Modeling the growth curve for Spirulina (Arthrospira) maxima, a versatile microalga for producing uniformly labelled compounds with stable isotopes

The paper presents a five-phase model to describe batch culture of Spirulina maxima under limitations of light and nutrients nitrogen andsulfur. The general equation for the exponential, linear, decelerating andstationary phases of the growth curve took into account that (i) the specificgrowth rate was proportional to the local light intensity in thephotobioreactor; (ii) light attenuation was due to cell's absorption andreflection and observed the Lambert-Beer's law with a total absorptioncoefficient (_T) that was the sum of absorption coefficient(_a) and reflection coefficient (_r); (iii) thecomposition of the alga and its absorption _a changed withtime and (iv) the specific growth rate was influenced by nutrients ofnitrogen and sulfur in the culture medium according to a Monod's law.Two successive equations describing the death phase were proposed basedon the hypothesis that the death rate accelerated with the %PSC until itreached its maximum. From that point the %PSC decreased and the deathrate reduced. Our model fitted very well the cultures grown in the photobioreactor developed in our laboratory.