Using machine learning tools to model complex toxic interactions with limited sampling regimes.

A major impediment to understanding the impact of environmental stress, including toxins and other pollutants, on organisms, is that organisms are rarely challenged by one or a few stressors in natural systems. Thus, linking laboratory experiments that are limited by practical considerations to a few stressors and a few levels of these stressors to real world conditions is constrained. In addition, while the existence of complex interactions among stressors can be identified by current statistical methods, these methods do not provide a means to construct mathematical models of these interactions. In this paper, we offer a two-step process by which complex interactions of stressors on biological systems can be modeled in an experimental design that is within the limits of practicality. We begin with the notion that environment conditions circumscribe an n-dimensional hyperspace within which biological processes or end points are embedded. We then randomly sample this hyperspace to establish experimental conditions that span the range of the relevant parameters and conduct the experiment(s) based upon these selected conditions. Models of the complex interactions of the parameters are then extracted using machine learning tools, specifically artificial neural networks. This approach can rapidly generate highly accurate models of biological responses to complex interactions among environmentally relevant toxins, identify critical subspaces where nonlinear responses exist, and provide an expedient means of designing traditional experiments to test the impact of complex mixtures on biological responses. Further, this can be accomplished with an astonishingly small sample size.