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.

Abstract
INTRODUCTION
MATERIAL AND METHODS
    1. Test algae and culture conditions
    2. Exposure experiments
    3. Dissolved, extracellular, and intracellularCu determination
    4. General kinetic models
    5. Long-term kinetic model development
RESULTS
    1. Evaluations of three general kinetic models
    2. Development of the long-term kineticmodel
    3. Model validation
DISCUSSION
REFERENCES

• Yongeun Kim(Ojeong Resilience Institute, Korea University)
• Minyoung Lee(Department of Environmental Science and Ecological Engineering, Korea University)
• Jinsol Hong(Department of Environmental Science and Ecological Engineering, Korea University)
• Kijong Cho(Department of Environmental Science and Ecological Engineering, Korea University) Corresponding author