the substrate is conserved, α 0 = 1/Y 0 and α m = 1/Y m where Y 0 and Y m are the maximum and minimum yields from the substrate, respectively.
Experimental tests of these relations applied to N (urea)-limited growth of Chlorella vulgaris in chemostat cultures showed satisfactory agreement between the results and the theory. For N uptake the growth constants were n = 5·5, L = 0·47, K
s = (LK
sh)1/n
= 82 μg N l–1, 
= K
sh
1/n
= 94 μg N l–1. The apparent departure of L from unity in N-limited growth can be accounted for by starch storage in the biomass.
For P (phosphate)-limited growth, n = 1·3, L = 0·15 and K s was about 28 μg P l–1. A discrepancy was found between the K sh value for P uptake obtained from the Q data and that from the α data. This discrepancy may be attributed to phosphate storage in the biomass, which is not allowed for in the model.
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© Society for General Microbiology 1978