Laboratory of Environmental Biotechnology, Institute of Microbiology of the CAS, v.v.i., Vídeňská 1083, Prague, 142 20, Czech Republic.
Laboratory of Environmental Biotechnology, Institute of Microbiology of the CAS, v.v.i., Vídeňská 1083, Prague, 142 20, Czech Republic; Institute for Environmental Studies, Faculty of Science, Charles University in Prague, Albertov 6, Prague, 128 43, Czech Republic.
Toxicology. 2019 May 15;420:21-28. doi: 10.1016/j.tox.2019.03.015. Epub 2019 Mar 29.
The equilibrium dissociation constant of competitive antagonists represents the affinity of the receptor-ligand interaction, and it is a key characteristic of many therapeutic drugs or toxic compounds. Two commonly used methods by which the affinity of the antagonist can be estimated are Schild analysis and the Cheng-Prusoff method. However, both methods yield different results when applied to systems with slopes not equal to one. The Gaddum equation, which is fundamental for both methods, should be extended to incorporate the slope parameter of the dose-response curves and this extension should diminish the differences between the Schild and Cheng-Prusoff methods. In this study, we derived a novel form of the Gaddum equation with a slope parameter (Hill coefficient) of agonist dose-response curve. We also derived the subsequent equations for Schild and Cheng-Prusoff analysis and we validated the proposed model by the measurement of several known estrogen receptor competitive antagonists. Standardized in vitro yeast reporter gene assay (BMAEREluc/ERα) has been used for the measurements and the range of used antagonist concentrations was 1.37-46.03 μM. By applying our mathematical model, both Schild and Cheng-Prusoff methods provide more similar values of antagonist affinity than the original mathematical approach. The correctness of the model has also been demonstrated by the measurement of a partial agonist with a known receptor affinity. The presented mathematical model significantly reduces the differences in values calculated by the Cheng-Prusoff and Schild methods and yields more accurate estimations of antagonist affinity.
竞争性拮抗剂的平衡解离常数代表受体-配体相互作用的亲和力，它是许多治疗药物或有毒化合物的关键特征。估计拮抗剂亲和力的两种常用方法是 Schild 分析和 Cheng-Prusoff 方法。然而，当应用于斜率不等于 1 的系统时，这两种方法都会产生不同的结果。Gaddum 方程是这两种方法的基础，应该扩展到包含剂量反应曲线的斜率参数，并且这种扩展应该减少 Schild 和 Cheng-Prusoff 方法之间的差异。在这项研究中，我们推导出了一种新的带有激动剂剂量反应曲线斜率参数（Hill 系数）的 Gaddum 方程形式。我们还推导出了随后的 Schild 和 Cheng-Prusoff 分析方程，并且通过测量几个已知的雌激素受体竞争性拮抗剂验证了所提出的模型。标准化的体外酵母报告基因测定（BMAEREluc/ERα）已用于测量，并且使用的拮抗剂浓度范围为 1.37-46.03 μM。通过应用我们的数学模型，Schild 和 Cheng-Prusoff 方法提供的拮抗剂亲和力值比原始数学方法更相似。该模型的正确性还通过测量具有已知受体亲和力的部分激动剂得到了证明。所提出的数学模型显著减少了 Cheng-Prusoff 和 Schild 方法计算值之间的差异，并产生了更准确的拮抗剂亲和力估计值。
