Simulating synergism or antagonism in binary mixtures with different modeling approaches - A case study focused on the effect of disinfection by-products on algal growth.

This paper aims to test several modeling approaches for predicting toxicity of binary mixtures with potential synergy and antagonism. The approach based on the construction of isoboles was first tested and criticized. In contrast to conventional approaches, and in order to be mathematically consistent with the additivity assumptions, non-linear isoboles have been constructed. This approach was compared with that proposed by Minto et al. (2000), which measures deviations from additivity by considering standardized variables and which considers the entire Hill concentration-response curves. The selected models were tested on a case study related to chlorine-based disinfectant by-products (DBPs), using experimental data describing the effect of five DBPs (monochloroacetic acid, dichloroacetic acid, trichloroacetic acid, bromochloroacetic acid and 1,1-dichloropropan-2-one) on a unicellular green algae Raphidocelis subcapitata. The approach based on the construction of isoboles has shown its limitations. Indeed, in cases where the individual substances involved have different slopes in terms of their Hill concentration-effect relationships, the so-called zone of indetermination can be large. Furthermore, conclusions drawn from isoboles based on EC₅₀s or EC₂₀s may not be consistent. Minto's approach makes it possible to construct interaction indicators that consider the entire Hill concentration-response curve. Response surfaces can be constructed to visualize the areas of concentration of the two substances involved that maximize the interaction effects.