Swansea University, Swansea, UK.
Leiden University, Leiden, The Netherlands.
J Pharmacokinet Pharmacodyn. 2024 Feb;51(1):39-63. doi: 10.1007/s10928-023-09870-y. Epub 2023 Jun 30.
Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions. Ordinary differential equation (ODE) models in receptor theory may be used to parameterise such interactions using timecourse data, but attention needs to be paid to the theoretical identifiability of the parameters of interest. Identifiability analysis is an often overlooked step in many bio-modelling works. In this paper we introduce structural identifiability analysis (SIA) to the field of receptor theory by applying three classical SIA methods (transfer function, Taylor Series and similarity transformation) to ligand-receptor binding models of biological importance (single ligand and Motulsky-Mahan competition binding at monomers, and a recently presented model of a single ligand binding at receptor dimers). New results are obtained which indicate the identifiable parameters for a single timecourse for Motulsky-Mahan binding and dimerised receptor binding. Importantly, we further consider combinations of experiments which may be performed to overcome issues of non-identifiability, to ensure the practical applicability of the work. The three SIA methods are demonstrated through a tutorial-style approach, using detailed calculations, which show the methods to be tractable for the low-dimensional ODE models.
数学建模已成为药理学分析的关键工具，有助于理解细胞信号动力学和量化配体-受体相互作用。受体理论中的常微分方程 (ODE) 模型可用于使用时程数据参数化此类相互作用，但需要注意感兴趣参数的理论可识别性。可识别性分析是许多生物建模工作中经常被忽视的步骤。在本文中，我们通过将三种经典的 SIA 方法（传递函数、泰勒级数和相似变换）应用于具有生物学重要性的配体-受体结合模型（单配体和 Motulsky-Mahan 竞争结合单体，以及最近提出的单配体结合受体二聚体模型），将结构可识别性分析 (SIA) 引入受体理论领域。得到了新的结果，这些结果表明对于 Motulsky-Mahan 结合和二聚体化受体结合的单个时程可识别参数。重要的是，我们进一步考虑了可以执行的实验组合，以克服不可识别性问题，确保工作的实际适用性。通过使用详细计算的教程式方法演示了这三种 SIA 方法，表明这些方法对于低维 ODE 模型是可行的。
