A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models

Computational models of the electrical potential across a cell membrane are longstanding and vital tools in electrophysiology research and applications. These models describe how ionic currents, internal fluxes, and buffering interact to determine membrane voltage and form action potentials (APs). Although this relationship is usually expressed as a differential equation, previous studies have shown it can be rewritten in an algebraic form, allowing direct calculation of membrane voltage. Rewriting in this form requires the introduction of a new parameter, called Γ(0) in this manuscript, which represents the net concentration of all charges that influence membrane voltage but are not considered in the model. Although several studies have examined the impact of Γ(0) on long-term stability and drift in model predictions, there has been little examination of its effects on model predictions, particularly when a model is refit to new data. In this study, we illustrate how Γ(0) affects important physiological properties such as action potential duration restitution, and examine the effects of (in)correctly specifying Γ(0) during model calibration. We show that, although physiologically plausible, the range of concentrations used in popular models leads to orders of magnitude differences in Γ(0), which can lead to very different model predictions. In model calibration, we find that using an incorrect value of Γ(0) can lead to biased estimates of the inferred parameters, but that the predictive power of these models can be restored by fitting Γ(0) as a separate parameter. These results show the value of making Γ(0) explicit in model formulations, as it forces modellers and experimenters to consider the effects of uncertainty and potential discrepancy in initial concentrations upon model predictions.