Keeping it short and (not so) simple: characterizing hERG kinetics with sinusoidal waves

Mathematical models and numerical simulation have tremendously enhanced our understanding of the mechanisms that underlie cardiac electrical and contractile function and their derangements, as well as the consequences of pharmacological intervention. Model development involves characterization of individual ionic current properties with square-wave voltage-clamp experiments, from which mathematical formulations are derived. Inherent limitations to this approach are being discussed and have started to be addressed by modellers and experimentalists (Krogh-Madsen et al. 2016; Grandi et al. 2017), and include the fact that (1) experimental datasets are typically collected for purposes other than model development, from different laboratories, and under different (sometimes non-physiological) experimental conditions, which often leads to incomplete datasets with large variances that do not necessarily reflect physiological variability; and (2) the traditional approach to fitting voltage-clamp protocols predominantly provides information about steady-state ion channel properties or time constants at fixed voltages, which is often insufficient to fully characterize channel kinetics during the complex action potential dynamics. As a result, predictions from various models can vary quite substantially, even when models are intended for replicating similar conditions. Furthermore, square-wave voltage-clamp protocols are time consuming and thus rarely performed in the same cell. There seems to be a consensus in our field that use of consistent, well-defined and distinct experimental datasets would be ideal to fit model parameters and validate model responses. Indeed, recent efforts in this direction have led to the development of new approaches to building cell-specific cardiac models. The Christini laboratory, for example, have designed condensed but dynamically rich experimental protocols consisting of (1) stochastic current-clamp stimulation to sample the rate-dependent cardiac dynamics and (2) multi-step voltage clamping using a tailored sequence of holding potentials, designed to highlight individual currents, which allow characterizing cardiac dynamics inherent to arrhythmias (Groenendaal et al. 2015). In this issue of The Journal of Physiology, Beattie et al. (2018) propose an innovative experimental and mathematical modelling method that allows the concise measurement of the dominant processes involved in human ether-à-go-go-related gene (hERG) channel gating probing a wide range of voltages and time scales. Rather than using traditional voltage-clamp step protocols, the authors developed a short (8 s-long) ‘sum of sinusoids’ voltage-clamp protocol so designed as to provoke a wider range of non-equilibrium behaviour than square voltage steps, thus allowing rich and complete characterization of hERG channel kinetics in the same cell and efficient model fitting. The authors then optimized mathematical models to cell-specific data and used a Bayesian inference method to obtain probability distributions for each model parameter and reveal (low) uncertainties in the best fit parameter sets. When applied to data acquired from multiple individual cells, the analysis showed only modest cell-to-cell variations in parameter values, thus attesting to the reproducibility of the method. Cell-to-cell variability was larger in certain parameters than others, perhaps reflecting greater physiological variability or sensitivities to experimental conditions. An additional strength of the study is that the new approach was rigorously validated and provided compelling evidence that the mathematical model so generated can recapitulate a wide array of additional experimental recordings (independent of the dataset used for model parameterization), including conventional voltage-clamp step protocols and complex action potential clamp protocols. The implications of this new technique are immediate and highly significant, given the importance of the rapidly activating delayed rectifier K+ current IKr, carried by hERG, as a major player in inherited and acquired (e.g. drug-induced) arrhythmia. The protocol could be used to characterize genetic mutations, with minimal required modifications if kinetic time scales are abundantly different from those of baseline hERG gating (i.e. the frequencies of the sine wave could be adapted or additional sinusoids could be added in). Similarly, the protocol could be used to measure whether channel kinetics have been altered in the presence of a drug compound. Indeed, Lee et al. (2017) recently discussed some of the challenges and limitations involved in modelling of the hERG channel and emphasized the need for improved voltage-clamp protocols to characterize drug–channel interaction in in vitro experiments. Furthermore, several recent studies have highlighted the importance of accurately describing state-dependence and kinetics of drug binding, instead of relying on steady-state concentration–response curves (Di Veroli et al. 2013; Grandi et al. 2017; Lee et al. 2017). Thus, an important next line of inquiry should be to determine whether this kind of approach can help to assess the kinetics (i.e. voltage- and state-dependence) of drug–channel interaction. As the authors have provided convincing results that the method is applicable to a range of ion channels and ion channel models, it is intriguing to speculate that it might also serve to discern what the ‘minimal model’ necessary to accurately describe a given channel behaviour should be. To this end, an additional iteration of modelling and experiments might be required, e.g. applying a protocol with optimized sine wave amplitudes and frequencies to distinguish among various model structures that have been previously parameterized. The experiments presented by Beattie et al. (2018) were performed in CHO cells overexpressing hERG1a. To develop a model that is more applicable for use in cardiac safety testing and multi-scale simulations it would be desirable to characterize native IKr kinetics by using the described methodology in cardiac myocytes. In the native environment, the presence of many larger voltage-dependent currents than observed in expression systems might make this challenging. It would be interesting to see if the dofetilide subtraction approach used here can still be applied successfully. If so, the significant brevity of the protocol will permit rapid characterization of native hERG channel regulation, by allowing more recordings in different experimental conditions (e.g. drug concentrations, temperatures, pH) within the same cell. This clever new technique, which outperforms traditional electrophysiological protocols by efficiently providing a dynamically rich dataset, is poised to substantially enhance hERG studies, e.g. in the context of congenital and drug-induced cardiac arrhythmia and drug safety testing. None. National Institutes of Health (NIH): Stimulating Peripheral Activity to Relieve Conditions (SPARC) grant 1OT2OD023848-01, and National Heart, Lung, and Blood Institute grant R01HL131517; American Heart Association grant 15SDG24910015.