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.
Highlights
Electrophysiology modelling has provided insights insights into physiological mechanisms, from the ion channel to whole organ scales
The NN-f model, where the entire a-gate was modelled with a neural network, was able to learn the dynamics of human Ether-à-go-go-Related Gene (hERG) activation
We see great potential in using neural ordinary differential equations (ODEs) modelling approaches that we demonstrated in this paper for ion channel modelling, we believe this approach is still in its infancy; there are several limitations that we have to overcome before these neural ODE models can be used as confidently as the standard ion channel models
Summary
Electrophysiology modelling has provided insights insights into physiological mechanisms, from the ion channel to whole organ scales. Mathematical models of many ion channels, pumps, and exchangers form models describing the cellular action potential, based on the pioneering work of Hodgkin and Huxley (1952) These models of ion channels are typically a collection of mathematical functions governed by systems of ordinary differential equations (ODEs), using the Hodgkin-Huxley formulation or the Markov model structure (Rudy and Silva, 2006; Whittaker et al, 2020), and form the foundation of many cellular action potential, including neurons (Hodgkin and Huxley, 1952; Traub et al, 1994; Kole et al, 2008; Hay et al, 2011), cardiomyocytes (Noble, 1962; ten Tusscher et al, 2004; Grandi et al, 2011; O’Hara et al, 2011), pancreatic islet cells (Chay and Keizer, 1983; Sherman et al, 1988; Fridlyand et al, 2003; Cha et al, 2011), etc. Each of the gates attempts to describe a different behaviour that gives rise to the characteristic dynamics of the currents
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