Modeling of chlorophyll $a$ content in microalgae cultures

The work focuses on mathematical modeling of light influence mechanisms on chlorophyll a content in microalgae biomass. The well-known qualitative models are based on concepts of synthesis and photodestructive oxidation of chlorophyll $a$, however the later for some microalgae species seems doubtful. We proposed an alternative approach to modeling the light-dependent chlorophyll $a$ content in microalgae biomass. The basic model is based on generally accepted two-stage photoautotrophic growth of microalgae. At the first stage, during photosynthesis a reserve part of biomass is formed, from which the biosynthesis of cell structures occurs at the second stage. Three partial solutions of the basic system of equations describing the dependence of chlorophyll $a$ content on the external light intensity are considered for various limiting conditions. Due to the equality of specific growth rates of formation of reserve and structural forms of biomass, the equations obtained can be used only for turbidostat cultures. Verification of the obtained equations for Arthrospira platensis allows us to estimate kinetic coefficients, the values of which are generally in good agreement with theoretically calculated ones. For approximate calculations, a simple equation is proposed that shows a good agreement with experimental data for Tetraselmis viridis ($R^2$ = 0.98), Dunaliella tertiolecta ($R^2$ = 0.92) and describes the results for Sceletonema costatum and Chlorella vulgaris ($R^2$ = 0.8) quite well. Chlorophyll $a$ refers to structural forms of biomass. The proportion of chlorophyll $a$ in the structural biomass is about 2.5–3.5 %, it is a species-specific parameter.