Many cellular responses are quantal; that is, they either take place or they do not. Examples of "either-or" responses include cell replication, differentiation and apoptosis. Surprisingly, induction of suites of genes and coordinated phenotypic changes in cells are also often quantal, where embedded molecular circuitry creates on-off switches. Mechanistic incidence-dose (ID) models need to account for the quantal characteristics of cellular switches that contribute, in turn, to dose thresholds and to the incidence of biological responses in individuals. Interdisciplinary systems biology approaches create mechanistic ID models based on: (i) detailed knowledge of the cellular circuitry controlling signal transduction; (ii) evolving biological modeling tools describing cellular circuits and their perturbations by chemicals and (iii) high throughput, high coverage "omic" screens for examining cell signaling pathways and biological responses. These interdisciplinary approaches should produce novel, quantitative ID models for biological responses and greatly improve the biological basis of safety and risk assessments.