Using many different voltage protocols to characterise discrepancy in mathematical ion channel models.

Abstract

The Kv11.1 protein encoded by the hERG gene forms the primary subunit of a voltage-sensitive ion channel responsible for IKr in cardiomyocytes. Mathematical models of the macroscopic current are fitted to data from patch-clamp experiments - in which the whole-cell current is recorded in response to an applied voltage protocol. These models are a valuable tool for understanding the proarrhythmic effects of drugs and mutations, as they can provide accurate, quantitative predictions of the macroscopic current. In recent years, information rich protocols (that do not rely on the channels returning to steady state between voltage pulses) were designed to calibrate mathematical IKr models using short, dense time series. These protocols have been adapted for use on high-throughput automated patch clamp machines in CHO cells overexpressing hERG at either room or physiological temperatures. There are many choices of such protocols to apply during a patch-clamp experiment. We designed twelve protocols under various criteria, all of which should provide enough information to fit simple models of IKr uniquely. However, the parameters in imperfect models are forced to make different compromises to fit data from different protocols. The results highlight the impact of model discrepancy (the difference between models and reality) on parameter estimation and prediction. In particular, we show that the parameter estimates obtained depend on the chosen protocol, and how parameters fitted to protocols which highlight a significant amount of model discrepancy can lead to poor predictions. These results motivate the need for new experimental design methods that account for model discrepancy and aid in model selection. Furthermore, we suggest cross-validation as a tool to help evaluate the trustworthiness of model predictions, which may help identify good models of IKr as well as other macroscopic currents.