Toxicity is described by classical dose-response (also called concentration-response) relationships that usually follow linear or sigmoidal trends. The toxicity of a compound is interpreted as the increase in intensity of the effect as a function of exposure concentration or time. This classic descriptor of toxicity was and is still successfully used in toxicology and pharmacology to describe various toxic responses (decreased survival) and sub-lethal effects at the organ or systemic levels (e.g., weight loss or decreased growth). The advent of biomarkers at the molecular level enabled a better understanding of the way chemicals negatively act at the fundamental level. In some cases, dose-response curves showed curious non-linear relationships which complicate the prediction of adverse toxic outcomes of biochemical/molecular changes. A close examination of the relationships between the intensity of biochemical markers and concentration suggests that biological effects are oscillatory (cyclic) in nature. Spectral analysis using Fourier transformation can decompose signal intensities as a combination of wave functions to describe the cyclic nature of biochemical changes. We tested this approach with a real case, exposing juvenile rainbow trout to seven rare earths using a gene expression quantitative real-time polymerase chain reactions (qPCR) array composed of 12 genes involved in toxic stress responses and compared those responses with the hepatic somatic index, fish condition and trout mortality endpoints. Multiple regression analysis on the classical endpoints (intensity of the 12 transcripts) showed only a few significant relationships between gene expression changes and toxicity. However, spectral analysis transformation of the gene expression data revealed highly significant relationships (r > 0.95) with liver weight data and mortality. This study proposes a data transformation based on the cyclic properties of molecular changes using spectral analysis with Fourier transformation. This novel approach considers the possibility that toxic responses could behave as waves providing a means to explore relationships between the mode of action of chemicals and adverse outcome pathways.
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