Mathematical modeling of PCB bioaccumulation in Perna viridis

In the present work, we built a mathematical model of polychlorinated biphenyl (PCB) bioaccumulation in Perna viridis, namely, a one-compartment model with a time dependent incorporation rate R (μgg^-1 lipid per ppb water per day), with positive substrate cooperativity as the underlying physical mechanism. The temporal change of the PCB concentration Q (μgg^-1 lipid) in the soft tissues of the mussel depends on the competition of the input rate RW and the output rate kQ, where W is the concentration of PCB in water (ppb water) and k is the elimination rate (per day). From our experimental data, k=0.181±0.017 d^-1. The critical concentration in water W_c for positive substrate cooperativity was found to be ∼2.4 ppb. Below W_c, R is a constant. For a water concentration of 0.5 ppb Aroclor 1254, R=24.0±2.4 μgg^-1 lipid ppb^-1d^-1. Above W_c, positive substrate cooperativity comes into effect and R becomes a function of time and dependent on the concentration Q in a form R=γQ/(Q+δ). This is the case for a water concentration of 5 ppb Aroclor 1254, where γ=15.1 μgg^-1 lipid ppb^-1d¹ and δ≈200 μgg^-1 lipid. From this model, the uptake is exponentially increasing when the PCB concentration in the mussel is small compared to 200 μgg^-1 lipid, and hyperbolically increasing when the concentration is large compared to 200 μgg^-1 lipid, which are consistent with the experimental data. The model is useful for understanding the true processes taking place during the bioaccumulation and for risk assessment with higher confidence. Future experimental data which challenge the present model are anticipated and in fact desirable for improvement and perfection of the model.