Le Bonniec B, Sauloy J, Ducrocq R, Elion J
Laboratoire de Biochimie B, Faculté Xavier Bichat, Université Paris 7, France.
Anal Biochem. 1988 Oct;174(1):280-90. doi: 10.1016/0003-2697(88)90547-7.
A method is proposed to set the parameters in a nonlinear regression procedure to determine the equilibrium dissociation constant (Kd) and the high affinity receptor concentration (Bmax) of systems consisting of one ligand, one high affinity receptor, and n low affinity binding sites. This method is suitable when neither bound or free ligand formal concentrations nor the maximum of the binding signal can be deduced from the experimental data. The method makes use of (i) the abscissa of the first inflection point of the plot of any signal proportional to the binding of ligand to receptors versus the logarithm of the total ligand concentration, and (ii) the initial slope of the saturation curve plotted in direct coordinates. We first demonstrate that when such an inflection point exists, its abscissa lies between Bmax/2 + Kd(1 + d) and Bmax + 2Kd(1 + d), where d is a parameter representative of the binding to the low affinity sites. Second, we demonstrate that the initial slopes of two saturation curves in direct coordinates, where Bmax varies by a known factor, allows an estimation of the Bmax/Kd ratio, within certain limits. From these two sets of data it is subsequently possible to define a precise window for the values of both Bmax and Kd. The performance of the method has been evaluated in representative cases using Monte Carlo studies. The results establish conditions for the existence of an inflection point as well as the influence of low affinity binding, whether or not proportional to Bmax.
提出了一种在非线性回归程序中设置参数的方法，以确定由一种配体、一种高亲和力受体和n个低亲和力结合位点组成的系统的平衡解离常数（Kd）和高亲和力受体浓度（Bmax）。当无法从实验数据中推导出结合或游离配体的形式浓度以及结合信号的最大值时，该方法适用。该方法利用（i）与配体与受体结合成正比的任何信号与总配体浓度对数的关系图的第一个拐点的横坐标，以及（ii）在直角坐标中绘制的饱和曲线的初始斜率。我们首先证明，当存在这样一个拐点时，其横坐标介于Bmax/2 + Kd(1 + d)和Bmax + 2Kd(1 + d)之间，其中d是代表与低亲和力位点结合的参数。其次，我们证明，在直角坐标中Bmax以已知因子变化的两条饱和曲线的初始斜率，在一定限度内允许估计Bmax/Kd比值。从这两组数据中，随后可以为Bmax和Kd的值定义一个精确的窗口。使用蒙特卡罗研究在代表性案例中评估了该方法的性能。结果确定了拐点存在的条件以及低亲和力结合的影响，无论其是否与Bmax成正比。
