To transfer toxicological findings from model systems, e.g. animals, to humans, standardized safety factors are applied to account for intra-species and inter-species variabilities. An alternative approach would be to measure and model the actual compound-specific uncertainties. This biological concept assumes that all observed toxicities depend not only on the exposure situation (environment = E), but also on the genetic (G) background of the model (G × E). As a quantitative discipline, toxicology needs to move beyond merely qualitative G × E concepts. Research programs are required that determine the major biological variabilities affecting toxicity and categorize their relative weights and contributions. In a complementary approach, detailed case studies need to explore the role of genetic backgrounds in the adverse effects of defined chemicals. In addition, current understanding of the selection and propagation of adverse outcome pathways (AOP) in different biological environments is very limited. To improve understanding, a particular focus is required on modulatory and counter-regulatory steps. For quantitative approaches to address uncertainties, the concept of "genetic" influence needs a more precise definition. What is usually meant by this term in the context of G × E are the protein functions encoded by the genes. Besides the gene sequence, the regulation of the gene expression and function should also be accounted for. The widened concept of past and present "gene expression" influences is summarized here as G _e . Also, the concept of "environment" needs some re-consideration in situations where exposure timing (E _t ) is pivotal: prolonged or repeated exposure to the insult (chemical, physical, life style) affects G _e . This implies that it changes the model system. The interaction of G _e with E _t might be denoted as G _e × E _t . We provide here general explanations and specific examples for this concept and show how it could be applied in the context of New Approach Methodologies (NAM).