Modelling ion channels with a view towards identifiability

Siekmann, I ORCID: 0000-0002-0706-6307 (2025) Modelling ion channels with a view towards identifiability. Bulletin of Mathematical Biology, 88 (1). pp. 1-37. ISSN 0092-8240

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Abstract

Aggregated Markov models provide a flexible framework for stochastic dynamics that develops on multiple timescales. For example, Markov models for ion channels often consist of multiple open and closed state to account for “slow” and “fast” openings and closings of the channel. The approach is a popular tool in the construction of mechanistic models of ion channels—instead of viewing model states as generators of sojourn times of a certain characteristic length, each individual model state is interpreted as a representation of a distinct biophysical state. We will review the properties of aggregated Markov models and discuss the implications for mechanistic modelling. First, we show how the aggregated Markov models with a given number of states can be calculated using Pólya enumeration. However, models with open and closed states that exceed the maximum number of parameters are non-identifiable. We will present two derivations of this classical result and investigate non-identifiability further via a detailed analysis of the non-identifiable fully connected three-state model. Finally, we will discuss the implications of non-identifiability for mechanistic modelling of ion channels. We will argue that instead of designing models based on assumed transitions between distinct biophysical states which are modulated by ligand binding, it is preferable to build models based on additional sources of data that give more direct insight into the dynamics of conformational changes.

Item Type:	Article
Uncontrolled Keywords:	Animals; Humans; Ion Channels; Markov Chains; Stochastic Processes; Ion Channel Gating; Models, Biological; Mathematical Concepts; Aggregated Markov model; Ion channel; Non-identifiability; Ion Channels; Markov Chains; Models, Biological; Mathematical Concepts; Stochastic Processes; Ion Channel Gating; Humans; Animals; 31 Biological Sciences; 49 Mathematical Sciences; 1.1 Normal biological development and functioning; Ion Channels; Markov Chains; Models, Biological; Mathematical Concepts; Stochastic Processes; Ion Channel Gating; Humans; Animals; 01 Mathematical Sciences; 06 Biological Sciences; Bioinformatics; 31 Biological sciences; 49 Mathematical sciences
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QH Natural history > QH301 Biology
Divisions:	Computer Science and Mathematics
Publisher:	Springer
Date of acceptance:	31 October 2025
Date of first compliant Open Access:	23 December 2025
Date Deposited:	23 Dec 2025 10:36
Last Modified:	23 Dec 2025 10:36
DOI or ID number:	10.1007/s11538-025-01558-3
URI:	https://researchonline.ljmu.ac.uk/id/eprint/27780

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