Atrial arrhythmogenicity of KCNJ2 mutations in short QT syndrome:Insights from virtual human atria

Gain-of-function mutations in KCNJ2-encoded Kir2.1 channels underlie variant 3 (SQT3) of the short QT syndrome, which is associated with atrial fibrillation (AF). Using biophysically-detailed human atria computer models, this study investigated the mechanistic link between SQT3 mutations and atrial arrhythmogenesis, and potential ion channel targets for treatment of SQT3. A contemporary model of the human atrial action potential (AP) was modified to recapitulate functional changes in IK1 due to heterozygous and homozygous forms of the D172N and E299V Kir2.1 mutations. Wild-type (WT) and mutant formulations were incorporated into multi-scale homogeneous and heterogeneous tissue models. Effects of mutations on AP duration (APD), conduction velocity (CV), effective refractory period (ERP), tissue excitation threshold and their rate-dependence, as well as the wavelength of re-entry (WL) were quantified. The D172N and E299V Kir2.1 mutations produced distinct effects on IK1 and APD shortening. Both mutations decreased WL for re-entry through a reduction in ERP and CV. Stability of re-entrant excitation waves in 2D and 3D tissue models was mediated by changes to tissue excitability and dispersion of APD in mutation conditions. Combined block of IK1 and IKr was effective in terminating re-entry associated with heterozygous D172N conditions, whereas IKr block alone may be a safer alternative for the E299V mutation. Combined inhibition of IKr and IKur produced a synergistic anti-arrhythmic effect in both forms of SQT3. In conclusion, this study provides mechanistic insights into atrial proarrhythmia with SQT3 Kir2.1 mutations and highlights possible pharmacological strategies for management of SQT3-linked AF

In silico Assessment of Pharmacotherapy for Human Atrial Patho-Electrophysiology Associated With hERG-Linked Short QT Syndrome

Short QT syndrome variant 1 (SQT1) arises due to gain-of-function mutations to the human Ether-à-go-go-Related Gene (hERG), which encodes the α subunit of channels carrying rapid delayed rectifier potassium current, IKr. In addition to QT interval shortening and ventricular arrhythmias, SQT1 is associated with increased risk of atrial fibrillation (AF), which is often the only clinical presentation. However, the underlying basis of AF and its pharmacological treatment remain incompletely understood in the context of SQT1. In this study, computational modeling was used to investigate mechanisms of human atrial arrhythmogenesis consequent to a SQT1 mutation, as well as pharmacotherapeutic effects of selected class I drugs–disopyramide, quinidine, and propafenone. A Markov chain formulation describing wild type (WT) and N588K-hERG mutant IKr was incorporated into a contemporary human atrial action potential (AP) model, which was integrated into one-dimensional (1D) tissue strands, idealized 2D sheets, and a 3D heterogeneous, anatomical human atria model. Multi-channel pharmacological effects of disopyramide, quinidine, and propafenone, including binding kinetics for IKr/hERG and sodium current, INa, were considered. Heterozygous and homozygous formulations of the N588K-hERG mutation shortened the AP duration (APD) by 53 and 86 ms, respectively, which abbreviated the effective refractory period (ERP) and excitation wavelength in tissue, increasing the lifespan and dominant frequency (DF) of scroll waves in the 3D anatomical human atria. At the concentrations tested in this study, quinidine most effectively prolonged the APD and ERP in the setting of SQT1, followed by disopyramide and propafenone. In 2D simulations, disopyramide and quinidine promoted re-entry termination by increasing the re-entry wavelength, whereas propafenone induced secondary waves which destabilized the re-entrant circuit. In 3D simulations, the DF of re-entry was reduced in a dose-dependent manner for disopyramide and quinidine, and propafenone to a lesser extent. All of the anti-arrhythmic agents promoted pharmacological conversion, most frequently terminating re-entry in the order quinidine > propafenone = disopyramide. Our findings provide further insight into mechanisms of SQT1-related AF and a rational basis for the pursuit of combined IKr and INa block based pharmacological strategies in the treatment of SQT1-linked AF

In silico Assessment of Pharmacotherapy for Human Atrial Patho-Electrophysiology Associated With hERG-Linked Short QT Syndrome

Short QT syndrome variant 1 (SQT1) arises due to gain-of-function mutations to the human Ether-à-go-go-Related Gene (hERG), which encodes the α subunit of channels carrying rapid delayed rectifier potassium current, IKr. In addition to QT interval shortening and ventricular arrhythmias, SQT1 is associated with increased risk of atrial fibrillation (AF), which is often the only clinical presentation. However, the underlying basis of AF and its pharmacological treatment remain incompletely understood in the context of SQT1. In this study, computational modeling was used to investigate mechanisms of human atrial arrhythmogenesis consequent to a SQT1 mutation, as well as pharmacotherapeutic effects of selected class I drugs–disopyramide, quinidine, and propafenone. A Markov chain formulation describing wild type (WT) and N588K-hERG mutant IKr was incorporated into a contemporary human atrial action potential (AP) model, which was integrated into one-dimensional (1D) tissue strands, idealized 2D sheets, and a 3D heterogeneous, anatomical human atria model. Multi-channel pharmacological effects of disopyramide, quinidine, and propafenone, including binding kinetics for IKr/hERG and sodium current, INa, were considered. Heterozygous and homozygous formulations of the N588K-hERG mutation shortened the AP duration (APD) by 53 and 86 ms, respectively, which abbreviated the effective refractory period (ERP) and excitation wavelength in tissue, increasing the lifespan and dominant frequency (DF) of scroll waves in the 3D anatomical human atria. At the concentrations tested in this study, quinidine most effectively prolonged the APD and ERP in the setting of SQT1, followed by disopyramide and propafenone. In 2D simulations, disopyramide and quinidine promoted re-entry termination by increasing the re-entry wavelength, whereas propafenone induced secondary waves which destabilized the re-entrant circuit. In 3D simulations, the DF of re-entry was reduced in a dose-dependent manner for disopyramide and quinidine, and propafenone to a lesser extent. All of the anti-arrhythmic agents promoted pharmacological conversion, most frequently terminating re-entry in the order quinidine > propafenone = disopyramide. Our findings provide further insight into mechanisms of SQT1-related AF and a rational basis for the pursuit of combined IKr and INa block based pharmacological strategies in the treatment of SQT1-linked AF.</p

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'

A nonlinear and time-dependent leak current in the presence of calcium fluoride patch-clamp seal enhancer [version 1; peer review: 2 approved with reservations]

Automated patch-clamp platforms are widely used and vital tools in both academia and industry to enable high-throughput studies such as drug screening. A leak current to ground occurs whenever the seal between a pipette and cell (or internal solution and cell in high-throughput machines) is not perfectly insulated from the bath (extracellular) solution. Over 1 GΩ seal resistance between pipette and bath solutions is commonly used as a quality standard for manual patch work. With automated platforms it can be difficult to obtain such a high seal resistance between the intra- and extra-cellular solutions. One suggested method to alleviate this problem is using an F− containing internal solution together with a Ca2+ containing external solution — so that a CaF2 crystal forms when the two solutions meet which ‘plugs the holes’ to enhance the seal resistance. However, we observed an unexpected nonlinear-in-voltage and time-dependent current using these solutions on an automated patch-clamp platform. We performed manual patch-clamp experiments with the automated patch-clamp solutions, but no biological cell, and observed the same nonlinear time-dependent leak current. The current could be completely removed by washing out F− ions to leave a conventional leak current that was linear and not time-dependent. We therefore conclude fluoride ions interacting with the CaF2 crystal are the origin of the nonlinear time-dependent leak current. The consequences of such a nonlinear and time-dependent leak current polluting measurements should be considered carefully if it cannot be isolated and subtracted

Effects of Taurine-Magnesium Coordination Compound on Type 2 Short QT Syndrome: A Simulation Study

Short QT Syndrome (SQTS)is an identified genetic arrhythmogenic disease associated with abnormally abbreviated QT intervals and an increased susceptibility to malignant arrhythmia and sudden cardiac death (SCD). SQT2 variant (linked to slow delayed rectifier, IKs) of SQTS, results from a gain-of-function (V307L) in the KCNQ1 subunit of the IKschannel. Pro-arrhythmogenic effects of SQT2 have been well characterized, but less is known about the pharmacological treatment of SQT2. We find that taurine-magnesium coordination compound (TMCC)exerted anti-arrhythmic effects with low toxicity. Therefore, this study aimed to assess the potential effects of TMCC on SQT2. The channel-blocking effect of TMCC on IKsin healthy and SQT2 cells were incorporated into computer models ofhuman ventricular action potential (AP) and into one dimensional transmural tissue simulations. In the single-cell model, TMCC prolonged cell AP duration at 90% repolarization (APD90). In the one dimensionalintact model, TMCC prolonged the QT interval on the pseudo-ECGs. Thus, the present study provides evidence that TMCC can extend the repolarization period and APD90and QT interval, thereby representing a therapeutic candidate for arrhythmia in SQT2

Ion channel model reduction using manifold boundaries

Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and parameters describing the voltage-dependent rates of transition between states. An open problem is selecting the appropriate degree of complexity and structure for an ion channel model given data availability. Here, we simplify a model of the cardiac human Ether-à-go-go Related Gene (hERG) potassium ion channel, which carries cardiac IKr, using the manifold boundary approximation method (MBAM). The MBAM approximates high-dimensional model-output manifolds by reduced models describing their boundaries, resulting in models with fewer parameters (and often variables). We produced a series of models of reducing complexity starting from an established 5-state hERG model with 15 parameters. Models with up to 3 fewer states and 8 fewer parameters were shown to retain much of the predictive capability of the full model and were validated using experimental hERG1a data collected in HEK293 cells at 37°C. The method provides a way to simplify complex models of ion channels that improves parameter identifiability and will aid in future model development

Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises—models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, ‘information-rich’ protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict—highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems

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