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.

中文翻译：

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对数剂量-反应曲线的更全面视图有助于更深入地了解胰岛素反应


刺激-反应曲线通常由 Hill 函数建模，因为它简单且分子机制清晰（Michaelis-Menten 类型的动力学）。不幸的是，这些机制并没有解释为什么刺激普遍是通过对数剂量而不是剂量本身来测量的，以及为什么对数（剂量）反应曲线具有对称性和广泛的可调性等精细特性。在这里，剂量反应是从跨越从分子到整个生物体的多个生物水平的整体角度考虑的，这表明对数（剂量）反应的合适模型是累积正态分布 （CND） 函数，它以前只有统计意义，但现在具有机械-统计二元性。目前的 CND 模型在单细胞全或无反应与组织/生物体水平的分级反应之间建立了联系，揭示了对数变换的存在理由，解释了为什么对数（剂量）反应曲线具有许多优良特性，并揭示了组织/生物体剂量反应的新机制，包括同质性诱导的敏感性。它还为重要的生物过程提供了新的见解，例如胰岛素剂量反应。