Quantitative regularities of growth of Arthrospira platensis batch culture

The work focuses on the modeling the light-dependent growth of Arthrospira platensis. During the experimental study, we obtained a batch curve, which characterizes the presence of a long linear phase. We showed that the constant culture productivity is determined by the light conditions in which cells are located. The simplest model of the light-dependent growth of a batch culture is proposed. The model is based on the assumption that the specific growth rate is determined by the surface irradiation, the light absorption coefficient, and the concentration of chlorophyll $a$. Verification of the obtained equations indicates that the constant productivity is observed only in the case of a hyperbolic decrease chlorophyll $a$ content and other structural compounds of microalgal biomass. A method for rapid assessment of the concentration of photosynthetic pigments in the A. platensis culture by its absorption spectrum using the sum of Gaussian curves is proposed. Mathematical decomposition of the absorption spectrum of A. platensis was carried out, all Gaussian parameters were calculated. For the red part of the spectrum, a simple expression is presented that allows one to estimate the concentration of chlorophyll $a$ and phycobiliproteins. The native extinction coefficient of chlorophyll $a$ at 678 nm was calculated to be 65 l$\cdot$ g$^{-1}\cdot$ cm$^{-1}$. We proposed an algorithm for determining the concentration of photosynthetic pigments directly from the true absorption spectrum of the A. platensis culture without interfering with its growth processes.