# DEVELOPMENT OF ALTERNATIVE MATHEMATICAL TOOLS TO ASSESS SYNERGISTIC MIXTURE EFFECTS Poster (konferens), 2015

Mixture effects are well known problems but chemical legislations are typically based on single chemical toxicity, which is unfortunate as chemicals occur as mixtures in the environment. There are mathematical models to assess additive mixture effects that are based on linear mixture effects such as toxicodynamic interactions. Chemicals with same or different mode-of-actions can also interfere with each other’s elimination pathways that can result in toxicokinetic interactions and cause indirect mixture effects. Therefore, chemicals that inhibit CYP enzymes in the elimination pathways of different classes of environmental pollutants can cause non-linear mixture effects that are more-than-additive. More-than-additive mixture effects have been observed between azoles and other classes of environmental pollutants such as estrogenic chemicals and aromatic hydrocarbons, as a result of toxicokinetic interactions via CYP1A/CYP3A inhibitions. There is need for new mathematical models to assess non-linear mixture effects. We have initiated the development of alternative mathematical tools to forecast non-linear mixture effects that are based on toxicokinetic interactions from earlier lab-studies in fish and fish cells. Time-dynamic is a key factor in toxicokinetic interactions and therefore we will combine multiple differential equations in the models. These equations describe how one chemical’s concentration changes over time in relationship to changes of another chemical’s concentration over time and how that affect biomarker responses such as CYP1A and vitellogenin. We will use statistical tools to quantitatively fit the suggested models with data from lab-studies. Non-linear models can be used to describe synergistic mixture effects. Those could be bottom-up-models, where we start from the different chemicals involved, or they could be top-down-models, where we fit a multi-dimension function to a given dataset using an auxiliary non-linear model. Our preliminary non-linear mathematical top-down model describes how the vitellogenin and the CYP1A biomarker responses can vary with concentrations of a synthetic estrogen and an antimycotic azole.

CYP

fish

biomarkers

: mixture toxicity

mathematical models

## Författare

#### Malin C. Celander

Göteborgs universitet

#### Kerstin Wiklander

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematisk statistik

#### Torbjörn Lundh

Göteborgs universitet

Chalmers, Matematiska vetenskaper

#### Ämneskategorier

Matematik

Biologiska vetenskaper

2017-10-08