**Modeling Growth and Photoadaptation of ***Porphyridium purpureum* Batch Culture
**Lelekov A.S.**^{1}, Klochkova V.S.^{2}
^{1}*A.O. Kovalevsky Institute of Biology of the Southern Seas of RAS, Russia*

^{2}*The Sevastopol State University, Department of Physics, Sevastopol, Russia*

**Abstract**. The work focuses on mathematical modeling of linear growth marine red algae *Porphyridium purpureum* batch culture under various surface irradiation. Before starting the batch culture *P. purpureum* was maintained for 3–5 days in turbidostat, which allowed the culture to adapt to a given light intensity. On each batch curve the maximum specific growth rate and maximum productivity are determined by approximating the exponential and linear growth phases with the appropriate equations. It is taken into account that at the beginning of the linear growth phase the integral light absorption coefficient, calculated from the true absorption spectrum in PAR range, exceeded 50 %. It is shown that with light intensity increase from 15 to 227 µmol photons m^{–2}·s^{–1} the maximum specific growth rate increased from 0.31 to 1 day^{–1}, the maximum productivity increased from 1.32 to 16.38 g DW m^{–2}·day^{–1}. Mathematical modeling of the linear growth of *P. purpureum* batch culture have showed that at any light intensity the specific growth rate is determined by the surface illumination, the light absorption coefficient and chlorophyll* a* concentration. The concept of reduced irradiation – the amount of absorbed light energy per chlorophyll *a* – was introduced. A linear dependence of the specific growth rate on reduced irradiation is given. The tangent of the angle of line slope is determined by the organization of the key multi-enzyme complex («metabolism bottleneck»). Parameters of this complex depend on the cells photoadaptation degree. For the first time a quantitative relationship between multi-enzyme complex parameters, light intensity and the chlorophyll / P700 ratio was established.

**Key words**: *microalgae, specific growth rate, chlorophyll a, productivity, reduced irradiance, photosynthetic unit size.*