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* Center for Cardiovascular Bioinformatics and Modeling, The Whitaker Biomedical Engineering Institute, Department of Medicine Division of Cardiology, and ¶ The Institute for Molecular Cardiobiology, The Johns Hopkins University School of Medicine and Whiting School of Engineering, Baltimore, Maryland
Correspondence: Address reprint requests to Antti Tanskanen, The Johns Hopkins University, Clark Hall, Rm. 204, 3400 N. Charles St., Baltimore, MD 21218. E-mail: atanskan{at}bme.jhu.edu.
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; Tsien et al., 1986; Yue et al., 1990). Mode 0 is a silent mode. Mode 0a is a low-activity mode characterized by sparse, brief openings. Modes 1 and 2 are high-activity modes displaying bursts of brief or long-lasting openings, respectively. Although first identified in experiments using barium (Ba2+) as the charge carrier (Hess et al., 1984; Yue et al., 1990), mode 2 gating of LCCs has been demonstrated recently to occur at physiological concentrations of extracellular calcium (Ca2+) (Josephson et al., 2002a).
Several phosphorylation-related events regulate the fraction of LCCs gating in each mode. ß-adrenergic receptor (ß-AR) agonists induce protein kinase A (PKA)-mediated phosphorylation of the LCC 
1C subunit at the Ser1928 residue (Gao et al., 1997; De Jongh et al., 1996; Yoshida et al., 1992). This phosphorylation increases both the fraction of LCCs available for gating as well as the fraction gating in mode 2 (Chen-Izu et al., 2000; Yue et al., 1990). The signaling molecule Ca2+/calmodulin-dependent protein kinase II (CaMKII), through phosphorylation of an as yet unidentified cell membrane protein(s), increases the fraction of LCCs gating in mode 2 relative to other modes (Dzhura et al., 2000). LCC agonists such as BayK8644 also increase mode 2 activity (Hess et al., 1984), potentially by inhibiting channel dephosphorylation or through allosteric interactions that mimic the effects of phosphorylation (Erxleben et al., 2003).
Early after-depolarizations (EADs) are depolarizations of membrane potential occurring during phases 2 or 3 of the cardiac action potential (AP). They are thought to be a possible trigger for development of polymorphic ventricular tachycardia (Roden, 1993; Zhou et al., 1992). Occurrence of EADs is often associated with prolongation of AP duration (APD, at 90% repolarization) produced, for example, by the action of LCC agonists (January and Riddle, 1989; January et al., 1988; Marbán et al., 1986) or by block of repolarizing potassium currents (Marbán et al., 1986). Cardiac myocytes can also exhibit EADs in response to ß-adrenergic agonists such as isoproterenol (ISO) (De Ferrari et al., 1995; Volders et al., 1997), even at ISO concentrations producing shortening of APD (Priori and Corr, 1990). Recently, Wu et al. (2002) investigated AP properties in cardiac ventricular myocytes isolated from transgenic mice expressing a constitutively active form of CaMKII, which would be expected to induce an increase in the number of LCCs gating in mode 2 (Dzhura et al., 2000). These mice exhibited APD prolongation accompanied by frequent EADs. A CaMKII inhibitory peptide AC3-I eliminated EADs with little APD shortening (Wu et al., 2002). In addition, blockers of PKA and CaMKII have been shown to eliminate EADs and torsade de pointes in ventricular myocytes isolated from rabbits (Mazur et al., 1999).
These data suggest the hypothesis that factors which promote mode 2 gating of LCCs may be linked with the generation of EADs. We test this hypothesis using an ionic model of the canine ventricular myocyte incorporating stochastic gating of LCCs and ryanodine-sensitive Ca2+ release channels (RyRs) (Greenstein and Winslow, 2002). The model is extended to describe mode 2 gating of LCCs, and is then used to simulate myocyte responses to 1 µM ISO.
Results demonstrate that random fluctuations in the number of open LCCs during the plateau phase of the AP can generate EADs. The most important fluctuations are those of LCCs gating in mode 2 and exhibiting long open times, which drive the slow-timescale fluctuations of L-type Ca2+ current (ICaL). EADs occur randomly, and the likelihood of occurrence is an increasing function of the fraction of LCCs gating in mode 2. These results suggest a novel mechanism whereby phosphorylation-induced changes in LCC gating properties contribute to EAD generation.
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). This model is able to reproduce experimentally measured properties of Ca2+-induced Ca2+ release such as graded release, voltage dependence of excitation-contraction coupling gain, stable release termination, and the relative magnitude of voltage- versus Ca2+-dependent inactivation of LCCs. The model has been extended to describe the action of 1 µM ISO on both Ca2+ regulatory proteins and ion channels of the cardiac ventricular myocyte (Greenstein et al., 2004). Details of model development, as well as a comparison of model Ca2+ transients and APs with and without ISO to those measured experimentally are provided in the following.
The local-control myocyte model
Simulations are performed using a canine ventricular myocyte model incorporating stochastic gating of LCCs and RyRs (Greenstein and Winslow, 2002). The model incorporates 1), sarcolemmal ion currents of the Winslow et al. (1999) canine ventricular cell model; 2), continuous-time Markov chain models of the rapidly activating delayed rectifier potassium (K+) current IKr (Mazhari et al., 2001), the Ca2+-independent transient outward K+ current Ito1 (Greenstein et al., 2000), and the Ca2+-dependent transient outward chloride (Cl–) current Ito2; 3), a continuous-time Markov chain model of ICaL in which Ca2+-mediated inactivation occurs via the mechanism of mode-switching (Imredy and Yue, 1994; Jafri et al., 1998); 4), an RyR channel model adapted from that of Keizer and Smith (Jafri et al., 1998; Keizer et al., 1998); and 5), locally controlled Ca2+-induced Ca2+ release from junctional sarcoplasmic reticulum (JSR) via inclusion of LCCs, RyRs, Cl– channels, and local JSR and diadic subspace compartments within Ca2+ release units (CaRUs).
The L-type Ca2+ channel gating scheme
The gating scheme of the LCC model is shown in Fig. 1 and has been described previously (Greenstein and Winslow, 2002; Jafri et al., 1998; Rice et al., 1999). Briefly, upper-row states encompass Mode Normal and lower-row states encompass Mode Ca. Each mode contains an open state (denoted O and OCa). Depolarization promotes transitions from left to right toward the open states. Elevation of subspace Ca2+ promotes transitions from Mode Normal to Mode Ca. When LCCs gate in Mode Ca, transitions into state OCa are infrequent. Mode Ca therefore corresponds to Ca2+-inactivated states. Transition rates from Mode Ca to Mode Normal (i.e., recovery from Ca2+-mediated inactivation) are Ca2+-independent. The LCC also contains a separate voltage-dependent inactivation gate (not shown in Fig. 1) whose open probability decreases with membrane depolarization.
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). The product NLCC x factive is chosen such that the amplitude of the whole-cell current agrees with that measured experimentally in canine myocytes (Hobai and O'Rourke, 2001). This approach yields a value of 50,000 for NLCC x factive, consistent with experimental estimates of active LCC density (McDonald et al., 1986; Rose et al., 1992) and corresponding to 12,500 active CaRUs.
The number of CaRUs simulated explicitly need not be equal to the actual number of CaRUs in a cell. In simulations including a reduced number of CaRUs, total fluxes between the cytosol and the population of simulated CaRUs are scaled by the ratio Nactual/Nsimulated to maintain an average flux independent of the number of CaRUs simulated. No variance-reduction methods were used, hence use of reduced numbers of CaRUs increases the standard deviation of the scaled currents/fluxes by a factor of 
(Nactual/Nsimulated)1/2. Unless stated otherwise, all simulations in this study are performed using a minimum of 10,000 simulated CaRUs, which results in no greater than an 2.2-fold increase in standard deviation of ICaL compared to the full 50,000-CaRU model. This approach was a necessary compromise between model accuracy and tractability.
Stochastic simulation
The algorithm for solving the stochastic ordinary differential equations defining the model has been described previously (Greenstein and Winslow, 2002). Briefly, transition rates for each channel are determined by their gating schemes and their dependence on local Ca2+ level. Stochastic simulation of CaRU dynamics is used to determine all Ca2+ flux into and out of each local subspace. The summation of all Ca2+ fluxes crossing the CaRU boundaries is taken as inputs to the global model, which is defined by a system of coupled ordinary differential equations. The dynamical equations defining the global model are solved using the Prince-Dormand algorithm (Engeln-Müllges and Uhlig, 1996) which has been modified to embed the stochastic CaRU simulations within each time step. The Mersenne Twister (Matsumoto and Nishimura, 1998) random number generator algorithm (period = 219,937 – 1) is used in stochastic computations.
This model provides the ability to investigate the ways in which LCC, RyR, and subspace properties impact on Ca2+-induced Ca2+ release and the integrative behavior of the myocyte. However, this ability is achieved at a high computational cost: up to 1 s of model activity was simulated in 3 min of simulation time with 1,250 CaRUs, and in 22 min with 12,500 CaRUs when running on 20 IBM Power4 processors configured with 4 gigabytes memory each.
Model of ß-AR responses
ß-AR agonists increase LCC availability (factive; Chen-Izu et al., 2000; Herzig et al., 1993; Yue et al., 1990). In guinea pig and human ventricular myocytes, baseline values of factive are relatively low and are increased by 2- to 2.5-fold in response to ß-AR stimulation (or in heart failure, in which there may be hyperphosphorylation of LCCs; Chen et al., 2002; Handrock et al., 1998; Herzig et al., 1993; Schröder et al., 1998; Yue et al., 1990). These data differ from those in rat, which show considerably higher baseline availability and a smaller change in factive in response to ß-AR stimulation (Chen-Izu et al., 2000). We have therefore elected to develop a "baseline" model of ß-AR action using data primarily from guinea pig, canine, and human ventricular myocytes (Greenstein et al., 2004). ß-AR-induced phosphorylation of LCCs is modeled by including populations of both active (phosphorylated) and inactive (unphosphorylated) LCCs. Model parameters are adjusted based on analyses of slow cycling between active and inactive modes in the presence of ISO, indicating that at 1 µM concentration, 25% of LCCs are available under control conditions, and that this increases to 60% in the presence of ISO (Herzig et al., 1993), which corresponds to 30,000 active CaRUs out of a total of 50,000 simulated CaRUs. The fraction of active CaRUs is set equal to the fraction of active LCCs (i.e., active CaRUs contain active LCCs).
Increased PKA-mediated phosphorylation of LCCs in response to ß-AR agonists has also been shown to shift the distribution of LCCs into high-activity gating modes (Chen-Izu et al., 2000; Herzig et al., 1993; Yue et al., 1990). In this study it has been assumed that mode 0a openings do not significantly contribute to whole-cell ICaL (see Herzig et al.,1993) and are therefore lumped into the inactive population of LCCs. Mode 1 gating of the LCC corresponds to the LCC model control parameter set. Mode 2 gating is defined as a modification of mode 1 parameters based on the data of Yue et al. (1990) in which mean LCC open time is increased from 0.5 ms to 5 ms. This is implemented by reducing the exit rate from the open state (g) (Fig. 1) by a factor of 10. LCC activation and inactivation is shifted by 2 mV in the hyperpolarizing direction in response to ISO consistent with experiments (Chen et al., 2002; Kääb et al., 1996). Under control conditions, all active LCCs are assumed to operate in mode 1, whereas in response to 1 µM ISO, 15% of the active population of LCCs are assumed to operate in mode 2, with 85% remaining in mode 1 (Yue et al., 1990).
ß-AR stimulation has also been shown to enhance SERCA2a function (Simmerman and Jones, 1998), reduce inactivation/rectification of IKr (Heath and Terrar, 2000), and increase amplitude of IKs (Kathofer et al., 2000). Functional increase in SERCA2a availability is modeled by simultaneous scaling of both the forward and reverse maximum pump rates Vmaxf and Vmaxr (Shannon et al., 2000) by a factor of 3.3. Reduction in the degree of steady-state inactivation of IKr is modeled by reducing rates entering the inactivation state (i and i3) by a factor of 4, and increasing the rates exiting the inactivation state (ßi and 
) by this same factor (Mazhari et al., 2001). Functional upregulation of IKs is modeled by scaling maximal conductance by a factor of 2.
Fig. 2 shows the ability of the baseline model to reproduce experimentally measured ß-AR responses to 1 µM ISO. Simultaneous measurements of APs and Ca2+ transients are shown in Fig. 2, A and B, respectively, for control (black lines) and after application of ISO (shaded lines). APD in response to ISO (Fig. 2 A) is shortened by 30%, plateau potential becomes 10–15 mV more depolarized, and phase 1 notch depth and duration are reduced. In addition, ISO produces an 3-fold increase in Ca2+ transient amplitude and speeds the relaxation rate of the Ca2+ transient 3-fold (Fig. 2 B). The AP generated by the baseline ß-AR model (Fig. 2 C) exhibits shortening of duration, depolarization of AP plateau, and reduction in phase 1 notch depth and duration similar to that seen experimentally (Fig. 2 A). Peak amplitude of the model Ca2+ transient (Fig. 2 D) is increased 3-fold and the rate of decay of the transient is increased (shortening its overall duration), as seen in experiments (Fig. 2 B).
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). Stochastic events during the plateau and "second plateau" following an EAD can trigger additional EADs. A non-EAD, a single-EAD, and a double-EAD AP are shown in Fig. 5 B. Using the single-EAD AP as a test case, the random number generator seed was reset at 150 ms and 180 ms (Fig. 5 B, arrows), leading to the elimination of the EAD and to the appearance of a second EAD, respectively. These results show that there appears to be a critical time during the late plateau of the AP, where the cell may either repolarize or depolarize (into an EAD), and that the outcome as to which of these events occurs is a random event determined by the stochastic gating of LCCs. Fig. 5 C shows ICaL associated with each of the three APs shown in Fig. 5 B. A large rapid increase of ICaL coincides with EAD onset. The time course of ICaL inactivation mechanisms corresponding to the single-EAD AP of Fig. 5 B is shown in Fig. 5 D. The ratio of LCCs that are not in an inactivated state (solid black line) reaches a minimum at 120 ms (corresponding to maximal LCC inactivation), and then proceeds to gradually increase. Both voltage- and Ca2+-dependent inactivation (dashed and dash-dotted lines, respectively) of the LCCs have partially recovered at the time of onset of the EAD (260 ms). The results of Fig. 5 D show that 10.2% of the LCC population recover from inactivation by the time of EAD onset. Of these, 9.5% recover from Ca2+-dependent inactivation, whereas only 1.4% recover from V-dependent inactivation. The overlap of these population subsets represents 0.7% of LCCs which recover from both Ca2+- and V-dependent inactivation. This demonstrates that preceding the EAD, LCC recovery from inactivation is due primarily to recovery from the Ca2+-mediated inactivation state (i.e., transitions from Mode Ca to Mode Normal in the model). This recovery from inactivation is necessary to provide a sufficient number of available LCCs, and hence a sufficient amount of inward current for an EAD to be triggered successfully.
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) for simulations with 0% (solid black line), 15% (dark shaded dashed line), and 25% (light shaded dashed line) of LCCs in mode 2. Currents are recorded during a voltage-clamp simulation, in which the cell is first held at –90 mV for 3 s, stepped to 40 mV for 10 ms, and then stepped to 5 mV for 7 s. Spectral analysis is performed on currents obtained during the final 5 s of this protocol and the results are shown in Fig. 7 A. The results indicate that the amplitude of slow-timescale (low-frequency) fluctuations of ICaL does not depend upon frequency and increases as the fraction of LCCs gating in mode 2 increases. There is an 7-dB/Hz, or fivefold, difference in power between ICaL composed purely of mode 1 channels and that containing 50% mode 2 channels. This corresponds to a 2.2-fold difference in current amplitude in the low-frequency range. At high frequencies, the power drops off as 1/fa where a is 2. These results agree with theoretical calculations, which predict that the power spectral density for a collection of ion channels with exponentially distributed open times is flat at low frequencies (i.e., white noise) and is decreasing at high frequencies with slope proportional to 1/f2. The boundary between these regions is expected to occur at a frequency which corresponds to the timescale of channel gating, and occurs in the range of 0.5–1.5 ms in this model. These results indicate that the presence of mode 2 channels significantly increases the amplitude of ICaL fluctuations at a timescale slower than 1 ms.
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; Dzhura et al., 2000; Yue et al., 1990), contribute to the generation of EADs (De Ferrari et al., 1995; Priori and Corr, 1990; Volders et al., 1997; Wu et al., 2002). We have tested the hypothesis that increased mode 2 gating induces EADs. Modeling results demonstrate that an increase in the ratio of LCCs gating in mode 2 favors the occurrence of EADs via a mechanism whereby the likelihood of such events is raised by stochastic prolongation of APD and subsequent reactivation of LCCs. Results of this study demonstrate that 1), the rate of EAD occurrence in response to long-term (150-s) 1-Hz pacing is a monotonic increasing function of the fraction of LCCs gating in mode 2, where no EADs occur if that fraction is zero (Fig. 2 A); 2), when the fraction of LCCs gating in mode 2 is >0, EAD occurrence is a stochastic event; and 3), the random opening of a sufficient number of LCCs gating in mode 2 can initiate an EAD (Figs. 3 and 7).
Mechanism of EAD formation
Generation of an EAD requires an inward current that is sufficiently large that total membrane current becomes inward. The main ionic current candidates that may be responsible for inducing EADs are therefore ICaL and INCX (Na+-Ca2+ exchanger). INCX did not play a significant role in EAD generation in this model (data not shown), whereas the role of ICaL is evident from Fig. 5, B and C, where the increase in magnitude of ICaL coincides with the onset of each EAD.
In the ß-AR stimulated model of the canine cardiac myocyte, EADs have been shown to be stochastic events (Fig. 3). Variation in ICaL due to stochastic gating of LCCs leads to variation in APD, and hence some APs are prolonged. These prolonged APs exhibit an increased likelihood of EAD occurrence since the time available for LCC to recover from Ca2+-mediated inactivation is extended during the AP plateau and recovered channels are likely to reopen, possibly triggering an EAD. Even when these conditions are present, however, an EAD is not guaranteed to occur because it is an inherently stochastic event that depends upon the number and duration of LCC openings during the late plateau of the AP. This is demonstrated in Fig. 5 B, where changes in the random number generator seeds late in the plateau of a single EAD-AP can either eliminate the EAD or produce an additional EAD within the same AP. This behavior demonstrates that the trajectory of an AP is bistable, as small changes in ICaL (of a magnitude comparable to the noise in this current) can dramatically alter the morphology of the AP. This behavior is a form of stochastic resonance (see, e.g., White et al., 2000) which relies upon intrinsic noise levels in ICaL and the fact that net membrane current is small during the plateau.
The effect of increasing the ratio of mode 2 LCCs can be separated into two components: 1), an increase in the mean amplitude of the sustained inward Ca2+ current during plateau, which prolongs AP in a deterministic manner (Fig. 4); and 2), an increase in slow-timescale fluctuations of total ICaL (Fig. 7 A), which enhances the likelihood of EAD triggering due to increased variation in APD (Figs. 3, B–D, and 7). Interestingly, the balance between mode 1 and mode 2 LCCs does not significantly influence the peak amplitude of ICaL.
The relationship between noise in ICaL and noise in membrane potential can be deduced from Fig. 7. The addition of mode 2 channels to ICaL enhances the amplitude of current fluctuations at timescales slower than 1 ms, whereas the enhancement of fluctuation in membrane potential is limited to timescales slower than 40 ms. This is a theoretically expected feature of this relationship since membrane impedance is low-pass in nature. In addition, the power spectrum of membrane potential may be influenced by time-dependent changes in membrane impedance during the AP. However, calculation of instantaneous I-V curves during the AP plateau time interval that was used to calculate power spectra indicates that membrane conductance does not change significantly over this interval (data not shown). The spectral properties of voltage noise are therefore largely determined by fluctuations of ICaL during the AP plateau, rather than fluctuation of membrane impedance.
Injection of an external current during the late plateau of an AP during ß-adrenergic stimulation can induce an EAD. The strength-duration relationship for an EAD-inducing square current pulse is quasihyperbolic, such that the current amplitude required to induce an EAD is quite small for a long duration pulse (data not shown). This system property suggests that modest amplification of slow-timescale fluctuations could effectively increase the likelihood of triggering EADs, and this is precisely what occurs as a fraction of the LCCs transition to mode 2 activity (Fig. 7). This result demonstrates that the appearance of LCCs with a long mean open time can have a profound impact on AP profile, even if only a small fraction of channels exhibit these high-activity gating dynamics.
To reduce computational load, not all simulations were run with the full 50,000-CaRU model. Reduction of the number of simulated CaRUs increases the variance of ICaL, which may in turn produce an increased frequency of EADs in the simulations presented in Fig. 3, B–D (compared to the full model). This increase in ICaL noise, however, does not influence the interpretation of the results regarding the mechanism of EAD generation. Both the full 50,000-CaRU model (Fig. 3 A) and the reduced 10,000-CaRU model (Fig. 3, B–D) exhibit EADs only in the presence of LCCs gating in mode 2. In the absence of mode 2 gating of LCCs both the full and the reduced models fail to exhibit EADs in runs as long as 400 s at 1 Hz (data not shown). Regardless of the number of CaRUs simulated, the mechanism of EAD generation was consistently observed to be dependent on stochastic gating of LCCs (Fig. 5, A and B).
Comparison with previous studies
In traditional approaches to myocyte modeling, it has often been assumed that it is sufficient to simulate the behavior of a large number (105–107) of ion channels using equations that describe the expected (average) behavior of the channel population. In this approach, fluctuations about the average behavior are assumed to be insignificant with respect to whole-cell dynamics.
Previous studies in the neuron (Chow and White, 1996; White et al., 1998, 2000) have shown that in the presence of a small number of stochastically gating ion channels, spontaneous action potentials can be triggered in a random pattern. For a population of independent identical channels, the central limit theorem states that as the number of channels (N) increases, the standard deviation in the signal will scale as N–1/2 (Feller, 1970), indicating that the amplitude of the gating noise may not be so small as to be considered inconsequential. This property coupled with the nonlinear bistability exhibited by the myocyte late in the AP plateau, results in a system where gating noise can contribute to the triggering of EADs in the presence of a physiological number of channels (40,000–200,000 LCCs).
Experimental measurements have demonstrated that gating noise may be the primary source of APD variability (Zaniboni et al., 2000). The coefficient of variation of APD in guinea pig ventricular myocytes (without ß-AR stimulation) has been measured to be 2.3 ± 0.9%, and 1.3 ± 0.4% in the absence of the late Na+ current (Zaniboni et al., 2000). In the baseline canine myocyte model (which does not include a late Na+ current), in the absence of ß-AR stimulation, coefficient of variation of APD is 1.4% with all 12,500 CaRUs included in the simulation, which agrees well with the experimental value.
Electrotonic coupling effects have been shown to have a major influence on the generation and propagation of EADs in myocardial tissue. A recent study by Zaniboni et al. (2000) demonstrated that EADs in single isolated myocytes were suppressed when the EAD-producing myocyte was electrically coupled to a normal myocyte. It is likely that in the presence of electrotonic loading, there must be a critical mass of cells that generate near simultaneous EADs for propagation to occur. This is an important consideration with respect to any mechanism of generation of EADs at the cellular level, including the mechanism considered here. However, it is important to understand all possible mechanisms by which EADs may be generated at the cellular level. It is known that EAD frequency is increased in ventricular myocytes isolated from the failing heart (Nuss et al., 1999), likely due to hyperphosphorylation of LCCs (Chen et al., 2002). Overexpression of CaMKII in isolated murine myocytes, which increases mode 2 gating of LCCs, leads to increased EAD frequency (Wu et al., 2002). Our results provide a possible explanation for these experimental data. Overexpression of CaMKII is also shown to produce EADs in murine ventricular tissue and these EADs are eliminated with application of CaMKII inhibitors, with little or no accompanying APD shortening (Wu et al., 2002). These data demonstrate that under these particular experimental conditions, EADs produced by increased mode 2 gating of LCCs may occur in tissue. The precise mechanism(s) by which EAD generation is supported at the tissue level remains an important issue that is central to the interpretation of our results. We are currently working on methods to further optimize simulation runtime, and plan to address this issue once more efficient algorithms have been developed.
In the LCC model used in this study, mode 2 activity differs from that of mode 1 only in channel mean open time. Recently, Josephson et al. (2002a,b) have found that mode 2 LCCs exhibit a 70% increase in unitary current amplitude compared to mode 1 channels, as well as a shift in the voltage dependence of channel opening. Mean open time was also observed to be 10–100 times greater for mode 2 channels than for mode 1 channels. Inclusion of these experimental findings would likely enhance the contribution of mode 2 LCC fluctuations to total ICaL, further supporting the idea that modal gating of LCCs is an important component of the mechanism of EAD generation.
Calmodulin kinase II and EADs
The effects of CaMKII on cardiac myocytes are under intensive investigation (reviewed in Anderson, 2004). Recent evidence obtained in the presence of constitutively active CaMKII indicate that 1), there is a significant shift in LCC gating from mode 1 to mode 2 (Dzhura et al., 2000); and 2), myocytes isolated from transgenic mice exhibit both EADs and enhanced LCC activity (open probability) (Wu et al., 2002). Both of these effects are eliminated by the CaMKII-inhibiting peptide AC3-I. The agreement of our simulation results with these experiments suggests that phosphorylation targets of CaMKII are likely similar to those of PKA as implemented in this study. Wu et al. (2002) also observed that the decrease in EAD frequency with CaMKII inhibition was not associated with a decrease in APD, suggesting that AP prolongation alone does not cause EADs. The modeling results presented here suggest that an altered distribution of LCCs among modes, combined with altered channel availability, can influence the frequency of EADs in the absence of a change in APD, and therefore may be an important mechanism underlying these experimental observations.
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Recent evidence indicates that in human heart failure, the number of LCCs expressed is reduced and the fraction of LCCs available for gating is increased (Schröder et al., 1998). It has been suggested that the phosphorylation of protein targets within the cellular microdomain between the t-tubule and the JSR may be regulated locally, and that the phosphorylation state of these molecules is increased in failing human ventricular myocytes, potentially as a result of decreased activity of phosphatases in the microdomain (Chen et al., 2002). We therefore speculate that the stochastic mechanism of EAD generation investigated in this simulation study may also be of importance in explaining the increased rate of EAD occurrence in failing ventricular myocytes (Nuss et al., 1999). There is as yet no evidence of any shift in the relative distribution of LCC gating modes in human heart failure. Experimental studies directed at understanding details of LCC modal gating in both normal and diseased human myocytes would be an important direction for future investigation.
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This work was supported by National Institutes of Health grants RO1 HL60133, RO1 HL61711, and P50 HL52307, the Falk Medical Trust, the Whitaker Foundation, and IBM.
Submitted on August 17, 2004; accepted for publication October 5, 2004.
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