One model to rule them all: Unification of voltage-gated potassium channel models via deep non-linear mixed effects modelling

Ion channels are essential for signal processing and propagation in neural cells. Voltage-gated ion channels permeable to potassium (Kv) form one of the most prominent channel families. Techniques used to model the voltage-dependent gating of Kv channels date back to Hodgkin and Huxley (1952). Different Kv types can display radically different kinetic properties, requiring different mathematical models. However, the construction of Hodgkin-Huxley-like (HH-like) models is generally complex and time consuming due to the number of parameters, their tuning and having to choose functional forms to model gating. In addition to the between-Kv type heterogeneity, there can be significant within-Kv type kinetic heterogeneity between different cells with genetically identical channels. Since HH-like models do not account for such variability, extensions to it are necessary. We use scientific machine learning (SciML), the integration of machine learning methodologies with existing scientific models, and non-linear mixed effects (NLME) modelling to bypass the limitations of HH-like modelling. NLME is a modelling methodology that takes into account both within- and between-subject variability. These tools allowed us to complement the HH-like modelling and construct a unified SciML HH-like model that fits the recordings from 20 different Kv types. The unified SciML HH-like model produced closer fits to the data compared to a set of seven previous HH-like models and was able to represent the highly heterogeneous data from different cells. Our model may be the first step in producing a SciML foundation model for ion channels that would be capable of modelling the gating kinetics of any ion channel type.Author summary: Ion channels are complex molecules embedded in the membranes of neurons – the cells responsible for signal propagation and processing in the brain. Ion channels can open and close in response to various types of stimuli, in particular the voltage difference across the cell membrane. Computational modelling, usage of mathematical techniques to represent a system and algorithmically solve for its dynamics, has been previously used to understand the dynamics of voltage-gated ion channels. However, computational modelling of voltage-gated ion channels requires costly and complex optimization routines to fit their structure and parameters. We utilize two tools new to the modelling of voltage-gated ion channels – scientific machine learning and non-linear mixed effects modelling – to bypass some limitations associated with the existing methods.