A model of the L-type Ca2+ channel in rat ventricular myocytes: ion selectivity and inactivation mechanisms

Local Control Model of a Human Ventricular Myocyte: An Exploration of Frequency-Dependent Changes and Calcium Sparks

Calcium (Ca2+) sparks are the elementary events of excitation-contraction coupling, yet they are not explicitly represented in human ventricular myocyte models. A stochastic ventricular cardiomyocyte human model that adapts to intracellular Ca2+ ([Ca2+]i) dynamics, spark regulation, and frequency-dependent changes in the form of locally controlled Ca2+ release was developed. The 20,000 CRUs in this model are composed of 9 individual LCCs and 49 RyRs that function as couplons. The simulated action potential duration at 1 Hz steady-state pacing is ~0.280 s similar to human ventricular cell recordings. Rate-dependence experiments reveal that APD shortening mechanisms are largely contributed by the L-type calcium channel inactivation, RyR open fraction, and [Ca2+]myo concentrations. The dynamic slow-rapid-slow pacing protocol shows that RyR open probability during high pacing frequency (2.5 Hz) switches to an adapted "nonconducting" form of Ca2+-dependent transition state. The predicted force was also observed to be increased in high pacing, but the SR Ca2+ fractional release was lower due to the smaller difference between diastolic and systolic [Ca2+]SR. Restitution analysis through the S1S2 protocol and increased LCC Ca2+-dependent activation rate show that the duration of LCC opening helps modulate its effects on the APD restitution at different diastolic intervals. Ultimately, a longer duration of calcium sparks was observed in relation to the SR Ca2+ loading at high pacing rates. Overall, this study demonstrates the spontaneous Ca2+ release events and ion channel responses throughout various stimuli.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

Understanding Calmodulin Variants Affecting Calcium-Dependent Inactivation of L-Type Calcium Channels through Whole-Cell Simulation of the Cardiac Ventricular Myocyte

Mutations in the calcium-sensing protein calmodulin (CaM) have been linked to two cardiac arrhythmia diseases, Long QT Syndrome 14 (LQT14) and Catecholaminergic Polymorphic Ventricular Tachycardia Type 4 (CPVT4), with varying degrees of severity. Functional characterization of the CaM mutants most strongly associated with LQT14 show a clear disruption of the calcium-dependent inactivation (CDI) of the L-Type calcium channel (LCC). CPVT4 mutants on the other hand are associated with changes in their affinity to the ryanodine receptor. In clinical studies, some variants have been associated with both CPVT4 and LQT15. This study uses simulations in a model for excitation-contraction coupling in the rat ventricular myocytes to understand how LQT14 variant might give the functional phenotype similar to CPVT4. Changing the CaM-dependent transition rate by a factor of 0.75 corresponding to the D96V variant and by a factor of 0.90 corresponding to the F142L or N98S variants, in a physiologically based stochastic model of the LCC prolonger, the action potential duration changed by a small amount in a cardiac myocyte but did not disrupt CICR at 1, 2, and 4 Hz. Under beta-adrenergic simulation abnormal excitation-contraction coupling was observed above 2 Hz pacing for the mutant CaM. The same conditions applied under beta-adrenergic stimulation led to the rapid onset of arrhythmia in the mutant CaM simulations. Simulations with the LQT14 mutations under the conditions of rapid pacing with beta-adrenergic stimulation drives the cardiac myocyte toward an arrhythmic state known as Ca2+ overload. These simulations provide a mechanistic link to a disease state for LQT14-associated mutations in CaM to yield a CPVT4 phenotype. The results show that small changes to the CaM-regulated inactivation of LCC promote arrhythmia and underscore the significance of CDI in proper heart function.

Pacing Dynamics Determines the Arrhythmogenic Mechanism of the CPVT2-Causing CASQ2G112+5X Mutation in a Guinea Pig Ventricular Myocyte Computational Model

Calsequestrin Type 2 (CASQ2) is a high-capacity, low-affinity, Ca2+-binding protein expressed in the sarcoplasmic reticulum (SR) of the cardiac myocyte. Mutations in CASQ2 have been linked to the arrhythmia catecholaminergic polymorphic ventricular tachycardia (CPVT2) that occurs with acute emotional stress or exercise can result in sudden cardiac death (SCD). CASQ2G112+5X is a 16 bp (339-354) deletion CASQ2 mutation that prevents the protein expression due to premature stop codon. Understanding the subcellular mechanisms of CPVT2 is experimentally challenging because the occurrence of arrhythmia is rare. To obtain an insight into the characteristics of this rare disease, simulation studies using a local control stochastic computational model of the Guinea pig ventricular myocyte investigated how the mutant CASQ2s may be responsible for the development of an arrhythmogenic episode under the condition of β-adrenergic stimulation or in the slowing of heart rate afterward once β-adrenergic stimulation ceases. Adjustment of the computational model parameters based upon recent experiments explore the functional changes caused by the CASQ2 mutation. In the simulation studies under rapid pacing (6 Hz), electromechanically concordant cellular alternans appeared under β-adrenergic stimulation in the CPVT mutant but not in the wild-type nor in the non-β-stimulated mutant. Similarly, the simulations of accelerating pacing from slow to rapid and back to the slow pacing did not display alternans but did generate early afterdepolarizations (EADs) during the period of second slow pacing subsequent acceleration of rapid pacing.

The Role of Ca2+ Sparks in Force Frequency Relationships in Guinea Pig Ventricular Myocytes

Calcium sparks are the elementary Ca2+ release events in excitation-contraction coupling that underlie the Ca2+ transient. The frequency-dependent contractile force generated by cardiac myocytes depends upon the characteristics of the Ca2+ transients. A stochastic computational local control model of a guinea pig ventricular cardiomyocyte was developed, to gain insight into mechanisms of force-frequency relationship (FFR). This required the creation of a new three-state RyR2 model that reproduced the adaptive behavior of RyR2, in which the RyR2 channels transition into a different state when exposed to prolonged elevated subspace [Ca2+]. The model simulations agree with previous experimental and modeling studies on interval-force relations. Unlike previous common pool models, this local control model displayed stable action potential trains at 7 Hz. The duration and the amplitude of the [Ca2+]myo transients increase in pacing rates consistent with the experiments. The [Ca2+]myo transient reaches its peak value at 4 Hz and decreases afterward, consistent with experimental force-frequency curves. The model predicts, in agreement with previous modeling studies of Jafri and co-workers, diastolic sarcoplasmic reticulum, [Ca2+]sr, and RyR2 adaptation increase with the increased stimulation frequency, producing rising, rather than falling, amplitude of the myoplasmic [Ca2+] transients. However, the local control model also suggests that the reduction of the L-type Ca2+ current, with an increase in pacing frequency due to Ca2+-dependent inactivation, also plays a role in the negative slope of the FFR. In the simulations, the peak Ca2+ transient in the FFR correlated with the highest numbers of SR Ca2+ sparks: the larger average amplitudes of those sparks, and the longer duration of the Ca2+ sparks.

Critical Requirements for the Initiation of a Cardiac Arrhythmia in Rat Ventricle: How Many Myocytes?

Cardiovascular disease is the leading cause of death worldwide due in a large part to arrhythmia. In order to understand how calcium dynamics play a role in arrhythmogenesis, normal and dysfunctional Ca²⁺ signaling in a subcellular, cellular, and tissued level is examined using cardiac ventricular myocytes at a high temporal and spatial resolution using multiscale computational modeling. Ca²⁺ sparks underlie normal excitation-contraction coupling. However, under pathological conditions, Ca²⁺ sparks can combine to form Ca²⁺ waves. These propagating elevations of (Ca²⁺)_i can activate an inward Na⁺-Ca²⁺ exchanger current (I_NCX) that contributes to early after-depolarization (EADs) and delayed after-depolarizations (DADs). However, how cellular currents lead to full depolarization of the myocardium and how they initiate extra systoles is still not fully understood. This study explores how many myocytes must be entrained to initiate arrhythmogenic depolarizations in biophysically detailed computational models. The model presented here suggests that only a small number of myocytes must activate in order to trigger an arrhythmogenic propagating action potential. These conditions were examined in 1-D, 2-D, and 3-D considering heart geometry. The depolarization of only a few hundred ventricular myocytes is required to trigger an ectopic depolarization. The number decreases under disease conditions such as heart failure. Furthermore, in geometrically restricted parts of the heart such as the thin muscle strands found in the trabeculae and papillary muscle, the number of cells needed to trigger a propagating depolarization falls even further to less than ten myocytes.

Cardiac Alternans Occurs through the Synergy of Voltage- and Calcium-Dependent Mechanisms

Cardiac alternans is characterized by alternating weak and strong beats of the heart. This signaling at the cellular level may appear as alternating long and short action potentials (APs) that occur in synchrony with alternating large and small calcium transients, respectively. Previous studies have suggested that alternans manifests itself through either a voltage dependent mechanism based upon action potential restitution or as a calcium dependent mechanism based on refractoriness of calcium release. We use a novel model of cardiac excitation-contraction (EC) coupling in the rat ventricular myocyte that includes 20,000 calcium release units (CRU) each with 49 ryanodine receptors (RyR2s) and 7 L-type calcium channels that are all stochastically gated. The model suggests that at the cellular level in the case of alternans produced by rapid pacing, the mechanism requires a synergy of voltage- and calcium-dependent mechanisms. The rapid pacing reduces AP duration and magnitude reducing the number of L-type calcium channels activating individual CRUs during each AP and thus increases the population of CRUs that can be recruited stochastically. Elevated myoplasmic and sarcoplasmic reticulum (SR) calcium, [Ca2+]myo and [Ca2+]SR respectively, increases ryanodine receptor open probability (Po) according to our model used in this simulation and this increased the probability of activating additional CRUs. A CRU that opens in one beat is less likely to open the subsequent beat due to refractoriness caused by incomplete refilling of the junctional sarcoplasmic reticulum (jSR). Furthermore, the model includes estimates of changes in Na+ fluxes and [Na+]i and thus provides insight into how changes in electrical activity, [Na+]i and sodium-calcium exchanger activity can modulate alternans. The model thus tracks critical elements that can account for rate-dependent changes in [Na+]i and [Ca2+]myo and how they contribute to the generation of Ca2+ signaling alternans in the heart.

Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats

Mathematical action potential (AP) modeling is a well-established but still-developing area of research to better understand physiological and pathological processes. In particular, changes in AP mechanisms in the isoproterenol (ISO) -induced hypertrophic heart model are incompletely understood. Here we present a mathematical model of the rat AP based on recordings from rat ventricular myocytes. In our model, for the first time, all channel kinetics are defined with a single type of function that is simple and easy to apply. The model AP and channels dynamics are consistent with the APs recorded from rats for both Control (absence of ISO) and ISO-treated cases. Our mathematical model helps us to understand the reason for the prolongation in AP duration after ISO application while ISO treatment helps us to validate our mathematical model. We reveal that the smaller density and the slower gating kinetics of the transient K⁺ current help explain the prolonged AP duration after ISO treatment and the increasing amplitude of the rapid and the slow inward rectifier currents also contribute to this prolongation alongside the flux in Ca²⁺ currents. ISO induced an increase in the density of the Na⁺ current that can explain the faster upstroke. We believe that AP dynamics from rat ventricular myocytes can be reproduced very well with this mathematical model and that it provides a powerful tool for improved insights into the underlying dynamics of clinically important AP properties such as ISO application.

Biophysical modeling of C. elegans neurons: Single ion currents and whole-cell dynamics of AWCon and RMD

C. elegans neuronal system constitutes the ideal framework for studying simple, yet realistic, neuronal activity, since the whole nervous system is fully characterized with respect to the exact number of neurons and the neuronal connections. Most recent efforts are devoted to investigate and clarify the signal processing and functional connectivity, which are at the basis of sensing mechanisms, signal transmission, and motor control. In this framework, a refined modelof whole neuron dynamics constitutes a key ingredient to describe the electrophysiological processes, both at thecellular and at the network scale. In this work, we present Hodgkin-Huxley-based models of ion channels dynamics black, built on data available both from C. elegans and from other organisms, expressing homologous channels. We combine these channel models to simulate the electrical activity oftwo among the most studied neurons in C. elegans, which display prototypical dynamics of neuronal activation, the chemosensory AWCON and the motor neuron RMD. Our model properly describes the regenerative responses of the two cells. We analyze in detail the role of ion currents, both in wild type and in in silico knockout neurons. Moreover, we specifically investigate the behavior of RMD, identifying a heterogeneous dynamical response which includes bistable regimes and sustained oscillations. We are able to assess the critical role of T-type calcium currents, carried by CCA-1 channels, and leakage currents in the regulation of RMD response. Overall, our results provide new insights in the activity of key C. elegans neurons. The developed mathematical framework constitute a basis for single-cell and neuronal networks analyses, opening new scenarios in the in silico modeling of C. elegans neuronal system.

Histone Deacetylase Inhibitors Relax Mouse Aorta Partly through Their Inhibitory Action on L-Type Ca2+ Channels

Histone deacetylase (HDAC) inhibitors modulate acetylation/deacetylation of histone and nonhistone proteins. They have been widely used for cancer treatment. However, there have been only a few studies investigating the effect of HDAC inhibitors on vascular tone regulation, most of which employed chronic treatment with HDAC inhibitors. In the present study, we found that two hydroxamate-based pan-HDAC inhibitors, suberoylanilide hydroxamic acid (SAHA) and trichostatin A (TSA), could partially but acutely relax high extracellular K⁺-contracted mouse aortas. SAHA and TSA also attenuated the high extracellular K⁺-induced cytosolic Ca²⁺ rise and inhibited L-type Ca²⁺ channel current in whole-cell patch-clamp. These data demonstrate that SAHA could inhibit L-type Ca²⁺ channels to cause vascular relaxation. In addition, SAHA and TSA dose dependently relaxed the arteries precontracted with phenylephrine. The relaxant effect of SAHA and TSA was greater in phenylephrine-precontracted arteries than in high K⁺-contracted arteries. Although part of the relaxant effect of SAHA and TSA on phenylephrine-precontracted arteries was related to L-type Ca²⁺ channels, both agents could also induce relaxation via a mechanism independent of L-type Ca²⁺ channels. Taken together, HDAC inhibitors SAHA and TSA can acutely relax blood vessels via their inhibitory action on L-type Ca²⁺ channels and via another L-type Ca²⁺ channel-independent mechanism.

A human ventricular myocyte model with a refined representation of excitation-contraction coupling

Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch et al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 μM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.

Ryanodine receptor sensitivity governs the stability and synchrony of local calcium release during cardiac excitation-contraction coupling

Calcium-induced calcium release is the principal mechanism that triggers the cell-wide [Ca(2+)]i transient that activates muscle contraction during cardiac excitation-contraction coupling (ECC). Here, we characterize this process in mouse cardiac myocytes with a novel mathematical action potential (AP) model that incorporates realistic stochastic gating of voltage-dependent L-type calcium (Ca(2+)) channels (LCCs) and sarcoplasmic reticulum (SR) Ca(2+) release channels (the ryanodine receptors, RyR2s). Depolarization of the sarcolemma during an AP stochastically activates the LCCs elevating subspace [Ca(2+)] within each of the cell's 20,000 independent calcium release units (CRUs) to trigger local RyR2 opening and initiate Ca(2+) sparks, the fundamental unit of triggered Ca(2+) release. Synchronization of Ca(2+) sparks during systole depends on the nearly uniform cellular activation of LCCs and the likelihood of local LCC openings triggering local Ca(2+) sparks (ECC fidelity). The detailed design and true SR Ca(2+) pump/leak balance displayed by our model permits investigation of ECC fidelity and Ca(2+) spark fidelity, the balance between visible (Ca(2+) spark) and invisible (Ca(2+) quark/sub-spark) SR Ca(2+) release events. Excess SR Ca(2+) leak is examined as a disease mechanism in the context of "catecholaminergic polymorphic ventricular tachycardia (CPVT)", a Ca(2+)-dependent arrhythmia. We find that that RyR2s (and therefore Ca(2+) sparks) are relatively insensitive to LCC openings across a wide range of membrane potentials; and that key differences exist between Ca(2+) sparks evoked during quiescence, diastole, and systole. The enhanced RyR2 [Ca(2+)]i sensitivity during CPVT leads to increased Ca(2+) spark fidelity resulting in asynchronous systolic Ca(2+) spark activity. It also produces increased diastolic SR Ca(2+) leak with some prolonged Ca(2+) sparks that at times become "metastable" and fail to efficiently terminate. There is a huge margin of safety for stable Ca(2+) handling within the cell and this novel mechanistic model provides insight into the molecular signaling characteristics that help maintain overall Ca(2+) stability even under the conditions of high SR Ca(2+) leak during CPVT. Finally, this model should provide tools for investigators to examine normal and pathological Ca(2+) signaling characteristics in the heart.

Modulation of L-type Ca²⁺ channel activity by neuronal nitric oxide synthase and myofilament Ca²⁺ sensitivity in cardiac myocytes from hypertensive rat

Neuronal nitric oxide synthase (nNOS) is important in cardiac protection in diseased heart. Recently, we have reported that nNOS is associated with myofilament Ca(2+) desensitization in cardiac myocytes from hypertensive rats. So far, the effect of myofilament Ca(2+) desensitization or nNOS on L-type Ca(2+) channel activity (I(Ca)) in cardiac myocyte is unclear. Here, we examined nNOS regulation of I(Ca) in left ventricular (LV) myocytes from sham and angiotensin II (Ang II)-induced hypertensive rats. Our results showed that basal I(Ca) was not different between sham and hypertension (from -60 to +40 mV, 0.1 Hz). S-methyl-L-thiocitrulline (SMTC), a selective nNOS inhibitor, increased peak I(Ca) similarly in both groups. However, chelation of intracellular Ca(2+) [Ca(2+)]i with BAPTA increased I(Ca) and abolished SMTC-augmentation of I(Ca) only in hypertension. Myofilament Ca(2+) desensitization with butanedione monoxime (BDM), a myosin ATPase inhibitor, decreased I(Ca) in both groups but to a greater extent in hypertension. Intracellular BAPTA or nNOS inhibition reinstated I(Ca) in the presence of BDM to the basal level, suggesting Ca(2+)-dependent inactivation of I(Ca) by nNOS and greater vulnerability in hypertension. Increasing stimulation frequencies (2, 4 and 8 Hz) attenuated myofilament Ca(2+) sensitivity in sham and reduced peak ICa in both groups. Nevertheless, SMTC or BAPTA exerted no effect on I(Ca) at high frequencies in either group. These results suggest that nNOS attenuates I(Ca) via Ca(2+)-dependent mechanism and the vulnerability is greater in hypertension subject to myofilament Ca(2+) desensitization. nNOS or [Ca(2+)]i does not affect I(Ca) at high stimulation frequencies. The results were recapitulated with computer simulation.

Theoretical study of L-type Ca(2+) current inactivation kinetics during action potential repolarization and early afterdepolarizations

Sarcoplasmic reticulum (SR) Ca(2+) release mediates excitation–contraction coupling (ECC) in cardiac myocytes. It is triggered upon membrane depolarization by entry of Ca(2+) via L-type Ca(2+) channels (LTCCs), which undergo both voltage- and Ca(2+)-dependent inactivation (VDI and CDI, respectively). We developed improved models of L-type Ca(2+) current and SR Ca(2+) release within the framework of the Shannon-Bers rabbit ventricular action potential (AP) model. The formulation of SR Ca(2+) release was modified to reproduce high ECC gain at negative membrane voltages. An existing LTCC model was extended to reflect more faithfully contributions of CDI and VDI to total inactivation. Ba(2+) current inactivation included an ion-dependent component (albeit small compared with CDI), in addition to pure VDI. Under physiological conditions (during an AP) LTCC inactivates predominantly via CDI, which is controlled mostly by SR Ca(2+) release during the initial AP phase, but by Ca(2+) through LTCCs for the remaining part. Simulations of decreased CDI or K(+) channel block predicted the occurrence of early and delayed after depolarizations. Our model accurately describes ECC and allows dissection of the relative contributions of different Ca(2+) sources to total CDI, and the relative roles of CDI and VDI, during normal and abnormal repolarization.

A computational model of cytosolic and mitochondrial [ca] in paced rat ventricular myocytes

We carried out a series of experiment demonstrating the role of mitochondria in the cytosolic and mitochondrial Ca(2+) transients and compared the results with those from computer simulation. In rat ventricular myocytes, increasing the rate of stimulation (1~3 Hz) made both the diastolic and systolic [Ca(2+)] bigger in mitochondria as well as in cytosol. As L-type Ca(2+) channel has key influence on the amplitude of Ca(2+)-induced Ca(2+) release, the relation between stimulus frequency and the amplitude of Ca(2+) transients was examined under the low density (1/10 of control) of L-type Ca(2+) channel in model simulation, where the relation was reversed. In experiment, block of Ca(2+) uniporter on mitochondrial inner membrane significantly reduced the amplitude of mitochondrial Ca(2+) transients, while it failed to affect the cytosolic Ca(2+) transients. In computer simulation, the amplitude of cytosolic Ca(2+) transients was not affected by removal of Ca(2+) uniporter. The application of carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone (FCCP) known as a protonophore on mitochondrial membrane to rat ventricular myocytes gradually increased the diastolic [Ca(2+)] in cytosol and eventually abolished the Ca(2+) transients, which was similarly reproduced in computer simulation. The model study suggests that the relative contribution of L-type Ca(2+) channel to total transsarcolemmal Ca(2+) flux could determine whether the cytosolic Ca(2+) transients become bigger or smaller with higher stimulus frequency. The present study also suggests that cytosolic Ca(2+) affects mitochondrial Ca(2+) in a beat-to-beat manner, however, removal of Ca(2+) influx mechanism into mitochondria does not affect the amplitude of cytosolic Ca(2+) transients.

High-throughput functional curation of cellular electrophysiology models

Effective reuse of a quantitative mathematical model requires not just access to curated versions of the model equations, but also an understanding of the functional capabilities of the model, and the advisable scope of its application. To enable this "functional curation" we have developed a simulation environment that provides high-throughput evaluation of a mathematical model's functional response to an arbitrary user-defined protocol, and optionally compares the results against experimental data. In this study we demonstrate the efficacy of this simulation environment on 31 cardiac electrophysiology cell models using two test cases. The S1-S2 response is evaluated to characterise the models' restitution curves, and their L-type calcium channel current-voltage curves are evaluated. The significant variation in the response of these models, even when the models represent the same species and temperature, demonstrates the importance of knowing the functional characteristics of a model prior to its reuse. We also discuss the wider implications for this approach, in improving the selection of models for reuse, enabling the identification of models that exhibit particular experimentally observed phenomena, and making the incremental development of models more robust.

Modeling CICR in rat ventricular myocytes: voltage clamp studies

Background

The past thirty-five years have seen an intense search for the molecular mechanisms underlying calcium-induced calcium-release (CICR) in cardiac myocytes, with voltage clamp (VC) studies being the leading tool employed. Several VC protocols including lowering of extracellular calcium to affect Ca²⁺ loading of the sarcoplasmic reticulum (SR), and administration of blockers caffeine and thapsigargin have been utilized to probe the phenomena surrounding SR Ca²⁺ release. Here, we develop a deterministic mathematical model of a rat ventricular myocyte under VC conditions, to better understand mechanisms underlying the response of an isolated cell to calcium perturbation. Motivation for the study was to pinpoint key control variables influencing CICR and examine the role of CICR in the context of a physiological control system regulating cytosolic Ca²⁺ concentration ([Ca²⁺]_myo).

Methods

The cell model consists of an electrical-equivalent model for the cell membrane and a fluid-compartment model describing the flux of ionic species between the extracellular and several intracellular compartments (cell cytosol, SR and the dyadic coupling unit (DCU), in which resides the mechanistic basis of CICR). The DCU is described as a controller-actuator mechanism, internally stabilized by negative feedback control of the unit's two diametrically-opposed Ca²⁺ channels (trigger-channel and release-channel). It releases Ca²⁺ flux into the cyto-plasm and is in turn enclosed within a negative feedback loop involving the SERCA pump, regulating[Ca²⁺]_myo.

Results

Our model reproduces measured VC data published by several laboratories, and generates graded Ca²⁺ release at high Ca²⁺ gain in a homeostatically-controlled environment where [Ca²⁺]_myo is precisely regulated. We elucidate the importance of the DCU elements in this process, particularly the role of the ryanodine receptor in controlling SR Ca²⁺ release, its activation by trigger Ca²⁺, and its refractory characteristics mediated by the luminal SR Ca²⁺ sensor. Proper functioning of the DCU, sodium-calcium exchangers and SERCA pump are important in achieving negative feedback control and hence Ca²⁺ homeostasis.

Conclusions

We examine the role of the above Ca²⁺ regulating mechanisms in handling various types of induced disturbances in Ca²⁺ levels by quantifying cellular Ca²⁺ balance. Our model provides biophysically-based explanations of phenomena associated with CICR generating useful and testable hypotheses.

Alteration in voltage-dependent calcium channels in dog basilar artery after subarachnoid hemorrhage

Object

The L-type Ca++ channel antagonists like nimodipine have limited efficacy against vasospasm after subarachnoid hemorrhage (SAH). The authors tested the hypothesis that this is because SAH alters these channels, rendering them less responsible for contraction.

Methods

Basilar artery smooth muscle cells were isolated 4, 7, and 21 days after SAH in dogs, and Ca++ channel currents were recorded in 10-mmol/L barium. Proteins for α1 subunits of L-type Ca++ channels were measured by immunoblotting and isometric tension recordings done on rings of the basilar artery.

Results

High voltage–activated (HVA) Ca++ channel currents were significantly decreased and low voltage–activated (LVA) currents increased during vasospasm 4, 7, and 21 days after SAH (p < 0.05). Vasospasm was associated with a significant decrease in the number of cells with negligible LVA current while the number of cells in which the LVA current formed greater than 50% of the maximal current increased (p < 0.01). Window currents through LVA and HVA channels were significantly reduced. All changes correlated with the severity of vasospasm. There was an increase in protein for Cav3.1 and Cav3.3 α1 subunits that comprise T-type Ca++ channels, a decrease in L-type (Cav1.2 and Cav1.3) and an increase in R-type (Cav2.3) Ca++ channel α1 subunits. Functionally, however, isometric tension studies showed vasospastic arteries still relaxed with nimodipine.

Conclusions

Voltage-dependent Ca++ channels are altered in cerebral arteries after SAH. While decreased L-type channels may account for the lack of efficacy of nimodipine clinically, there may be other reasons such as inadequate dose, effect of nimodipine on other cellular targets, and mechanisms of vasospasm other than smooth muscle contraction mediated by activation of L-type Ca++ channels.

Interplay of voltage and Ca-dependent inactivation of L-type Ca current

Inactivation of L-type Ca channels (LTCC) is regulated by both Ca and voltage-dependent processes (CDI and VDI). To differentiate VDI and CDI, several experimental and theoretical studies have considered the inactivation of Ba current through LTCC (I(Ba)) as a measure of VDI. However, there is evidence that Ba can weakly mimic Ca, such that I(Ba) inactivation is still a mixture of CDI and VDI. To avoid this complication, some have used the monovalent cation current through LTCC (I(NS)), which can be measured when divalent cation concentrations are very low. Notably, I(NS) inactivation rate does not depend on current amplitude, and hence may reflect purely VDI. However, based on analysis of existent and new data, and modeling, we find that I(NS) can inactivate more rapidly and completely than I(Ba), especially at physiological temperature. Thus VDI that occurs during I(Ba) (or I(Ca)) must differ intrinsically from VDI during I(NS). To account for this, we have extended a previously published LTCC mathematical model of VDI and CDI into an excitation-contraction coupling model, and assessed whether and how experimental I(Ba) inactivation results (traditionally used in VDI experiments and models) could be recapitulated by modifying CDI to account for Ba-dependent inactivation. Thus, the view of a slow and incomplete I(NS) inactivation should be revised, and I(NS) inactivation is a poor measure of VDI during I(Ca) or I(Ba). This complicates VDI analysis experimentally, but raises intriguing new questions about how the molecular mechanisms of VDI differ for divalent and monovalent currents through LTCCs.

Cooperative regulation of Ca(v)1.2 channels by intracellular Mg(2+), the proximal C-terminal EF-hand, and the distal C-terminal domain

L-type Ca(2+) currents conducted by Ca(v)1.2 channels initiate excitation-contraction coupling in cardiac myocytes. Intracellular Mg(2+) (Mg(i)) inhibits the ionic current of Ca(v)1.2 channels. Because Mg(i) is altered in ischemia and heart failure, its regulation of Ca(v)1.2 channels is important in understanding cardiac pathophysiology. Here, we studied the effects of Mg(i) on voltage-dependent inactivation (VDI) of Ca(v)1.2 channels using Na(+) as permeant ion to eliminate the effects of permeant divalent cations that engage the Ca(2+)-dependent inactivation process. We confirmed that increased Mg(i) reduces peak ionic currents and increases VDI of Ca(v)1.2 channels in ventricular myocytes and in transfected cells when measured with Na(+) as permeant ion. The increased rate and extent of VDI caused by increased Mg(i) were substantially reduced by mutations of a cation-binding residue in the proximal C-terminal EF-hand, consistent with the conclusion that both reduction of peak currents and enhancement of VDI result from the binding of Mg(i) to the EF-hand (K(D) approximately 0.9 mM) near the resting level of Mg(i) in ventricular myocytes. VDI was more rapid for L-type Ca(2+) currents in ventricular myocytes than for Ca(v)1.2 channels in transfected cells. Coexpression of Ca(v)beta(2b) subunits and formation of an autoinhibitory complex of truncated Ca(v)1.2 channels with noncovalently bound distal C-terminal domain (DCT) both increased VDI in transfected cells, indicating that the subunit structure of the Ca(v)1.2 channel greatly influences its VDI. The effects of noncovalently bound DCT on peak current amplitude and VDI required Mg(i) binding to the proximal C-terminal EF-hand and were prevented by mutations of a key divalent cation-binding amino acid residue. Our results demonstrate cooperative regulation of peak current amplitude and VDI of Ca(v)1.2 channels by Mg(i), the proximal C-terminal EF-hand, and the DCT, and suggest that conformational changes that regulate VDI are propagated from the DCT through the proximal C-terminal EF-hand to the channel-gating mechanism.

Physiological modulation of voltage-dependent inactivation in the cardiac muscle L-type calcium channel: A modelling study

The inactivation of the L-type Ca2+ current is composed of voltage-dependent and calcium-dependent mechanisms. The relative contribution of these processes is still under dispute and the idea that the voltage-dependent inactivation could be subject to further modulation by other physiological processes had been ignored. This study sought to model physiological modulation of inactivation of the current in cardiac ventricular myocytes, based upon the recent detailed experimental data that separated total and voltage-dependent inactivation (VDI) by replacing extracellular Ca2+ with Mg2+ and monitoring L-type Ca2+ channel behaviour by outward K+ current flowing through the channel in the absence of inward current flow. Calcium-dependent inactivation (CDI) was based upon Ca2+ influx and formulated from data that was recorded during beta-adrenergic stimulation of the myocytes. Ca2+ influx and its competition with non-selective monovalent cation permeation were also incorporated into channel permeation in the model. The constructed model could closely reproduce the experimental Ba2+ and Ca2+ current results under basal condition where no beta-stimulation was added after a slight reduction of the development of fast voltage-dependent inactivation with depolarization. The model also predicted that under beta-adrenergic stimulation voltage-dependent inactivation is lost and calcium-dependent inactivation largely compensates it. The developed model thus will be useful to estimate the respective roles of VDI and CDI of L-type Ca2+ channels in various physiological and pathological conditions of the heart which would otherwise be difficult to show experimentally.

Mechanisms of the negative inotropic effects of sphingosine-1-phosphate on adult mouse ventricular myocytes

Sphingosine-1-phosphate (S1P) induces a transient bradycardia in mammalian hearts through activation of an inwardly rectifying K(+) current (I(K(ACh))) in the atrium that shortens action potential duration (APD) in the atrium. We have investigated probable mechanisms and receptor-subtype specificity for S1P-induced negative inotropy in isolated adult mouse ventricular myocytes. Activation of S1P receptors by S1P (100 nM) reduced cell shortening by approximately 25% (vs. untreated controls) in field-stimulated myocytes. S1P(1) was shown to be involved by using the S1P(1)-selective agonist SEW2871 on myocytes isolated from S1P(3)-null mice. However, in these myocytes, S1P(3) can modulate a somewhat similar negative inotropy, as judged by the effects of the S1P(1) antagonist VPC23019. Since S1P(1) activates G(i) exclusively, whereas S1P(3) activates both G(i) and G(q), these results strongly implicate the involvement of mainly G(i). Additional experiments using the I(K(ACh)) blocker tertiapin demonstrated that I(K(ACh)) can contribute to the negative inotropy following S1P activation of S1P(1) (perhaps through G(ibetagamma) subunits). Mathematical modeling of the effects of S1P on APD in the mouse ventricle suggests that shortening of APD (e.g., as induced by I(K(ACh))) can reduce L-type calcium current and thus can decrease the intracellular Ca(2+) concentration ([Ca(2+)](i)) transient. Both effects can contribute to the observed negative inotropic effects of S1P. In summary, these findings suggest that the negative inotropy observed in S1P-treated adult mouse ventricular myocytes may consist of two distinctive components: 1) one pathway that acts via G(i) to reduce L-type calcium channel current, blunt calcium-induced calcium release, and decrease [Ca(2+)](i); and 2) a second pathway that acts via G(i) to activate I(K(ACh)) and reduce APD. This decrease in APD is expected to decrease Ca(2+) influx and reduce [Ca(2+)](i) and myocyte contractility.

Effects of N-n-butyl haloperidol iodide on L-type calcium channels and intracellular free calcium in rat ventricular myocytes

The ability of N-n-butyl haloperidol iodide (F2) to cause vasodilation, and thereby produce a cardioprotective effect, has been well documented. The aim of this study was to investigate whether F2 might act as a Ca2+ antagonist. Myocytes were obtained from rat heart, and the whole-cell patch-clamp technique was used to record Ca2+ current. Laser scanning confocal microscopy was used to measure intracellular free calcium ([Ca2+]i). The results obtained from this study demonstrate that F2 reduced calcium current (ICa) in a concentration-dependent manner with an IC50 of 1.19 micromol/L, upshifted the current-voltage curve of ICa, shifted the inactivation kinetics of ICa leftward, and slowed down the recovery of ICa from inactivation. F2 decreased the fluorescent intensity of [Ca2+]i elevation induced by KCl with an IC50 of 1.61 micromol/L, and had no effects on the intracellular calcium release induced by caffeine and inositol-1,4,5-trisphosphate. These findings indicate that F2 may act as a calcium antagonist, which could account for its cardiovascular benefits.

Gating of the HypoPP-1 mutations: II. Effects of a calcium-channel agonist BayK 8644

L-type calcium-channel mutations causing hypokalemic periodic paralysis type 1 (HypoPP-1) have pronounced "loss-of-function" features and stabilize the less-selective second open state O(2), as we demonstrated in the companion paper. Here, we compared the effects of the L-type calcium-channel activator (+/-)BayK 8644 (BayK) on the heterologously expressed wild-type (WT) calcium channel, rabbit Cav1.2 HypoPP-1 analogs, and two double mutants (R650H/R1362H, R650H/R1362G). Our goal was to elucidate (1) whether the "loss-of-function" in HypoPP-1 can be compensated by BayK application, (2) how the less-selective open state is affected by BayK in WT and HypoPP-1 mutants, as well as (3) to gain an insight into BayK mechanism of action. Ionic currents were examined by whole-cell patch-clamp and analyzed by the global-fitting procedure. Our results imply that (1) BayK promotes channel activation, but equalized the differences among the WT and mutants, thus attenuating HypoPP-related effects on activation and deactivation; (2) BayK binds to the first open state O(1), and then serves as a catalyst for O(2) formation; (3) binding of BayK is impaired in the HypoPP mutants, thus affecting the formation of the less-selective second open state; (4) BayK affects cooperativity between the single HypoPP-1 mutations at all stages of the channel gating; and (5) BayK favoring of O(2) lowers calcium-channel selectivity.

Gating of the HypoPP-1 mutations: I. Mutant-specific effects and cooperativity

Hypokalemic periodic paralysis type 1 (HypoPP-1) is a hereditary muscular disorder caused by point mutations in the gene encoding the voltage-gated Ca(2+) channel alpha subunit (Ca(v)1.1). Despite extensive research, the results on HypoPP-1 mutations are minor and controversial, as it is difficult to analyse Ca(2+) channel activation macroscopically due to an existence of two open states. In this study, we heterologously expressed the wild-type and HypoPP-1 mutations introduced into the rabbit cardiac Ca(2+) channel (R650H, R1362H, R1362G) in HEK-293 cells. To examine the cooperative effects of the mutations on channel gating, we expressed two double mutants (R650H/R1362H, R650H/R1362G). We performed whole-cell patch-clamp and, to obtain more information, applied a global fitting procedure whereby several current traces elicited by different potentials were simultaneously fit to the kinetic model containing four closed, two open and two inactivated states. We found that all HypoPP-1 mutations have "loss-of-function" features: D4/S4 mutations shift the equilibrium to the closed states, which results in reduced open probability, shorter openings and, therefore, in smaller currents, and the D2/S4 mutant slows the activation. In addition, HypoPP-1 histidine mutants favored the second open state O(2) with a possibly lower channel selectivity. Cooperativity between the D2/S4 and D4/S4 HypoPP-1 mutations manifested in dominant effects of the D4/S4 mutations on kinetics of the double mutants, suggesting different roles of D2/S4 and D4/S4 voltage sensors in the gating of voltage-gated calcium channels.

Voltage-dependent calcium channels of dog basilar artery

Electrophysiological and molecular characteristics of voltage-dependent calcium (Ca(2+)) channels were studied using whole-cell patch clamp, polymerase chain reaction and Western blotting in smooth muscle cells freshly isolated from dog basilar artery. Inward currents evoked by depolarizing steps from a holding potential of -50 or -90 mV in 10 mm barium consisted of low- (LVA) and high-voltage activated (HVA) components. LVA current comprised more than half of total current in 24 (12%) of 203 cells and less than 10% of total current in 52 (26%) cells. The remaining cells (127 cells, 62%) had LVA currents between one tenth and one half of total current. LVA current was rapidly inactivating, slowly deactivating, inhibited by high doses of nimodipine and mibefradil (> 0.3 microM), not affected by omega-agatoxin GVIA (gamma100 nM), omega-conotoxin IVA (1 microM) or SNX-482 (200 nM) and probably carried by T-type Ca(2+) channels based on the presence of messenger ribonucleic acid (mRNA) and protein for Ca(v3.1) and Ca(v3.3) alpha(1) subunits of these channels. LVA currents exhibited window current with a maximum of 13% of the LVA current at -37.4 mV. HVA current was slowly inactivating and rapidly deactivating. It was inhibited by nimodipine (IC(50) = 0.018 microM), mibefradil (IC(50) = 0.39 microM) and omega-conotoxin IV (1 microM). Smooth muscle cells also contained mRNA and protein for L- (Ca(v1.2) and Ca(v1.3)), N- (Ca(v2.2)) and T-type (Ca(v3.1) and Ca(v3.3)) alpha(1) Ca(2+) channel subunits. Confocal microscopy showed Ca(v1.2) and Ca(v1.3) (L-type), Ca(v2.2) (N-type) and Ca(v3.1) and Ca(v3.3) (T-type) protein in smooth muscle cells. Relaxation of intact arteries under isometric tension in vitro to nimodipine (1 microM) and mibefradil (1 microM) but not to omega-agatoxin GVIA (100 nM), omega-conotoxin IVA (1 microM) or SNX-482 (1 microM) confirmed the functional significance of L- and T-type voltage-dependent Ca(2+) channel subtypes but not N-type. These results show that dog basilar artery smooth muscle cells express functional voltage-dependent Ca(2+) channels of multiple types.

The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes

The morphology of the cardiac transverse-axial tubular system (TATS) has been known for decades, but its function has received little attention. To explore the possible role of this system in the physiological modulation of electrical and contractile activity, we have developed a mathematical model of rat ventricular cardiomyocytes in which the TATS is described as a single compartment. The geometrical characteristics of the TATS, the biophysical characteristics of ion transporters and their distribution between surface and tubular membranes were based on available experimental data. Biophysically realistic values of mean access resistance to the tubular lumen and time constants for ion exchange with the bulk extracellular solution were included. The fraction of membrane in the TATS was set to 56%. The action potentials initiated in current-clamp mode are accompanied by transient K+ accumulation and transient Ca2+ depletion in the TATS lumen. The amplitude of these changes relative to external ion concentrations was studied at steady-state stimulation frequencies of 1-5 Hz. Ca2+ depletion increased from 7 to 13.1% with stimulation frequency, while K+ accumulation decreased from 4.1 to 2.7%. These ionic changes (particularly Ca2+ depletion) implicated significant decrease of intracellular Ca2+ load at frequencies natural for rat heart.

Effect of resveratrol on L-type calcium current in rat ventricular myocytes

AIM

To study the effect of resveratrol on L-type calcium current (I(Ca-L)) in isolated rat ventricular myocytes and the mechanisms underlying these effects.

METHODS

I(Ca-L) was examined in isolated single rat ventricular myocytes by using the whole cell patch-clamp recording technique.

RESULTS

Resveratrol (10-40 micromol/L) reduced the peak amplitude of I(Ca-L) and shifted the current-voltage (I-V) curve upwards in a concentration-dependent manner. Resveratrol (10, 20, 40 micromol/L) decreased the peak amplitude of I(Ca-L) from -14.2+/-1.5 pA/pF to -10.5+/-1.5 pA/pF (P<0.05), -7.5+/-2.4 pA/pF (P<0.01), and -5.2+/-1.2 pA/pF (P<0.01), respectively. Resveratrol (40 micromol/L) shifted the steady-state activation curve of I(Ca-L) to the right and changed the half-activation potential (V0.5) from -19.4+/-0.4 mV to -15.4+/-1.9 mV (P<0.05). Resveratrol at a concentration of 40 micromol/L did not affect the steady-state inactivation curve of I(Ca-L), but did markedly shift the time-dependent recovery curve of I(Ca-L) to the right, and slow down the recovery of I(Ca-L) from inactivation. Sodium orthovanadate (Na(3)VO(4); 1 mmol/L), a potent inhibitor of tyrosine phosphatase, significantly inhibited the effects of resveratrol (P<0.01).

CONCLUSION

Resveratrol inhibited I(Ca-L) mainly by inhibiting the activation of L-type calcium channels and slowing down the recovery of L-type calcium channels from inactivation. This inhibitory effect of resveratrol was mediated by the inhibition of protein tyrosine kinase in rat ventricular myocytes.

Analysis of the modal hypothesis of Ca2+-dependent inactivation of L-type Ca2+ channels

A kinetic model of Ca2+-dependent inactivation (CDI) of L-type Ca2+ channels was developed. The model is based on the hypothesis that postulates the existence of four short-lived modes with lifetimes of a few hundreds of milliseconds. Our findings suggest that the transitions between the modes is primarily determined by the binding of Ca2+ to two intracellular allosteric sites located in different motifs of the CI region, which have greatly differing binding rates for Ca2+ (different k(on)). The slow-binding site is controlled by local Ca2+ near a single open channel that is consistent with the "domain" CDI model, and Ca2+ binding to the fast-binding site(s) depends on Ca2+ arising from distant sources that is consistent with the "shell" CDI model. The model helps to explain numerous experimental findings that are poorly understood so far.

Variability in couplon size in rabbit ventricular myocytes

Variation in couplon size is thought to be essential for graded Ca(2+) transients in cardiac myocytes. We examined this variation by investigating spark appearance in rabbit ventricular myocytes at various locations and at potentials from -20 to 0 mV. At 0 mV, sparks appeared at the beginning of the voltage step with a probability of unity. On the other hand, at -20 mV, sparks appeared later during the voltage step with a lower probability. The cumulative spark probabilities at various potentials were fitted with exponential functions of both time and voltage. Spark latency became longer as spark probability decreased at more negative potentials. At -20 mV, the cumulative spark probability and the mean spark latency were not only variable among locations but also inversely related. Under the assumption that a single opening of an L-type Ca(2+) channel triggers a spark, we suggest a simple mathematical explanation for the distribution of spark appearance. The variation in spark probability and latency with location suggests that the couplon size, and hence the number of L-type Ca(2+) channels in a couplon is variable.

Ca2+- and voltage-dependent inactivation of the expressed L-type Ca(v)1.2 calcium channel

Ca2+-dependent regulation of the ion current through the alpha1Cbeta2aalpha2delta-1 (L-type) calcium channel transiently expressed in HEK 293 cells was investigated using whole cell patch clamp method. Ca2+ or Na+ ions were used as a charge carrier. Intracellular Ca2+ was either buffered by 10 mM EGTA or 200 microM Ca2+ was added into non-buffered intracellular solution. Free intracellular Ca2+ inactivated permanently about 80% of the L-type calcium current. The L-type calcium channel inactivated during a depolarizing pulse with two time constants, tau(fast) and tau(slow). Free intracellular calcium accelerated both time constants. Effect on the tau(slow) was more pronounced. About 80% of the channel inactivation during brief depolarizing pulse could be attributed to a Ca2+-dependent mechanism and 20% to a voltage-dependent mechanism. When Na+ ions were used as a charge carrier, the L-type current still inactivated with two time constants that were 10 times slower and were virtually voltage-independent. Ca2+ ions stabilized the inactivated state of the channel in a concentration-dependent manner.

Physiological modulation of inactivation in L-type Ca2+ channels: one switch

The relative contributions of voltage- and Ca(2+)-dependent mechanisms of inactivation to the decay of L-type Ca(2+) channel currents (I(CaL)) is an old story to which recent results have given an unexpected twist. In cardiac myocytes voltage-dependent inactivation (VDI) was thought to be slow and Ca(2+)-dependent inactivation (CDI) resulting from Ca(2+) influx and Ca(2+)-induced Ca(2+)-release (CICR) from the sarcoplasmic reticulum provided an automatic negative feedback mechanism to limit Ca(2+) entry and the contribution of I(CaL) to the cardiac action potential. Physiological modulation of I(CaL) by Beta-adrenergic and muscarinic agonists then involved essentially more or less of the same by enhancing or reducing Ca(2+) channel activity, Ca(2+) influx, sarcoplasmic reticulum load and thus CDI. Recent results on the other hand place VDI at the centre of the regulation of I(CaL). Under basal conditions it has been found that depolarization increases the probability that an ion channel will show rapid VDI. This is prevented by Beta-adrenergic stimulation. Evidence also suggests that a channel which shows rapid VDI inactivates before CDI can become effective. Therefore the contributions of VDI and CDI to the decay of I(CaL) are determined by the turning on, by depolarization, and the turning off, by phosphorylation, of the mechanism of rapid VDI. The physiological implications of these ideas are that under basal conditions the contribution of I(CaL) to the action potential will be determined largely by voltage and by Ca(2+) following Beta-adrenergic stimulation.

Molecular determinants of Ca(2+)/calmodulin-dependent regulation of Ca(v)2.1 channels

Ca2+-dependent facilitation and inactivation (CDF and CDI) of Cav2.1 channels modulate presynaptic P/Q-type Ca2+ currents and contribute to activity-dependent synaptic plasticity. This dual feedback regulation by Ca2+ involves calmodulin (CaM) binding to the alpha1 subunit (alpha12.1). The molecular determinants for Ca2+-dependent modulation of Cav2.1 channels reside in CaM and in two CaM-binding sites in the C-terminal domain of alpha12.1, the CaM-binding domain (CBD) and the IQ-like domain. In transfected tsA-201 cells, CDF and CDI were both reduced by deletion of CBD. In contrast, alanine substitution of the first two residues of the IQ-like domain (IM-AA) completely prevented CDF but had little effect on CDI, and glutamate substitutions (IM-EE) greatly accelerated voltage-dependent inactivation but did not prevent CDI. Mutational analyses of the Ca2+ binding sites of CaM showed that both the N- and C-terminal lobes of CaM were required for full development of facilitation, but only the N-terminal lobe was essential for CDI. In biochemical assays, CaM12 and CaM34 were unable to bind CBD, whereas CaM34 but not CaM12 retained Ca2+-dependent binding to the IQ-like domain. These findings support a model in which Ca2+ binding to the C-terminal EF-hands of preassociated CaM initiates CDF via interaction with the IQ-like domain. Further Ca2+ binding to the N-terminal EF-hands promotes secondary CaM interactions with CBD, which enhance facilitation and cause a conformational change that initiates CDI. This multifaceted mechanism allows positive regulation of Cav2.1 in response to local Ca2+ increases (CDF) and negative regulation during more global Ca2+ increases (CDI).

A model of graded calcium release and L-type Ca2+ channel inactivation in cardiac muscle

We have developed a model of Ca(2+) handling in ferret ventricular myocytes. This model includes a novel L-type Ca(2+) channel, detailed intracellular Ca(2+) movements, and graded Ca(2+)-induced Ca(2+) release (CICR). The model successfully reproduces data from voltage-clamp experiments, including voltage- and time-dependent changes in intracellular Ca(2+) concentration ([Ca(2+)](i)), L-type Ca(2+) channel current (I(CaL)) inactivation and recovery kinetics, and Ca(2+) sparks. The development of graded CICR is critically dependent on spatial heterogeneity and the physical arrangement of calcium channels in opposition to ryanodine-sensitive release channels. The model contains spatially distinct subsystems representing the subsarcolemmal regions where the junctional sarcoplasmic reticulum (SR) abuts the T-tubular membrane and where the L-type Ca(2+) channels and SR ryanodine receptors (RyRs) are localized. There are eight different types of subsystems in our model, with between one and eight L-type Ca(2+) channels distributed binomially. This model exhibits graded CICR and provides a quantitative description of Ca(2+) dynamics not requiring Monte-Carlo simulations. Activation of RyRs and release of Ca(2+) from the SR depend critically on Ca(2+) entry through L-type Ca(2+) channels. In turn, Ca(2+) channel inactivation is critically dependent on the release of stored intracellular Ca(2+). Inactivation of I(CaL) depends on both transmembrane voltage and local [Ca(2+)](i) near the channel, which results in distinctive inactivation properties. The molecular mechanisms underlying many I(CaL) gating properties are unclear, but [Ca(2+)](i) dynamics clearly play a fundamental role.

Ionic mechanisms mediating oscillatory membrane potentials in wide-field retinal amacrine cells

Particular types of amacrine cells of the vertebrate retina show oscillatory membrane potentials (OMPs) in response to light stimulation. Historically it has been thought the oscillations arose as a result of circuit properties. In a previous study we found that in some amacrine cells, the ability to oscillate was an intrinsic property of the cell. Here we characterized the ionic mechanisms responsible for the oscillations in wide-field amacrine cells (WFACs) in an effort to better understand the functional properties of the cell. The OMPs were found to be calcium (Ca2+) dependent; blocking voltage-gated Ca2+ channels eliminated the oscillations, whereas elevating extracellular Ca2+ enhanced them. Strong intracellular Ca2+ buffering (10 mM EGTA or bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid) eliminated any attenuation in the OMPs as well as a Ca2+-dependent inactivation of the voltage-gated Ca2+ channels. Pharmacological and immunohistochemical characterization revealed that WFACs express L- and N-type voltage-sensitive Ca2+ channels. Block of the L-type channels eliminated the OMPs, but omega-conotoxin GVIA did not, suggesting a different function for the N-type channels. The L-type channels in WFACs are functionally coupled to a set of calcium-dependent potassium (K(Ca)) channels to mediate OMPs. The initiation of OMPs depended on penitrem-A-sensitive (BK) K(Ca) channels, whereas their duration is under apamin-sensitive (SK) K(Ca) channel control. The Ca2+ current is essential to evoke the OMPs and triggering the K(Ca) currents, which here act as resonant currents, enhances the resonance as an amplifying current, influences the filtering characteristics of the cell membrane, and attenuates the OMPs via CDI of the L-type Ca2+ channel.

Two components of voltage-dependent inactivation in Ca(v)1.2 channels revealed by its gating currents

Voltage-dependent inactivation (VDI) was studied through its effects on the voltage sensor in Ca(v)1.2 channels expressed in tsA 201 cells. Two kinetically distinct phases of VDI in onset and recovery suggest the presence of dual VDI processes. Upon increasing duration of conditioning depolarizations, the half-distribution potential (V(1/2)) of intramembranous mobile charge was negatively shifted as a sum of two exponential terms, with time constants 0.5 s and 4 s, and relative amplitudes near 50% each. This kinetics behavior was consistent with that of increment of maximal charge related to inactivation (Qn). Recovery from inactivation was also accompanied by a reduction of Qn that varied with recovery time as a sum of two exponentials. The amplitudes of corresponding exponential terms were strongly correlated in onset and recovery, indicating that channels recover rapidly from fast VDI and slowly from slow VDI. Similar to charge "immobilization," the charge moved in the repolarization (OFF) transient became slower during onset of fast VDI. Slow VDI had, instead, hallmarks of interconversion of charge. Confirming the mechanistic duality, fast VDI virtually disappeared when Li(+) carried the current. A nine-state model with parallel fast and slow inactivation pathways from the open state reproduces most of the observations.

Ca2+ entry-dependent inactivation of L-type Ca current: a novel formulation for cardiac action potential models

Cardiac L-type Ca current (I(Ca,L)) is controlled not only by voltage but also by Ca(2+)-dependent mechanisms. Precise implementation of I(Ca,L) in cardiac action potential models therefore requires thorough understanding of intracellular Ca(2+) dynamics, which is not yet available. Here, we present a novel formulation of I(Ca,L) for action potential models that does not explicitly require the knowledge of local intracellular Ca(2+) concentration ([Ca(2+)](i)). In this model, whereas I(Ca,L) is obtained as the product of voltage-dependent gating parameters (d and f), Ca(2+)-dependent inactivation parameters (f(Ca): f(Ca-entry) and f(Ca-SR)), and Goldman-Hodgkin-Katz current equation as in previous studies, f(Ca) is not a instantaneous function of [Ca(2+)](i) but is determined by two terms: onset of inactivation proportional to the influx of Ca(2+) and time-dependent recovery (dissociation). We evaluated the new I(Ca,L) subsystem in the framework of the standard cardiac action potential model. The new formulation produced a similar temporal profile of I(Ca,L) as the standard, but with different gating mechanisms. Ca(2+)-dependent inactivation gradually proceeded throughout the plateau phase, replacing the voltage-dependent inactivation parameter in the LRd model. In typical computations, f declined to approximately 0.7 and f(Ca-entry) to approximately 0.1, whereas deactivation caused fading of I(Ca,L) during final repolarization. These results support experimental findings that Ca(2+) entering through I(Ca,L) is essential for inactivation. After responses to standard voltage-clamp protocols were examined, the new model was applied to analyze the behavior of I(Ca,L) when action potential was prolonged by several maneuvers. Our study provides a basis for theoretical analysis of I(Ca,L) during action potentials, including the cases encountered in long QT syndromes.

Voltage-dependent inactivation of L-type Ca2+ currents in guinea-pig ventricular myocytes

The objective of this study was to describe the kinetics of voltage-dependent inactivation of native cardiac L-type Ca(2+) currents. Whole-cell currents were recorded from guinea-pig isolated ventricular myocytes. Voltage-dependent inactivation was separated from Ca(2+)-dependent inactivation by replacing extracellular Ca(2+) with Mg(2+) and recording outward currents through Ca(2+) channels. Voltage-dependent inactivation accelerated from slow monophasic decay at -30 mV to maximal rapid biphasic decay at +20 mV. Maximal voltage-dependent inactivation occurred with tau(f) approximately equal 30 ms and tau(s) approximately equal 300 ms, the fast component of decay accounted for 70 % of the current amplitude. In basal conditions Ca(2+) current availability was sigmoid. Isoproterenol (isoprenaline) evoked a large increase in a time-independent component of the Ca(2+) current which also increased with depolarisation. This was responsible for the apparent recovery of Ca(2+) channel current availability at positive membrane potentials and thus a U-shaped availability-voltage (A-V) relationship. It is concluded that beta-adrenergic stimulation altered the reaction of native cardiac L-type Ca(2+) channels to membrane voltage. In basal conditions, voltage accelerated inactivation. In isoproterenol, voltage could also reduce inactivation.

An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.

Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell

We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models.

beta-Adrenergic stimulation modulates Ca2+- and voltage-dependent inactivation of L-type Ca2+ channel currents in guinea-pig ventricular myocytes

The objective of this study was to examine the effect of beta-adrenergic stimulation upon voltage- and Ca2+-induced inactivation of native cardiac L-type Ca2+ channels. Whole-cell currents were recorded from guinea-pig isolated ventricular myocytes. Total and voltage-dependent inactivation was separated by replacing extracellular Ca2+ with Mg2+. L-type Ca2+ channel behaviour was monitored with outward Ca2+ channel currents. First, the voltage dependence of inactivation was studied at fixed times (50 and 1000 ms) after activation. This showed that under control conditions Ca2+ contributed little to inactivation. In isoproterenol (isoprenaline), voltage-dependent inactivation was markedly reduced and Ca2+ contributed largely to total inactivation. Second, the time dependence of inactivation was studied at a fixed voltage (+10 mV). In control conditions the fast phase of inactivation (tau(f) approximately 15 ms) was reduced to the same extent by ryanodine (tau(f) approximately 30 ms) and the absence of Ca2+ (tau(f) approximately 30 ms) while the slow phase of inactivation (tau(s) approximately 70 ms) was reduced by ryanodine (tau(s) approximately 160 ms) and further reduced in the absence of Ca2+ (tau(s) approximately 300 ms). In isoproterenol, biphasic inactivation of Ca2+ currents (tau(f) approximately 4 ms, tau(s) approximately 60 ms) was replaced by a single slow (tau approximately 450 ms) phase of inactivation in the absence of Ca2+. It is concluded that, under control conditions Ca2+ channel current decay is largely dominated by rapid voltage-dependent inactivation, while in isoproterenol this is replaced by Ca2+-induced inactivation.

Voltage- and cation-dependent inactivation of L-type Ca2+ channel currents in guinea-pig ventricular myocytes

L-type Ca2+ channel currents in native ventricular myocytes inactivate according to voltage- and Ca2+-dependent processes. This study sought to examine the effect of beta-adrenergic stimulation on the contributions of voltage and Ca2+ to Ca2+ current decay. Ventricular myocytes were enzymatically isolated from guinea-pig hearts. Inward whole-cell Cd2+-sensitive L-type Ca2+ channel currents were recorded with the patch clamp technique and comparison was made between inward currents carried by Ca2+ and either Ba2+, Sr2+ or Na+. In control conditions the decay of Ca2+ currents was faster than Ba2+, Sr2+ or Na+ currents at negative voltages while at positive voltages there was no difference. The relationship between voltage and inactivation for Ca2+ currents was bell-shaped, while that for Ba2+, Sr2+, and Na+ currents was sigmoid. Thus depolarisation progressively replaced Ca2+-dependent inactivation in the fast phase of decay of Ca2+ channel currents with rapid voltage-dependent inactivation. In the presence of isoproterenol (isoprenaline) the decay of Ca2+ currents was faster than Ba2+, Sr2+ or Na+ currents at all measured voltages (-40 to +30 mV). The relationship between voltage and inactivation for Ca2+, Ba2+ and Sr2+ currents was bell-shaped, while that for Na+ currents was sigmoid with less inactivation than under control conditions. Therefore the fast phase of decay of Ca2+ channel currents was now almost entirely due to Ca2+. It is concluded that the relative contributions of Ca2+- and voltage-dependent mechanisms of inactivation of L-type Ca2+ channels in native cardiac myocytes are modulated by beta-adrenergic stimulation influencing the amount of rapid voltage-dependent inactivation.

A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes

Mathematical models were developed to reconstruct the action potentials (AP) recorded in epicardial and endocardial myocytes isolated from the adult rat left ventricle. The main goal was to obtain additional insight into the ionic mechanisms responsible for the transmural AP heterogeneity. The simulation results support the hypothesis that the smaller density and the slower reactivation kinetics of the Ca(2+)-independent transient outward K(+) current (I(t)) in the endocardial myocytes can account for the longer action potential duration (APD), and more prominent rate dependence in that cell type. The larger density of the Na(+) current (I(Na)) in the endocardial myocytes results in a faster upstroke (dV/dt(max)). This, in addition to the smaller magnitude of I(t), is responsible for the larger peak overshoot of the simulated endocardial AP. The prolonged APD in the endocardial cell also leads to an enhanced amplitude of the sustained K(+) current (I(ss)), and a larger influx of Ca(2+) ions via the L-type Ca(2+) current (I(CaL)). The latter results in an increased sarcoplasmic reticulum (SR) load, which is mainly responsible for the higher peak systolic value of the Ca(2+) transient [Ca(2+)](i), and the resultant increase in the Na(+)-Ca(2+) exchanger (I(NaCa)) activity, associated with the simulated endocardial AP. In combination, these calculations provide novel, quantitative insights into the repolarization process and its naturally occurring transmural variations in the rat left ventricle.