Abstract
Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data.This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
Highlights
Mathematical modelling and computational simulations have been remarkably successful in providing mechanistic insight into many electrophysiological phenomena
After analysing the local sensitivity of the voltage-clamp experiment model, we found that the effects of voltage offset (Vo†ff) and imperfect Rs compensation are most apparent in the observed current
We validated the mathematical model through experiments using two types of electrical model cells, where we showed that our mathematical model is able to rectify imperfect amplifier estimations; applied it to account for artefacts whilst inferring parameters of an IKr model from hERG1a Chinese hamster ovary (CHO) cell data
Summary
Mathematical modelling and computational simulations have been remarkably successful in providing mechanistic insight into many electrophysiological phenomena. Quantitative models of the action potential have demonstrated their usefulness in basic research and are beginning to be used in safety-critical applications [1,2,3]. Mathematical models of ion channels constitute indispensable components of these action potential models. Identifying and quantifying sources of uncertainty enables informed decision making when using models in safety-critical applications [5]. Whole-cell patch-clamp experiments (in voltage-clamp configuration) are a common source of data for calibrating ion channel models. To study the dynamics of ion channels, currents through the cell membrane are often measured with a patch-clamp amplifier. Typical peak current magnitudes are of the order of pA to μA, depending on the size and type of cell; the voltage across the cell membrane (potential inside minus outside) typically is within the range −140 to +60 mV
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