Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments

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’.

Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments

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.

Four ways to fit an ion channel model

ABSTRACTComputational models of the cardiac action potential are increasingly being used to investigate the effects of genetic mutations, predict pro-arrhythmic risk in drug development, and to guide clinical interventions. These safety-critical applications, and indeed our understanding of the cardiac action potential, depend on accurate characterisation of the underlying ionic currents. Four different methods can be found in the literature to fit ionic current models to single-cell measurements: (Method 1) fitting model equations directly to time constant, steady-state, and I-V summary curves; (Method 2) fitting by comparing simulated versions of these summary curves to their experimental counterparts; (Method 3) fitting to the current traces themselves from a range of protocols; and (Method 4) fitting to a single current trace from an information-rich voltage clamp protocol. We compare these methods using a set of experiments in which hERG1a current from single Chinese Hamster Ovary (CHO) cells was characterised using multiple fitting protocols and an independent validation protocol. We show that Methods 3 and 4 provide the best predictions on the independent validation set, and that the short information-rich protocols of Method 4 can replace much longer conventional protocols without loss of predictive ability. While data for Method 2 is most readily available from the literature, we find it performs poorly compared to Methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.Statement of SignificanceMathematical models have been constructed to capture and share our understanding of the kinetics of ion channel currents for almost 70 years, and hundreds of models have been developed, using a variety of techniques. We compare how well four of the main methods fit data, how reliable and efficient the process of fitting is, and how predictive the resulting models are for physiological situations. The most widely-used traditional approaches based on current-voltage and time constant-voltage curves do not produce the most predictive models. Short, optimised experimental voltage clamp protocols can be used to create models that are as predictive as ones derived from traditional protocols, opening up possibilities for measuring ion channel kinetics faster, more accurately and in single cells. As these models often form part of larger multi-scale action potential and tissue electrophysiology models, improved ion channel kinetics models could influence the findings of thousands of simulation studies.

Sinusoidal voltage protocols for rapid characterisation of ion channel kinetics

Understanding the roles of ion currents is crucial to predict the action of pharmaceuticals and mutations in different scenarios, and thereby to guide clinical interventions in the heart, brain and other electrophysiological systems. Our ability to predict how ion currents contribute to cellular electrophysiology is in turn critically dependent on our characterisation of ion channel kinetics — the voltage-dependent rates of transition between open, closed and inactivated channel states. We present a new method for rapidly exploring and characterising ion channel kinetics, applying it to the hERG potassium channel as an example, with the aim of generating a quantitatively predictive representation of the ion current. We fit a mathematical model to currents evoked by a novel 8 second sinusoidal voltage clamp in CHO cells over-expressing hERG1a. The model is then used to predict over 5 minutes of recordings in the same cell in response to further protocols: a series of traditional square step voltage clamps, and also a novel voltage clamp comprised of a collection of physiologically-relevant action potentials. We demonstrate that we can make predictive cell-specific models that outperform the use of averaged data from a number of different cells, and thereby examine which changes in gating are responsible for cell-cell variability in current kinetics. Our technique allows rapid collection of consistent and high quality data, from single cells, and produces more predictive mathematical ion channel models than traditional approaches.Table of Contents CategoryTechniques for Physiology1Key PointsIon current kinetics are commonly represented by current-voltage relationships, time-constant voltage relationships, and subsequently mathematical models fitted to these. These experiments take substantial time which means they are rarely performed in the same cell.Rather than traditional square-wave voltage clamps, we fit a model to the current evoked by a novel sum-of-sinusoids voltage clamp that is only 8 seconds long.Short protocols that can be performed multiple times within a single cell will offer many new opportunities to measure how ion current kinetics are affected by changing conditions.The new model predicts the current under traditional square-wave protocols well, with better predictions of underlying currents than literature models. The current under a novel physiologically-relevant series of action potential clamps is predicted extremely well.The short sinusoidal protocols allow a model to be fully fitted to individual cells, allowing us to examine cell-cell variability in current kinetics for the first time.

Mapping the function of neuronal ion channels in model and experiment

Ion channel models are the building blocks of computational neuron models. Their biological fidelity is therefore crucial for the interpretation of simulations. However, the number of published models, and the lack of standardization, make the comparison of ion channel models with one another and with experimental data difficult. Here, we present a framework for the automated large-scale classification of ion channel models. Using annotated metadata and responses to a set of voltage-clamp protocols, we assigned 2378 models of voltage- and calcium-gated ion channels coded in NEURON to 211 clusters. The IonChannelGenealogy (ICGenealogy) web interface provides an interactive resource for the categorization of new and existing models and experimental recordings. It enables quantitative comparisons of simulated and/or measured ion channel kinetics, and facilitates field-wide standardization of experimentally-constrained modeling.