{"title":"Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory.","authors":"Carla White, Vivi Rottschäfer, Lloyd Bridge","doi":"10.1007/s10928-023-09870-y","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":" ","pages":"39-63"},"PeriodicalIF":2.2000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10884104/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pharmacokinetics and Pharmacodynamics","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1007/s10928-023-09870-y","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/6/30 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"PHARMACOLOGY & PHARMACY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
数学模型已成为药理学分析的重要工具,可用于了解细胞信号的动态和量化配体与受体的相互作用。受体理论中的常微分方程(ODE)模型可用于利用时程数据对这种相互作用进行参数化,但需要注意相关参数的理论可识别性。在许多生物建模工作中,可识别性分析往往是一个被忽视的步骤。在本文中,我们将结构可识别性分析(SIA)引入受体理论领域,将三种经典的 SIA 方法(传递函数、泰勒级数和相似性变换)应用于具有重要生物学意义的配体-受体结合模型(单体上的单配体和莫图尔斯基-马汉竞争结合,以及最近提出的受体二聚体上的单配体结合模型)。我们获得的新结果表明了莫图尔斯基-马汉结合和二聚受体结合的单一时间历程的可识别参数。重要的是,我们进一步考虑了为克服不可识别性问题而可能进行的实验组合,以确保这项工作的实际应用性。我们通过教程式的方法演示了三种 SIA 方法,并进行了详细计算,结果表明这些方法对于低维 ODE 模型是可行的。
期刊介绍:
Broadly speaking, the Journal of Pharmacokinetics and Pharmacodynamics covers the area of pharmacometrics. The journal is devoted to illustrating the importance of pharmacokinetics, pharmacodynamics, and pharmacometrics in drug development, clinical care, and the understanding of drug action. The journal publishes on a variety of topics related to pharmacometrics, including, but not limited to, clinical, experimental, and theoretical papers examining the kinetics of drug disposition and effects of drug action in humans, animals, in vitro, or in silico; modeling and simulation methodology, including optimal design; precision medicine; systems pharmacology; and mathematical pharmacology (including computational biology, bioengineering, and biophysics related to pharmacology, pharmacokinetics, orpharmacodynamics). Clinical papers that include population pharmacokinetic-pharmacodynamic relationships are welcome. The journal actively invites and promotes up-and-coming areas of pharmacometric research, such as real-world evidence, quality of life analyses, and artificial intelligence. The Journal of Pharmacokinetics and Pharmacodynamics is an official journal of the International Society of Pharmacometrics.