Oscillations of algal cell quota: Considering two-stage phosphate uptake kinetics

Elucidating the mechanism of effect of phosphate (PO3-4 ) uptake on the growth of algal cells helps understand the frequent outbreaks of algal blooms caused by eutrophication. In this study, we develop a comprehensive mathematical model that incorporates two stages of PO3-4 uptake and accounts for transport time delay. The model parameter values are determined by fitting experimental data of Prorocentrum donghaiense and the model is validated using experimental data of Karenia mikimotoi. The numerical results demonstrate that the model successfully captures the general characteristics of algal growth and PO3-4 uptake under PO3-4 sufficient conditions. Significantly, the experimental and mathematical findings suggest that the time delay associated with the transfer of PO3-4 from the surface -adsorbed PO3-4 (Ps) pool to the intracellular PO3- 4 (Pi) pool may serve as a physiologically plausible mechanism leading to oscillations of algal cell quota. These results have important implications for resource managers, enabling them to predict and deepen their understanding of harmful algal blooms.