Advancing analytical and graphical methods for binary and ternary mixtures: The toxic interactions of divalent metal...

Humans are exposed to various environmental chemicals, particles, and pathogens that can cause adverse health outcomes. These exposures are rarely homogenous but rather complex mixtures in which the components may interact, such as through synergism or antagonism. Toxicologists have conducted preliminary investigations into binary mixtures of two components, but little work has been done to understand mixtures of three or more components. We investigated mixtures of divalent metal ions, quantifying the toxic interactions in a human lung model. Eight metals were chosen: heavy metals cadmium, copper, lead, and tin, as well as transition metals iron, manganese, nickel, and zinc. Human alveolar epithelial cells (A549) were exposed to individual metals and sixteen binary and six ternary combinations. The dose-response was modeled using logistic regression in R to extract LC₅₀ values. Among the individual metals, the highest and lowest toxicity were observed with copper at an LC₅₀ of 102 μM and lead at an LC₅₀ of 5639 μM, respectively. First and second-order interaction coefficients were obtained using machine learning-based linear regression in Python. The resulting second-degree polynomial model formed either a hyperbolic or elliptical conic section, and the positive quadrant was used to produce isobolograms and contour plots. The strongest synergism and antagonism were observed in cadmium-copper and iron-zinc, respectively. A three-way interaction term was added to produce full ternary isobologram surfaces, which, to our knowledge, are a significant first in the toxicology literature.