A multiscale investigation of repolarization variability and its role in cardiac arrhythmogenesis

Enhanced temporal and spatial variability in cardiac repolarization has been related to increased arrhythmic risk both clinically and experimentally. Causes and modulators of variability in repolarization and their implications in arrhythmogenesis are however not well understood. At the ionic level, the slow component of the delayed rectifier potassium current (I_Ks) is an important determinant of ventricular repolarization. In this study, a combination of experimental and computational multiscale studies is used to investigate the role of intrinsic and extrinsic noise in I_Ks in modulating temporal and spatial variability in ventricular repolarization in human and guinea pig. Results show that under physiological conditions: i), stochastic fluctuations in I_Ks gating properties (i.e., intrinsic noise) cause significant beat-to-beat variability in action potential duration (APD) in isolated cells, whereas cell-to-cell differences in channel numbers (i.e., extrinsic noise) also contribute to cell-to-cell APD differences; ii), in tissue, electrotonic interactions mask the effect of I_Ks noise, resulting in a significant decrease in APD temporal and spatial variability compared to isolated cells. Pathological conditions resulting in gap junctional uncoupling or a decrease in repolarization reserve uncover the manifestation of I_Ks noise at cellular and tissue level, resulting in enhanced ventricular variability and abnormalities in repolarization such as afterdepolarizations and alternans.     

Determinants of Beat-to-Beat Variability of Repolarization Duration in the Canine Ventricular Myocyte: A Computational Analysis

Beat-to-beat variability of repolarization duration (BVR) is an intrinsic characteristic of cardiac function and a better marker of proarrhythmia than repolarization prolongation alone. The ionic mechanisms underlying baseline BVR in physiological conditions, its rate dependence, and the factors contributing to increased BVR in pathologies remain incompletely understood. Here, we employed computer modeling to provide novel insights into the subcellular mechanisms of BVR under physiological conditions and during simulated drug-induced repolarization prolongation, mimicking long-QT syndromes type 1, 2, and 3. We developed stochastic implementations of 13 major ionic currents and fluxes in a model of canine ventricular-myocyte electrophysiology. Combined stochastic gating of these components resulted in short- and long-term variability, consistent with experimental data from isolated canine ventricular myocytes. The model indicated that the magnitude of stochastic fluctuations is rate dependent due to the rate dependence of action-potential (AP) duration (APD). This process (the “active” component) and the intrinsic nonlinear relationship between membrane current and APD (“intrinsic component”) contribute to the rate dependence of BVR. We identified a major role in physiological BVR for stochastic gating of the persistent Na⁺ current (I_Na) and rapidly activating delayed-rectifier K⁺ current (I_Kr). Inhibition of I_Kr or augmentation of I_Na significantly increased BVR, whereas subsequent β-adrenergic receptor stimulation reduced it, similar to experimental findings in isolated myocytes. In contrast, β-adrenergic stimulation increased BVR in simulated long-QT syndrome type 1. In addition to stochastic channel gating, AP morphology, APD, and beat-to-beat variations in Ca²⁺ were found to modulate single-cell BVR. Cell-to-cell coupling decreased BVR and this was more pronounced when a model cell with increased BVR was coupled to a model cell with normal BVR. In conclusion, our results provide new insights into the ionic mechanisms underlying BVR and suggest that BVR reflects multiple potentially proarrhythmic parameters, including increased ion-channel stochasticity, prolonged APD, and abnormal Ca²⁺ handling.     

Quantal charge redistributions accompanying the structural transitions of sodium channels

Asymmetric displacement currents, I _g , associated with the gating of nerve sodium channels have been recorded in cell-attached macropatches of Xenopus laevis oocytes injected with exogenous mRNA coding for rat-brain-II sodium channels. The I _g properties were found to be similar to those of gating currents previously observed in native nerve preparations. I _g fluctuations were measured in order to ascertain the discreteness of the conformational changes which precede the channel opening. The autocorrelation of the fluctuations is consistent with a shot-like character of the elementary I _g contributions. The variance of the fluctuations indicates that most of the gating-charge movement that accompanies the activation of a single sodium channel occurs in 2 to 3 brief packets, each carrying an equivalent of about 2.3 electron charges.     

Mechanism of Ion Permeation in Skeletal Muscle Chloride Channels

Voltage-gated Cl⁻ channels belonging to the ClC family exhibit unique properties of ion permeation and gating. We functionally probed the conduction pathway of a recombinant human skeletal muscle Cl⁻ channel (hClC-1) expressed both in Xenopus oocytes and in a mammalian cell line by investigating block by extracellular or intracellular I⁻ and related anions. Extracellular and intracellular I⁻ exert blocking actions on hClC-1 currents that are both concentration and voltage dependent. Similar actions were observed for a variety of other halide (Br⁻) and polyatomic (SCN⁻, NO₃ ⁻, CH₃SO₃ ⁻) anions. In addition, I⁻ block is accompanied by gating alterations that differ depending on which side of the membrane the blocker is applied. External I⁻ causes a shift in the voltage-dependent probability that channels exist in three definable kinetic states (fast deactivating, slow deactivating, nondeactivating), while internal I⁻ slows deactivation. These different effects on gating properties can be used to distinguish two functional ion binding sites within the hClC-1 pore. We determined K _D values for I⁻ block in three distinct kinetic states and found that binding of I⁻ to hClC-1 is modulated by the gating state of the channel. Furthermore, estimates of electrical distance for I⁻ binding suggest that conformational changes affecting the two ion binding sites occur during gating transitions. These results have implications for understanding mechanisms of ion selectivity in hClC-1, and for defining the intimate relationship between gating and permeation in ClC channels.     

Stochastic Model of Gap Junctions Exhibiting Rectification and Multiple Closed States of Slow Gates

Gap-junction (GJ) channels formed from connexin (Cx) proteins provide direct pathways for electrical and metabolic cell-cell communication. Earlier, we developed a stochastic 16-state model (S16SM) of voltage gating of the GJ channel containing two pairs of fast and slow gates, each operating between open (o) and closed (c) states. However, experimental data suggest that gates may in fact contain two or more closed states. We developed a model in which the slow gate operates according to a linear reaction scheme, o↔c₁↔c₂, where c₁ and c₂ are initial-closed and deep-closed states that both close the channel fully, whereas the fast gate operates between the open state and the closed state and exhibits a residual conductance. Thus, we developed a stochastic 36-state model (S36SM) of GJ channel gating that is sensitive to transjunctional voltage (V_j). To accelerate simulation and eliminate noise in simulated junctional conductance (g_j) records, we transformed an S36SM into a Markov chain 36-state model (MC36SM) of GJ channel gating. This model provides an explanation for well-established experimental data, such as delayed g_j recovery after V_j gating, hysteresis of g_j-V_j dependence, and the low ratio of functional channels to the total number of GJ channels clustered in junctional plaques, and it has the potential to describe chemically mediated gating, which cannot be reflected using an S16SM. The MC36SM, when combined with global optimization algorithms, can be used for automated estimation of gating parameters including probabilities of c₁↔c₂ transitions from experimental g_j-time and g_j-V_j dependencies.     

CaMKII-Induced Shift in Modal Gating Explains L-Type Ca Current Facilitation: A Modeling Study

Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) plays an important role in L-type Ca²⁺ channel (LCC) facilitation: the Ca²⁺-dependent augmentation of Ca²⁺ current (I_CaL) exhibited during rapid repeated depolarization. Multiple mechanisms may underlie facilitation, including an increased rate of recovery from Ca²⁺-dependent inactivation and a shift in modal gating distribution from mode 1, the dominant mode of LCC gating, to mode 2, a mode in which openings are prolonged. We hypothesized that the primary mechanism underlying facilitation is the shift in modal gating distribution resulting from CaMKII-mediated LCC phosphorylation. We developed a stochastic model describing the dynamic interactions among CaMKII, LCCs, and phosphatases as a function of dyadic Ca²⁺ and calmodulin levels, and we incorporated it into an integrative model of the canine ventricular myocyte. The model reproduces behaviors at physiologic protein levels and allows for dynamic transition between modes, depending on the LCC phosphorylation state. Simulations showed that a CaMKII-dependent shift in LCC distribution toward mode 2 accounted for the I_CaL positive staircase. Moreover, simulations demonstrated that experimentally observed changes in LCC inactivation and recovery kinetics may arise from modal gating shifts, rather than from changes in intrinsic inactivation properties. The model therefore serves as a powerful tool for interpreting I_CaL experiments.     

Simulation of Ca-calmodulin-dependent protein kinase II on rabbit ventricular myocyte ion currents and action potentials

Ca-calmodulin-dependent protein kinase II (CaMKII) was recently shown to alter Na⁺ channel gating and recapitulate a human Na⁺ channel genetic mutation that causes an unusual combined arrhythmogenic phenotype in patients: simultaneous long QT syndrome and Brugada syndrome. CaMKII is upregulated in heart failure where arrhythmias are common, and CaMKII inhibition can reduce arrhythmias. Thus, CaMKII-dependent channel modulation may contribute to acquired arrhythmic disease. We developed a Markovian Na⁺ channel model including CaMKII-dependent changes, and incorporated it into a comprehensive myocyte action potential (AP) model with Na⁺ and Ca²⁺ transport. CaMKII shifts Na⁺ current (I_Na) availability to more negative voltage, enhances intermediate inactivation, and slows recovery from inactivation (all loss-of-function effects), but also enhances late noninactivating I_Na (gain of function). At slow heart rates, with long diastolic time for I_Na recovery, late I_Na is the predominant effect, leading to AP prolongation (long QT syndrome). At fast heart rates, where recovery time is limited and APs are shorter, there is little effect on AP duration, but reduced availability decreases I_Na, AP upstroke velocity, and conduction (Brugada syndrome). CaMKII also increases cardiac Ca²⁺ and K⁺ currents (I_Ca and I_to), complicating CaMKII-dependent AP changes. Incorporating I_Ca and I_to effects individually prolongs and shortens AP duration. Combining I_Na, I_Ca, and I_to effects results in shortening of AP duration with CaMKII. With transmural heterogeneity of I_to and I_to downregulation in heart failure, CaMKII may accentuate dispersion of repolarization. This provides a useful initial framework to consider pathways by which CaMKII may contribute to arrhythmogenesis.     

Mechanisms of Transition from Normal to Reentrant Electrical Activity in a Model of Rabbit Atrial Tissue: Interaction of Tissue Heterogeneity and Anisotropy

Experimental evidence suggests that regional differences in action potential (AP) morphology can provide a substrate for initiation and maintenance of reentrant arrhythmias in the right atrium (RA), but the relationships between the complex electrophysiological and anatomical organization of the RA and the genesis of reentry are unclear. In this study, a biophysically detailed three-dimensional computer model of the right atrial tissue was constructed to study the role of tissue heterogeneity and anisotropy in arrhythmogenesis. The model of Lindblad et al. for a rabbit atrial cell was modified to incorporate experimental data on regional differences in several ionic currents (primarily, I_Na, I_CaL, I_K1, I_to, and I_sus) between the crista terminalis and pectinate muscle cells. The modified model was validated by its ability to reproduce the AP properties measured experimentally. The anatomical model of the rabbit RA (including tissue geometry and fiber orientation) was based on a recent histological reconstruction. Simulations with the resultant electrophysiologically and anatomically detailed three-dimensional model show that complex organization of the RA tissue causes breakdown of regular AP conduction patterns at high pacing rates (>11.75 Hz): as the AP in the crista terminalis cells is longer, and electrotonic coupling transverse to fibers of the crista terminalis is weak, high-frequency pacing at the border between the crista terminalis and pectinate muscles results in a unidirectional conduction block toward the crista terminalis and generation of reentry. Contributions of the tissue heterogeneity and anisotropy to reentry initiation mechanisms are quantified by measuring action potential duration (APD) gradients at the border between the crista terminalis and pectinate muscles: the APD gradients are high in areas where both heterogeneity and anisotropy are high, such that intrinsic APD differences are not diminished by electrotonic interactions. Thus, our detailed computer model reconstructs complex electrical activity in the RA, and provides new insights into the mechanisms of transition from focal atrial tachycardia into reentry.     

Modifying L-type calcium current kinetics: consequences for cardiac excitation and arrhythmia dynamics

The L-type Ca current (I_Ca,L), essential for normal cardiac function, also regulates dynamic action potential (AP) properties that promote ventricular fibrillation. Blocking I_Ca,L can prevent ventricular fibrillation, but only at levels suppressing contractility. We speculated that, instead of blocking I_Ca,L, modifying its shape by altering kinetic features could produce equivalent anti-fibrillatory effects without depressing contractility. To test this concept experimentally, we overexpressed a mutant Ca-insensitive calmodulin (CaM₁₂₃₄) in rabbit ventricular myocytes to inhibit Ca-dependent I_Ca,L inactivation, combined with the ATP-sensitive K current agonist pinacidil or I_Ca,L blocker verapamil to maintain AP duration (APD) near control levels. Cell shortening was enhanced in pinacidil-treated myocytes, but depressed in verapamil-treated myocytes. Both combinations flattened APD restitution slope and prevented APD alternans, similar to I_Ca,L blockade. To predict the arrhythmogenic consequences, we simulated the cellular effects using a new AP model, which reproduced flattening of APD restitution slope and prevention of APD/Ca_i transient alternans but maintained a normal Ca_i transient. In simulated two-dimensional cardiac tissue, these changes prevented the arrhythmogenic spatially discordant APD/Ca_i transient alternans and spiral wave breakup. These findings provide a proof-of-concept test that I_Ca,L can be targeted to increase dynamic wave stability without depressing contractility, which may have promise as an antifibrillatory strategy.     

A New TASK for Dipeptidyl Peptidase-like Protein 6

Dipeptidyl Peptidase-like Protein 6 (DPP6) is widely expressed in the brain where it co-assembles with Kv4 channels and KChIP auxiliary subunits to regulate the amplitude and functional properties of the somatodendritic A-current, I_SA. Here we show that in cerebellar granule (CG) cells DPP6 also regulates resting membrane potential and input resistance by increasing the amplitude of the I_K(SO) resting membrane current. Pharmacological analysis shows that DPP6 acts through the control of a channel with properties matching the K_2P channel TASK-3. Heterologous expression and co-immunoprecipitation shows that DPP6 co-expression with TASK-3 results in the formation of a protein complex that enhances resting membrane potassium conductance. The co-regulation of resting and voltage-gated channels by DPP6 produces coordinate shifts in resting membrane potential and A-current gating that optimize the sensitivity of I_SA inactivation gating to subthreshold fluctuations in resting membrane potential.     

Differential Expression of hERG1 Channel Isoforms Reproduces Properties of Native I Kr and Modulates Cardiac Action Potential Characteristics

Background

The repolarizing cardiac rapid delayed rectifier current, I _Kr, is composed of ERG1 channels. It has been suggested that two isoforms of the ERG1 protein, ERG1a and ERG1b, both contribute to I _Kr. Marked heterogeneity in the kinetic properties of native I _Kr has been described. We hypothesized that the heterogeneity of native I _Kr can be reproduced by differential expression of ERG1a and ERG1b isoforms. Furthermore, the functional consequences of differential expression of ERG1 isoforms were explored as a potential mechanism underlying native heterogeneity of action potential duration (APD) and restitution.

Methodology/Principal Findings

The results show that the heterogeneity of native I _Kr can be reproduced in heterologous expression systems by differential expression of ERG1a and ERG1b isoforms. Characterization of the macroscopic kinetics of ERG1 currents demonstrated that these were dependent on the relative abundance of ERG1a and ERG1b. Furthermore, we used a computational model of the ventricular cardiomyocyte to show that both APD and the slope of the restitution curve may be modulated by varying the relative abundance of ERG1a and ERG1b. As the relative abundance of ERG1b was increased, APD was gradually shortened and the slope of the restitution curve was decreased.

Conclusions/Significance

Our results show that differential expression of ERG1 isoforms may explain regional heterogeneity of I _Kr kinetics. The data demonstrate that subunit dependent changes in channel kinetics are important for the functional properties of ERG1 currents and hence I _Kr. Importantly, our results suggest that regional differences in the relative abundance of ERG1 isoforms may represent a potential mechanism underlying the heterogeneity of both APD and APD restitution observed in mammalian hearts.     

Using Multi-Compartment Ensemble Modeling As an Investigative Tool of Spatially Distributed Biophysical Balances: Application to Hippocampal Oriens-Lacunosum/Moleculare (O-LM) Cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron''s output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron''s biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (I _h). Although dendritic I _h could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of I _h on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic I _h. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic I _h. These findings inform future experiments that differentiate between somatic and dendritic I _h, thereby continuing a cycle between model and experiment.     

Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion

Ca²⁺-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca²⁺ channel gating, Ca²⁺ diffusion, and Ca²⁺ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca²⁺ diffusion, buffering, and sensing if Ca²⁺ channel gating is not Ca²⁺ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca²⁺ dynamics downstream of Ca²⁺ channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca²⁺-bound state of a vesicle fusion sensor, following a brief Ca²⁺ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ～50 Ca²⁺ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca²⁺ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca²⁺ sensor from local Ca²⁺ fluctuations. Thus, fluctuations in the Ca²⁺ sensor’s state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca²⁺ concentration around its average, deterministically computable value.     

The Contribution of Ionic Currents to Rate-Dependent Action Potential Duration and Pattern of Reentry in a Mathematical Model of Human Atrial Fibrillation

Persistent atrial fibrillation (PeAF) in humans is characterized by shortening of action potential duration (APD) and attenuation of APD rate-adaptation. However, the quantitative influences of particular ionic current alterations on rate-dependent APD changes, and effects on patterns of reentry in atrial tissue, have not been systematically investigated. Using mathematical models of human atrial cells and tissue and performing parameter sensitivity analysis, we evaluated the quantitative contributions to action potential (AP) shortening and APD rate-adaptation of ionic current remodeling seen with PeAF. Ionic remodeling in PeAF was simulated by reducing L-type Ca²⁺ channel current (I_CaL), increasing inward rectifier K⁺ current (I_K1) and modulating five other ionic currents. Parameter sensitivity analysis, which quantified how each ionic current influenced APD in control and PeAF conditions, identified interesting results, including a negative effect of Na⁺/Ca²⁺ exchange on APD only in the PeAF condition. At high pacing rate (2 Hz), electrical remodeling in I_K1 alone accounts for the APD reduction of PeAF, but at slow pacing rate (0.5 Hz) both electrical remodeling in I_CaL alone (-70%) and I_K1 alone (+100%) contribute equally to the APD reduction. Furthermore, AP rate-adaptation was affected by I_Kur in control and by I_NaCa in the PeAF condition. In a 2D tissue model, a large reduction (-70%) of I_CaL becomes a dominant factor leading to a stable spiral wave in PeAF. Our study provides a quantitative and unifying understanding of the roles of ionic current remodeling in determining rate-dependent APD changes at the cellular level and spatial reentry patterns in tissue.     

Exact Stochastic Simulation of a Calcium Microdomain Reveals the Impact of Ca2+ Fluctuations on IP3R Gating

In this study, we numerically analyzed the nonlinear Ca²⁺-dependent gating dynamics of a single, nonconducting inositol 1,4,5-trisphosphate receptor (IP₃R) channel, using an exact and fully stochastic simulation algorithm that includes channel gating, Ca²⁺ buffering, and Ca²⁺ diffusion. The IP₃R is a ubiquitous intracellular Ca²⁺ release channel that plays an important role in the formation of complex spatiotemporal Ca²⁺ signals such as waves and oscillations. Dynamic subfemtoliter Ca²⁺ microdomains reveal low copy numbers of Ca²⁺ ions, buffer molecules, and IP₃Rs, and stochastic fluctuations arising from molecular interactions and diffusion do not average out. In contrast to models treating calcium dynamics deterministically, the stochastic approach accounts for this molecular noise. We varied Ca²⁺ diffusion coefficients and buffer reaction rates to tune the autocorrelation properties of Ca²⁺ noise and found a distinct relation between the autocorrelation time τ_ac, the mean channel open and close times, and the resulting IP₃R open probability P_O. We observed an increased P_O for shorter noise autocorrelation times, caused by increasing channel open times and decreasing close times. In a pure diffusion model the effects become apparent at elevated calcium concentrations, e.g., at [Ca²⁺] = 25 μM, τ_ac = 0.082 ms, the IP₃R open probability increased by ≈20% and mean open times increased by ≈4 ms, compared to a zero noise model. We identified the inactivating Ca²⁺ binding site of IP₃R subunits as the primarily noise-susceptible element of the De Young and Keizer model. Short Ca²⁺ noise autocorrelation times decrease the probability of Ca²⁺ association and consequently increase IP₃R activity. These results suggest a functional role of local calcium noise properties on calcium-regulated target molecules such as the ubiquitous IP₃R. This finding may stimulate novel experimental approaches analyzing the role of calcium noise properties on microdomain behavior.     

Pronounced Effects of HERG-Blockers E-4031 and Erythromycin on APD,Spatial APD Dispersion and Triangulation in Transgenic Long-QT Type 1 Rabbits

Background

Prolongation of action potential duration (APD), increased spatial APD dispersion, and triangulation are major factors promoting drug-induced ventricular arrhythmia. Preclinical identification of HERG/I_Kr-blocking drugs and their pro-arrhythmic potential, however, remains a challenge. We hypothesize that transgenic long-QT type 1 (LQT1) rabbits lacking repolarizing I_Ks current may help to sensitively detect HERG/I_Kr-blocking properties of drugs.

Methods

Hearts of adult female transgenic LQT1 and wild type littermate control (LMC) rabbits were Langendorff-perfused with increasing concentrations of HERG/I_Kr-blockers E-4031 (0.001–0.1 µM, n = 9/7) or erythromycin (1–300 µM, n = 9/7) and APD, APD dispersion, and triangulation were analyzed.

Results

At baseline, APD was longer in LQT1 than in LMC rabbits in LV apex and RV mid. Erythromycin and E-4031 prolonged APD in LQT1 and LMC rabbits in all positions. However, erythromycin-induced percentaged APD prolongation related to baseline (%APD) was more pronounced in LQT1 at LV base-lateral and RV mid positions (100 µM, LQT1, +40.6±9.7% vs. LMC, +24.1±10.0%, p<0.05) and E-4031-induced %APD prolongation was more pronounced in LQT1 at LV base-lateral (0.01 µM, LQT1, +29.6±10.6% vs. LMC, +19.1±3.8%, p<0.05) and LV base-septal positions. Moreover, erythromycin significantly increased spatial APD dispersion only in LQT1 and increased triangulation only in LQT1 in LV base-septal and RV mid positions. Similarly, E-4031 increased triangulation only in LQT1 in LV apex and base-septal positions.

Conclusions

E-4031 and erythromycin prolonged APD and increased triangulation more pronouncedly in LQT1 than in LMC rabbits. Moreover, erythromycin increased APD dispersion only in LQT1, indicating that transgenic LQT1 rabbits could serve as sensitive model to detect HERG/I_Kr-blocking properties of drugs.     

A Stochastic Four-State Model of Contingent Gating of Gap Junction Channels Containing Two “Fast” Gates Sensitive to Transjunctional Voltage

Connexins, a family of membrane proteins, form gap junction (GJ) channels that provide a direct pathway for electrical and metabolic signaling between cells. We developed a stochastic four-state model describing gating properties of homotypic and heterotypic GJ channels each composed of two hemichannels (connexons). GJ channel contain two “fast” gates (one per hemichannel) oriented opposite in respect to applied transjunctional voltage (V_j). The model uses a formal scheme of peace-linear aggregate and accounts for voltage distribution inside the pore of the channel depending on the state, unitary conductances and gating properties of each hemichannel. We assume that each hemichannel can be in the open state with conductance γ_h,o and in the residual state with conductance γ_h,res, and that both γ_h,o and γ_h,res rectifies. Gates can exhibit the same or different gating polarities. Gating of each hemichannel is determined by the fraction of V_j that falls across the hemichannel, and takes into account contingent gating when gating of one hemichannel depends on the state of apposed hemichannel. At the single-channel level, the model revealed the relationship between unitary conductances of hemichannels and GJ channels and how this relationship is affected by γ_h,o and γ_h,res rectification. Simulation of junctions containing up to several thousands of homotypic or heterotypic GJs has been used to reproduce experimentally measured macroscopic junctional current and V_j-dependent gating of GJs formed from different connexin isoforms. V_j-gating was simulated by imitating several frequently used experimental protocols: 1), consecutive V_j steps rising in amplitude, 2), slowly rising V_j ramps, and 3), series of V_j steps of high frequency. The model was used to predict V_j-gating of heterotypic GJs from characteristics of corresponding homotypic channels. The model allowed us to identify the parameters of V_j-gates under which small changes in the difference of holding potentials between cells forming heterotypic junctions effectively modulates cell-to-cell signaling from bidirectional to unidirectional. The proposed model can also be used to simulate gating properties of unapposed hemichannels.     

A comparative analysis of models of Na+ channel gating for mammalian and invertebrate nonmyelinated axons: Relationship to energy efficient action potentials

The rapidly activating, voltage gated Na⁺ current, I_Na, has recently been measured in mammalian nonmyelinated axons. Those results have been incorporated in simulations of the action potential, results that demonstrate a significant separation in time during the spike between I_Na and the repolarizing K⁺ current, I_K. The original Hodgkin and Huxley (1952) model of Na⁺ channel gating, m³h, where m and h are channel activation and inactivation, respectively, has been used in this analysis. This model was originally developed for invertebrate nonmyelinated axons, squid giant axons in particular. The model has not survived challenges based on results from invertebrate preparations using a double-step voltage clamp protocol and measurements of gating currents, results that demonstrate a kinetic link between activation and inactivation leading to a delayed onset of inactivation following a voltage step. These processes are independent of each other in the Hodgkin and Huxley (1952) model. Application of the double-step protocol to the m³h model for mammalian I_Na results reveals a surprising prediction, an apparent delay in onset of inactivation even though activation and inactivation are uncoupled in the model. Other results, most notably gating currents, will be required to demonstrate such a link, if indeed it exists for mammalian Na⁺ channels. The information obtained will be significant in determining the way in which the Na⁺ channel is sequestered away from its open state during repolarization, thereby allowing for a separation in time between I_Na and I_K during a spike, an energetically efficient mechanism of neuronal signaling in the mammalian brain.     

Alk7 Depleted Mice Exhibit Prolonged Cardiac Repolarization and Are Predisposed to Ventricular Arrhythmia

We aimed to investigate the role of activin receptor-like kinase (ALK7) in regulating cardiac electrophysiology. Here, we showed that Alk7^-/- mice exhibited prolonged QT intervals in telemetry ECG recordings. Furthermore, Langendorff-perfused Alk7^-/- hearts had significantly longer action potential duration (APD) and greater incidence of ventricular arrhythmia (AV) induced by burst pacing. Using whole-cell patch clamp, we found that the densities of repolarizing K⁺ currents I_to and I_K1 were profoundly reduced in Alk7^-/- ventricular cardiomyocytes. Mechanistically, the expression of Kv4.2 (a major subunit of I_to carrying channel) and KCHIP2 (a key accessory subunit of I_to carrying channel), was markedly decreased in Alk7^-/- hearts. These findings suggest that endogenous expression of ALK7 is necessary to maintain repolarizing K⁺ currents in ventricular cardiomyocytes, and finally prevent action potential prolongation and ventricular arrhythmia.     

Single-Channel Characteristics of Wild-Type IKs Channels and Channels formed with Two MinK Mutants that Cause Long QT Syndrome

I_Ks channels are voltage dependent and K⁺ selective. They influence cardiac action potential duration through their contribution to myocyte repolarization. Assembled from minK and KvLQT1 subunits, I_Ks channels are notable for a heteromeric ion conduction pathway in which both subunit types contribute to pore formation. This study was undertaken to assess the effects of minK on pore function. We first characterized the properties of wild-type human I_Ks channels and channels formed only of KvLQT1 subunits. Channels were expressed in Xenopus laevis oocytes or Chinese hamster ovary cells and currents recorded in excised membrane patches or whole-cell mode. Unitary conductance estimates were dependent on bandwidth due to rapid channel “flicker.” At 25 kHz in symmetrical 100-mM KCl, the single-channel conductance of I_Ks channels was ∼16 pS (corresponding to ∼0.8 pA at 50 mV) as judged by noise-variance analysis; this was fourfold greater than the estimated conductance of homomeric KvLQT1 channels. Mutant I_Ks channels formed with D76N and S74L minK subunits are associated with long QT syndrome. When compared with wild type, mutant channels showed lower unitary currents and diminished open probabilities with only minor changes in ion permeabilities. Apparently, the mutations altered single-channel currents at a site in the pore distinct from the ion selectivity apparatus. Patients carrying these mutant minK genes are expected to manifest decreased K⁺ flux through I_Ks channels due to lowered single-channel conductance and altered gating.