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. 2013 Sep 23;8(9):e74456. doi: 10.1371/journal.pone.0074456

Table 1. Simple dynamic model describing the feedbacks.

State variables Inline graphic Chlorophyll-a in algal population (µg-Chl-a L−1)
D Dissolved organic carbon (DOC) concentration (mg-C L−1)
Inline graphic Concentration of dissolved silver (mg-Ag L−1)
Inline graphic Concentration of bioavailable AgNPs (mg-Ag L−1)
Inline graphic Concentration of inactivated AgNPs (mg-Ag L−1)
q “quota” of bioaccumulated Ag in algae (mg-Ag (µg-Chl-a)−1)
Rates Inline graphic exposure-related specific mortality rate of algae (day−1)
Inline graphic rate of dissolution of AgNPs (mg-Ag L−1 day−1)
Inline graphic rate of inactivation of ionic silver (mg-Ag L−1 day−1)
Inline graphic rate of inactivation of AgNPs (mg-Ag L−1 day−1)
P rate of production of DOC by algae (mg-C day−1)
Balance Equations Inline graphic Algae
Inline graphic Dissolved organic carbon (DOC)
Inline graphic Bioavailable AgNPs
Inline graphic Inactivated AgNPs
Inline graphic Ionic silver
Inline graphic Quota
Model functions Inline graphic Exposure-induced mortality
Inline graphic AgNP dissolution
Inline graphic AgNP inactivation by DOC
Inline graphic Inactivation of ionic silver
Inline graphic DOC production
Inline graphic Chl-a in control population

Subscripts used are N:silver nanoparticles; I: ionic silver; U: non-bioavailable (inactivated) silver. In the balance equations, Inline graphicdenotes the rate of transformation of silver in state n to state m. Parameters are defined in Table 2. Note: the notation [x]+ means use the value of x if it is positive, otherwise set to zero.