Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory.

Area of Science:

• Pharmacological analysis
• Mathematical modeling
• Receptor theory

Background:

• Mathematical modeling, particularly ordinary differential equation (ODE) models, is crucial for understanding cell signaling and ligand-receptor interactions in pharmacology.
• Parameter identifiability is a critical but often overlooked aspect of bio-modeling, impacting the reliability of model-based analyses.
• Existing receptor theory models require robust methods to ensure their parameters can be uniquely determined from experimental data.

Purpose of the Study:

• To introduce and apply structural identifiability analysis (SIA) methods to important ligand-receptor binding models within receptor theory.
• To determine which parameters in specific ligand-receptor binding models are identifiable from experimental timecourse data.
• To propose experimental strategies to address non-identifiability issues and enhance the practical applicability of receptor theory models.

Main Methods:

• Application of three classical SIA methods: transfer function, Taylor Series, and similarity transformation.
• Analysis of ODE models for single ligand binding, Motulsky-Mahan competition binding at monomers, and single ligand binding at receptor dimers.
• Tutorial-style demonstration with detailed calculations to illustrate the tractability of SIA methods for low-dimensional ODE models.

Main Results:

• Identification of parameters that are structurally identifiable for Motulsky-Mahan binding and dimerised receptor binding models using a single timecourse.
• Demonstration of the practical application of SIA methods to biologically relevant receptor binding models.
• Validation of the tractability and utility of SIA for parameter estimation in complex pharmacological models.

Conclusions:

• Structural identifiability analysis is a vital tool for validating receptor theory models in pharmacological research.
• Specific parameters in Motulsky-Mahan and dimerised receptor binding models can be identified, but experimental design is key.
• The applied SIA methods provide a robust framework for ensuring the reliability and practical utility of mathematical models in pharmacology.