A more holistic view of the logarithmic dose–response curve offers greater insights into insulin responses

The stimulus-response curve is usually modeled by the Hill function due to its simplicity and clear molecular mechanisms (Michaelis-Menten type of kinetics). Unfortunately, the mechanisms do not explain why the stimulus is ubiquitously measured by logarithmic dose rather than the dose itself and why the log(dose)-response curve possesses such fine properties as symmetry and wide adjustability. Here, the dose-response is considered from a holistic perspective spanning multiple biological levels from molecules to the whole organism, which reveals that an appropriate model for log(dose) response is the cumulative normal distribution (CND) function, which had only statistical implication previously but now possess mechanistic-statistical duality. The present CND model establishes a connection between single-cell all-or-none responses and the graded response at the tissue/organism level, reveals the raison d'être of the logarithmic transformation, explains why log(dose)-response curve possesses many fine properties, and reveals new mechanisms of tissue/organism dose-response, including homogeneity-induced sensitivity. It also provides new insights into vital biological processes, such as the insulin dose-response.