Models of HERG gating

Beta-Barrel Channel Response to High Electric Fields: Functional Gating or Reversible Denaturation?

Ion channels exhibit gating behavior, fluctuating between open and closed states, with the transmembrane voltage serving as one of the essential regulators of this process. Voltage gating is a fundamental functional aspect underlying the regulation of ion-selective, mostly α-helical, channels primarily found in excitable cell membranes. In contrast, there exists another group of larger, and less selective, β-barrel channels of a different origin, which are not directly associated with cell excitability. Remarkably, these channels can also undergo closing, or "gating", induced by sufficiently strong electric fields. Once the field is removed, the channels reopen, preserving a memory of the gating process. In this study, we explored the hypothesis that the voltage-induced closure of the β-barrel channels can be seen as a form of reversible protein denaturation by the high electric fields applied in model membranes experiments-typically exceeding twenty million volts per meter-rather than a manifestation of functional gating. Here, we focused on the bacterial outer membrane channel OmpF reconstituted into planar lipid bilayers and analyzed various characteristics of the closing-opening process that support this idea. Specifically, we considered the nearly symmetric response to voltages of both polarities, the presence of multiple closed states, the stabilization of the open conformation in channel clusters, the long-term gating memory, and the Hofmeister effects in closing kinetics. Furthermore, we contemplate the evolutionary aspect of the phenomenon, proposing that the field-induced denaturation of membrane proteins might have served as a starting point for their development into amazing molecular machines such as voltage-gated channels of nerve and muscle cells.

Noncanonical electromechanical coupling paths in cardiac hERG potassium channel

Voltage-gated potassium channels are involved in many physiological processes such as nerve impulse transmission, the heartbeat, and muscle contraction. However, for many of them the molecular determinants of the gating mechanism remain elusive. Here, using a combination of theoretical and experimental approaches, we address this problem focusing on the cardiac hERG potassium channel. Network analysis of molecular dynamics trajectories reveals the presence of a kinematic chain of residues that couples the voltage sensor domain to the pore domain and involves the S4/S1 and S1/S5 subunit interfaces. Mutagenesis experiments confirm the role of these residues and interfaces in the activation and inactivation mechanisms. Our findings demonstrate the presence of an electromechanical transduction path crucial for the non-domain-swapped hERG channel gating that resembles the noncanonical path identified in domain-swapped K+ channels.

Calibration of ionic and cellular cardiac electrophysiology models

Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Modulation of hERG K+ Channel Deactivation by Voltage Sensor Relaxation

The hERG (human-ether-à-go-go-related gene) channel underlies the rapid delayed rectifier current, I_kr, in the heart, which is essential for normal cardiac electrical activity and rhythm. Slow deactivation is one of the hallmark features of the unusual gating characteristics of hERG channels, and plays a crucial role in providing a robust current that aids repolarization of the cardiac action potential. As such, there is significant interest in elucidating the underlying mechanistic determinants of slow hERG channel deactivation. Recent work has shown that the hERG channel S4 voltage sensor is stabilized following activation in a process termed relaxation. Voltage sensor relaxation results in energetic separation of the activation and deactivation pathways, producing a hysteresis, which modulates the kinetics of deactivation gating. Despite widespread observation of relaxation behaviour in other voltage-gated K⁺ channels, such as Shaker, Kv1.2 and Kv3.1, as well as the voltage-sensing phosphatase Ci-VSP, the relationship between stabilization of the activated voltage sensor by the open pore and voltage sensor relaxation in the control of deactivation has only recently begun to be explored. In this review, we discuss present knowledge and questions raised related to the voltage sensor relaxation mechanism in hERG channels and compare structure-function aspects of relaxation with those observed in related ion channels. We focus discussion, in particular, on the mechanism of coupling between voltage sensor relaxation and deactivation gating to highlight the insight that these studies provide into the control of hERG channel deactivation gating during their physiological functioning.

Four Ways to Fit an Ion Channel Model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current 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 a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are 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.

Steady-State Activation and Modulation of the Concatemeric α1β2γ2L GABAA Receptor

The two-state coagonist model has been successfully used to analyze and predict peak current responses of the γ-aminobutyric acid type A (GABA_A) receptor. The goal of the present study was to provide a model-based description of GABA_A receptor activity under steady-state conditions after desensitization has occurred. We describe the derivation and properties of the cyclic three-state resting-active-desensitized (RAD) model. The relationship of the model to receptor behavior was tested using concatemeric α1β2γ2 GABA_A receptors expressed in Xenopus oocytes. The receptors were activated by the orthosteric agonists GABA or β-alanine, the allosteric agonist propofol, or combinations of GABA, propofol, pentobarbital, and the steroid allopregnanolone, and the observed steady-state responses were compared with those predicted by the model. A modified RAD model was employed to analyze and describe the actions on steady-state current of the inhibitory steroid pregnenolone sulfate. The findings indicate that the steady-state activity in the presence of multiple active agents that interact with distinct binding sites follows standard energetic additivity. The derived equations enable prediction of peak and steady-state activity in the presence of orthosteric and allosteric agonists, and the inhibitory steroid pregnenolone sulfate. SIGNIFICANCE STATEMENT: The study describes derivation and properties of a three-state resting-active-desensitized model. The model and associated equations can be used to analyze and predict peak and steady-state activity in the presence of one or more active agents.

Temperature Dependence of the Biophysical Mechanisms Underlying the Inhibition and Enhancement Effect of Amiodarone on hERG Channels

hERG K⁺ channel is important for controlling the duration of cardiac action potentials. Amiodarone (AMD), a widely prescribed class III antiarrhythmic, could inhibit hERG currents with relatively few tachyarrhythmic adverse events. We use injected Xenopus oocyte with two-electrode voltage clamp techniques to characterize the action of AMD on hERG channels. We found that AMD binds to the resting hERG channel with an apparent dissociation constant of ∼1.4 μM, and inhibits hERG currents at mild and strong depolarization pulses by slowing activation and enhancing inactivation, respectively, at 22°C. The activation kinetics of hERG channel activation are much faster, but inactivation kinetics are slower at 37°C. AMD accordingly has a 15% to 20% weaker and stronger inhibitory effect at mild and strong depolarization (e.g., -60 and +30 mV, 0.3-second pulse), respectively. In the meanwhile, the resurgent hERG tail currents are dose-dependently inhibited by AMD without altering the kinetics of current decay at both 22°C and 37°C, indicating facilitation of recovery from inactivation via the silent route. Most importantly, AMD no longer inhibits but enhances hERG currents at a mild pulse shortly after a prepulse at 37°C, but not so much at 22°C. We conclude that AMD is an effective hERG channel-gating modifier capable of lengthening the plateau phase of cardiac action potential (without increasing the chance of afterdepolarization). AMD, however, should be used with caution in hypothermia or the other scenarios that slow hERG channel activation. SIGNIFICANCE STATEMENT: It is known that amiodarone (AMD) acts on hERG K⁺ channels to treat cardiac arrhythmias with relatively little arrhythmogenicity. We found that AMD enhances hERG channel inactivation but slows activation as well as recovery from inactivation, and thus has a differential inhibition and enhancement effect on hERG currents at different phases of membrane voltage changes, especially at 37°C, but not so much at 22°C. AMD is therefore a relatively ideal agent against tachyarrhythmia at 37°C, but should be more cautiously used at lower temperatures or relevant pathophysiological/pharmacological scenarios associated with slower hERG channel activation because of the increased chances of adverse events.

The influence of hERG1a and hERG1b isoforms on drug safety screening in iPSC-CMs

The human Ether-à-go-go Related Gene (hERG) encodes the pore forming subunit of the channel that conducts the rapid delayed rectifier potassium current I_Kr. I_Kr drives repolarization in the heart and when I_Kr is dysfunctional, cardiac repolarization delays, the QT interval on the electrocardiogram (ECG) prolongs and the risk of developing lethal arrhythmias such as Torsade de Pointes (TdP) increases. TdP risk is incorporated in drug safety screening for cardiotoxicity where hERG is the main target since the I_Kr channels appear highly sensitive to blockage. hERG block is also included as an important read-out in the Comprehensive in Vitro Proarrhythmia Assay (CiPA) initiative which aims to combine in vitro and in silico experiments on induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) to screen for cardiotoxicity. However, the hERG channel has some unique features to consider for drug safety screening, which we will discuss in this study. The hERG channel consists of different isoforms, hERG1a and hERG1b, which individually influence the kinetics of the channel and the drug response in the human heart and in iPSC-CMs. hERG1b is often underappreciated in iPSC-CM studies, drug screening assays and in silico models, and the fact that its contribution might substantially differ between iPSC-CM and healthy but also diseased human heart, adds to this problem. In this study we show that the activation kinetics in iPSC-CMs resemble hERG1b kinetics using Cs⁺ as a charge carrier. Not including hERG1b in drug safety testing might underestimate the actual role of hERG1b in repolarization and drug response, and might lead to inappropriate conclusions. We stress to focus more on including hERG1b in drug safety testing concerning I_Kr.

Sinusoidal voltage protocols for rapid characterisation of ion channel kinetics

Key points

Ion 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 fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s 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.

Abstract

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 fitted a mathematical model to currents evoked by a novel 8 second sinusoidal voltage clamp in CHO cells overexpressing hERG1a. The model was 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 comprising 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.

Ion 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 fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s 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.

Determinants of Isoform-Specific Gating Kinetics of hERG1 Channel: Combined Experimental and Simulation Study

I_Kr is the rapidly activating component of the delayed rectifier potassium current, the ion current largely responsible for the repolarization of the cardiac action potential. Inherited forms of long QT syndrome (LQTS) (Lees-Miller et al., 1997) in humans are linked to functional modifications in the Kv11.1 (hERG) ion channel and potentially life threatening arrhythmias. There is little doubt now that hERG-related component of I_Kr in the heart depends on the tetrameric (homo- or hetero-) channels formed by two alternatively processed isoforms of hERG, termed hERG1a and hERG1b. Isoform composition (hERG1a- vs. the b-isoform) has recently been reported to alter pharmacologic responses to some hERG blockers and was proposed to be an essential factor pre-disposing patients for drug-induced QT prolongation. Very little is known about the gating and pharmacological properties of two isoforms in heart membranes. For example, how gating mechanisms of the hERG1a channels differ from that of hERG1b is still unknown. The mechanisms by which hERG 1a/1b hetero-tetramers contribute to function in the heart, or what role hERG1b might play in disease are all questions to be answered. Structurally, the two isoforms differ only in the N-terminal region located in the cytoplasm: hERG1b is 340 residues shorter than hERG1a and the initial 36 residues of hERG1b are unique to this isoform. In this study, we combined electrophysiological measurements for HEK cells, kinetics and structural modeling to tease out the individual contributions of each isoform to Action Potential formation and then make predictions about the effects of having various mixture ratios of the two isoforms. By coupling electrophysiological data with computational kinetic modeling, two proposed mechanisms of hERG gating in two homo-tetramers were examined. Sets of data from various experimental stimulation protocols (HEK cells) were analyzed simultaneously and fitted to Markov-chain models (M-models). The minimization procedure presented here, allowed assessment of suitability of different Markov model topologies and the corresponding parameters that describe the channel kinetics. The kinetics modeling pointed to key differences in the gating kinetics that were linked to the full channel structure. Interactions between soluble domains and the transmembrane part of the channel appeared to be critical determinants of the gating kinetics. The structures of the full channel in the open and closed states were compared for the first time using the recent Cryo-EM resolved structure for full open hERG channel and an homology model for the closed state, based on the highly homolog EAG1 channel. Key potential interactions which emphasize the importance of electrostatic interactions between N-PAS cap, S4-S5, and C-linker are suggested based on the structural analysis. The derived kinetic parameters were later used in higher order models of cells and tissue to track down the effect of varying the ratios of hERG1a and hERG1b on cardiac action potentials and computed electrocardiograms. Simulations suggest that the recovery from inactivation of hERG1b may contribute to its physiologic role of this isoform in the action potential. Finally, the results presented here contribute to the growing body of evidence that hERG1b significantly affects the generation of the cardiac I_kr and plays an important role in cardiac electrophysiology. We highlight the importance of carefully revisiting the Markov models previously proposed in order to properly account for the relative abundance of the hERG1 a- and b- isoforms.

Pro-arrhythmic effects of low plasma [K+] in human ventricle: An illustrated review

Potassium levels in the plasma, [K⁺]_o, are regulated precisely under physiological conditions. However, increases (from approx. 4.5 to 8.0mM) can occur as a consequence of, e.g., endurance exercise, ischemic insult or kidney failure. This hyperkalemic modulation of ventricular electrophysiology has been studied extensively. Hypokalemia is also common. It can occur in response to diuretic therapy, following renal dialysis, or during recovery from endurance exercise. In the human ventricle, clinical hypokalemia (e.g., [K⁺]_o levels of approx. 3.0mM) can cause marked changes in both the resting potential and the action potential waveform, and these may promote arrhythmias. Here, we provide essential background information concerning the main K⁺-sensitive ion channel mechanisms that act in concert to produce prominent short-term ventricular electrophysiological changes, and illustrate these by implementing recent mathematical models of the human ventricular action potential. Even small changes (~1mM) in [K⁺]_o result in significant alterations in two different K⁺ currents, I_K1 and HERG. These changes can markedly alter in resting membrane potential and/or action potential waveform in human ventricle. Specifically, a reduction in net outward transmembrane K⁺ currents (repolarization reserve) and an increased substrate input resistance contribute to electrophysiological instability during the plateau of the action potential and may promote pro-arrhythmic early after-depolarizations (EADs). Translational settings where these insights apply include: optimal diuretic therapy, and the interpretation of data from Phase II and III trials for anti-arrhythmic drug candidates.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

Potassium channels in the heart: structure, function and regulation

This paper is the outcome of the fourth UC Davis Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias Symposium, a biannual event that aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The theme of the 2016 symposium was 'K⁺ Channels and Regulation'. Experts in the field contributed their experimental and mathematical modelling perspectives and discussed emerging questions, controversies and challenges on the topic of cardiac K⁺ channels. This paper summarizes the topics of formal presentations and informal discussions from the symposium on the structural basis of voltage-gated K⁺ channel function, as well as the mechanisms involved in regulation of K⁺ channel gating, expression and membrane localization. Given the critical role for K⁺ channels in determining the rate of cardiac repolarization, it is hardly surprising that essentially every aspect of K⁺ channel function is exquisitely regulated in cardiac myocytes. This regulation is complex and highly interrelated to other aspects of myocardial function. K⁺ channel regulatory mechanisms alter, and are altered by, physiological challenges, pathophysiological conditions, and pharmacological agents. An accompanying paper focuses on the integrative role of K⁺ channels in cardiac electrophysiology, i.e. how K⁺ currents shape the cardiac action potential, and how their dysfunction can lead to arrhythmias, and discusses K⁺ channel-based therapeutics. A fundamental understanding of K⁺ channel regulatory mechanisms and disease processes is fundamental to reveal new targets for human therapy.

A computational model predicts adjunctive pharmacotherapy for cardiac safety via selective inhibition of the late cardiac Na current

Background

The QT interval is a phase of the cardiac cycle that corresponds to action potential duration (APD) including cellular repolarization (T-wave). In both clinical and experimental settings, prolongation of the QT interval of the electrocardiogram (ECG) and related proarrhythmia have been so strongly associated that a prolonged QT interval is largely accepted as surrogate marker for proarrhythmia. Accordingly, drugs that prolong the QT interval are not considered for further preclinical development resulting in removal of many promising drugs from development. While reduction of drug interactions with hERG is an important goal, there are promising means to mitigate hERG block. Here, we examine one possibility and test the hypothesis that selective inhibition of the cardiac late Na current (I_NaL) by the novel compound GS-458967 can suppress proarrhythmic markers.

Methods and results

New experimental data has been used to calibrate I_NaL in the Soltis-Saucerman computationally based model of the rabbit ventricular action potential to study effects of GS-458967 on I_NaL during the rabbit ventricular AP. We have also carried out systematic in silico tests to determine if targeted block of I_NaL would suppress proarrhythmia markers in ventricular myocytes described by TRIaD: Triangulation, Reverse use dependence, beat-to-beat Instability of action potential duration, and temporal and spatial action potential duration Dispersion.

Conclusions

Our computer modeling approach based on experimental data, yields results that suggest that selective inhibition of I_NaL modifies all TRIaD related parameters arising from acquired Long-QT Syndrome, and thereby reduced arrhythmia risk. This study reveals the potential for adjunctive pharmacotherapy via targeted block of I_NaL to mitigate proarrhythmia risk for drugs with significant but unintended off-target hERG blocking effects.

Computational cardiology and risk stratification for sudden cardiac death: one of the grand challenges for cardiology in the 21st century

Risk stratification in the context of sudden cardiac death has been acknowledged as one of the major challenges facing cardiology for the past four decades. In recent years, the advent of high performance computing has facilitated organ-level simulation of the heart, meaning we can now examine the causes, mechanisms and impact of cardiac dysfunction in silico. As a result, computational cardiology, largely driven by the Physiome project, now stands at the threshold of clinical utility in regards to risk stratification and treatment of patients at risk of sudden cardiac death. In this white paper, we outline a roadmap of what needs to be done to make this translational step, using the relatively well-developed case of acquired or drug-induced long QT syndrome as an exemplar case.

NS1643 interacts around L529 of hERG to alter voltage sensor movement on the path to activation

Activators of hERG1 such as NS1643 are being developed for congenital/acquired long QT syndrome. Previous studies identify the neighborhood of L529 around the voltage-sensor as a putative interacting site for NS1643. With NS1643, the V1/2 of activation of L529I (-34 ± 4 mV) is similar to wild-type (WT) (-37 ± 3 mV; P > 0.05). WT and L529I showed no difference in the slope factor in the absence of NS1643 (8 ± 0 vs. 9 ± 0) but showed a difference in the presence of NS1643 (9 ± 0.3 vs. 22 ± 1; P < 0.01). Voltage-clamp-fluorimetry studies also indicated that in L529I, NS1643 reduces the voltage-sensitivity of S4 movement. To further assess mechanism of NS1643 action, mutations were made in this neighborhood. NS1643 shifts the V1/2 of activation of both K525C and K525C/L529I to hyperpolarized potentials (-131 ± 4 mV for K525C and -120 ± 21 mV for K525C/L529I). Both K525C and K525C/K529I had similar slope factors in the absence of NS1643 (18 ± 2 vs. 34 ± 5, respectively) but with NS1643, the slope factor of K525C/L529I increased from 34 ± 5 to 71 ± 10 (P < 0.01) whereas for K525C the slope factor did not change (18 ± 2 at baseline and 16 ± 2 for NS1643). At baseline, K525R had a slope factor similar to WT (9 vs. 8) but in the presence of NS1643, the slope factor of K525R was increased to 24 ± 4 vs. 9 ± 0 mV for WT (P < 0.01). Molecular modeling indicates that L529I induces a kink in the S4 voltage-sensor helix, altering a salt-bridge involving K525. Moreover, docking studies indicate that NS1643 binds to the kinked structure induced by the mutation with a higher affinity. Combining biophysical, computational, and electrophysiological evidence, a mechanistic principle governing the action of some activators of hERG1 channels is proposed.

Parameter Estimation of Ion Current Formulations Requires Hybrid Optimization Approach to Be Both Accurate and Reliable

Computational models of cardiac electrophysiology provided insights into arrhythmogenesis and paved the way toward tailored therapies in the last years. To fully leverage in silico models in future research, these models need to be adapted to reflect pathologies, genetic alterations, or pharmacological effects, however. A common approach is to leave the structure of established models unaltered and estimate the values of a set of parameters. Today's high-throughput patch clamp data acquisition methods require robust, unsupervised algorithms that estimate parameters both accurately and reliably. In this work, two classes of optimization approaches are evaluated: gradient-based trust-region-reflective and derivative-free particle swarm algorithms. Using synthetic input data and different ion current formulations from the Courtemanche et al. electrophysiological model of human atrial myocytes, we show that neither of the two schemes alone succeeds to meet all requirements. Sequential combination of the two algorithms did improve the performance to some extent but not satisfactorily. Thus, we propose a novel hybrid approach coupling the two algorithms in each iteration. This hybrid approach yielded very accurate estimates with minimal dependency on the initial guess using synthetic input data for which a ground truth parameter set exists. When applied to measured data, the hybrid approach yielded the best fit, again with minimal variation. Using the proposed algorithm, a single run is sufficient to estimate the parameters. The degree of superiority over the other investigated algorithms in terms of accuracy and robustness depended on the type of current. In contrast to the non-hybrid approaches, the proposed method proved to be optimal for data of arbitrary signal to noise ratio. The hybrid algorithm proposed in this work provides an important tool to integrate experimental data into computational models both accurately and robustly allowing to assess the often non-intuitive consequences of ion channel-level changes on higher levels of integration.

Kinetic model for NS1643 drug activation of WT and L529I variants of Kv11.1 (hERG1) potassium channel

Congenital and acquired (drug-induced) forms of the human long-QT syndrome are associated with alterations in Kv11.1 (hERG) channel-controlled repolarizing IKr currents of cardiac action potentials. A mandatory drug screen implemented by many countries led to a discovery of a large group of small molecules that can activate hERG currents and thus may act as potent antiarrhythmic agents. Despite significant progress in identification of channel activators, little is known about their mechanism of action. A combination of electrophysiological studies with molecular and kinetic modeling was used to examine the mechanism of a model activator (NS1643) action on the hERG channel and its L529I mutant. The L529I mutant has gating dynamics similar to that of wild-type while its response to application of NS1643 is markedly different. We propose a mechanism compatible with experiments in which the model activator binds to the closed (C3) and open states (O). We suggest that NS1643 is affecting early gating transitions, probably during movements of the voltage sensor that precede the opening of the activation gate.

The utility of simple mathematical models in understanding gene regulatory dynamics

In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960's. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting.

Structural insight into the transmembrane segments 3 and 4 of the hERG potassium channel

The hERG (human ether-a-go-go related gene) potassium channel is a voltage-gated potassium channel containing an N-terminal domain, a voltage-sensor domain, a pore domain and a C-terminal domain. The transmembrane segment 4 (S4) is important for sensing changes of membrane potentials through positively charge residues. A construct containing partial S2-S3 linker, S3, S4 and the S4-S5 linker of the hERG channel was purified into detergent micelles. This construct exhibits good quality NMR spectrum when it was purified in lyso-myristoyl phosphatidylglycerol (LMPG) micelles. Structural study showed that S3 contains two short helices with a negatively charged surface. The S4 and S4-S5 linker adopt helical structures. The six positively charged residues in S4 localize at different sides, suggesting that they may have different functions in channel gating. Relaxation studies indicated that S3 is more flexible than S4. The boundaries of S3-S4 and S4-S4-S5 linker were identified. Our results provided structural information of the S3 and S4, which will be helpful to understand their roles in channel gating.

Hydrophobic interactions between the voltage sensor and pore mediate inactivation in Kv11.1 channels

Kv11.1 channels are critical for the maintenance of a normal heart rhythm. The flow of potassium ions through these channels is controlled by two voltage-regulated gates, termed "activation" and "inactivation," located at opposite ends of the pore. Crucially in Kv11.1 channels, inactivation gating occurs much more rapidly, and over a distinct range of voltages, compared with activation gating. Although it is clear that the fourth transmembrane segments (S4), within each subunit of the tetrameric channel, are important for controlling the opening and closing of the activation gate, their role during inactivation gating is much less clear. Here, we use rate equilibrium free energy relationship (REFER) analysis to probe the contribution of the S4 "voltage-sensor" helix during inactivation of Kv11.1 channels. Contrary to the important role that charged residues play during activation gating, it is the hydrophobic residues (Leu529, Leu530, Leu532, and Val535) that are the key molecular determinants of inactivation gating. Within the context of an interconnected multi-domain model of Kv11.1 inactivation gating, our REFER analysis indicates that the S4 helix and the S4-S5 linker undergo a conformational rearrangement shortly after that of the S5 helix and S5P linker, but before the S6 helix. Combining REFER analysis with double mutant cycle analysis, we provide evidence for a hydrophobic interaction between residues on the S4 and S5 helices. Based on a Kv11.1 channel homology model, we propose that this hydrophobic interaction forms the basis of an intersubunit coupling between the voltage sensor and pore domain that is an important mediator of inactivation gating.

Computational tools to investigate genetic cardiac channelopathies

The aim of this perspective article is to share with the community of ion channel scientists our thoughts and expectations regarding the increasing role that computational tools will play in the future of our field. The opinions and comments detailed here are the result of a 3-day long international exploratory workshop that took place in October 2013 and that was supported by the Swiss National Science Foundation.

Mechanism of hERG channel block by the psychoactive indole alkaloid ibogaine

Ibogaine is a psychoactive indole alkaloid. Its use as an antiaddictive agent has been accompanied by QT prolongation and cardiac arrhythmias, which are most likely caused by human ether a go-go-related gene (hERG) potassium channel inhibition. Therefore, we studied in detail the interaction of ibogaine with hERG channels heterologously expressed in mammalian kidney tsA-201 cells. Currents through hERG channels were blocked regardless of whether ibogaine was applied via the extracellular or intracellular solution. The extent of inhibition was determined by the relative pH values. Block occurred during activation of the channels and was not observed for resting channels. With increasing depolarizations, ibogaine block grew and developed faster. Steady-state activation and inactivation of the channel were shifted to more negative potentials. Deactivation was slowed, whereas inactivation was accelerated. Mutations in the binding site reported for other hERG channel blockers (Y652A and F656A) reduced the potency of ibogaine, whereas an inactivation-deficient double mutant (G628C/S631C) was as sensitive as wild-type channels. Molecular drug docking indicated binding within the inner cavity of the channel independently of the protonation of ibogaine. Experimental current traces were fit to a kinetic model of hERG channel gating, revealing preferential binding of ibogaine to the open and inactivated state. Taken together, these findings show that ibogaine blocks hERG channels from the cytosolic side either in its charged form alone or in company with its uncharged form and alters the currents by changing the relative contribution of channel states over time.

Allocryptopine and benzyltetrahydropalmatine block hERG potassium channels expressed in HEK293 cells

AIM

Allocryptopine (ALL) is an alkaloid extracted from Corydalis decumbens (Thunb) Pers. Papaveraceae, whereas benzyltetrahydropalmatine (BTHP) is a derivative of tetrahydropalmatine extracted from Corydalis ambigua (Pall) Cham et Schlecht. The aim of this study was to investigate the effects of ALL and BTHP on the human ether-a-go-go related gene (hERG) current expressed in HEK293 cells.

METHODS

Cultured HEK293 cells were transiently transfected with hERG channel cDNA plasmid pcDNA3.1 using Lipofectamine. The whole-cell current IHERG was evoked and recorded using Axon MultiClamp 700B amplifier. The drugs were applied via supserfusion.

RESULTS

Both ALL and BTHP reversibly suppressed the amplitude and density of IHERG in concentration- and voltage-dependent manners (the respective IC50 value was 49.65 and 22.38 μmol/L). BTHP (30 μmol/L) caused a significant negative shift of the steady-state inactivation curve of IHERG, while ALL (30 μmol/L) did not affect the steady-state inactivation of IHERG. Furthermore, BTHP, but not ALL, shortened the time constants of fast inactivation and slow time constants of deactivation of IHERG. But both the drugs markedly lengthened the time constants for recovery of IHERG from inactivation. Using action potential waveform pulses, it was found that both the drugs at 30 μmol/L significantly suppressed the current densities in the late phase of action potential, but did not significantly affect the current densities in the early phase of action potential.

CONCLUSION

Both ALL and BTHP derived from Chinese herbs potently block hERG current.

Effects of the small molecule HERG activator NS1643 on Kv11.3 channels

NS1643 is one of the small molecule HERG (Kv11.1) channel activators and has also been found to increase erg2 (Kv11.2) currents. We now investigated whether NS1643 is also able to act as an activator of Kv11.3 (erg3) channels expressed in CHO cells. Activation of rat Kv11.3 current occurred in a dose-dependent manner and maximal current increasing effects were obtained with 10 µM NS1643. At this concentration, steady-state outward current increased by about 80% and the current increase was associated with a significant shift in the voltage dependence of activation to more negative potentials by about 15 mV. In addition, activation kinetics were accelerated, whereas deactivation was slowed. There was no significant effect on the kinetics of inactivation and recovery from inactivation. The strong current-activating agonistic effect of NS1643 did not result from a shift in the voltage dependence of Kv11.3 channel inactivation and was independent from external Na⁺ or Ca²⁺. At the higher concentration of 20 µM, NS1643 induced clearly less current increase. The left shift in the voltage dependence of activation reversed and the voltage sensitivity of activation dramatically decreased along with a slowing of Kv11.3 channel activation. These data show that, in comparison to other Kv11 family members, NS1643 exerts distinct effects on Kv11.3 channels with especially pronounced partial antagonistic effects at higher concentration.

Voltage-dependent gating of HERG potassium channels

The mechanisms by which voltage-gated channels sense changes in membrane voltage and energetically couple this with opening of the ion conducting pore has been the source of significant interest. In voltage-gated potassium (Kv) channels, much of our knowledge in this area comes from Shaker-type channels, for which voltage-dependent gating is quite rapid. In these channels, activation and deactivation are associated with rapid reconfiguration of the voltage-sensing domain unit that is electromechanically coupled, via the S4-S5 linker helix, to the rate-limiting opening of an intracellular pore gate. However, fast voltage-dependent gating kinetics are not typical of all Kv channels, such as Kv11.1 (human ether-à-go-go related gene, hERG), which activates and deactivates very slowly. Compared to Shaker channels, our understanding of the mechanisms underlying slow hERG gating is much poorer. Here, we present a comparative review of the structure-function relationships underlying activation and deactivation gating in Shaker and hERG channels, with a focus on the roles of the voltage-sensing domain and the S4-S5 linker that couples voltage sensor movements to the pore. Measurements of gating current kinetics and fluorimetric analysis of voltage sensor movement are consistent with models suggesting that the hERG activation pathway contains a voltage independent step, which limits voltage sensor transitions. Constraints upon hERG voltage sensor movement may result from loose packing of the S4 helices and additional intra-voltage sensor counter-charge interactions. More recent data suggest that key amino acid differences in the hERG voltage-sensing unit and S4-S5 linker, relative to fast activating Shaker-type Kv channels, may also contribute to the increased stability of the resting state of the voltage sensor.

Increased vulnerability of human ventricle to re-entrant excitation in hERG-linked variant 1 short QT syndrome

The short QT syndrome (SQTS) is a genetically heterogeneous condition characterized by abbreviated QT intervals and an increased susceptibility to arrhythmia and sudden death. This simulation study identifies arrhythmogenic mechanisms in the rapid-delayed rectifier K⁺ current (I_Kr)-linked SQT1 variant of the SQTS. Markov chain (MC) models were found to be superior to Hodgkin-Huxley (HH) models in reproducing experimental data regarding effects of the N588K mutation on KCNH2-encoded hERG. These ionic channel models were then incorporated into human ventricular action potential (AP) models and into 1D and 2D idealised and realistic transmural ventricular tissue simulations and into a 3D anatomical model. In single cell models, the N588K mutation abbreviated ventricular cell AP duration at 90% repolarization (APD₉₀) and decreased the maximal transmural voltage heterogeneity (δV) during APs. This resulted in decreased transmural heterogeneity of APD₉₀ and of the effective refractory period (ERP): effects that are anticipated to be anti-arrhythmic rather than pro-arrhythmic. However, with consideration of transmural heterogeneity of I_Kr density in the intact tissue model based on the ten Tusscher-Noble-Noble-Panfilov ventricular model, not only did the N588K mutation lead to QT-shortening and increases in T-wave amplitude, but δV was found to be augmented in some local regions of ventricle tissue, resulting in increased tissue vulnerability for uni-directional conduction block and predisposing to formation of re-entrant excitation waves. In 2D and 3D tissue models, the N588K mutation facilitated and maintained re-entrant excitation waves due to the reduced substrate size necessary for sustaining re-entry. Thus, in SQT1 the N588K-hERG mutation facilitates initiation and maintenance of ventricular re-entry, increasing the lifespan of re-entrant spiral waves and the stability of scroll waves in 3D tissue.

Sudden cardiac death may arise in individuals with diseased heart tissue, or in apparently healthy subjects who suffer from genetic defects in ‘ion channel’ proteins, which increase cardiac arrhythmia risk and are associated with significant morbidity and mortality. One rare, though serious, genetic condition is the ‘short QT syndrome’ (SQTS). Although it is now known that the KCNH2-encoded N588K-hERG mutation is associated with the main (SQT1) variant of the SQTS, the mechanisms by which ventricular arrhythmia is initiated and sustained are still unclear due to lack of genotypically accurate experimental models. In this study, we used sophisticated multi-scale computer models of human ventricles in order to investigate the pro-arrhythmic effects of the N588K hERG mutation. It was found that the mutation accelerated the ventricular repolarization process, produced augmented electrical heterogeneity in some local regions of the tissue, leading to increased risk of arrhythmia genesis. It was also found that accelerated ventricular repolarization reduced the substrate size of the tissue required to sustain re-entrant circuits in both two and three dimensions. This study provides new mechanistic insight into understanding of how changes to hERG channel function in SQT1 lead to exacerbated ventricular arrhythmia risk in this inherited arrhythmia syndrome.