Motulsky H J, Mahan L C
Mol Pharmacol. 1984 Jan;25(1):1-9.
Although equilibrium competitive radioligand binding studies are often used to characterize hormone and neurotransmitter receptors, the kinetics of such experiments have not been extensively explored. The interactions of the radioligand and competitor with the receptors can be described by two differential equations which can be solved to yield a single equation describing the binding of the radioligand as a function of time. This equation has several applications: First, it can be used to simulate competitive binding reactions under defined conditions. Second, fitting experimental data to this equation allows one to determine the association and dissociation rate constants of the competing ligand, parameters that cannot be derived from equilibrium experiments. Furthermore, this method can be used to determine the KI of the competing drug from data acquired before equilibrium is reached. Third, mathematical analysis of the binding equation allowed us to answer two specific questions regarding the kinetics of competitive radioligand binding: how long such an incubation takes to equilibrate, and how the IC50 varies over time. The answers to these questions depended, to a large extent, on the relative values of the dissociation rate constants of the radioligand and competitor, which can be determined as noted above. When the competitor dissociates from the receptors more rapidly than the radioligand, the IC50 first decreases and then increases, but never has a value less than the KI. At low radioligand concentrations, equilibrium is reached in the same amount of time required of the radioligand to dissociate completely from the receptors as determined in an "off-rate experiment." At higher concentrations of radioligand this time is halved. When the competitor dissociates from the receptor more slowly than does the radioligand, then the time required to equilibrate depends only on the dissociation rate constant of the competitor, and the IC50 decreases over time.
尽管平衡竞争性放射性配体结合研究常用于表征激素和神经递质受体，但此类实验的动力学尚未得到广泛探索。放射性配体和竞争者与受体的相互作用可用两个微分方程来描述，求解这两个方程可得到一个描述放射性配体结合量随时间变化的单一方程。该方程有几个应用：第一，它可用于模拟特定条件下的竞争性结合反应。第二，将实验数据拟合到该方程可使人们确定竞争配体的结合和解离速率常数，这些参数无法从平衡实验中得出。此外，该方法可用于根据平衡达到之前获取的数据确定竞争药物的抑制常数（KI）。第三，对结合方程的数学分析使我们能够回答关于竞争性放射性配体结合动力学的两个具体问题：这样的孵育需要多长时间达到平衡，以及半数抑制浓度（IC50）如何随时间变化。这些问题的答案在很大程度上取决于放射性配体和竞争者解离速率常数的相对值，如上文所述，这些值是可以确定的。当竞争者从受体上解离的速度比放射性配体快时，IC50先降低然后升高，但从未低于KI值。在低放射性配体浓度下，达到平衡所需的时间与在“解离速率实验”中确定的放射性配体从受体上完全解离所需的时间相同。在较高的放射性配体浓度下，这个时间减半。当竞争者从受体上解离的速度比放射性配体慢时，达到平衡所需的时间仅取决于竞争者的解离速率常数，且IC50随时间降低。
