Neural Network Differential Equations For Ion Channel Modelling

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.

The impact of uncertainty in hERG binding mechanism on in silico predictions of drug‐induced proarrhythmic risk

“…Also, our approach was able to highlight compounds, such as tamoxifen, loratadine, and https://www.guidetopharmacology.org/GRAC/LigandDisplayForward?ligandId=2334, where none of the models (not even the CiPA 1.0 model) were able to fit the data satisfactorily. On closer inspection (Supporting Information) the data of loratadine, and nitrendipine showed a slight increase of the (percentage) current over time during the 0 m V pulses, raising potential data quality issues (Lei, Clerx, et al, 2020; Montnach et al, 2021; Raba, et al, 2013) or the need for methods to account for inadequacy of the models (Lei, Ghosh, et al, 2020; Lei & Mirams, 2021) and/or new (un)binding mechanisms to explain this observation; whilst for tamoxifen, there was a more obvious data quality issue for one of the concentrations. In Figure S26, we also included the results of fitting all the binding models whilst assuming the Hill coefficient (number of binding sites) to be .…”

Robust Hybrid Learning With Expert Augmentation

“…Hybrid Learning (HyL), or gray box modelling as called in its early days in the 90's (Psichogios & Ungar, 1992;Rico-Martinez et al, 1994;Thompson & Kramer, 1994;Rivera-Sampayo & Vélez-Reyes, 2001;Braun & Chaturvedi, 2002), has been an appropriate method to learn models that are both expressive and interpretable, while also allowing them to be learnt on fewer data. The interest for HyL (Mehta et al, 2020;Lei & Mirams, 2021;Reichstein et al, 2019;Saha et al, 2020;Guen & Thome, 2020;Levine & Stuart, 2021;Espeholt et al, 2021) has greatly renewed since the outbreak of recent neural network architectures that simplify the combination of physical equations within ML models. As an example, Neural ODE (Chen et al, 2018) and convolutional neural networks (LeCun et al, 1995, CNN) are privileged architectures to work with dynamical systems described by ODEs or PDEs.…”

“…In this work, we decided to study Yin et al (2021) and Takeishi & Kalousis (2021) for two reasons that distinguish them from the rest of the HyL literature. First, these are notable examples of HyL algorithms that can be applied to a broad class of problems in contrast to papers that focus on specific applications (Lei & Mirams, 2021;Reichstein et al, 2019). Second, those methods also learn a reliable inference model for the physical parameters, suggesting that the expert model is used properly in the generative model, which is a key assumption for our augmentation.…”

“…In recent work (Yin et al, 2021;Takeishi & Kalousis, 2021;Qian et al, 2021;Mehta et al, 2020;Lei & Mirams, 2021;Reichstein et al, 2019), HyL demonstrated success in complementing partial physical models and improving the inference of the corresponding parameters. However, contrarily to the common belief that HyL achieves better generalization than black box ML models, we argue that hybrid models do not meet their promise regarding robustness.…”

Neural network emulation of the human ventricular cardiomyocyte action potential for more efficient computations in pharmacological studies

“…In contrast, it has been proven that neural networks (NN) can approximate even discontinuous functions with arbitrary precision in theory ( Hornik et al, 1989 ), while recent works using NNs show empirically promising results for modeling partial differential equations containing discontinuities ( Jagtap et al, 2020 ). These features render NN emulators suitable emulation candidates and while Lei and Mirams, 2021 have recently investigated NN emulation of hERG channel kinetics, Jeong et al, 2023 proposed a neural network using AP shapes as input for the prediction of a drug’s proarrhythmic risk. However, to the best of our knowledge, NN emulators have not yet been used as surrogate for cardiomyocyte EP models.…”