Mathematical modeling to simulate the adsorption and internalization of copper in two freshwater algae species, Pseudokirchneriella subcapitata and Chlorella vulgaris

Abstract

Prediction of the behavior of heavy metals over time is important to evaluate the heavy metal toxicity in algae species. Various modeling studies have been well established, but there is a need for an improved model for predicting the chronic effects of metals on algae species to combine the metal kinetics and biological response of algal cells. In this study, a kinetic dynamics model was developed to predict the copper behavior (5 μg L-1, 10 μg L-1, and 15 μg L-1) for two freshwater algae (Pseudokirchneriella subcapitata and Chlorella vulgaris) in the chronic exposure experiments (8 d and 21 d). In the experimental observations, the rapid change in copper mass between the solutions, extracellular and intracellular sites occurred within initial exposure periods, and then it was slower although the algal density changed with time. Our model showed a good agreement with the measured copper mass in each part for all tested conditions with an elapsed time (R 2 for P. subcapitata: 0.928, R 2 for C. vulgaris: 0.943). This study provides a novel kinetic dynamics model that is compromised between practical simplicity and realistic complexity, and it can be used to investigate the chronic effects of heavy metals on the algal population.