Neural Network Differential Equations For Ion Channel Modelling

Lei, Chon Lok; Mirams, Gary R.

doi:10.3389/fphys.2021.708944

Neural Network Differential Equations For Ion Channel Modelling

Lei, Chon Lok; Mirams, Gary R.

Authors

Chon Lok Lei

Prof. GARY MIRAMS GARY.MIRAMS@NOTTINGHAM.AC.UK
Professor of Mathematical Biology

Abstract

Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality—termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications.

Citation

Lei, C. L., & Mirams, G. R. (2021). Neural Network Differential Equations For Ion Channel Modelling. Frontiers in Physiology, 12, Article 708944. https://doi.org/10.3389/fphys.2021.708944

Journal Article Type	Article
Acceptance Date	Jul 5, 2021
Online Publication Date	Aug 4, 2021
Publication Date	2021-08
Deposit Date	Jul 16, 2021
Publicly Available Date	Aug 4, 2021
Journal	Frontiers in Physiology
Electronic ISSN	1664-042X
Publisher	Frontiers Media
Peer Reviewed	Peer Reviewed
Volume	12
Article Number	708944
DOI	https://doi.org/10.3389/fphys.2021.708944
Public URL	https://nottingham-repository.worktribe.com/output/5787337
Publisher URL	https://www.frontiersin.org/articles/10.3389/fphys.2021.708944/full