Kubinyi H
Arzneimittelforschung. 1976;26(11):1991-7.
A new model is derived for the dependence of biological activity on hydrophobic character from a simple hypothetical system. Unlike the parabolic Hansch model this model can explain the peculiar effect that for homologous series of compounds the logarithms of biological activities of the lower homologs are linearly dependent on hydrophobic character, while for the higher homologs the relationship between biological activities and hydrophobic character changes to a parabola. Although these relationships are known and several appropriate models were proposed, the bilinear model presented in this paper is the first which can be described by a simple and generally valid equation: log 1/C = a log P--b log (beta - P + 1) + c While the parameters a, b and c can be calculated by linear multiple regression analysis, the non-linear term beta must be derived by a stepwise iteration process or ty Taylor series iteration. Examples are given for comparison of the bilinear model and the parabolic Hansch model.
从一个简单的假设系统中推导出了一个关于生物活性与疏水特性关系的新模型。与抛物线型的汉斯奇模型不同，该模型能够解释这样一种特殊效应：对于同系物系列化合物，较低同系物的生物活性对数与疏水特性呈线性相关，而对于较高同系物，生物活性与疏水特性之间的关系则变为抛物线型。尽管这些关系是已知的，并且已经提出了几个合适的模型，但本文提出的双线性模型是第一个能用一个简单且普遍有效的方程描述的模型：log 1/C = a log P - b log (β - P + 1) + c。虽然参数a、b和c可以通过线性多元回归分析计算得出，但非线性项β必须通过逐步迭代过程或泰勒级数迭代来推导。给出了双线性模型与抛物线型汉斯奇模型比较的实例。
