Current Conductances Research Articles

Circular current in a one-dimensional open quantum ring in the presence of magnetic field and spin–orbit interaction

In an open quantum system having a channel in the form of loop geometry, the current inside the channel, namely circular current, and overall junction current, namely transport current, can be different. A quantum ring has doubly degenerate eigen energies due to periodic boundary condition that is broken in an asymmetric ring where the ring is asymmetrically connected to the external electrodes. Kramers’ degeneracy and spin degeneracy can be lifted by considering non-zero magnetic field and spin–orbit interaction (SOI), respectively. Here, we find that symmetry breaking impacts the circular current conductance vs energy (E) spectra in addition to lifting the degeneracy. For charge and spin current conductances, the corresponding effects are not the same. Under symmetry-breaking they may remain symmetric or anti-symmetric or asymmetric around E = 0 whereas the transmission function (which is proportional to the junction current conductance) vs energy characteristic remains symmetric around E = 0. This study leads us to estimate the qualitative nature of the circular current and the choices of Fermi-energy/chemical potential to have a net non-zero current. As a result, we may manipulate the system to generate pure currents of charge, spin, or both, which is necessary for any spintronic and electronic applications.

Optimization of a cardiomyocyte model illuminates role of increased INa,L in repolarization reserve.

Cardiac ion currents may compensate for each other when one is compromised by a congenital or drug-induced defect. Such redundancy contributes to a robust repolarization reserve that can prevent the development of lethal arrhythmias. Most efforts made to describe this phenomenon have quantified contributions by individual ion currents. However, it is important to understand the interplay between all major ion-channel conductances, as repolarization reserve is dependent on the balance between all ion currents in a cardiomyocyte. Here, a genetic algorithm was designed to derive profiles of nine ion-channel conductances that optimize repolarization reserve in a mathematical cardiomyocyte model. Repolarization reserve was quantified using a previously defined metric, repolarization reserve current, i.e., the minimum constant current to prevent normal action potential repolarization in a cell. The optimization improved repolarization reserve current up to 84% compared to baseline in a human adult ventricular myocyte model and increased resistance to arrhythmogenic insult. The optimized conductance profiles were not only characterized by increased repolarizing current conductances but also uncovered a previously unreported behavior by the late sodium current. Simulations demonstrated that upregulated late sodium increased action potential duration, without compromising repolarization reserve current. The finding was generalized to multiple models. Ultimately, this computational approach, in which multiple currents were studied simultaneously, illuminated mechanistic insights into how the metric's magnitude could be increased and allowed for the unexpected role of late sodium to be elucidated.NEW & NOTEWORTHY Genetic algorithms are typically used to fit models or extract desired parameters from data. Here, we use the tool to produce a ventricular cardiomyocyte model with increased repolarization reserve. Since arrhythmia mitigation is dependent on multiple cardiac ion-channel conductances, study using a comprehensive, unbiased, and systems-level approach is important. The use of this optimization strategy allowed us to find robust profiles that illuminated unexpected mechanistic determinants of key ion-channel conductances in repolarization reserve.

Characterization of Spatio-Temporal Cardiac Action Potential Variability at Baseline and Under $\beta$-Adrenergic Stimulation by Combined Unscented Kalman Filter and Double Greedy Dimension Reduction

Elevated spatio-temporal variability of human ventricular repolarization has been related to increased risk for ventricular arrhythmias and sudden cardiac death, particularly under β-adrenergic stimulation ( β-AS). This work presents a methodology for theoretical characterization of temporal and spatial repolarization variability at baseline conditions and in response to β-AS. For any measured voltage trace, the proposed methodology estimates the parameters and state variables of an underlying human ventricular action potential (AP) model by combining Double Greedy Dimension Reduction (DGDR) with automatic selection of biomarkers and the Unscented Kalman Filter (UKF). Such theoretical characterization can facilitate subsequent characterization of underlying variability mechanisms. Given an AP trace, initial estimates for the ionic conductances in a stochastic version of the baseline human ventricular O'Hara etal. model were obtained by DGDR. Those estimates served to initialize and update model parameter estimates by the UKF method based on formulation of an associated nonlinear state-space representation and joint estimation of model parameters and state variables. Similarly, β-AS-induced phosphorylation levels of cellular substrates were estimated by the DGDR-UKF methodology. Performance was tested by building an experimentally-calibrated population of virtual cells, from which synthetic AP traces were generated for baseline and β-AS conditions. The combined DGDR-UKF methodology led to 25% reduction in the error associated with estimation of ionic current conductances at baseline conditions and phosphorylation levels under β-AS with respect to individual DGDR and UKF methods. This improvement was not at the expense of higher computational load, which was diminished by 90% with respect to the individual UKF method. Both temporal and spatial AP variability of repolarization were accurately characterized by the DGDR-UKF methodology. A combined DGDR-UKF methodology is proposed for parameter and state variable estimation of human ventricular cell models from available AP traces at baseline and under β-AS. This methodology improves the estimation performance and reduces the convergence time with respect to individual DGDR and UKF methods and renders a suitable approach for computational characterization of spatio-temporal repolarization variability to be used for ascertainment of variability mechanisms and its relation to arrhythmogenesis.

Heterogeneous Effects of Fibroblast-Myocyte Coupling in Different Regions of the Human Atria Under Conditions of Atrial Fibrillation.

Background: Atrial fibrillation (AF), the most common cardiac arrhythmia, is characterized by alteration of the action potential (AP) propagation. Under persistent AF, myocytes undergo electrophysiological and structural remodeling, which involves fibroblast proliferation and differentiation, modifying the substrate for AP propagation. The aim of this study was to analyze the effects on the AP of fibroblast-myocyte coupling during AF and its propagation in different regions of the atria.Methods: Isolated myocytes were coupled to different numbers of fibroblasts using the established AP models and tissue simulations were performed by randomly distributing fibroblasts. Fibroblast formulations were updated to match recent experimental data. Major ion current conductances of the myocyte model were modified to simulate AP heterogeneity in four different atrial regions (right atrium posterior wall, crista terminalis, left atrium posterior wall, and pulmonary vein) according to experimental and computational studies.Results: The results of the coupled myocyte-fibroblast simulations suggest that a more depolarized membrane potential and higher fibroblast membrane capacitance have a greater impact on AP duration and myocyte maximum depolarization velocity. The number of coupled fibroblasts and the stimulation frequency are determining factors in altering myocyte AP. Strand simulations show that conduction velocity tends to homogenize in all regions, while the left atrium is more likely to be affected by fibroblast and AP propagation block is more likely to occur. The pulmonary vein is the most affected region, even at low fibroblast densities. In 2D sheets with randomly placed fibroblasts, wavebreaks are observed in the low density (10%) central fibrotic zone and when fibroblast density increases (40%) propagation in the fibrotic region is practically blocked. At densities of 10 and 20% the width of the vulnerable window increases with respect to control but is decreased at 40%.Conclusion: Myocyte-fibroblast coupling characteristics heterogeneously affect AP propagation and features in the different atrial zones, and myocytes from the left atria are more sensitive to fibroblast coupling.

Intragenic duplication of KCNQ5 gene results in aberrant splicing leading to a premature termination codon in a patient with intellectual disability

The KCNQ5 gene, widely expressed in the brain, encodes a voltage-gated potassium channel (Kv7.5) important for neuronal function. Here, we report a novel KCNQ5 intragenic duplication at 6q13 spanning about 239 Kb of genomic DNA, identified by array comparative genomic hybridization (array-CGH). The duplication was found in heterozygosity in an adult patient affected by mild intellectual disability with history of absence epilepsy in adolescence, with no EEG nor MRI alterations. By in vitro analyses we demonstrated that this copy number variation (CNV) led to an aberrant transcript with exon 2–11 skipping and a premature stop codon causing, most likely, haploinsufficiency.The Kv7.5 channel plays an important role in the regulation of M-type current and afterhyperpolarization conductances which contribute to neuronal excitability. A recently published paper described KCNQ5 missense mutations in individuals with intellectual disability and treatment-resistant epilepsy that were thought to act through either loss-of-function or gain-of-function mechanisms, associated in both cases with altered neuronal excitability.In the case reported here, we showed that no functional protein can be produced from the allele involved by the intragenic duplication. This evidence strongly supports the hypothesis of KCNQ5 haploinsufficiency, which could lead to altered neuronal excitability, thus contributing to seizure susceptibility and intellectual disability.

A response surface optimization approach to adjust ionic current conductances of cardiac electrophysiological models. Application to the study of potassium level changes.

Cardiac electrophysiological computational models are often developed from previously published models. The new models may incorporate additional features to adapt the model to a different species or may upgrade a specific ionic formulation based on newly available experimental data. A relevant challenge in the development of a new model is the estimation of certain ionic current conductances that cannot be reliably identified from experiments. A common strategy to estimate those conductances is by means of constrained non-linear least-squares optimization. In this work, a novel methodology is proposed for estimation of ionic current conductances of cardiac electrophysiological models by using a response surface approximation-based constrained optimization with trust region management. Polynomial response surfaces of a number of electrophysiological markers were built using statistical sampling methods. These markers included action potential duration (APD), triangulation, diastolic and systolic intracellular calcium concentration, and time constants of APD rate adaptation. The proposed methodology was applied to update the Carro et al. human ventricular action potential model after incorporation of intracellular potassium ([K+]i) dynamics. While the Carro et al. model was well suited for investigation of arrhythmogenesis, it did not allow simulation of [K+]i changes. With the methodology proposed in this study, the updated Carro et al. human ventricular model could be used to simulate [K+]i changes in response to varying extracellular potassium ([K+]o) levels. Additionally, it rendered values of evaluated electrophysiological markers within physiologically plausible ranges. The optimal values of ionic current conductances in the updated model were found in a notably shorter time than with previously proposed methodologies. As a conclusion, the response surface optimization-based approach proposed in this study allows estimating ionic current conductances of cardiac electrophysiological computational models while guaranteeing replication of key electrophysiological features and with an important reduction in computational cost with respect to previously published approaches. The updated Carro et al. model developed in this study is thus suitable for the investigation of arrhythmic risk-related conditions, including those involving large changes in potassium concentration.

Ethyl Vanillin Activates TRPA1.

The nonselective cation channel transient receptor potential ankryn subtype family 1 (TRPA1) is expressed in neurons of dorsal root ganglia and trigeminal ganglia and also in vagal afferent neurons that innervate the lungs and gastrointestinal tract. Many TRPA1 agonists are reactive electrophilic compounds that form covalent adducts with TRPA1. Allyl isothiocyanate (AITC), the common agonist used to identify TRPA1, contains an electrophilic group that covalently binds with cysteine residues of TRPA1 and confers a structural change on the channel. There is scientific motivation to identify additional compounds that can activate TRPA1 with different mechanisms of channel gating. We provide evidence that ethyl vanillin (EVA) is a TRPA1 agonist. Using fluorescent calcium imaging and whole-cell patch-clamp electrophysiology on dissociated rat vagal afferent neurons and TRPA1-transfected COS-7 cells, we discovered that EVA activates cells also activated by AITC. Both agonists display similar current profiles and conductances. Pretreatment with A967079, a selective TRPA1 antagonist, blocks the EVA response as well as the AITC response. Furthermore, EVA does not activate vagal afferent neurons from TRPA1 knockout mice, showing selectivity for TRPA1 in this tissue. Interestingly, EVA appears to be pharmacologically different from AITC as a TRPA1 agonist. When AITC is applied before EVA, the EVA response is occluded. However, they both require intracellular oxidation to activate TRPA1. These findings suggest that EVA activates TRPA1 but via a distinct mechanism that may provide greater ease for study in native systems compared with AITC and may shed light on differential modes of TRPA1 gating by ligand types.

A balance of outward and linear inward ionic currents is required for generation of slow-wave oscillations.

Regenerative inward currents help produce slow oscillations through a negative-slope conductance region of their current-voltage relationship that is well approximated by a linear negative conductance. We used dynamic-clamp injections of a linear current with such conductance, INL, to explore why some neurons can generate intrinsic slow oscillations whereas others cannot. We addressed this question in synaptically isolated neurons of the crab Cancer borealis after blocking action potentials. The pyloric network consists of a distinct pacemaker and follower neurons, all of which express the same complement of ionic currents. When the pyloric dilator (PD) neuron, a member of the pacemaker group, was injected with INL with dynamic clamp, it consistently produced slow oscillations. In contrast, all follower neurons failed to oscillate with INL To understand these distinct behaviors, we compared outward current levels of PD with those of follower lateral pyloric (LP) and ventral pyloric (VD) neurons. We found that LP and VD neurons had significantly larger high-threshold potassium currents (IHTK) than PD and LP had lower-transient potassium current (IA). Reducing IHTK pharmacologically enabled both LP and VD neurons to produce INL-induced oscillations, whereas modifying IA levels did not affect INL-induced oscillations. Using phase-plane and bifurcation analysis of a simplified model cell, we demonstrate that large levels of IHTK can block INL-induced oscillatory activity whereas generation of oscillations is almost independent of IA levels. These results demonstrate the general importance of a balance between inward pacemaking currents and high-threshold K+ current levels in determining slow oscillatory activity.NEW & NOTEWORTHY Pacemaker neuron-generated rhythmic activity requires the activation of at least one inward and one outward current. We have previously shown that the inward current can be a linear current (with negative conductance). Using this simple mechanism, here we demonstrate that the inward current conductance must be in relative balance with the outward current conductances to generate oscillatory activity. Surprisingly, an excess of outward conductances completely precludes the possibility of achieving such a balance.

Ionospheric conductances and currents of a morning sector auroral arc from Swarm‐A electric and magnetic field measurements

AbstractWe show the first ionospheric Hall and Pedersen conductances derived from Swarm magnetic and electric field measurements during a crossing of a morning sector auroral arc. Only Swarm‐A was used, with assumptions of negligible azimuthal gradients and vanishing eastward electric field. We find upward field‐aligned current, enhanced Hall and Pedersen conductances, and relatively weak electric field coincident with the arc. Poleward of the arc, the field‐aligned current was downward, conductances lower, and the electric field enhanced. The arc was embedded in a westward electrojet, immediately equatorward of the peak current density. The equatorward portion of the electrojet could thus be considered conductance dominant and the poleward portion electric field dominant. Although the electric field measured by Swarm was intense, resulting in conductances lower than those typically reported, comparable electric fields have been observed earlier. These results demonstrate how Swarm data can significantly contribute to our understanding of the ionospheric electrodynamics.

Current Noise and AC Response of a Back-Gated Single-Molecule Junction

Current noise and ac response properties of single-molecule junctions (SMJs) are essential for their potential application as nanoscale electron devices. We first study I-V characteristics of electronic transport through a back-gated benzene-type SMJ based on the nonequilibrium Green's function formalism within a tight-binding model, and then present analytical expressions and numerical calculations for current noises and ac conductances of the SMJ. We show that the noise power density in the high-frequency region is independent of the applied bias voltage, and will be significantly suppressed and have dip structures at the frequencies where electron transitions from the occupied molecular states to the unoccupied ones are excited. It is found that both the bias voltage and the back-gate voltage can affect current noise spectra and ac conductances drastically in the low-frequency region. The low-frequency part of the ac conductance can be enhanced by applying a bias voltage, but an opposite behavior with suppression of conductances is observed for the system without the particle-hole symmetry. AC conductances for the source and the drain leads also show distinct characteristics for this SMJ system. It is expected that our results will provide some bases for the ac application of SMJ nanodevices.

The role of linear and voltage-dependent ionic currents in the generation of slow wave oscillations

Neuronal oscillatory activity is generated by a combination of ionic currents, including at least one inward regenerative current that brings the cell towards depolarized voltages and one outward current that repolarizes the cell. Such currents have traditionally been assumed to require voltage-dependence. Here we test the hypothesis that the voltage dependence of the regenerative inward current is not necessary for generating oscillations. Instead, a current I NL that is linear in the biological voltage range and has negative conductance is sufficient to produce regenerative activity. The current I NL can be considered a linear approximation to the negative-conductance region of the current-voltage relationship of a regenerative inward current. Using a simple conductance-based model, we show that I NL , in conjunction with a voltage-gated, non-inactivating outward current, can generate oscillatory activity. We use phase-plane and bifurcation analyses to uncover a rich variety of behaviors as the conductance of I NL is varied, and show that oscillations emerge as a result of destabilization of the resting state of the model neuron. The model shows the need for well-defined relationships between the inward and outward current conductances, as well as their reversal potentials, in order to produce stable oscillatory activity. Our analysis predicts that a hyperpolarization-activated inward current can play a role in stabilizing oscillatory activity by preventing swings to very negative voltages, which is consistent with what is recorded in biological neurons in general. We confirm this prediction of the model experimentally in neurons from the crab stomatogastric ganglion.

Population of Computational Rabbit-Specific Ventricular Action Potential Models for Investigating Sources of Variability in Cellular Repolarisation

Variability is observed at all levels of cardiac electrophysiology. Yet, the underlying causes and importance of this variability are generally unknown, and difficult to investigate with current experimental techniques. The aim of the present study was to generate populations of computational ventricular action potential models that reproduce experimentally observed intercellular variability of repolarisation (represented by action potential duration) and to identify its potential causes. A systematic exploration of the effects of simultaneously varying the magnitude of six transmembrane current conductances (transient outward, rapid and slow delayed rectifier K+, inward rectifying K+, L-type Ca2+, and Na+/K+ pump currents) in two rabbit-specific ventricular action potential models (Shannon et al. and Mahajan et al.) at multiple cycle lengths (400, 600, 1,000 ms) was performed. This was accomplished with distributed computing software specialised for multi-dimensional parameter sweeps and grid execution. An initial population of 15,625 parameter sets was generated for both models at each cycle length. Action potential durations of these populations were compared to experimentally derived ranges for rabbit ventricular myocytes. 1,352 parameter sets for the Shannon model and 779 parameter sets for the Mahajan model yielded action potential duration within the experimental range, demonstrating that a wide array of ionic conductance values can be used to simulate a physiological rabbit ventricular action potential. Furthermore, by using clutter-based dimension reordering, a technique that allows visualisation of multi-dimensional spaces in two dimensions, the interaction of current conductances and their relative importance to the ventricular action potential at different cycle lengths were revealed. Overall, this work represents an important step towards a better understanding of the role that variability in current conductances may play in experimentally observed intercellular variability of rabbit ventricular action potential repolarisation.

Functional expression of SK channels in murine detrusor PDGFRα+ cells

We sought to characterize molecular expression and ionic conductances in a novel population of interstitial cells (PDGFRα(+) cells) in murine bladder to determine how these cells might participate in regulation of detrusor excitability. PDGFRα(+) cells and smooth muscle cells (SMCs) were isolated from detrusor muscles of PDGFRα(+)/eGFP and smMHC/Cre/eGFP mice and sorted by FACS. PDGFRα(+) cells were highly enriched in Pdgfra (12 fold vs. unsorted cell) and minimally positive for Mhc (SMC marker), Kit (ICC marker) and Pgp9.5 (neuronal marker). SK3 was dominantly expressed in PDGFRα(+) cells in comparison to SMCs. αSlo (BK marker) was more highly expressed in SMCs. SK3 protein was observed in PDGFRα(+) cells by immunohistochemistry but could not be resolved in SMCs. Depolarization evoked voltage-dependent Ca(2+) currents in SMCs, but inward current conductances were not activated in PDGFRα(+) cells under the same conditions. PDGFRα(+) cells displayed spontaneous transient outward currents (STOCs) at potentials positive to -60 mV that were inhibited by apamin. SK channel modulators, CyPPA and SKA-31, induced significant hyperpolarization of PDGFRα(+) cells and activated SK currents under voltage clamp. Similar responses were not resolved in SMCs at physiological potentials. Single channel measurements confirmed the presence of functional SK3 channels (i.e. single channel conductance of 10 pS and sensitivity to intracellular Ca(2+)) in PDGFRα(+) cells. The apamin-sensitive stabilizing factor regulating detrusor excitability is likely to be due to the expression of SK3 channels in PDGFRα(+) cells because SK agonists failed to elicit resolvable currents and hyperpolarization in SMCs at physiological potentials.

Stability and sustained oscillations in a ventricular cardiomyocyte model

The Luo-Rudy I model, describing the electrophysiology of a ventricular cardiomyocyte, is associated with an 8-dimensional discontinuous dynamical system with logarithmic and exponential non-linearities depending on 15 parameters. The associated stationary problem was reduced to a nonlinear system in only two unknowns, the transmembrane potential V and the intracellular calcium concentration [Ca]( i ). By numerical approaches appropriate to bifurcation problems, sections in the static bifurcation diagram were determined. For a variable steady depolarizing or hyperpolarizing current (I (st)), the corresponding projection of the static bifurcation diagram in the (I (st), V) plane is complex, featuring three branches of stationary solutions joined by two limit points. On the upper branch oscillations can occur, being either damped at a stable focus or diverted to the lower branch of stable stationary solutions when reaching the unstable manifold of a homoclinic saddle, thus resulting in early after-depolarizations (EADs). The middle branch of solutions is a series of unstable saddle points, while the lower one a series of stable nodes. For variable slow inward and K(+) current maximal conductances (g (si) and g (K)), in a range between 0 and 4-fold normal values, the dynamics is even more complex, and in certain instances sustained oscillations tending to a limit cycle appear. All these types of behavior were correctly predicted by linear stability analysis and bifurcation theory methods, leading to identification of Hopf bifurcation points, limit points of cycles and period doubling bifurcations. In particular settings, e.g. one-fifth-of-normal g (si), EADs and sustained high amplitude oscillations due to an unstable resting state may occur simultaneously.

Impact of Multiple Ionic Changes in Arrhythmic Risk Biomarkers in Human Ventricular Electrophysiology

Electrophysiological variability represents an important challenge in evaluating cardiac response to disease and drug action. Our goal is to quantitatively evaluate the sensitivity of biomarkers to the simultaneous alteration of several ionic current in human cardiomyocytes. Computer simulations of human ventricular electrophysiology are conducted using an action potential (AP) model proposed by Carro et al.Ionic current conductances and kinetics were simultaneously varied by +/-30%. Model output was evaluated by quantifying biomarkers including AP duration (APD) and triangulation. Statistical techniques based on experiments design along with a second order response surface model were used.Figure 1. A) AP duration, B) AP triangulation. Marked area indicates physiological rangeView Large Image | View Hi-Res Image | Download PowerPoint SlideResults reveal that simultaneous alteration of several ionic properties results in nonlinear effects in biomarkers response. APD is more sensitive than triangulation to changes in ionic properties. 30% changes in sodium/potassium pump and in calcium inactivation result in APD values outside the physiological range (287-350ms; Fig. 1A). In contrast, 30% changes in most ionic properties result in triangulation within physiological range (70-86ms). However, simultaneous reduction of GKr and GCaL by 30% significantly increases triangulation (Fig. 1B).

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

Global sensitivity analysis is critical in understanding the role of ionic currents variability in modulating cellular electrophysiological properties of ventricular myocytes as well as in assessing the cardiac single cell arrhythmic risk biomarkers. This work involves a systematic investigation into the sensitivity of various preclinical cellular biomarkers of arrhythmic risk to changes in ionic current conductances and kinetics. We compare local and global sensitivity analysis approaches. The nonlinearity of the system is confirmed to play an important role when considering the effect of parameters on markers that involve information from different frequencies. In the case of such biomarkers as action potential duration (APD), maxima Cai and Nai concentrations, we find no significant changes in the overall order of the parameters' significance between local and global sensitivity studies. However, even for these single frequency markers we are able to give a more precise relative contribution of each parameter. Importantly, in the case of maximum S1-S2 slope marker, which integrates the information across a spectrum of frequencies of electrical stimuli, we find significant changes in the order of parameters as compared to the previously used methods for studying the sensitivity of cellular biomarkers. Moreover, the models consistently identify the L-type Calcium current (ICaL) as one of the dominant currents affecting the plateau of the action potential. Furthermore, in consistence with experimental data, the simulation results show that variation in conductances and kinetics of other channels does not affect the significance of ICaL's contribution. We demonstrate the critical role of global (vs local) sensitivity analysis in providing insights into the sensitivity of preclinical biomarkers, and hence mechanisms of repolarization and their rate dependence.

Systematic characterization of the ionic basis of rabbit cellular electrophysiology using two ventricular models

Several mathematical models of rabbit ventricular action potential (AP) have been proposed to investigate mechanisms of arrhythmias and excitation-contraction coupling. Our study aims at systematically characterizing how ionic current properties modulate the main cellular biomarkers of arrhythmic risk using two widely-used rabbit ventricular models, and comparing simulation results using the two models with experimental data available for rabbit. A sensitivity analysis of AP properties, Ca2+ and Na+ dynamics, and their rate dependence to variations (±15% and ±30%) in the main transmembrane current conductances and kinetics was performed using the Shannon et al. (2004) and the Mahajan et al. (2008a,b) AP rabbit models. The effects of severe transmembrane current blocks (up to 100%) on steady-state AP and calcium transients, and AP duration (APD) restitution curves were also simulated using both models. Our simulations show that, in both virtual rabbit cardiomyocytes, APD is significantly modified by most repolarization currents, AP triangulation is regulated mostly by the inward rectifier K+ current (IK1) whereas APD rate adaptation as well as [Na+]i rate dependence is influenced by the Na+/K+ pump current (INaK). In addition, steady-state [Ca2+]i levels, APD restitution properties and [Ca2+]i rate dependence are strongly dependent on INaK, the L-Type Ca2+ current (ICaL) and the Na+/Ca2+ exchanger current (INaCa), although the relative role of these currents is markedly model dependent. Furthermore, our results show that simulations using both models agree with many experimentally-reported electrophysiological characteristics. However, our study shows that the Shannon et al. model mimics rabbit electrophysiology more accurately at normal pacing rates, whereas Mahajan et al. model behaves more appropriately at faster rates. Our results reinforce the usefulness of sensitivity analysis for further understanding of cellular electrophysiology and validation of cardiac AP models.

Ionic mechanisms of electrophysiological properties and repolarization abnormalities in rabbit Purkinje fibers

Purkinje cells play an important role in drug-induced arrhythmogenesis and are widely used in preclinical drug safety assessments. Repolarization abnormalities such as action potential (AP) prolongation and early afterdeploarizations (EAD) are often observed in vitro upon pharmacological interventions. However, because drugs do not act on only one defined target, it is often difficult to fully explain the mechanisms of action and their potential arrhythmogenicity. Computational models, when appropriately detailed and validated, can be used to gain mechanistic insights into the mechanisms of action of certain drugs. Nevertheless, no model of Purkinje electrophysiology that is able to reproduce characteristic Purkinje responses to drug-induced changes in ionic current conductances such as AP prolongation and EAD generation currently exists. In this study, a novel biophysically detailed model of rabbit Purkinje electrophysiology was developed by integration of data from voltage-clamp and AP experimental recordings. Upon validation, we demonstrate that the model reproduces many key electrophysiological properties of rabbit Purkinje cells. These include: AP morphology and duration, both input resistance and rate dependence properties as well as response to hyperkalemia. Pharmacological interventions such as inward rectifier K(+) current and rapid delayed rectifier K(+) current block as well as late Na(+) current increase result in significant AP changes. However, enhanced L-type Ca(2+) current (i(CaL)) dominates in EAD genesis in Purkinje fibers. In addition, i(CaL) inactivation dynamics and intercellular coupling in tissue strongly modulate EAD formation. We conclude that EAD generation in Purkinje cells is mediated by an increase in i(CaL) and modulated by its inactivation kinetics.

Stability and Self-Sustained Oscillations in a Ventricular Cardiomyocyte Model

The Luo-Rudy I model, describing the electrophysiology of a ventricular cardiomyocyte, is associated with an 8-dimensional discontinuous dynamical system with logarithmic and exponential non-linearities depending on 15 parameters. By numerical approaches appropriate to bifurcation problems, sections in the static bifurcation diagram were determined. For different values of a steady depolarizing/hyperpolarizing current (Ist), the corresponding projection of the static bifurcation diagram in the (Ist, V) plane is complex, featuring three branches of stationary solutions delimited by two saddle-node bifurcation points. In addition, on the upper branch oscillations can occur within an Ist range [−4.45, −0.51 μA/cm2] where the Jacobian of the linearized system features two complex conjugated eigenvalues. Oscillations are either damped at a stable focus or amplified until the system trajectory is diverted to the lower branch of stable stationary solutions when reaching the unstable manifold of a homoclinic saddle. The middle branch of solutions is a series of unstable saddle points, while the lower one a series of stable nodes. For variable slow inward and K+ current maximal conductances (gsi and gK), in a range between 0 and 4-fold normal values, the dynamics is even more complex, and in certain instances self-sustained oscillations tending to a stable limit cycle appear. All these types of behavior were correctly predicted by linear stability analysis and bifurcation theory methods based on numerical continuation algorithms. Both unsustained oscillations, resulting in early after-depolarizations, and sustained oscillations may trigger dangerous ventricular arrhythmias by multiple mechanisms. In particular settings, e.g. for a normal gK and one-fifth-of-normal gsi, these two arrhythmia-threatening conditions may occur simultaneously.

Accurate Prediction of Alternans in Cardiac Cells Using Stochastic Pacing and Transfer Function Analysis

Alternans of action potential duration (APD) is a well-known arrhythmogenic mechanism. Studies based on eigenmode analysis demonstrated that alternans occurs when the eigenvalue λ_alt of the alternant eigenmode is < −1, providing an exact marker in contrast to the APD restitution slope. However, no method has been designed to estimate λ_alt experimentally. We hypothesized that λ_alt can be obtained by pacing at cycle lengths (CLs) varying stochastically around a basic CL (BCL) and analyzing the transfer function between the time series of CLs and APDs. We expected that the pole of this transfer function closest to −1 corresponds to λ_alt. We tested this hypothesis using a canine ventricular cell model in which alternans can be caused by unstable dynamics of membrane potential or of Ca2+ cycling. Control values of λ_alt were obtained analytically as a function of BCL. Stochastic pacing protocols were simulated for different BCLs and the poles and zeros of the corresponding transfer functions were estimated by fitting an autoregressive-moving-average (ARMA) model describing APD as a function of previous APDs and CLs. In all model versions, the pole closest to −1 provided an accurate estimation of λ_alt and required the analysis of 30 successive APDs and CLs. During slow ramp decreases of BCL or slow changes of ion current conductances simulating drug application, small stochastic CL variations and ARMA model identification permitted to predict the onset of alternans by extrapolating the time course of the estimated λ_alt to −1. In conclusion, stochastic pacing combined with ARMA model identification represents a novel approach to accurately evaluate the propensity to alternans. This method does not make any assumptions about the ionic mechanism of alternans and should be applicable experimentally for any type of myocardial cell.