Hoffman A, Goldberg A
Department of Pharmacy, School of Pharmacy, Hebrew University of Jerusalem, Israel.
J Pharmacokinet Biopharm. 1994 Dec;22(6):449-68. doi: 10.1007/BF02353789.
The apparent concentration-effect relationship is the ensemble of many effector units (such as individual cells or channels) that do not always exhibit a uniform stimulus-effect relationship. This concept is substantiated by many observations of heterogeneity in receptor-effector populations including hormone secreting cells, response to hormonal stimuli, activity pattern of second messengers, stimulus-evoked synaptic currents, and single ion channels. The relationship between drug concentration and magnitude of pharmacologic response is commonly described by the sigmoidal Emax model which was derived from the Hill equation. The sigmoidicity factor (N) in this model is assumed to be a pure mathematical parameter without physiological connotations. This work demonstrates that the numerical value of N (measured empirically) is the product of two factors: (i) the degree of heterogeneity of the effector subunits, i.e., the elemental component that upon drug stimulus contributes its pharmacological effect independently and does not interact with other subunits (it could range from a single receptor up to a whole tissue), and (ii) value of N*--the shape factor of the subunits' concentration-effect relationship. A special case of this approach occurs when N* > 5, which is an on-off case. Here N is determined by the distribution (density equation) of the subunit values. In case of heterogeneity of the microparameters of the effector subunits the apparent N will always have a lower value than N*. According to this theory it can be concluded that without knowledge of the distribution of the microparameters no mechanistic interpretation can be deduced from the apparent N value. If in the future N* can be determined by theoretical or experimental methods, the distribution function relating N* to N can be calculated. The relevance of this theory is increased in view of the progress being made in advanced research techniques which may enable us to determine the concentration-effect relationship at the level of the individual effector unit.
表观浓度 - 效应关系是由许多效应单元（如单个细胞或通道）组成的集合，这些效应单元并不总是呈现统一的刺激 - 效应关系。这一概念通过许多关于受体 - 效应器群体异质性的观察得到证实，包括激素分泌细胞、对激素刺激的反应、第二信使的活性模式、刺激诱发的突触电流以及单离子通道。药物浓度与药理反应强度之间的关系通常用从希尔方程推导而来的S形Emax模型来描述。该模型中的S形因子（N）被假定为一个没有生理内涵的纯数学参数。这项研究表明，N的数值（通过实验测量）是两个因素的乘积：（i）效应亚基的异质性程度，即药物刺激后独立产生药理效应且不与其他亚基相互作用的基本组成部分（其范围可以从单个受体到整个组织），以及（ii）N的值——亚基浓度 - 效应关系的形状因子。当N > 5时会出现这种方法的一个特殊情况，这是一个开关情况。在这里，N由亚基值的分布（密度方程）决定。在效应亚基微观参数存在异质性的情况下，表观N值总是低于N*。根据这一理论可以得出结论，如果不知道微观参数的分布，就无法从表观N值推导出任何机制性解释。如果未来可以通过理论或实验方法确定N*，那么可以计算出将N*与N相关联的分布函数。鉴于先进研究技术的进展，这一理论的相关性得到了增强，这些技术可能使我们能够在单个效应单元水平上确定浓度 - 效应关系。
