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Computer model of action potential of mouse ventricular myocytes

¹Department of Physiology and Biophysics, School of Medicine and Biomedical Sciences, University at Buffalo, State University of New York, Buffalo, New York 14214-3078; and ²Cell Biology and Molecular Medicine Cardiovascular Research Institute, University of Medicine and Dentistry of New Jersey-New Jersey Medical School, Newark, New Jersey 07103

Submitted 28 February 2003 ; accepted in final form 11 May 2004

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 
We have developed a mathematical model of the mouse ventricular myocyte action potential (AP) from voltage-clamp data of the underlying currents and Ca²⁺ transients. Wherever possible, we used Markov models to represent the molecular structure and function of ion channels. The model includes detailed intracellular Ca²⁺ dynamics, with simulations of localized events such as sarcoplasmic Ca²⁺ release into a small intracellular volume bounded by the sarcolemma and sarcoplasmic reticulum. Transporter-mediated Ca²⁺ fluxes from the bulk cytosol are closely matched to the experimentally reported values and predict stimulation rate-dependent changes in Ca²⁺ transients. Our model reproduces the properties of cardiac myocytes from two different regions of the heart: the apex and the septum. The septum has a relatively prolonged AP, which reflects a relatively small contribution from the rapid transient outward K⁺ current in the septum. The attribution of putative molecular bases for several of the component currents enables our mouse model to be used to simulate the behavior of genetically modified transgenic mice.

cardiac myocytes; computer modeling

The pioneering model of DiFrancesco and Noble (27) was the first to incorporate active transport and secondary active transport mechanisms. These were included in response to the growing experimental evidence that these electrogenic processes were important in repolarization. Development of the whole cell patch-clamp technique gave rise to a number of animal- and region-specific models, based on detailed descriptions of ionic currents from isolated single-myocyte experiments (41, 55, 62, 63, 76, 77, 91, 98). These models began to address the basis for the diverse AP behavior observed in different species and regions of the heart. Models of bullfrog atrial and cardiac pacemaker cells (76, 77) replicated the lack of a significant intracellular Ca²⁺ release contribution in these cells. Similarly, models of the guinea pig ventricular myocyte (62, 63, 98) reflected the absence of the transient outward current in these cells. Lindblad et al. (55) developed a model of the rabbit atrial cell with prominent transient outward (I_to) and rapid delayed rectifier (I_Kr) currents. Human atrial models were developed by Nygren et al. (72) and Courtemanche et al. (25), based partially on measurements from atrial appendage tissue obtained from bypass surgery. I_to had a prominent role in these AP models, reflecting the experimentally obtained data. Recently, a rat ventricular myocyte model was published by Pandit et al. (73). The rat AP has a short AP duration (APD) and relatively dominant transient outward current.

APs of cardiac cells from different animals and different heart regions have different shapes, durations, and sets of ionic currents. These variations reflect corresponding differences in the molecular basis of repolarization and hence pharmacological responses (32, 37, 56). For example, APD at 50% of repolarization (APD₅₀) in guinea pig and canine ventricular myocytes is 300 ms (41, 62, 63, 91), whereas APD₅₀ for rat ventricular myocytes from the epicardial region is only 13 ms (73). The guinea pig ventricular myocyte AP has an elevated plateau (41, 62, 63, 91), whereas rat and mouse ventricular APs are relatively short, with a "triangular" shape (11, 93). The human atrial AP has a relatively sharp, short peak followed by a slow repolarization phase, which takes up to 250 ms (33, 72). In general, APD seems to be correlated to the size of the heart or the heart rate for a particular species, with smaller, faster-beating hearts having shorter APDs than larger, slower-beating hearts. The shape and underlying currents for the various APs have considerable variability. This variability is less related to heart size than it is to the species and region of the heart. Presumably, the restitution patterns, pharmacology, and arrhythmogenic potential of each waveform reflects the different molecular bases and timing of underlying currents. Understanding the timing of these currents under different situations can be critical. For example, one of the arrhythmogenic defects in human ether-à-go-go-related gene (HERG) (which encodes the rapid delayed rectifier current I_Kr) may be spontaneously triggered arrhythmias resulting from a complex interaction of I_Kr with the L-type Ca²⁺ current and subcellular Ca²⁺-handling mechanisms during repolarization (67). Clearly, understanding abnormalities in cardiac repolarization requires an understanding of the functioning of the cell as an integrated system. The many complex potential interactions of transmembrane currents and intracellular ions (particularly Ca²⁺) leave computer modeling as the only method currently available to synthesize and understand these multiple nonlinear interactions.

In general, most models simulate sarcolemmal currents, pumps, and exchangers and combine them with intracellular ionic homeostasis to reproduce an AP. One limitation of many older models is their description of intracellular Ca²⁺ dynamics (55, 62, 63, 76, 77, 98). These older models did not take into account the importance of spatial localization in Ca²⁺ cellular dynamics, which results in generation of relatively high-amplitude Ca²⁺ sparks (see, for example, Ref. 11) and can only roughly approximate the relationship between Ca²⁺ release and Ca²⁺ channel inactivation. More recent models (12, 41, 91) have begun to address this issue. Our model builds on the strengths of these previous models and was developed to reproduce a mouse myocyte with a characteristically short AP.

There is a great diversity of anatomic and electrophysiological features in myocytes from different species, e.g., transverse tubules, Ca²⁺-handling systems, as well as the specific properties of the major ionic currents. Wherever possible, we developed our model of the mouse ventricular myocytes with experimental data from adult mouse ventricular cardiac cells. This has been possible largely because of the increase in detailed examination of currents in various transgenic mice.

Although a majority of the most important currents and parameters are well constrained by this large body of data, there is still uncertainty in the exact kinetic parameters of some current systems. Where there was uncertainty or an absence of mouse data, we used data from less closely related species and heterologously expressed clones and adjusted them to match related mouse data.

Our mouse model is specifically designed to make use of the information from recent advances in molecular biology. The mouse is the most widely used animal in genetic research. There is now an abundance of transgenic mice with genetic defects associated with human diseases. Where possible, the component currents of the model have been assigned putative molecular bases, so the model can be used to test predictions about the consequences of transgenic experiments with relative ease. Our model mouse myocyte has a diversity of K⁺ channels, not all of which may be present in the same cell, depending on the region from which the cells were isolated. The model has seven distinct K⁺ currents: a rapid transient outward K⁺ current (I_Kto,f), a slow transient outward K⁺ current (I_Kto,s), a time-independent K⁺ current (I_K1), an ultrarapidly activating delayed rectifier K⁺ current (I_Kur), a noninactivating steady-state K⁺ current (I_Kss), a rapid delayed rectifier K⁺ current (I_Kr), and a slow delayed rectifier K⁺ current (I_Ks).

Molecular biology has provided considerable information on the structure and function of ion channels, e.g., mechanistic information concerning ion channel gating and its modification by either genetic disease or pharmacological intervention. To be able to assess the consequences of these modifications, we used Markov models for several important currents: the Na⁺ current (I_Na), the L-type Ca²⁺ current (I_CaL), and I_Kr. Many genetic manipulations and diseases alter the kinetic properties of a single ion channel and can be related to changes in specific rate constants in the Markov models for these channels. Our mouse model can therefore be used to predict the kinetic consequences of many transgenic or pharmacological modifications on channel properties.

The main goal of this paper was to develop a computer model of the mouse ventricular AP that will provide insight into the ionic basis of AP behavior. We modeled the behavior of myocytes from the apex and the septum regions of the heart (36, 37, 69, 92) to demonstrate that the different regional expression of I_Kto,f, I_Kto,s, I_Kur, and I_Kss can account for regional differences in myocyte repolarization in the mouse heart. The model contains transmembrane pumps, currents, and exchangers and a detailed intracellular Ca²⁺-handling system based on data from voltage-clamp experiments on individual currents (e.g., steady-state inactivation, recovery from inactivation). We developed Markov models for the fast Na⁺ current (I_Na), the L-type Ca²⁺ current (I_CaL) and I_Kr. These formalisms allow for future investigation of the cellular mechanisms of arrhythmia generation due to genetic mutations or state-dependent binding that alter functional electrical properties such as restitution.

	METHODS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 
All animal procedures conformed to the "Guiding Principles for Research Involving Animals and Human Beings" of the American Physiological Society.

Preparation of Left Ventricular Myocytes

Mouse cardiac myocytes were prepared as described previously (48). Briefly, the heart was rapidly excised and submerged in Ca²⁺-free Tyrode solution containing (in mM) 140 NaCl, 5.4 KCl, 1 MgCl₂, 0.33 NaH₂PO₄, 10 glucose, and 5 HEPES adjusted to pH 7.4. The aorta was cannulated with a blunt-tip needle (20 gauge) placed on a perfusion apparatus. The heart was retrogradely perfused for 3 min with Tyrode solution and then perfused for 18 min with Tyrode solution with 2% calf serum (Sigma-Aldrich) and 75 U/ml each of collagenase type I and type II (Worthington). All solutions were continuously bubbled with 95% O₂-5% CO₂ at 37°C. Isolated myocytes were stored at room temperature in low-Cl^–, high-K⁺ solution (in mM: 70 KOH, 147 L-glutamic acid, 40 KCl, 20 taurine, 20 KH₂PO₄, 10 glucose, 10 HEPES, and 0.5 EGTA, adjusted to pH 7.3 with Tris base) before experiments. Calcium-tolerant, rod-shaped ventricular myocytes with clear striations were randomly selected for electrophysiological studies.

Cellular Electrophysiological Studies

Cell-attached patch-clamp macroscopic currents were recorded with an Axopatch 1D amplifier (Axon Instruments). A DigiData 1200 (Axon Instruments) controlled by pCLAMP software (Axon Instruments) was used to generate command pulses and acquire data. Electrodes (Garner Glass) had tip resistances of 1–4 M. For Na⁺ current measurement, the following extracellular solution was used (in mM): 40 NaCl, 5 CsCl, 20 TEA-Cl, 2.5 MgCl₂, 5 CoCl₂, 5 4-aminopyridine (4-AP), 10 glucose, 80 sucrose, and 5 HEPES adjusted to pH 7.3. The Na⁺ current intracellular solution contained (in mM) 110 CsCl, 20 TEA-Cl, 100 aspartic acid, 5 EGTA, 2 MgCl₂, 5 HEPES, 2 MgATP, and 0.1 Na₃GTP adjusted to pH 7.3. For Ca²⁺ current measurement, the extracellular solution contained (in mM) 130 TEA-Cl, 2 CaCl₂, 1 MgCl₂, 10 HEPES, 5 4-AP, and 10 sucrose adjusted to pH 7.3. The intracellular solution was the same as that used for I_Na measurement. For K⁺ current measurement, the pipette was filled with a standard internal solution containing (in mM) 100 L-aspartic acid, 110 KOH, 20 KCl, 2 MgCl₂, 5 EGTA, 5 HEPES, 2 Mg₂ATP, and 0.3 Na₃GTP, with pH adjusted to 7.2 with Tris base. Mouse ventricular myocytes were superfused at room temperature (20–22°C) with a HEPES-buffered Tyrode solution containing (in mM) 135 NaCl, 5.4 KCl, 1 MgCl, 2 CaCl₂, 5 HEPES, and 10 glucose, with pH adjusted to 7.3 with NaOH. I_CaL was blocked by 1 µM nifedipine, and Mg₂ATP in the pipettes suppressed the ATP-sensitive K⁺ current.

Simulation Methods and Simulated Voltage-Clamp Protocols

The model is based on a set of 40 ordinary differential equations solved by a fourth-order Runge-Kutta method, with a time step of 0.0001 ms. A summary of the equations, model parameters, and initial conditions is given in the APPENDIX. The model is nominally adjusted for room temperature of 25°C (298 K). Steady-state initial conditions were obtained by running the model until changes in all variables did not exceed 0.01%. Ryanodine receptor modulation factor P_RyR was set to 0 at the beginning of each AP.

We used two types of simulated voltage-clamp protocols: a double-pulse steady-state inactivation protocol and a variable-interval gapped pulse protocol. Usually, the double-pulse steady-state inactivation protocol involved a pulse (P1) to a voltage between the holding potential and + 50 mV (in 10-mV intervals), followed immediately by a second pulse (P2) to a holding potential specific to the current under investigation. The durations of the two pulses were set appropriately for the gating time constants of the given current. Other protocols are described in the text and figures. For I_CaL, P1 and P2 were separated by a 2-ms return to the holding potential, to match experimental protocols. APs were simulated for at least 100 cycles until a steady state was established, except for simulation of the negative staircase of Ca²⁺ transients, which began from a quiescent steady state.

The variable-interval gapped pulse protocol was used to determine the rate of recovery from inactivation. A P1 pulse was applied to activate and inactivate the channel, followed by a second pulse after a variable time interval. The degree of recovery from inactivation was calculated by comparing the peak P2 current to the peak P1 current. The depolarization, duration, and range of interpulse intervals used were specific to the current being studied. Unstimulated ventricular myocytes are quiescent, so we used an 0.5-ms 80 pA/pF stimulus current (I_stim) applied at a frequency of 0.5–6.7 Hz to trigger simulated APs.

Data Analysis

The electrophysiological data were analyzed by using Clampfit (Axon Instruments), Excel (Microsoft), and Origin (OriginLab). Clampfit was used for the exponential fitting of inactivation kinetics. Other nonlinear curve fittings were performed in Origin. The quality of the fit was evaluated by visual inspection and comparison of ²-values.

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 
We modeled cellular electrical activity in the mouse by using a nondistributed equivalent electrical circuit with subcellular compartmental spaces. This assumes that there are no electrical gradients within the cell itself, i.e., the membrane potential is spatially homogeneous and all subcellular compartments are uniform or "well stirred." A schematic representation of the currents, fluxes, and physical compartments of the model is shown in Fig. 1. In generating APs, the model mouse membrane potential (V) was determined by the following differential equation:

(1)

where C_m is membrane capacitance, I_Na is the fast Na⁺ current, I_CaL is the L-type Ca²⁺ current, I_Kto,f is the rapidly recovering transient outward K⁺ current, I_Kto,s is the slowly recovering transient outward K⁺ current, I_Kr is the rapid delayed rectifier K⁺ current (mERG), I_Kur is the ultrarapidly activating delayed rectifier K⁺ current, I_Kss is the noninactivating steady-state voltage-activated K⁺ current, I_K1 is the time-independent inwardly rectifying K⁺ current, I_Ks is the slow delayed rectifier K⁺ current, I_NaCa is the Na⁺/Ca²⁺ exchange current, I_p(Ca) is the Ca²⁺ pump current, I_NaK is the Na⁺/K⁺ pump current, I_Cl,Ca is the Ca²⁺-activated Cl^– current, I_Cab and I_Nab are the background Ca²⁺ and Na⁺ currents, and I_stim is the externally applied stimulation current. Our model has differential expression of I_Kto,f, I_Kto,s, I_Kur, and I_Kss in myocytes from the apex and the septum region of the mouse heart.

View larger version (28K): [in this window] [in a new window]   Fig. 1. Schematic diagram of the mouse model ionic currents and Ca2+ fluxes. Transmembrane currents are the fast Na+ current (INa), the L-type Ca2+ current (ICaL), the sarcolemmal Ca2+ pump [Ip(Ca)], the Na+/Ca2+ exchanger (INaCa), the rapidly recovering transient outward K+ current (IKto,f), the slowly recovering transient outward K+ current (IKto,s), the rapid delayed rectifier K+ current (IKr), the ultrarapidly activating delayed rectifier K+ current (IKur), the noninactivating steady-state voltage activated K+ current (IKss), the time-independent K+ current (IK1), the slow delayed rectifier K+ current (IKs), the Na+/K+ pump (INaK), the Ca2+-activated Cl– current (ICl,Ca), and the Ca2+ and Na+ background currents (ICab and INab). Istim is the external stimulation current. The Ca2+ fluxes within the cell are uptake of Ca2+ from the cytosol to the network sarcoplasmic reticulum (SR) (Jup), Ca2+ release from the junctional SR (Jrel), Ca2+ flux from the network SR (NSR) to junctional SR (JSR) (Jtr), Ca2+ leak from the SR to the cytosol (Jleak), Ca2+ flux from the subspace volume to the bulk myoplasm (Jxfer), and Ca2+ flux to troponin (Jtrpn). The model includes Ca2+ buffering by troponin and calmodulin in the cytosol and by calsequestrin in the SR. [Ca2+]i, [Na+]i, [K+]i, intracellular Ca2+, Na+, and K+ concentrations; [Ca2+]o, [Na+]o, [K+]o, extracellular Ca2+, Na+, and K+ concentrations.

Fast Na⁺ current I_Na. The fast transient Na⁺ current drives rapid depolarization at the upstroke of the ventricular AP. Most older models of I_Na were based on the Hodgkin and Huxley formalism of the neuronal AP, where inactivation is a single independent and completely absorbing state. I_Na inactivation is fast and relatively complete after depolarization, so the exact gating mechanisms of this channel were not considered in most previous AP reconstructions, despite evidence that a small noninactivated component of I_Na might play a role in repolarization (20, 22–24). Na⁺ channel inactivation has at least two components: fast and slow. Na⁺ channel mutations in the mouse heart that alter the slow component of inactivation can underlie a form of long QT syndrome (a frequently fatal genetic disease in other species). This suggests an important role for I_Na in the pathophysiology of arrhythmias (71). Consequently, more advanced Markov-type models are now beginning to be used to characterize I_Na during the AP (20, 22, 23, 29).

We used a Markov model for I_Na (22) with three closed states (C_Na1, C_Na2, and C_Na3), an open state (O_Na), a fast (IF_Na) and two intermediate (I1_Na and I2_Na) inactivated states, and two closed inactivation states (IC_Na2 and IC_Na3), as shown in Fig. 2. There is a reversible fast inactivation O_Na IF_Na transition, which we have attributed to the initial binding of the inactivation domain to the core domain. The second inactivation transition, IF_Na I1_Na, would then represent stabilization of the inactivation domain-receptor complex. Only a few channels enter the I2_Na state via slow transitions (22). A direct transition pathway between IF_Na, the fast-inactivated state, and the C_Na1 closed state was introduced to match inactivation recovery data (29). Inclusion of two closed-inactivation states, IC_Na2 and IC_Na3, allows for more accurate representation of Na⁺ channel availability (22). The transition rates were based on the model of Clancy and Rudy (22), with parameters adjusted to match mouse data. The transition rates and dynamic equations for I_Na are detailed in the APPENDIX. I_Na is described by the equation:

(2)

where G_Na is the whole cell conductance (mS/µF), E_Na is the Na⁺ reversal potential, and O_Na is the probability of the Na⁺ channel being in the open state.

View larger version (15K): [in this window] [in a new window]   Fig. 2. State diagram of the Markov model for the Na+ channel. CNa1, CNa2, and CNa3 are closed states; ONa is the open state; IFNa is the fast inactivated state; I1Na and I2Na are the intermediate inactivated states; and ICNa2 and ICNa3 are the closed-inactivation states (22). and are the transition rates between the states, as given in the APPENDIX.

View larger version (24K): [in this window] [in a new window]   Fig. 3. The fast Na+ current INa. A: a family of simulated current traces in response to a step depolarization. A 500-ms depolarizing pulse to between –130 and +50 mV was applied (in 10-mV increments) from a holding potential of –140 mV. Only the first 30 ms are shown to demonstrate details of activation and inactivation. B: peak INa-voltage relationship for simulated and experimental data. Data were simulated with 1.8 mM [Ca2+]o and 10 mM (solid line I), 52.5 mM (solid line II), or 140 mM [Na+]o (solid line III). , Our experimental data on mice (n = 20). Simulations with 10 mM (dashed line I) and 52.5 mM [Na+]o (dashed line II) have activation time constants negatively shifted by 15 mV to mimic experimental conditions with 0.5 mM [Ca2+]o [ (86), (51), (9)]. C: INa steady-state inactivation relationship. The simulated (solid line) and experimental steady-state inactivation data from double-pulse protocols are plotted against voltage. Experimental data from mice: (86), (51), (9). D: time constant of inactivation (Na) vs. voltage for simulated (solid line) and experimental data [ (86)]. Dashed line shows calculations of Na with activation time constants negatively shifted by 15 mV to simulate experimental conditions with [Ca2+]o = 0.5 mM, as predicted by surface charge effects (see Ref. 38 for a review).

Recovery from inactivation in the Na⁺ channel was simulated by using a gapped-pulse protocol with steps to –20 mV with an interstimulus holding potential of either –80 mV or –100 mV. The rate of recovery from inactivation is strongly dependent on the interstimulus holding potential, so two very different interpulse intervals (1–50 ms in 1-ms steps and 10–500 ms in 10-ms steps) were used. Fitting simulated recovery curves with a single exponential function showed that the time constant of recovery increased by a factor of 8 when the holding potential was reduced from –80 mV (time constant for recovery from inactivation _rec,Na = 71.5 ms) to –100 mV (_rec,Na = 8.6 ms). This compares well with our data from mouse myocytes (_rec,Na = 66.0 ± 1.9 at –80 mV; n = 5).

One of the advantages of using a Markov model is that transition rates can be modified to simulate the effects of mutations on gating. However, our model of I_Na gating has several important limitations. The most important of these stems from the size of I_Na and the consequential difficulty in measuring this current. I_Na is large and can cause resistive drops of 10 mV or more across the microelectrode tip, resulting in loss of voltage clamp control. Most investigators, therefore, partially block the channel or otherwise reduce conductance to maintain voltage clamp. These manipulations (e.g., reducing [Na⁺]_o or applying partial doses of blocker) are known to alter gating kinetics and equilibrium. Consequently, we also validated our model parameters for I_Na by comparing the calculated and experimental rate of maximal upstroke velocity (dV/dt_max) due to I_Na AP upstroke (see Mouse Action Potential below).

L-type Ca²⁺ current I_CaL. Perturbations in the amplitude and gating kinetics of I_CaL have been associated with many arrhythmias and pathological states such as failing, hypertrophic, stunned, ischemic, and hibernating myocardium (47). Activation of the L-type Ca²⁺ channel is a purely voltage-dependent process, similar to Na⁺ and K⁺ channel activation. The molecular basis of L-type Ca²⁺ channel inactivation is not fully understood. Inactivation of the L-type Ca²⁺ channel is both a time-dependent (i.e., apparently voltage dependent because of its coupling to activation) and a Ca²⁺-dependent process (43, 52). Ca²⁺-induced inactivation of the Ca²⁺ channel appears to be modulated by calmodulin (74), which may bind to the Ca²⁺-binding motif (EF hand) on the carboxy tail of the main _1C-subunit (53), thus transducing calmodulin binding into channel inactivation (75).

Describing the complex inactivation behavior of the L-type Ca²⁺ channel requires assumptions about coupling and inactivation biophysics. Jafri et al. (41) used a mode-switching Markov model for Ca²⁺ inactivation of the L-type Ca²⁺ channel to link inactivation to subspace [Ca²⁺]. The channel is modeled with four independent subunits that can close the channel and whose mode of operation is determined by intracellular Ca²⁺ binding. Transitions between the two modes are controlled by a Ca²⁺-dependent factor, . The probability of entering the Ca²⁺ mode is dependent on voltage, conformation, and subspace [Ca²⁺]. This model makes little use of the emerging structure and function information from voltage-gated channels and fails to model recovery from inactivation.

We developed a new Markov model to describe L-type Ca²⁺ channel dynamics (Fig. 4), based on homology and extrapolated structure-function relationships of Shaker B voltage-gated K⁺ channels. Our model has two inactivation states, one of which is a Markov representation of "ball and chain" inactivation in which the ball binding is Ca²⁺ dependent (74, 75). The model Ca²⁺ channel has four closed states (C₁, C₂, C₃, and C₄), one open state (O), and three inactivated states (I₁, I₂, and I₃). Activation is controlled by the voltage-dependent rate constants, and . Transitions from O to I₁ correspond to a relatively fast Ca²⁺-dependent inactivation, controlled by the Ca²⁺-dependent rate constant . Transitions from O to I₂ represent relatively slow voltage-dependent inactivation and are controlled by the rate constants and K_pcf (forward voltage-insensitive rate constant). The I₃ inactivated state represents a channel with both Ca²⁺- and voltage-dependent inactivation. Direct transitions between the closed state C₄ and the inactivated states I₁, I₂, and I₃ result in a voltage-dependent recovery from inactivation. All rate constants fulfill the condition of thermodynamic reversibility (for review see Ref. 38), i.e., the product of the rate constants in any clockwise loop is equal to that of the same loop measured in a counterclockwise direction.

View larger version (17K): [in this window] [in a new window]   Fig. 4. State diagram of the model L-type Ca2+ channel. C1, C2, C3, and C4 are closed states; O is the open state; and I1, I2, and I3 are inactivated states. The rate constants and are voltage dependent, and is calcium dependent. Kpcf and Kpcb are the forward and backward voltage-insensitive rate constants, respectively.

(3)

where G_CaL is the whole cell conductance (mS/µF), E_Ca,L is the L-type Ca²⁺ channel reversal potential, and O is the channel open probability.

Sarcoplasmic reticulum. No matter how well the Ca²⁺ channel is modeled, it cannot be considered in isolation from its surroundings. In ventricular myocytes, L-type Ca²⁺ channels are found mostly in clusters in the T-tubules directly opposed to the ryanodine receptors on the sarcoplasmic reticulum (SR) (13). Ca²⁺ that enters the cell as part of I_CaL initiates Ca²⁺-induced Ca²⁺ release from the SR, which then contributes to Ca²⁺-dependent inactivation of the Ca²⁺ channel (10, 30, 31). A more physiologically realistic model of the L-type Ca²⁺ channel must therefore include an appropriate representation of the SR release channels and the local [Ca²⁺] near the L-type Ca²⁺ channel.

Ca²⁺ fluxes in and around the SR are shown in Fig. 1. Ca²⁺ entering the cell via through I_CaL results in a localized increase in [Ca²⁺] ([Ca²⁺]_ss) in a restricted subsarcolemmal space. [Ca²⁺]_ss both inactivates the L-type Ca²⁺ channel and initiates Ca²⁺-induced Ca²⁺ release, which further adds to Ca²⁺ channel inactivation. Ca²⁺ diffuses from the subsarcolemmal space to the general cytosol, where it binds to contractile proteins and initiates contraction. Ca²⁺ is removed from the cytosol by translocation across the sarcolemmal membrane by the Na⁺/Ca²⁺ exchanger and the sarcolemmal Ca²⁺ pump and taken back into the network SR by Ca²⁺-ATPase. Ca²⁺ diffuses from the network SR to the junctional SR, where it can be released into the subsarcolemmal space once more. The equations governing the time dependence of the ryanodine receptor are based on those of Keizer and Levine (45). We also modified the Jafri et al. (41) model of Ca²⁺ dynamics to match Ca²⁺ transients reported for the mouse. A Gaussian distribution function and integral of the time course of I_CaL were used to modulate Ca²⁺ release and simulate graded release of Ca²⁺ from the intracellular store (Eq. A15, APPENDIX). Incorporation of local effects of Ca²⁺ release in our mouse model allowed simulation of Ca²⁺ sparks, the elementary units of Ca²⁺ signaling, and a precise description of Ca²⁺ handling and Ca²⁺ channel inactivation that resembles that of more complex biophysically based models (12).

Simulated I_CaL voltage-clamp studies are shown in Fig. 5. A conventional double-pulse protocol was used with a 250-ms P1 pulse stepping from –80 to between –70 and +40 mV followed by a 2-ms return to –80 mV and then a 250-ms P2 pulse to +10 mV. The biexponential current decay is typical for I_CaL from mouse myocytes (see, for example, Ref. 88). The half-time of simulated I_CaL decay at +10 mV was 4.2 ms, which is smaller than the corresponding experimental value of 8 ms obtained by Wang et al. (90). However, the calculated fast inactivation time constant _1,CaL = 4.45 ms compares well to the experimental value of 4.7 ± 0.2 ms obtained by Kirchhefer et al. (49), but is somewhat smaller than 12.28 ± 1.29 ms (82) and 7.92 ± 0.74 ms (81) obtained by Santana et al. The simulated slow inactivation time constant _2,CaL = 16.1 ms is close to the value of 22.47 ± 1.89 ms obtained by Santana et al. (82); however, it is somewhat smaller than the measured values of 56.1 ± 2.6 ms observed by Kirchhefer et al. (49) and 48 ± 1.35 ms recorded by Santana et al. (81). The variability in time constants for the components of inactivation between laboratories probably reflect different experimental conditions (e.g., amount of EGTA, effectiveness of perfusion through electrode tip, isolation procedures, ionic conditions) that can effect both Ca²⁺- and voltage-dependent inactivation. The simulated traces in Fig. 5A mimic control conditions without EGTA or other nonintrinsic buffers and so are closest to the fastest time constants, which we assumed had the least perturbation from altered Ca²⁺ handling. When Ca²⁺-release flux during simulation is decreased by 20-fold to mimic the effect of strong buffering by EGTA, the rate of decay of I_CaL is reduced, with fast and slow time constants equal to 8.8 and 57.3 ms, respectively (V = +10 mV).

View larger version (20K): [in this window] [in a new window]   Fig. 5. The L-type Ca2+ current ICaL. A: a family of simulated current traces. A 250-ms depolarizing first pulse to between –70 and +40 mV (in 10-mV increments) was applied from a holding potential of –80 mV. This was followed by a brief 2-ms return to –80 mV before a second 250-ms pulse to +10 mV. B: peak ICaL voltage relationships for simulated and experimental data. The solid line shows data from simulations under normal physiological extracellular ion concentrations (see APPENDIX), and the dashed line shows data simulating the experimental conditions of Yatani et al. (96). , Our mouse data (n = 5). Other experimental results: (48), (96), (88), (15), (50). C: steady-state inactivation relationships for 500-ms P1 pulse simulations (dashed line), and 5-s P1 pulse simulations with buffered Ca2+ (solid line). , Our data from 5-s P1 pulses and [Ca2+]i buffered with 5 mM EGTA (n = 5); , experimental measurements of Yatani et al. (96), which were buffered with 10 mM BAPTA. D: voltage dependence of simulated fast and slow inactivation time constants 1,CaL and 2,CaL.

Figure 6A shows the bulk intracellular [Ca²⁺] ([Ca²⁺]_i) and subspace volume [Ca²⁺]_ss transients in response to a step depolarization to 0 mV and corresponding experimental data (42). The simulated [Ca²⁺]_i time to peak of 14.8 ms and half-time of decay of 33.6 ms compare well with the experimental values of 17 ms and 34 ms, respectively (90).

View larger version (18K): [in this window] [in a new window]   Fig. 6. Intracellular Ca2+ transients. A: simulated [Ca2+]i transients and Ca2+ subspace volume concentration ([Ca2+]ss) in response to a step depolarization to 0 mV. , Experimental data for [Ca2+]i transients from Ref. 42, normalized to peak simulated concentration. B: voltage dependence of simulated [Ca2+]i () and peak ICaL (). These data show graded release of Ca2+ from the SR.

Figure 7 shows the results of a simulated variable-gap double-pulse protocol. Two 250-ms pulses to 0 mV were applied with an interstimulus interval of between 2 and 500 ms for three different interpulse holding potentials. Recovery from inactivation was approximated by a single exponential function with time constants _rec,Ca equal to 19, 39, and 77 ms for three holding potentials, –90, –80, and –70 mV, respectively. These simulations suggest a moderate voltage dependence of recovery. However, no data exist on the voltage-dependent recovery of I_CaL in mouse myocytes. The L-type Ca²⁺ channel in bullfrog sinus venosus and atrium (17) and in rat and rabbit ventricles (97) shows voltage dependence in this range, with recovery becoming faster with hyperpolarization. Voltage-dependent recovery is also consistent with the general properties of recovery from other voltage-gated channels (see Ref. 38 for a review).

View larger version (21K): [in this window] [in a new window]   Fig. 7. ICaL recovery from inactivation. A: simulated currents from a gapped-pulse protocol used to measure recovery from inactivation. A 250-ms pulse (P1) to 0 mV from the holding potential of –80 mV was followed by a 100-ms pulse (P2) to 0 mV after an interstimulus interval of between 2 and 502 ms, in 25-ms increments. B: peak P2 current plotted against time was fitted with a single exponential function (solid line). , , and , Interpulse holding potentials of –90, –80, and –70 mV, respectively.

(4)

where G_Kto,f is the maximum whole cell conductance (mS/µF), E_K is the K⁺ reversal potential, and a_to,f and i_to,f are the activation and inactivation gating variables. Equations for a_to,f and i_to,f are given in the APPENDIX. This current is equivalent to I_to,f in mouse ventricular myocytes (92).

Mouse ventricular myocytes show substantial regional heterogeneity in repolarization characteristics and can be divided into several types depending on both the anatomic location and the number and type of K⁺ currents present (37, 92). We modeled ventricular myocytes from two regions: the apex and the septum. The fundamental differences between these cells are the APD and density of K⁺ currents present (37, 92).

Figure 8 shows the combined depolarization-activated simulated K⁺ currents (I_K,sum) from the apex and septum when depolarized from a holding potential of –80 mV to between –70 and +50 mV in 10-mV steps. Both simulations are in qualitative and quantitative agreement with the experimental results (92). In our model, there are seven types of K⁺ currents: the rapid transient outward K⁺ current (I_Kto,f), the slow transient outward K⁺ current (I_Kto,s), the rapid delayed rectifier K⁺ current (I_Kr), the ultrarapidly activating delayed rectifier current (I_Kur), the noninactivating steady-state K⁺ current (I_Kss), a very small slow delayed rectifier (I_Ks), and the time-independent K⁺ current (I_K1).

View larger version (14K): [in this window] [in a new window]   Fig. 8. Total depolarization-activated K+ currents (IK,sum) from different regions of mouse heart. Simulated currents were elicited by a 5-s depolarizing step to between –70 and +50 mV in 10-mV increments from a holding potential of –80 mV. A: model apical cell. B: model septal cell.

View larger version (21K): [in this window] [in a new window]   Fig. 9. The rapidly inactivating transient outward K+ current IKto,f. A: simulated double-pulse protocol current traces from a 500-ms pulse to between –100 and +50 mV (in 10-mV increments) from the holding potential of –80 mV followed by a 500-ms second pulse to +50 mV. B: peak IKto,f-voltage relationships for the apex and the septum. Simulated results from the apex and septum are shown as solid lines; , experimental data (apex; Ref. 92). Activation is shifted slightly negative to compensate for the effects of divalent ions used to block Ca2+ currents during the experiments (1). C: steady-state inactivation relationships. The simulated (solid line) relationships were calculated from a double-pulse protocol. Experimental results from mouse: (92) and (87). D: time constants of activation and inactivation (act and inact). Simulated results are shown by bold solid lines. Mouse experimental data for inactivation: (87), (100), and (1 data point only at +40 mV; Ref. 92). Experimental data for activation: (92) and (93). The dashed line shows the calculated activation time constant, shifted positive to fit the experimental conditions (92) with divalent ions.

A simulated gapped-pulse protocol was used to determine the rate of recovery of I_Kto,f from inactivation. Two pulses to +50 mV from the holding potential of –70 mV were applied with an interstimulus interval of 10–500 ms. The simulated recovery time constant was _rec,Kto,f = 27.4 ms, which is close to the experimental value of 27 ms recorded in the mouse (92). The time constants of recovery are identical for I_Kto,f from the apex and the septum (92).

Slow-inactivating transient outward K⁺ current I_Kto,s. The slow-inactivating K⁺ current, I_Kto,s, presumably encoded by Kv1.4, is present in cardiac myocytes from the septum region, but largely absent from other regions of the heart (92). The slowly recovering inactivating K⁺ current might be considered a compensatory current, because it is present in septal cells where there is a considerably smaller I_Kto,f and in ventricular myocytes from mice in which I_Kto,f has been transgenically deleted (7, 36, 69). The model formulation of I_Kto,s is:

(5)

where G_Kto,s is the maximum whole cell conductance (mS/µF) and a_to,s and i_to,s are the activation and inactivation gating variables.

Figure 10A shows simulated current traces in response to a series of step depolarizations from –100 to between –90 and +50 mV in 10-mV increments. The inactivation rate of I_Kto,s is voltage independent, with a time constant of 270 ms that corresponds to the experimental value of 258 ± 15 ms (92). The simulated and experimental peak current-voltage relationships are shown in Fig. 10B. Figure 10C shows the simulated and experimental steady-state activation and inactivation functions of I_Kto,s. Our model was developed to simulate experimental currents recorded in the absence of Ca²⁺ channel blockers (16). Data obtained in the presence of divalent ionic blockers of the Ca²⁺ channel, such as 2 mM CoCl₂, showed a positive shift in activation and inactivation due to the surface charge effect (99). We therefore adjusted our model gating parameters to fit data and account for the shift in activation and inactivation. Figure 10D shows the voltage dependence of time constants of activation for I_Kto,s. The simulated time constant for recovery from inactivation is 1.306 s, which compares well with the experimental value of 1.298 s (92).

View larger version (18K): [in this window] [in a new window]   Fig. 10. The slow inactivating transient outward K+ current IKto,s. A: families of simulated traces for IKto,s for the septum. Depolarizing pulses of 5 s were applied to between –90 and +50 mV in 10-mV increments from the holding potential of –100 mV. B: peak IKto,s-voltage relationships for the septum. Simulated results are shown as a solid line; , experimental data (92). C: steady-state activation and inactivation relationships for the IKto,s. Solid lines show simulated results, and circles with dashed lines show data from Ref. 99. Note that the experimental data (99) are shifted because of the effect of divalent ions (Co2+). D: time constant of activation for IKto,s. , Experimental data from Ref. 99; solid lines, simulated data.

(6)

I_Kr is described by the following equation:

(7)

where G_Kr is the whole cell conductance (mS/µF), O_K is the probability of the channel being in the open state, R is the ideal gas constant, F is the Faraday constant, and [K⁺]_o and [K⁺]_i are the K⁺ concentrations outside and inside the cell, respectively. The driving force for permeation through I_Kr has some permeability to Na⁺ to account for the experimentally observed reversal potential in ventricular myocytes (10 mV positive to E_K). Simulated I_Kr in response to a double-pulse voltage-clamp protocol is shown in Fig. 11. P1 was a 1-s pulse from the holding potential (–80 mV) to between –70 and +50 mV in 10-mV steps, and P2 was a second 1-s pulse to –40 mV. The simulated currents are comparable to experimental results from I_Kr (57). The calculated value of maximum I_Kr amplitude of 0.25 pA/pF was chosen to be close to experimentally observed value in adult mice (57). Our representation of I_Kr as a linear Markov model does not permit inactivation from closed states. Single-channel experiments suggest that these transitions can occur (46), and they have been included in other I_Kr models (21). Kiehn et al. (46) described a relatively rapid flicker state, which allows the channel to inactivate without opening when inactivation is sufficiently fast and complete at positive potentials. There is no experimental evidence that the flicker state is part of the activation process or that it has any consequences for drug binding or burst duration. For macroscopic currents, this flicker is readily addressed as a reduced conductance with a mean lifetime equal to burst duration. We have treated it as such in this model, so as not to complicate the model with a rapid time constant.

View larger version (14K): [in this window] [in a new window]   Fig. 11. The rapid delayed rectifier K+ current IKr: a family of simulated IKr current traces. A 1-s depolarizing pulse from –70 to +60 mV was applied (in 10-mV increments) from a holding potential of –80 mV followed by a 1-s second pulse to –40 mV.

(8)

(9)

where G_Kur and G_Kss are the maximum whole cell conductances (mS/µF), a_ur and a_Kss are activation gates, and i_ur and i_Kss are inactivation gates, described in detail in the APPENDIX. I_Kur and I_Kss correspond to I_K,slow and I_ss, respectively (92). We chose to use the I_Kur terminology to emphasize the rapid activation, as opposed to the slow inactivation that is characteristic of these channels. Use of this terminology also emphasizes the similarity of this current to I_Kur in human atrium (for review, see Ref. 68). These currents are present in both the apex and the septum, but with different expression levels. The model parameters were chosen to fit mouse experimental data (92).

Figure 12 shows simulated currents in response to a series of step depolarizations from –100 to between –90 and +50 mV in 10-mV intervals. The inactivation rate of I_Kur is voltage independent and can be fit with a single exponential function (92). The simulated time constant of inactivation is 1,198 ms, which compares well with the experimental value of 1,180 ± 45 ms (92). I_Kss shows little inactivation in either simulation or experiment (92).

View larger version (14K): [in this window] [in a new window]   Fig. 12. Families of simulated traces for the ultrarapidly activating delayed rectifier current (IKur; A) and the noninactivating steady-state K+ current (IKss; B) for the septum. Depolarizing pulses of 5 s were applied to between –90 and +50 mV in 10-mV increments from the holding potential of –100 mV.

View larger version (20K): [in this window] [in a new window]   Fig. 13. The ultrarapidly activating delayed rectifier K+ current IKur and the noninactivating steady-state K+ current IKss. Simulated peak current-voltage relationships for IKur (circles) and IKss (triangles) are shown. Data from the apex are open symbols; data from the septum are filled symbols. A: simulated data. B: experimental data from Xu et al. (92). C: steady-state inactivation relationships for IKur. Solid line is simulated steady-state inactivation; squares with dashed line show experimental data from Ref. 16. D: IKur and IKss activation time constants. and , Experimental data for IKur and IKss, respectively (92); solid lines, simulated results.

(10)

The equations governing the activation gate, n_Ks, are shown in the APPENDIX. Simulated voltage-clamp data for I_Ks are shown in Fig. 14. I_Ks does not significantly affect AP shape under control conditions; however, it can be of potential importance in experiments where other K⁺ currents are knocked out.

View larger version (15K): [in this window] [in a new window]   Fig. 14. The slow delayed rectifier K+ current IKs: A family of simulated current traces. Depolarizing pulses were applied to between –70 and +50 mV (in 10-mV increments) from the holding potential of –80 mV.

(11)

where G_Cl,Ca is the maximum whole cell conductance (mS/µF), O_Cl,Ca is the probability of the channel being in the open state, K_m,Cl is the half-saturation constant, and E_Cl is the Cl^– reversal potential. This small-amplitude current was recently discovered by Xu et al. (94). Experiments (94) and simulations (not shown) suggest that the current does not affect the AP shape under control conditions. However, the current may be important under pathophysiological conditions that result in abnormal cellular Ca²⁺ loading.

Time-independent K⁺ current I_K1. The I_K1 equation in our model is based on that of DiFrancesco and Noble (27):

(12)

Figure 15 shows simulated and experimental (7, 50, 88) peak current-voltage relationships in response to a pulse from the holding potential of –80 mV to voltages from –150 to –40 mV. Simulated and experimental results give currents of similar magnitude.

View larger version (11K): [in this window] [in a new window]   Fig. 15. The time-independent potassium current IK1. The current-voltage relationship for IK1 from simulations is shown as a solid line with experimental data for comparison [ (88), (50), at –120 mV only (7), and (our data)].

(13)

(14)

where G_Cab is the background Ca²⁺ conductance, G_Nab is the background Na⁺ conductance, E_CaN is the Ca²⁺ reversal potential, and E_Na is the Na⁺ reversal potential. These currents normally maintain ionic homeostasis.

Na⁺/Ca²⁺ exchange current I_NaCa. The equation representing I_NaCa is based on that of Luo and Rudy (62):

(15)

where K_m,Na is the Na⁺ half-saturation constant for I_NaCa, K_m,Ca is the Ca²⁺ half-saturation constant, k_sat is the saturation factor at very negative potentials, and = 0.35 is the position of the energy barrier that controls the voltage dependence of I_NaCa. I_NaCa plays an important role in mouse myocyte Ca²⁺ dynamics (84). The absolute value of I_NaCa does not exceed 1.0 pA/pF within the range –120 to +40 mV. The scaling factor k_NaCa was chosen to ensure equilibrium intracellular ionic concentrations of Na⁺ and Ca²⁺ within experimental values and to match the experimental ratio of Ca²⁺ extruded by the SR ATPase to Ca²⁺ expelled from the cell via I_NaCa during a myocyte twitch.

Sarcolemmal Ca²⁺ pump current I_p(Ca). I_p(Ca) is taken from the Luo and Rudy (62) model:

(16)

where I_p(Ca)^max is the maximum Ca²⁺ pump current and K_m,p(Ca) is the Ca²⁺ half-saturation constant.

Na⁺/K⁺ pump current I_NaK. I_NaK was modeled by using the Luo and Rudy (62) formulation:

(17)

(18)

(19)

where I_NaK^max is the maximum pump current, K_m,Nai is the Na⁺ half-saturation constant, and K_m,Ko is the K⁺ half-saturation constant. This current maintains Na⁺ and K⁺ electrochemical gradients across the cell membrane. I_NaK^max was optimized to reproduce experimental values of quiescent [Na⁺]_i and [K⁺]_i for mouse myocytes.

Quiescent Cellular Properties

To calculate the steady-state resting cellular parameters, the mouse model was allowed to run for at least 1,000 s with no external stimulation. The currents that determine the resting membrane potential are I_K1, I_NaCa, I_p(Ca), I_NaK, and the background currents I_Cab and I_Nab. The reversal potential of the time-independent K⁺ current is the major determinant of the resting potential of the quiescent model myocyte. The resting potential of the cell is only 1.8 mV positive to the reversal potential for I_K1. I_NaK pumps Na⁺ out of and K⁺ into the cell, thus maintaining [Na⁺]_i and [K⁺]_i. At rest, I_NaCa extrudes Ca²⁺ and brings Na⁺ into the myocyte, contributing to equilibration of intracellular ion concentrations. The sarcolemmal Ca²⁺ pump carries Ca²⁺ out of cell. The magnitudes of these currents were chosen so that the resting potential and equilibrium intracellular ion concentrations were within experimental values (see Table 8 in APPENDIX).

The mouse APD is region dependent (37), with cells from the septum in general having longer APDs than those from the apex (37). Figure 16 , A and D, shows simulated APs for these two regions obtained with a 1-Hz stimulation rate. APs were obtained after at least 100 s of continuous simulation to ensure that a steady-state solution has been reached. In the apex, the experimental value of APD₅₀ is 4.5 ± 0.3 ms, which is somewhat longer than the simulated value of 4.0 ms. In the septum, the experimental APD₅₀ is 8.5 ± 0.3 ms and the simulated APD₅₀ is 7.6 ms. Regional differences in AP shape are also evident at other potentials. There is close agreement at APD at 25% of repolarization (APD₂₅), with simulated values of 2.0 and 3.4 ms for apex and septum, respectively, compared with the experimentally observed values of 2.3 ± 0.1 and 4.0 ± 0.2 ms (37). There is also close agreement at APD at 75% of repolarization (APD₇₅), with simulated values of 11.3 and 16.1 ms for apex and septum, respectively, compared with the experimental values of 10.0 ± 1.2 and 20.9 ± 1.3 ms (37). These data are presented in Table 1.

View larger version (26K): [in this window] [in a new window]   Fig. 16. Simulated action potentials (APs) and underlying currents of the mouse ventricular myocyte model. A: the apical AP. B and C: currents underlying the apical AP. D: the septal AP. E and F: currents underlying the septal AP. The scale for the relatively large Na+ current INa is given on axis on right in B and E. All other currents are scaled to the axis on left. Pacing frequency was 1 Hz.

Immediately after depolarization, the membrane potential falls to approximately –20 mV and the shape of the AP is determined by competition between several currents. The major contributors in apical myocytes are I_Kto,f, I_Kur, I_Kss, and I_CaL. In septal cells, I_Kto,s also contributes to repolarization. The outward K⁺ currents slow the rate of depolarization and initiate repolarization, opposing and dominating the depolarizing inward current, I_CaL. I_Kto,f is relatively large in the apex, where the membrane potential decreases rapidly, resulting in an APD₅₀ of 4.0 ms. In the septum, I_Kto,f is relatively small and comparable to I_Kur and I_Kss. This results in the longer septal AP (APD₅₀ 7.6 ms). This relatively prolonged depolarization affects other voltage-dependent currents, which in turn affect cellular Ca²⁺ dynamics and excitation-contraction coupling. The maintained depolarization decreases the amplitude but increases the duration of I_CaL. It also increases the duration of Ca²⁺ influx via I_NaCa (Fig. 16, C and F).

The final stage of repolarization is relatively slow and is controlled by the slower K⁺ currents and the Na⁺/Ca²⁺ exchanger (I_Kto,s, I_Kur, I_Kss, I_K1, and I_NaCa). I_Kur and I_Kss are slightly larger in the apex than in the septum. However, the septum has an additional K⁺ current, I_Kto,s (4.2 pA/pF), and a relatively small I_Kto,f (6.8 pA/pF) compared with the apex (25.9 pA/pF). These differences in K⁺ current magnitudes result in differing repolarization rates and APDs. The resting potential is maintained by the balance between inward (I_Cab, I_Nab, and I_NaCa) and outward [I_p(Ca), I_K1, and I_NaK] currents (Fig. 16, C and F). Our model suggests that the regional difference in shape and duration of the mouse cardiac AP is a result of the relative magnitudes of I_Kto,f and I_Kto,s. I_Kto,f dominates the rapid repolarization of the apex where I_Kto,s is absent, whereas the smaller I_Kto,f and additional I_Kto,s mediate the slower septal repolarization.

Ca²⁺ Dynamics During AP

Figure 17 shows simulated APs from the apex and septum for different pacing periods, ranging from 150 to 2,000 ms. Simulated data were obtained after 100 s of stimulation. There is little change in AP shape with stimulation frequency, which is consistent with experimental data (36). Rat epicardial myocytes show a similar rate insensitivity (73). The simulated time course of decay of [Ca²⁺]_i after an action potential is 183 and 165 ms for the apex and the septum, respectively. These values are well within the range of experimental observations of 126 ± 11 (34), 188 ± 14 (54), 190 (39), 184 ± 22 (95), 210 (15), and 293 ± 19 (64) ms.

View larger version (25K): [in this window] [in a new window]   Fig. 17. Simulated APs (A, C) and intracellular Ca2+ transients (B, D) for the apex (A, B) and the septum (C, D). Pacing periods were 150, 250, 500, 1,000, and 2,000 ms. There was little change in AP shape with pacing frequency. However, once the model reached steady state, there was a decrease in the magnitude of the [Ca2+]i transients as the stimulation frequency increased because of changes in Ca2+ accumulation in the SR.

View larger version (16K): [in this window] [in a new window]   Fig. 18. Experimental peak (open symbols) and basal (filled symbols) [Ca2+]i transients during mouse AP excitation vs. stimulation frequency. Circles and triangles show simulated data for the apex and septum, respectively. Squares and diamonds show experimental data from Refs. 2 and 40, respectively, which were not regionally isolated. [Ca2+]i transients show a minimum at pacing frequencies of 1 Hz in experimental data (40) and between 1 and 2 Hz in simulated data.

View larger version (23K): [in this window] [in a new window]   Fig. 19. The negative staircase of electrically evoked [Ca2+]i transients. After a protracted quiescent period, the initial Ca2+ transient is large, and it decreases with continued pacing. A: experimental data. Image modified with permission from Ref. 39. B: simulation for apical cells. C: simulation for septal cells. Pacing period is 1.3 s.

View larger version (27K): [in this window] [in a new window]   Fig. 20. Calcium handling during one cardiac cycle. Ca2+ fluxes (A, C) during the AP and the integral of the Ca2+ fluxes (B, D) for various Ca2+-handling pathways. A and B: apex. C and D: septum. Ca2+ release flux (Jrel) is shown on the right axis. Simulations are shown for 1 cycle at 1 Hz after 10 stimulations. Data in A and C show the fluxes during the first 60 ms after the stimulus. B and D show the integral of the net fluxes over the entire 1-s cycle.

	DISCUSSION

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 
Development of Model

The aim of this study was to develop a model of the isolated mouse ventricular myocyte that reproduces the cellular AP. The model is based on available experimental voltage-clamp data from various membrane currents present in the mouse heart. Wherever possible, the currents have been related to structure and function data, including regional heterogeneity. We tested the model currents against experimental voltage-clamp data and used molecularly based Markov models for the fast Na⁺ (I_Na), L-type Ca²⁺ (I_CaL), and rapid delayed-rectifier K⁺ (I_Kr) channels. Simulations of AP upstroke dV_m/dt, decline of [Ca²⁺]_i transients during twitch, or APD₂₅, APD₅₀, and APD₇₅ served as additional validation of the model. We included a variety of optional K⁺ channel types to account for the experimentally observed regional diversity in AP shape and duration.

The simulated AP was relatively short, which is characteristic of the mouse myocyte. The kinetic behavior of the currents present in our mouse model are similar to those found in other mammalian cardiac myocytes with much longer APDs, consistent with the molecular similarity of these currents. The main factor in generating the short mouse AP is not differing channel kinetics but the relative magnitude of the currents present. Mouse ventricular myocytes have large outward K⁺ currents, which ensure rapid repolarization. An additional factor, which has been noted previously (11), is that mice, like other rodents, have extremely fast Ca²⁺-handling mechanisms. This means that they require significantly less Ca²⁺ influx via sarcolemmal mechanisms to trigger Ca²⁺ release from the intracellular stores. The released Ca²⁺ leads to a rise in systolic Ca²⁺ and ultimately triggers contraction. In mammalian models with longer APDs (25, 55, 62, 63, 72, 91), a larger percentage of the systolic Ca²⁺ transient is due to transsarcolemmal sources rather than to Ca²⁺ release from intracellular stores. In summary, it appears that multiple ionic mechanisms are adapted to the rapid beating required of a mouse heart.

A model of the mouse ventricular myocyte is an important tool in understanding the many type of transgenic mice that have been created to mimic various aspects of abnormal electrical behavior in the heart (7, 42, 48, 60, 69, 93, 100). Gene knockout experiments on ion channels almost invariably lead to compensatory changes and upregulation of other ion channels (7, 37, 69). For example, an -myosin mutation (associated with human atrial arrhythmias) alters ionic homeostasis when expressed in the mouse ventricle. This illustrates the limitations of the reductionist approach to understanding biological function. A primary defect may be localized to only a few atoms on a single molecule. However, the final phenotype resulting from the mutation is a consequence of both the defect and the response of the organism, which may result in seemingly unrelated pathologies. This pattern of adaptation of multiple subcellular systems to fit the physiological requirements for function carries through to the cellular responses to transgenic manipulation.

The lack of complete knowledge about cellular parameters may be a limitation in some respects, but dealing with this uncertainty has also been one of the strengths of systems biology in general and the study of repolarization in particular. In cardiac muscle, models of repolarization have long played an important role. The models have been developed in parallel with or even in advance of experimental validation. The earliest model of cardiac repolarization was made by postulating the presence of a diminished outward K⁺ current with slow kinetics, coupled with a sustained inward current (70). Although the exact nature of the K⁺ currents has changed and the inward current is generally thought to be carried primarily by Ca²⁺ instead of Na⁺, the general concepts spurred further investigation. Similarly, subsequent models, such as those of McAllister, Noble, and Tsien (66), Beeler and Reuter (8), DiFrancesco and Noble (27), and Luo and Rudy (62, 63, 98), all had severe limitations in parameters and descriptions of component currents but provided an essential framework in which the behavior of the cell and repolarization as a system could be quantitatively and qualitatively discussed and potential mechanisms could be evaluated and explained.

Our model, and the formulations within it, reflects advances in our understanding of how the mouse ventricular myocyte functions during excitation and repolarization. Equally importantly, the formulations within this model have been developed to parallel advances in our ability to manipulate the cellular system. Thus the main currents and transporters have been associated with specific molecular bases. Although this renders the model more complex in terms of the total number of currents included, it allows the model to be used to interpret data from molecular biology and transgenic experiments.

Incorporation of structure and function information from molecular biophysics is another important component of this cellular model. For many channels, we have moved away from the Hodgkin and Huxley type of formalism in favor of Markov-type models. Markov models have the advantage of being more closely related to the underlying structure and conformation of the ion channel proteins. Clancy and Rudy (20) demonstrated that this is extremely important for relating genetic defects that result in altered channel function to the pathological phenotype. In other cases, e.g., HERG or the L-type Ca²⁺ channel, conventional Hodgkin and Huxley formalisms simply fail to reproduce channel behavior (58). However, models of individual ion channels and subcellular systems are, by themselves, areas of intense research interest. For example, there is considerable debate as to how the Ca²⁺ channel and its coupling to the Ca²⁺-release subsystem should be modeled. We had to make choices between alternative formulations, some of which are clearly controversial. Some of these choices and their relationship to other models and mechanisms of repolarization in other cardiac myocytes are discussed in Mechanisms, Formalisms, and Limitations.

Mechanisms, Formalisms, and Limitations

Different species have APs with differing AP shapes and durations, with various mechanisms of repolarization. The molecular basis for AP initiation in atrial and ventricular myocytes of working myocardium is consistently the fast Na⁺ current I_Na (8, 41, 62, 63, 66, 70, 72, 73, 76). Its role in initiating depolarization and sustaining conduction is similar to that originally described for the squid axon AP. On a molecular level, cardiac I_Na is mediated by a cardiac-specific -subunit isoform that is relatively insensitive to the neurotoxin TTX. Many of the kinetic properties of I_Na are dependent on coassembly of the -subunit with ancillary subunits. These subunits strongly modify the inactivation and recovery properties of the -subunit of the channel. I_Na has two types of inactivation with differing molecular bases, termed "fast" and "slow." Fast inactivation is strongly dependent on a small "flap" of cytoplasmic-facing lipophilic amino acids, and slow inactivation is related to other regions. These two mechanisms have been suggested to be similar to the N- and C-type inactivation mechanisms studied in the distantly related voltage-gated K⁺ channels (78).

Although early cardiac models hypothesized a major role for a noninactivating component of I_Na during repolarization, later models considered I_Na to inactivate completely and contribute little to the plateau phase of repolarization. However, the discovery of a human Na⁺ channel defect that alters the slow component of inactivation and results in QT prolongation generated new interest in the role of I_Na and slow inactivation during repolarization. The role of slow inactivation in producing this phenotype was elegantly described by Clancy and Rudy (20) and demonstrated the importance of the use of Markov models that relate to the molecular basis of gating.

Recent advances in the molecular basis of voltage-gated ion channels indicates that activation and inactivation are not independent processes (38). Furthermore, similar mechanisms of inactivation appear to operate across a wide variety of channels. In Ca²⁺ channels, the Ca²⁺ dependence of inactivation is mediated by the highly localized increase of [Ca²⁺] that binds to calmodulin, which is constitutively bound to the Ca²⁺ channel (74, 75). Our model assumes that this regulation is mediated by an N-type-like inactivation "ball" associated with the channel. The Markov model implementation of this mechanism produces inactivation behavior that cannot be reproduced by a gating-variable type model and is distinct in its molecular basis from the allosteric model of Ca²⁺ channel inactivation used in other recent formulations.

Our model is able to reproduce experimental observations of Ca²⁺ fluxes in mouse myocytes. As with other animals, the Ca²⁺ cycle in the mouse begins with activation of L-type Ca²⁺ current I_CaL, which transports a relatively small amount of Ca²⁺ across the sarcolemmal membrane into a small subspace volume, where it triggers Ca²⁺ release from the SR (10, 30). The Ca²⁺ released from the SR is considerably larger (40 µM) than the Ca²⁺ influx through L-type Ca²⁺ channels. Additional amounts of Ca²⁺ also enter the cell through a reverse mode of the Na⁺/Ca²⁺ exchanger. Ultimately, the elevation in [Ca²⁺]_i leads to Ca²⁺ binding to troponin C and activation of myocyte contraction (10, 30). During the diastolic phase, Ca²⁺ gradually unbinds from troponin and other buffers, resulting in muscle relaxation. Excess Ca²⁺ is removed from the cytosol mostly through the SR Ca²⁺ pump and the Na⁺/Ca²⁺ exchanger. For mice and rats 90% of Ca²⁺ is pumped back to the SR and 10% of Ca²⁺ is extruded from the cell via the Na⁺/Ca²⁺ exchanger (15, 54). In rabbits, cats, dogs, and ferrets, all of which have longer APs, a considerably larger fraction of Ca²⁺ (30–40%) is extruded from the myocyte by the Na⁺/Ca²⁺ exchanger (11). In our model, 90% of the total Ca²⁺ transported during myocyte relaxation is carried by the SR Ca²⁺ pump and 10% by the sarcolemmal Na⁺/Ca²⁺ exchanger.

Many currents are more accurately described by Markov models rather than Hodgkin-Huxley formulations. For example, the complex voltage-dependent kinetics of the rapid delayed-rectifier current, I_Kr, can more accurately be reproduced by a Markovian model. I_Kr is encoded by the ether-à-go-go-related gene, HERG in humans and mERG in mouse. A number of familial and spontaneous mutations of the HERG channel are associated with arrhythmias in humans (44). We used the HERG model developed by Wang et al. (89) to reproduce mouse I_Kr (57). I_Kr is not consistently observed in mouse ventricular myocytes, and expression appears to vary with age. It is more prominent in embryonic and neonatal myocytes than in the adult. In adult myocytes, I_Kr is small relative to other currents (57). Accordingly, in our model of the mouse ventricular myocytes I_Kr is very small and does not significantly alter the shape and duration of AP under control conditions. However, the HERG current plays an important role in myocyte repolarization in the other species [guinea pig (41, 98), rabbit (55), and human (25, 72)] and may play an important role in species-dependent toxicity to K⁺ channel blockers. It may also underlie differences in restitution properties.

In the mouse ventricle, as in human and rabbit atrial cells, the rapid transient outward K⁺ current, I_Kto,f, dominates repolarization. Elimination of I_Kto,f can result in a marked increase in mouse ventricular APD and cardiac remodeling (7, 93). I_Kto,f plays an important role in repolarization of both the apex and the septum in the mouse (37). To evaluate the contribution of I_Kto,f in these regions, a point mutation (Trp to Phe) was introduced at position 362 in the -subunit of Kv4.2 channels to produce a nonconducting mutant subunit (7). This "dominant negative" mutation eliminated I_Kto,f and increased APD₉₀ from 36 ± 10 ms in wild-type mice to 116 ± 14 ms in transgenic mice (37). In our model eliminating I_Kto,f resulted in significant APD prolongation, but the effect was larger than that observed experimentally. The difference may be due to upregulation of other channels in the mouse.

There is a correlation between the amplitude of I_Kto,f and APD. In the apex, peak I_Kto,f is 34.5 ± 2.3 pA/pF and APD₅₀ is 4.5 ± 0.3 ms, whereas in the septum peak I_Kto,f is only 6.8 ± 0.4 pA/pF and APD₅₀ is 8.5 ± 0.3 ms (37). We used the experimentally determined amplitudes for I_Kto,f to simulate regional APs. The difference between the simulated APD₅₀ from the septum and the apex was 3.6 ms, which is close to the corresponding experimental value of 4.0 ms (37).

The slow transient outward K⁺ current, I_Kto,s, also makes a substantial contribution to the heterogeneity of myocyte repolarization from apical and septal regions. I_Kto,s is absent in apical cells, but is especially important in the septum, where its amplitude is comparable to that of I_Kto,f. Most likely, I_Kto,s plays a compensatory role in repolarization in the septum because of the relatively small amplitude of I_Kto,f. I_Kto,s has been tentatively given a molecular basis of Kv1.4 and has been called I_to,s in some cases (36, 37). The inactivation rate of I_Kto,s is somewhat slower than the heterologously expressed -subunit of the Kv1.4 channel, but I_Kto,s has the characteristic slow recovery properties of this channel.

The ultrarapidly activating delayed rectifier K⁺ current, I_Kur, and the noninactivating steady-state K⁺ current, I_Kss, both play a substantial role in repolarization. I_Kur has a tentative molecular basis of Kv1.5 (59). The mediator(s) for I_Kss is controversial (69, 92). Our model allows simulation of AP modification in knockout mice with modulation of I_Kur and I_Kss. However, it should be remembered that this is only an approximation of a "knockout" experiment, and several other currents are likely to show compensatory changes in addition to removal or modification of the target current (7, 37, 69).

Our model of the mouse ventricular AP reconciles regional differences in repolarization with the measured differential expression of I_Kto,f, I_Kto,s, I_Kur, and I_Kss. In the apex I_Kto,f is dominant, leading to a rapid early repolarization and a relatively short AP. In the septum I_Kto,s prevails. Differential expression and recovery from inactivation of the transient outward K⁺ current are also responsible for heterogeneity in rat ventricular AP (73). The rat AP is short compared with other species, with APD₅₀ 13 and 38 ms for model epicardial and endocardial cells, respectively (73).

Heterogeneity of expression of I_Kto also contributes to heterogeneity of repolarization in larger animals, e.g., canine ventricle (56), although a clear I_Kto,f and I_Kto,s distinction has not been made in larger animals. Regional differences in I_Kto have also been found in cat, rabbit, and human ventricular myocytes (3). I_Kto is prominent in both canine epicardial and midmyocardial (M) cells, which have a "notch" in the AP. Conversely, endocardial cells have relatively small I_Kto and a less clear notch. There is a similar comparative reduction in I_Kto and notch in left versus right ventricular myocytes in dogs (26). There is also a difference in APD between epicardial and M cells. M cells have smaller I_Ks expression and a longer APD₅₀ compared with epicardial myocytes (56), a mechanism that is unlikely to be active in adult mouse ventricles.

I_Kto,f is the dominant outward current in early repolarization or the notch phase of repolarization in mouse, rat, and human cardiac cells. It is absent, however, in bullfrog and guinea pig myocytes (41, 62, 63, 76, 77) and does not play an important role in the early repolarization of rabbit atrial cells (55). During the later phases of repolarization in mouse and rat ventricular and human atrial myocytes, I_Kur and I_CaL act in opposite directions and play a more important role in repolarization. I_Kur repolarizes membrane potential, whereas I_CaL depolarizes the cell to form a plateau (25) or slow down repolarization (72, 73). In rabbit atrial cells, the interplay between I_Kto,f and I_CaL is responsible for the decaying plateau just after early stage of repolarization (55). In the guinea pig ventricular myocyte, the plateau is supported by the interaction of outward K⁺ currents [the plateau K⁺ current (I_Kp), I_Kr, and I_Ks; Ref. 98] and total inward Ca²⁺ current, which includes L-type and T-type Ca²⁺ currents (62, 63). In bullfrog atrial cells, the middle to late plateau is formed by the activation of the outward delayed-rectifier K⁺ current and reactivation of the inward Ca²⁺ current (76).

Mouse and rat APs do not have an elevated plateau, so after inactivation of I_Kur and I_CaL final repolarization is mediated by a balance between I_K1, I_NaCa, I_NaK, and the background currents. This is similar to the final stage of repolarization in human atrial myocytes, which involves I_Kr, I_Ks, and I_K1 (25, 72). In rabbit atrial and guinea pig ventricular myocytes, I_Kr and I_Ks speed up repolarization after the plateau phase, with the role of I_K1 and I_NaCa increasing at the end of repolarization (55, 62, 63, 98).

Late repolarization in the mouse ventricular AP (often measured as APD₉₀) can be highly variable. It is arguable whether this phase represents a true repolarization "plateau" or an "afterdepolarization." The high current densities and fast rate of beating of the mouse ventricle put a large demand on the ionic homeostasis mechanisms, especially the Na⁺/K⁺ pump and the Na⁺/Ca²⁺ exchanger. In this sense, it resembles the DiFrancesco and Noble (27) mechanism of repolarization, in which I_NaCa contributes significantly to the plateau phase of repolarization in Purkinje fibers. Late repolarization is relatively slow, with small dV_m/dt and net membrane current. As a consequence, it is a limitation of the model that this phase may be sensitive to physiological and experimental factors, including accumulation and depletion of ions in restricted extracellular spaces, or buffering of [Ca²⁺]_i by indicator dyes, such as BAPTA or fura-2. Similarly, pump and exchanger current densities may be altered indirectly in cells by activation of electroneutral transport mechanisms not included in the model, such as Cl^–/HCO₃^– exchange or furosemide-sensitive Na⁺-K⁺-2Cl^– cotransport.

Extracellular and intracellular ion accumulation can be an additional confounding factor. Flux through the Na⁺ channel is large and localized to the transverse tubule system (13). Flux through I_Kto,f is also large, further complicating quantitative measurement. Local accumulation and depletion artifacts can occur for both Na⁺ and K⁺ in the restricted extracellular space. Changes in ionic concentrations in these extracellular spaces have been reported to be of physiological and experimental significance. We have chosen to model extracellular ions as being in a well-stirred single extracellular space. With the exception of colocalization of Ca²⁺ channels and ryanodine receptors in narrow diadic spaces, the cytosol is also treated as lumped well-mixed space. This may limit the performance of the model in the face of sustained depolarization or fast repetitive firing.

One limitation of any model of cardiac cellular activity is reconciling disparate experimental data obtained under widely different experimental conditions. All of these data must be "corrected" by the modeler to correspond to some "physiological" reference state. Voltage-clamp data are obtained under experimental conditions different from those used to measure action potentials. For example, I_Kto,f is measured in the presence of divalent Ca²⁺ channel blockers. In many cases we have used several strategies to validate the "corrections" made. The magnitude and kinetics of the Na⁺ current were at least partially validated by simulation for dV_m/dt and comparison with the corresponding experimental measurements. Voltage-clamp measurements of I_CaL were performed in the presence of Ca²⁺ buffers (EGTA, BAPTA) that substantially change I_CaL gating properties. Therefore, the mechanism of Ca²⁺ handling, including I_CaL and the Ca²⁺-release system, was validated with the time course of [Ca²⁺]_i transients measured during myocyte twitch. However, this measurement is at least partially affected by the binding of Ca²⁺ to the Ca²⁺ indicator. The gating properties of K⁺ currents responsible for the AP shape and duration at different levels of repolarization were tested with APs from different heart regions (the apex and the septum), where particular K⁺ channels have differential expression. For example, the gating properties of I_Kto,f obtained in the presence of divalent ions during voltage-clamp experiments were adjusted in accordance with experimental data (1) and validated by the APD₅₀ from the apical cells, where it is primarily responsible for the early stage of repolarization.

Thus our computer model of the mouse ventricular myocyte successfully reproduces experimental voltage-clamp data for the major ionic currents: a fast Na⁺ current, an L-type Ca²⁺ current, a Na⁺/Ca²⁺ exchange current, transient outward K⁺ currents, a rapid delayed rectifier K⁺ current, an ultrarapid delayed rectifier K⁺ current, a noninactivating steady-state K⁺ current, a time-independent K⁺ current, and a slow delayed rectifier K⁺ current. It closely describes experimentally observed Ca²⁺ transients and Ca²⁺ fluxes during the AP and myocyte relaxation. Our model also reproduces the characteristically short-duration mouse AP and can account for the heterogeneity of AP shape from the apex and the septum. The heterogeneity in our model arises through simulated differential expression of transient outward and ultrarapid delayed-rectifier K⁺ channels. Our model uses Markov representations that are related to structure-function data, so it will provide an important tool for interpreting the complex changes observed in experiments on transgenic mouse myocytes.

	APPENDIX: MOUSE MODEL SUMMARY

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 
Model parameters are defined in Tables 2–8.

(A1)

Calcium Dynamics

Calcium concentration.

(A2)

(A3)

(A4)

(A5)

(A6)

(A7)

(A8)

Calcium fluxes.

(A9)

(A10)

(A11)

(A12)

(A13)

(A14)

(A15)

Calcium buffering.

(A16)

(A17)

Ryanodine receptors.

(A18)

(A19)

(A20)

(A21)

Calcium currents.
l-type calcium current.

(A22)

(A23)

(A24)

(A25)

(A26)

(A27)

(A28)

(A29)

(A30)

(A31)

(A32)

(A33)

(A34)

calcium pump current.

(A35)

na⁺/ca²⁺ exchange current.

(A36)

calcium background current.

(A37)

(A38)

Na⁺ Dynamics

Na⁺ concentration.

(A39)

Fast Na⁺ current.

(A40)

(A41)

(A42)

(A43)

(A44)

(A45)

(A46)

(A47)

(A48)

(A49)

(A50)

(A51)

(A52)

(A53)

(A54)

(A55)

(A56)

(A57)

(A58)

(A59)

(A60)

(A61)

(A62)

(A63)

(A64)

Background Na⁺ current.

(A65)

K⁺ Dynamics

K⁺ concentration.

(A66)

Transient outward K⁺ current I_Kto,f.

(A67)

(A68)

(A69)

(A70)

(A71)

(A72)

(A73)

(A74)

Transient outward K⁺ current I_Kto,s.

(A75)

(A76)

(A77)

(A78)

(A79)

(A80)

(A81)

Time-independent K⁺ current.

(A82)

Slow delayed rectifier K⁺ current.

(A83)

(A84)

(A85)

(A86)

Ultrarapidly activating delayed rectifier K⁺ current.

(A87)

(A88)

(A89)

(A90)

(A91)

Noninactivating steady-state K⁺ current.

(A92)

(A93)

(A94)

(A95)

Rapid delayed rectifier K⁺ current (mERG).

(A96)

(A97)

(A98)

(A99)

(A100)

(A101)

(A102)

(A103)

(A104)

(A105)

(A106)

(A107)

Na⁺/K⁺ Pump Current

(A108)

(A109)

(A110)

Ca²⁺-Activated Cl^– Current

(A111)

(A112)

	GRANTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 
This work was supported in part by the National Heart, Lung, and Blood Institute (R01-HL-59526-01 to R. L. Rasmusson; HL-59139, HL-69020, and HL-33107 to S. F. Vatner; and HL-62442 to S.-J. Kim); an Established Investigator Award to R. L. Rasmusson (9940185N) and a Scientist Development Grant to G. C. L. Bett (0430051N) from the American Heart Association; a National Science Foundation Knowledge and Distributed Intelligence Grant (DBI-9873173); R01-HL-59614; and a Pittsburgh Supercomputer Center Grant to V. E. Bondarenko (MCB010020P).

	ACKNOWLEDGMENTS

	FOOTNOTES

 

Address for reprint requests and other correspondence: R. L. Rasmusson, Dept. of Physiology and Biophysics, School of Medicine and Biomedical Sciences, Univ. at Buffalo, State Univ. of New York, 124 Sherman Hall, 3435 Main St., Buffalo, NY 14214-3078 (E-mail: rr32{at}buffalo.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

	REFERENCES

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX: MOUSE MODEL SUMMARY GRANTS REFERENCES

 

1. Agus ZS, Dukes ID, and Morad M. Divalent cations modulate the transient outward current in rat ventricular myocytes. Am J Physiol Cell Physiol 261: C310–C318, 1991.[Abstract/Free Full Text]
2. Antoons G, Mubagwa K, Nevelsteen I, and Sipido KR. Mechanisms underlying the frequency dependence of contraction and [Ca²⁺]_i transients in mouse ventricular myocytes. J Physiol 543: 889–898, 2002.[Abstract/Free Full Text]
3. Antzelevitch C, Shimizu W, Yan GX, Sicouri S, Weissenburger J, Nesterenko VV, Burashnikov A, Di Diego J, Saffitz J, and Thomas GP. The M cell: its contribution to the ECG and to normal and abnormal electrical function of the heart. J Cardiovasc Electrophysiol 10: 1124–1152, 1999.[Web of Science][Medline]
4. Anumonwo JMB, Tallini YN, Vetter FJ, and Jalife J. Action potential characteristics and arrhythmogenic properties of the cardiac conduction system of the murine heart. Circ Res 89: 329–335, 2001.[Abstract/Free Full Text]
5. Balasubramaniam R, Grace AA, Saumarez RC, Vandenberg JI, and Huang CL. Electrogram prolongation and nifedipine-suppressible ventricular arrhythmias in mice following targeted disruption of KCNE1. J Physiol 552: 535–546, 2003.[Abstract/Free Full Text]
6. Barhanin J, Lesagne F, Guillemare E, Fink M, Lazdunski M, and Romey G. K_vLQT1 and IsK (minK) proteins associate to form the I_Ks cardiac potassium current. Nature 384: 78–80, 1996.[CrossRef][Web of Science][Medline]
7. Barry DM, Xu H, Schuessler RB, and Nerbonne JM. Functional knockout of the transient outward current, long-QT syndrome, and cardiac remodeling in mice expressing a dominant-negative Kv4 subunit. Circ Res 83: 560–567, 1998.[Abstract/Free Full Text]
8. Beeler GW and Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268: 177–210, 1977.[Abstract/Free Full Text]
9. Benndorf K, Boldt W, and Nilius B. Sodium current in single myocardial mouse cells. Pflügers Arch 404: 190–196, 1985.[CrossRef][Web of Science][Medline]
10. Bers DM. Calcium fluxes involved in control of cardiac myocyte contraction. Circ Res 87: 275–281, 2000.[Free Full Text]
11. Bers DM. Excitation-Contraction Coupling and Cardiac Contractile Force (2nd ed.). Dordrecht, The Netherlands: Kluwer Academic, 2001.
12. Bondarenko VE, Bett GCL, and Rasmusson RL. A model of graded calcium release and L-type Ca²⁺ channel inactivation in cardiac muscle. Am J Physiol Heart Circ Physiol 286: H1154–H1169, 2004.[Abstract/Free Full Text]
13. Brette F and Orchard C. T-tubule function in mammalian cardiac myocytes. Circ Res 92: 1182–1192, 2003.[Abstract/Free Full Text]
14. Bridge JHB, Ershler PR, and Cannell MB. Properties of Ca²⁺ sparks evoked by action potentials in mouse ventricular myocytes. J Physiol 518: 469–478, 1999.[Abstract/Free Full Text]
15. Brittsan AG, Ginsburg KS, Chu G, Yatani A, Wolska BM, Schmidt AG, Asahi M, MacLennan DH, Bers DM, and Kranias EG. Chronic SR Ca²⁺-ATPase inhibition causes adaptive changes in cellular Ca²⁺ transport. Circ Res 92: 769–776, 2003.[Abstract/Free Full Text]
16. Brouillette J, Trepanier-Boulay V, and Fiset C. Effect of androgen deficiency on mouse ventricular repolarization. J Physiol 546: 403–413, 2003.[Abstract/Free Full Text]
17. Campbell DL, Giles WR, Hume JR, and Shibata EF. Inactivation of calcium currents in bull-frog atrial myocytes. J Physiol 403: 287–315, 1988.[Abstract/Free Full Text]
18. Campbell DL, Rasmusson RL, Qu Y, and Strauss HC. The calcium-independent transient outward potassium current in isolated ferret right ventricular myocytes. I. Basic characterization and kinetic analysis. J Gen Physiol 101: 571–601, 1993.[Abstract/Free Full Text]
19. Chiello Tracy C, Cabo C, Coromilas J, Kurokawa J, Kass RS, and Wit AL. Electrophysiological consequences of human I_Ks channel expression in adult murine heart. Am J Physiol Heart Circ Physiol 284: H168–H175, 2003.[Abstract/Free Full Text]
20. Clancy CE and Rudy Y. Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia. Nature 400: 566–569, 1999.[CrossRef][Medline]
21. Clancy CE and Rudy Y. Cellular consequences of HERG mutations in the long QT syndrome: precursors to sudden cardiac death. Cardiovasc Res 50: 301–313, 2001.[Abstract/Free Full Text]
22. Clancy CE and Rudy Y. Na⁺ channel mutation that causes both Brugada and long-QT syndrome phenotypes: a simulation study of mechanism. Circulation 105: 1208–1213, 2002.[Abstract/Free Full Text]
23. Clancy CE, Tateyama M, and Kass RS. Insights into the molecular mechanisms of bradycardia-triggered arrhythmias in long QT-3 syndrome. J Clin Invest 110: 1251–1262, 2002.[CrossRef][Web of Science][Medline]
24. Clancy CE, Tateyama M, Liu H, Wehrens XH, and Kass RS. Non-equilibrium gating in cardiac Na⁺ channels: an original mechanism of arrhythmia. Circulation 107: 2233–2237, 2003.[Abstract/Free Full Text]
25. Courtemanche M, Ramirez RJ, and Nattel S. Ionic mechanisms underlying human atrial potential properties: insights from a mathematical model. Am J Physiol Heart Circ Physiol 275: H301–H321, 1998.[Abstract/Free Full Text]
26. Di Diego JM, Sun ZQ, and Antzelevitch C. I_to and action potential notch are smaller in left vs. right canine ventricular epicardium. Am J Physiol Heart Circ Physiol 271: H548–H561, 1996.[Abstract/Free Full Text]
27. DiFrancesco D and Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond B Biol Sci 307: 353–398, 1985.[Abstract/Free Full Text]
28. Drici MD, Arrighi I, Chouabe C, Mann JR, Lazdunski M, Romey G, and Barhanin J. Involvement of IsK-associated K⁺ channel in heart rate control of repolarization in a murine engineered model of Jervell and Lange-Nielsen syndrome. Circ Res 83: 95–102, 1998.[Abstract/Free Full Text]
29. Dumaine R, Wang Q, Keating MT, Hartmann HA, Schwartz PJ, Brown AM, and Kirsch GE. Multiple mechanisms of Na⁺ channel-linked long-QT syndrome. Circ Res 78: 916–924, 1996.[Abstract/Free Full Text]
30. Eisner DA, Choi HS, Diaz ME, O'Neill SC, and Trafford AW. Integrative analysis of calcium cycling in cardiac muscle. Circ Res 87: 1087–1094, 2000.[Abstract/Free Full Text]
31. Eisner DA, Trafford AW, Diaz ME, Overend CL, and O'Neill SC. The control of Ca release from the cardiac sarcoplasmic reticulum: regulation versus autoregulation. Cardiovasc Res 38: 589–604, 1998.[Abstract/Free Full Text]
32. Fedida D and Giles WR. Regional variations in action potentials and transient outward current in myocytes isolated from rabbit left ventricle. J Physiol 442: 191–209, 1991.[Abstract/Free Full Text]
33. Firek L and Giles WR. Outward currents underlying repolarization in human atrial myocytes. Cardiovasc Res 30: 31–38, 1995.[CrossRef][Web of Science][Medline]
34. Gao WD, Perez NG, and Marban E. Calcium cycling and contractile activation in intact mouse cardiac muscle. J Physiol 507: 175–184, 1998.[Abstract/Free Full Text]
35. Gao WD, Perez NG, Seidman CE, Seidman JG, and Marban E. Altered cardiac excitation-contraction coupling in mutant mice with familial hypertrophic cardiomyopathy. J Clin Invest 103: 661–666, 1999.[Web of Science][Medline]
36. Guo W, Li H, London B, and Nerbonne JM. Functional consequences of elimination of I_to,f and I_to,s: early afterdepolarizations, atrioventricular block, and ventricular arrhythmias in mice lacking Kv1.4 and expressing a dominant-negative Kv4 subunit. Circ Res 87:73–79, 2000.[Abstract/Free Full Text]
37. Guo W, Xu H, London B, and Nerbonne JM. Molecular basis of transient outward K⁺ current diversity in mouse ventricular myocytes. J Physiol 521: 587–599, 1999.[Abstract/Free Full Text]
38. Hille B. Ionic Channels of Excitable Membranes (3rd ed.). Sunderland, MA: Sinauer, 2001.
39. Huser J, Bers DM, and Blatter LA. Subcellular properties of [Ca²⁺]_i transients in phospholamban-deficient mouse ventricular cells. Am J Physiol Heart Circ Physiol 274: H1800–H1811, 1998.[Abstract/Free Full Text]
40. Ito K, Yan X, Tajima M, Su Z, Barry WH, and Lorell BH. Contractile reserve and intracellular calcium regulation in mouse myocytes from normal and hypertrophied failing hearts. Circ Res 87: 588–595, 2000.[Abstract/Free Full Text]
41. Jafri MS, Rice JJ, and Winslow RL. Cardiac Ca²⁺ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74: 1149–1168, 1998.[Web of Science][Medline]
42. Jones LR, Suzuki YJ, Wang W, Kobayashi YM, Ramesh V, Franzini-Armstrong C, Cleemann L, and Morad M. Regulation of Ca²⁺ signaling in transgenic mouse cardiac myocytes overexpressing calsequestrin. J Clin Invest 101: 1385–1393, 1998.[Web of Science][Medline]
43. Kass RS and Sanguinetti MC. Inactivation of calcium channel current in the calf cardiac Purkinje fiber. Evidence for voltage- and calcium-mediated mechanisms. J Gen Physiol 84: 705–726, 1984.[Abstract/Free Full Text]
44. Keating MT and Sanguinetti MC. Molecular genetic insights into cardiovascular disease. Science 272: 681–685, 1996.[Abstract]
45. Keizer J and Levine L. Ryanodine receptor adaptation and Ca²⁺-induced Ca²⁺ release-dependent Ca²⁺ oscillations. Biophys J 71: 3477–3487, 1996.[Web of Science][Medline]
46. Kiehn J, Lacerda AE, and Brown AM. Pathways of HERG inactivation. Am J Physiol Heart Circ Physiol 277: H199–H210, 1999.[Abstract/Free Full Text]
47. Kim SJ, Depre C, and Vatner SF. Novel mechanisms mediating stunned myocardium. Heart Fail Rev 8: 143–153, 2003.[CrossRef][Web of Science][Medline]
48. Kim SJ, Yatani A, Vatner DE, Yamamoto S, Ishikawa Y, Wagner TE, Shannon RP, Kim YK, Takagi G, Asai K, Homcy CJ, and Vatner SF. Differential regulation of inotropy and lusitropy in overexpressed Gs myocytes through cAMP and Ca²⁺ channel pathways. J Clin Invest 103: 1089–1097, 1999.[Web of Science][Medline]
49. Kirchhefer U, Neumann J, Bers DM, Buchwalow IB, Fabritz L, Hanske G, Justus I, Riemann B, Schmitz W, and Jones LR. Impaired relaxation in transgenic mice overexpressing junctin. Cardiovasc Res 59: 369–379, 2003.[Abstract/Free Full Text]
50. Knollmann BC, Knollmann-Ritschel BEC, Weissman NJ, Jones LR, and Morad M. Remodelling of transgenic mice overexpressing calsequestrin. J Physiol 525: 483–498, 2000.[Abstract/Free Full Text]
51. Lee HC, Patel MK, Mistry DJ, Wang Q, Reddy S, Moorman JR, and Mounsey JP. Abnormal Na channel gating in murine cardiac myocytes deficient in myotonic dystrophy protein kinase. Physiol Genomics 12: 147–157, 2003.[Abstract/Free Full Text]
52. Lee KS, Marban E, and Tsien RW. Inactivation of calcium channels in mammalian heart cells: joint dependence on membrane potential and intracellular calcium. J Physiol 364: 395–411, 1985.[Abstract/Free Full Text]
53. De Leon M, Wang Y, Jones L, Perez-Reyes E, Wei X, Soong TW, Snutch TP, and Yue DT. Essential Ca²⁺-binding motif for Ca²⁺-sensitive inactivation of L-type Ca²⁺ channels. Science 270: 1502–1506, 1995.[Abstract/Free Full Text]
54. Li L, Chu G, Kranias EG, and Bers DM. Cardiac myocyte calcium transport in phospholamban knockout mouse: relaxation and endogenous CaMKII effects. Am J Physiol Heart Circ Physiol 274: H1335–H1347, 1998.[Abstract/Free Full Text]
55. Lindblad DS, Murphey CR, Clark JW, and Giles WR. A model of the action potential and underlying membrane currents in a rabbit atrial cell. Am J Physiol Heart Circ Physiol 271: H1666–H1696, 1996.[Abstract/Free Full Text]
56. Liu DW and Antzelevitch C. Characteristics of the delayed rectifier current (I_Kr and I_Ks) in canine ventricular epicardial, midmyocardial, and endocardial myocytes: a weaker I_Ks contributes to the longer action potential of the M cell. Circ Res 76: 351–365, 1995.[Abstract/Free Full Text]
57. Liu GX, Zhou J, Nattel S, and Koren G. Single-channel recordings of a rapid delayed rectifier current in adult mouse ventricular myocytes: basic properties and effects of divalent cations. J Physiol 556: 401–413, 2004.[Abstract/Free Full Text]
58. Liu S and Rasmusson RL. Hodgkin-Huxley and partially coupled inactivation models yield different voltage dependence of block. Am J Physiol Heart Circ Physiol 272: H2013–H2022, 1997.[Abstract/Free Full Text]
59. London B, Guo W, Pan XH, Lee JS, Shusterman V, Rocco CJ, Logothetis DA, Nerbonne JM, and Hill JA. Targeted replacement of Kv1.5 in the mouse leads to loss of the 4-aminopyridine-sensitive component of I_K,slow and resistance to drug-induced QT prolongation. Circ Res 88: 940–946, 2001.[Abstract/Free Full Text]
60. London B, Jeron A, Zhou J, Buckett P, Han X, Mitchell GF, and Koren G. Long QT and ventricular arrhythmias in transgenic mice expressing the N terminus and first transmembrane segment of a voltage-gated potassium channel. Proc Natl Acad Sci USA 95: 2926–2931, 1998.[Abstract/Free Full Text]
61. Lukyanenko V, Wiesner TF, and Gyorke S. Termination of Ca²⁺ release during Ca²⁺ sparks in rat ventricular myocytes. J Physiol 507: 667–677, 1998.[Abstract/Free Full Text]
62. Luo CH and Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res 74: 1071–1096, 1994.[Abstract/Free Full Text]
63. Luo CH and Rudy Y. A dynamic model of the cardiac ventricular action potential. II. Afterdepolarization, triggered activity, and potentiation. Circ Res 74: 1097–1113, 1994.[Abstract/Free Full Text]
64. Maier LS, Zhang T, Chen L, DeSantiago J, Brown JH, and Bers DM. Transgenic CaMKII_C overexpression uniquely alters cardiac myocyte Ca²⁺ handling: reduced SR Ca²⁺ load and activated SR Ca²⁺ release. Circ Res 92: 904–911, 2003.[Abstract/Free Full Text]
65. Marx SO, Kurokawa J, Reiken S, Motoike H, D'Armiento J, Marks AR, and Kass RS. Requirement of a macromolecular signaling complex for adrenergic receptor modulation of the KCNQ1-KCNE1 potassium channel. Science 295: 496–499, 2002.[Abstract/Free Full Text]
66. McAllister RE, Noble D, and Tsien RW. Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol 251: 1–59, 1975.[Abstract/Free Full Text]
67. Muraki K, Imaizumi Y, Watanabe M, Habuchi Y, and Giles WR. Delayed rectifier K⁺ current in rabbit atrial myocytes. Am J Physiol Heart Circ Physiol 269: H524–H532, 1995.[Abstract/Free Full Text]
68. Nattel S, Yue L, and Wang Z. Cardiac ultrarapid delayed rectifiers: a novel potassium current family of functional similarity and molecular diversity. Cell Physiol Biochem 9: 217–226, 1999.[CrossRef][Web of Science][Medline]
69. Nerbonne JM, Nichols CG, Schwarz TL, and Escande D. Genetic manipulation of cardiac K⁺ channel function in mice: what have we learned, and where do we go from here? Circ Res 89: 944–956, 2001.[Abstract/Free Full Text]
70. Noble D. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potentials. J Physiol 160: 317–352, 1962.[Free Full Text]
71. Nuyens D, Stengl M, Dugarmaa S, Rossenbacker T, Compernolle V, Rudy Y, Smits JF, Flameng W, Clancy CE, Moons L, Vos MA, Dewerchin M, Benndorf K, Collen D, Carmeliet E, and Carmeliet P. Abrupt rate accelerations or premature beats cause life-threatening arrhythmias in mice with long-QT3 syndrome. Nat Med 7: 1021–1027, 2001.[CrossRef][Web of Science][Medline]
72. Nygren A, Ficet C, Firek L, Clark JW, Lindblad DS, Clark RB, and Giles WR. Mathematical model of an adult human atrial cell: the role of K⁺ currents in repolarization. Circ Res 82: 63–81, 1998.[Abstract/Free Full Text]
73. Pandit SV, Clark RB, Giles WR, and Demir SS. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys J 81:3029–3051, 2001.[Web of Science][Medline]
74. Peterson BZ, DeMaria CD, Adelman JP, and Yue DT. Calmodulin is the Ca²⁺ sensor for Ca²⁺-dependent inactivation of L-type calcium channels. Neuron 22: 549–558, 1999.[CrossRef][Web of Science][Medline]
75. Peterson BZ, Lee JS, Mulle JG, Wang Y, de Leon M, and Yue DT. Critical determinants of Ca²⁺-dependent inactivation within an EF-hand motif of L-type Ca²⁺ channels. Biophys J 78: 1906–1920, 2000.[Web of Science][Medline]
76. Rasmusson RL, Clark JW, Giles WR, Robinson K, Clark RB, Shibata EF, and Campbell DL. A mathematical model of electrophysiological activity in a bullfrog atrial cell. Am J Physiol Heart Circ Physiol 259: H370–H389, 1990.[Abstract/Free Full Text]
77. Rasmusson RL, Clark JW, Giles WR, Shibata EF, and Campbell DL. A mathematical model of a bullfrog cardiac pacemaker cell. Am J Physiol Heart Circ Physiol 259: H352–H369, 1990.[Abstract/Free Full Text]
78. Rasmusson RL, Morales MJ, Wang S, Liu S, Campbell DL, Brahmajothi MV, and Strauss HC. Inactivation of voltage-gated cardiac K⁺ channels. Circ Res 82: 739–750, 1998.[Abstract/Free Full Text]
79. Reuter H. The dependence of the slow inward current in Purkinje fibres on the extracellular calcium concentration. J Physiol 192: 479–492, 1967.[Abstract/Free Full Text]
80. Ritter M, Su Z, Xu S, Shelby J, and Barry WH. Cardiac unloading alters contractility and calcium homeostasis in ventricular myocytes. J Mol Cell Cardiol 32: 577–584, 2000.[CrossRef][Web of Science][Medline]
81. Santana LF, Chase EG, Votaw VS, Nelson MT, and Greven R. Functional coupling of calcineurin and protein kinase A in mouse ventricular myocytes. J Physiol 544: 57–69, 2002.[Abstract/Free Full Text]
82. Santana LF, Kranias EG, and Lederer WJ. Calcium sparks and excitation-contraction coupling in phospholamban-deficient mouse ventricular myocytes. J Physiol 503: 21–29, 1997.[Abstract/Free Full Text]
83. Su Z, Sugishita K, Ritter M, Li F, Spitzer KW, and Barry WH. The sodium pump modulates the influence of I_Na on [Ca²⁺]_i transients in mouse ventricular myocytes. Biophys J 80: 1230–1237, 2001.[Web of Science][Medline]
84. Su Z, Zou A, Nonaka A, Zubair I, Sanguinetti MC, and Barry WH. Influence of prior Na⁺ pump activity on pump and Na⁺/Ca²⁺ exchange currents in mouse ventricular myocytes. Am J Physiol Heart Circ Physiol 275: H1808–H1817, 1998.[Abstract/Free Full Text]
85. Thomas SP, Kucera JP, Bircher-Lehmann L, Rudy Y, Saffitz JE, and Kleber AG. Impulse propagation in synthetic strands of neonatal cardiac myocytes with genetically reduced levels of connexin43. Circ Res 92: 1209–1216, 2003.[Abstract/Free Full Text]
86. Ufret-Vincenty CA, Baro DJ, Lederer WJ, Rockman HA, Quinones LE, and Santana LF. Role of sodium channel deglycosylation in the genesis of cardiac arrhythmias in heart failure. J Biol Chem 276: 28197–28203, 2001.[Abstract/Free Full Text]
87. Wang L and Duff HJ. Developmental changes in transient outward current in mouse ventricle. Circ Res 81: 120–127, 1997.[Abstract/Free Full Text]
88. Wang L, Feng ZP, and Duff HJ. Glucocorticoid regulation of cardiac K⁺ currents and L-type Ca²⁺ current in neonatal mice. Circ Res 85: 168–173, 1999.[Abstract/Free Full Text]
89. Wang S, Liu S, Morales MJ, Strauss HC, and Rasmusson RL. A quantitative analysis of the activation and inactivation kinetics of HERG expressed in Xenopus oocytes. J Physiol 502: 45–60, 1997.[Abstract/Free Full Text]
90. Wang W, Cleemann L, Jones LR, and Morad M. Modulation of focal and global Ca²⁺ release in calsequestrin-overexpressing mouse cardiomyocytes. J Physiol 524: 399–414, 2000.[Abstract/Free Full Text]
91. Winslow RL, Rice J, Jafri S, Marban E, and O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure. II. Model studies. Circ Res 84: 571–586, 1999.[Abstract/Free Full Text]
92. Xu H, Guo W, and Nerbonne JM. Four kinetically distinct depolarization-activated K⁺ currents in adult mouse ventricular myocytes. J Gen Physiol 113: 661–677, 1999.[Abstract/Free Full Text]
93. Xu H, Li H, and Nerbonne JM. Elimination of the transient outward current and action potential prolongation in mouse atrial myocytes expressing a dominant negative Kv4 subunit. J Physiol 519: 11–21, 1999.[Abstract/Free Full Text]
94. Xu Y, Dong PH, Zhang Z, Ahmmed GU, and Chiamvimonvat N. Presence of a calcium-activated chloride current in mouse ventricular myocytes. Am J Physiol Heart Circ Physiol 283: H302–H314, 2002.[Abstract/Free Full Text]
95. Yao A, Su Z, Nonaka A, Zubair I, Lu L, Philipson KD, Bridge JHB, and Barry WH. Effects of overexpression of the Na⁺-Ca²⁺ exchanger on [Ca²⁺]_i transients in murine ventricular myocytes. Circ Res 82: 657–665, 1998.[Abstract/Free Full Text]
96. Yatani A, Frank K, Sako H, Kranias EG, and Dorn GW II. Cardiac-specific overexpression of Gq alters excitation-contraction coupling in isolated cardiac myocytes. J Mol Cell Cardiol 31: 1327–1336, 1999.[CrossRef][Web of Science][Medline]
97. Yuan W, Ginsburg KS, and Bers DM. Comparison of sarcolemmal calcium channel current in rabbit and rat ventricular myocytes. J Physiol 493: 733–746, 1996.[Abstract/Free Full Text]
98. Zeng J, Laurita KR, Rosenbaum DS, and Rudy Y. Two components of the delayed rectifier K⁺ current in ventricular myocytes of the guinea pig type: theoretical formulation and their role in repolarization. Circ Res 77: 140–152, 1995.[Abstract/Free Full Text]
99. Zhou J, Jeron A, London B, Han X, and Koren G. Characterization of a slowly inactivating outward current in adult mouse ventricular myocytes. Circ Res 83: 806–814, 1998.[Abstract/Free Full Text]
100. Zhou J, Kodirov S, Murata M, Buckett PD, Nerbonne JM, and Koren G. Regional upregulation of Kv2.1-encoded current, I_K,slow2, in Kv1DN mice is abolished by crossbreeding with Kv2DN mice. Am J Physiol Heart Circ Physiol 284: H491–H500, 2003.[Abstract/Free Full Text]

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