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

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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), i.e., Q = QmSn/(Sn + Ksh), where S is substrate concentration, n is the Hill number and Ksh is a constant. For substrates such as N or P, which are conserved in the biomass, the substrate content of the biomass (.alpha.) will vary according to the relation (.alpha.-.alpha.0)/(.alpha.m-.alpha.0) = Sn/(Sn + Ksh), where .alpha.0 is the minimum substrate content of the biomass, occurring when S .fwdarw. 0, and .alpha.m is the maximum substrate content of the biomass, occurring when the biomass is saturated with substrate. The specific growth rate is given by .mu. = .mu.mSn/(Sn + LKsh), where L is a constant given by .alpha.0/.alpha.m. If the substrate is conserved, .alpha.0 = 1/Y0 and .mu. = 1/Ym where Y0 and Ym are the maximum and minimum yields from the substrate, respectively. Experimental tests of these relations applied to N (urea)-limited growth of C. 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, Ks = (LKsh)1/n = 82 .mu.g N 1-1, .**GRAPHIC**. = Ksh1/n = 94 .mu.g N 1-1. 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 Ks was about 28 .mu.g P 1-1. A discrepancy was found between the Ksh value for P uptake obtained from the Q data and that from the .alpha. data. This discrepancy may be attributed to phosphate storage in the biomass, which is not allowed for in the model.

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