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 (), that is, = /( + )

where is substrate concentration, is the Hill number and is a constant. For substrates such as N or P, which are conserved in the biomass, the substrate content of the biomass v(α) will vary according to the relation (α—α)/(α—α)= /( + )

where α, is the hinimum substrate content of the biomass, occurring when ≤ O, and α, 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 /( + )

where is a constant given by α. If the substrate is conserved, α, = 1/ and α =1/ where and 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 = 5·5, = 0·47, = ( ) = 82 μg N 1, i = Kshlln = 94 pgN1-l. 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, and was about 28 μ P 1-l. A discrepancy was found between the value for P uptake obtained from the 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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