Methods that allow quantification of receptor binding (occupancy) by measuring response (effect) data only are of interest as they can be used to allow characterization of binding properties (e.g., dissociation constant, K_d) without having to perform explicit ligand binding experiments that require different setups (e.g., use of labeled ligands). However, since response depends not just on the binding affinity-determined receptor occupancy, but also on receptor activation, which is affected by ligand efficacy (plus constitutive activity, if present), and downstream pathway amplification, this requires the acquisition and fitting of multiple concentration-response data. Here, two alternative methods, which both are straightforward to implement using nonlinear regression software, are described to fit such multiple responses measured at different receptor levels that can be obtained, for example, by partial irreversible receptor inactivation (i.e., Furchgott method) or different expression levels. One is a simple method via straightforward fitting of each response with sigmoid functions and estimation of K_d from the obtained E_max and EC₅₀ values as K_d=(E_max·EC’₅₀−E’_max·EC₅₀)/(E_max−E’_max). This is less error-prone than the original Furchgott method of double-reciprocal fit and simpler than alternatives that require concentration interpolations, thus, should allow more widespread use of this so-far underutilized approach to estimate binding properties. Relative efficacies can then be compared using E_max·K_d/EC₅₀ values. The other is a complex method that uses the SABRE receptor model to obtain a unified fit of the multiple concentration-response curves with a single set of parameters that include binding affinity K_d, efficacy ε, amplification γ, and Hill coefficient n. Illustrations with simulated and experimental data are presented including with activity data of three muscarinic agonists measured in rabbit myocardium.

中文翻译：

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从不同受体水平获得的响应数据量化受体结合：简单的个体 Sigmoid 拟合和统一的 SABRE 方法

仅通过测量响应（效果）数据来量化受体结合（占有率）的方法是令人感兴趣的，因为它们可用于表征结合特性（例如，解离常数，K _d) 无需执行需要不同设置（例如，使用标记的配体）的显式配体结合实验。然而，由于反应不仅取决于结合亲和力决定的受体占有率，还取决于受体激活，受配体功效（加上组成活性，如果存在）和下游通路放大的影响，这需要获取和拟合多个浓度反应数据。在这里，描述了两种替代方法，它们都可以直接使用非线性回归软件实现，以拟合在不同受体水平上测量的这种多重反应，例如，通过部分不可逆受体失活（即，Furchgott 方法）或不同表达水平。K _d从获得的E _max和 EC ₅₀值作为K _d =( E _max ·EC' ₅₀ - E ' _max ·EC ₅₀ )/( E _max - E ' _max )。这比双倒数拟合的原始 Furchgott 方法更不容易出错，并且比需要浓度插值的替代方法更简单，因此，应该允许更广泛地使用这种迄今为止未充分利用的方法来估计结合特性。然后可以使用E _max · K _{d比较相对功效}/EC ₅₀值。另一种是一种复杂的方法，它使用 SABER 受体模型来获得多个浓度-反应曲线的统一拟合，其中包含一组参数，包括结合亲和力K _d、功效ε、放大γ和希尔系数n。展示了模拟和实验数据的插图，包括在兔心肌中测量的三种毒蕈碱激动剂的活性数据。