Otago Pharmacometrics Group, National School of Pharmacy, University of Otago, Dunedin, New Zealand.
Department of Pharmacology and Clinical Pharmacology, Faculty of Medical and Health Sciences, University of Auckland, Auckland, New Zealand.
Br J Pharmacol. 2018 May;175(10):1654-1668. doi: 10.1111/bph.14171. Epub 2018 Mar 30.
Functional selectivity describes the ability of ligands to differentially regulate multiple signalling pathways when coupled to a single receptor, and the operational model is commonly used to analyse these data. Here, we assess the mathematical properties of the operational model and evaluate the outcomes of fixing parameters on model performance.
The operational model was evaluated using both a mathematical identifiability analysis and simulation.
Mathematical analysis revealed that the parameters R and K were not independently identifiable which can be solved by considering their ratio, τ. The ratio parameter, τ, was often imprecisely estimated when only functional assay data were available and generally only the transduction coefficient R ( τKA) could be estimated precisely. The general operational model (that includes baseline and the Hill coefficient) required either the parameters E or K to be fixed. The normalization process largely cancelled out the mean error of the calculated Δlog (R) caused by fixing these parameters. From this analysis, it was determined that we can avoid the need for a full agonist ligand to be included in an experiment to determine Δlog (R).
This analysis has provided a ready-to-use understanding of current methods for quantifying functional selectivity. It showed that current methods are generally tolerant to fixing parameters. A new method was proposed that removes the need for including a high efficacy ligand in any given experiment, which allows application to large-scale screening to identify compounds with desirable features of functional selectivity.
功能选择性描述了配体与单个受体结合时，区分调节多个信号通路的能力，而操作模型通常用于分析这些数据。在这里，我们评估了操作模型的数学性质，并评估了固定参数对模型性能的影响。
使用数学可识别性分析和模拟对操作模型进行了评估。
数学分析表明，参数 R 和 K 不能独立识别，可以通过考虑它们的比值 τ 来解决。当仅具有功能测定数据时，比值参数 τ 通常估计不准确，通常只能准确估计转导系数 R（τKA）。一般的操作模型（包括基线和希尔系数）需要固定参数 E 或 K。归一化过程在很大程度上消除了由于固定这些参数而导致的计算 Δlog（R）的平均误差。通过该分析，确定可以避免在实验中包含完全激动剂配体来确定 Δlog（R）。
该分析为定量功能选择性的当前方法提供了易于理解的理解。它表明当前的方法通常对固定参数具有容忍性。提出了一种新方法，该方法不需要在任何给定的实验中包含高功效配体，从而允许应用于大规模筛选以识别具有功能选择性所需特征的化合物。
