The Effects of Cooperativity and Growth Yield Variation on the Kinetics of Nitrogen or Phosphate Limited Growth of Chlorella in a Chemostat Culture

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, Q = Q m S n / ( S n + K sh ) 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 ( α − α 0 ) / ( α m − α 0 ) = S n / ( S n + K sh ) 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 μ = μ m S n / ( S n + L K sh ) 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 s ′ = 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.