Cardiovascular Research

Cardiovascular Research 2006 69(1):116-127; doi:10.1016/j.cardiores.2005.08.015

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Copyright © 2005, European Society of Cardiology

A multi-modal composition of the late Na⁺ current in human ventricular cardiomyocytes

Victor A. Maltsev¹ and Albertas I. Undrovinas^*

Henry Ford Heart and Vascular Institute, Henry Ford Hospital, Cardiovascular Research Bldg. Room 4015, 2799 West Grand Boulevard Detroit, MI 48202-2689, United States

^* Corresponding author. Tel.: +1 313 916 1321; fax: +1 313 916 3001. Email address: aundrov1{at}hfhs.org

Received 28 January 2005; revised 12 July 2005; accepted 5 August 2005

	Abstract

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
Objective: We reported an ultraslow late Na⁺ current (I_NaL) in ventricular cardiomyocytes of human hearts. I_NaL has been implicated in regulation of action potential duration in normal hearts and repolarization abnormalities in failing hearts. We have also identified sodium channel (NaCh) gating modes including bursts (BM) and late scattered openings (LSM) that together comprise I_NaL; however, the contribution of these gating modes to Na⁺ current (I_Na) remains unknown. In the present study, the late NaCh activity was recorded, analyzed, and modeled for heterologously expressed NaCh, Na_v1.5, and for the native NaCh of ventricular mid-myocardial cardiomyocytes from normal and failing hearts.

Methods and results: We found that LSM gating was significantly slower in failing compared to normal myocytes and Na_v1.5 (=474 ± 10 vs. 299 ± 9, and 229 ± 12 ms, m ± SEM; P<0.05, n=5–6). Total burst length of BM decreased with depolarization and was larger in failing compared to normal myocytes and Na_v1.5. A complete I_Na decay was then numerically approximated as composed of NaCh populations operating in three gating modes described by separate Markov kinetic schemes: transient mode (TM), LSM, and BM. The populations of NaCh operating in each gating mode were estimated as 79.8% for TM, 20% for LSM, and 0.2% for BM, yielding an apparent four-exponential I_Na decay at –30 mV (maximum I_Na) (_i0.4, 4, 50, and 500 ms). Whole-cell recordings confirmed the existence of all four predicted components. The model also predicted voltage and temperature dependence of I_NaL as well as I_NaL increase and slower decay in failing hearts and acceleration by amiodarone.

Conclusions: The early phase of Na⁺ current decay (<40 ms) involves all three NaCh gating modes, the intermediate phase (from 40 to 300 ms) is produced by BM+LSM, although the contribution of BM decreases with depolarization, and ultra-late decay (>300 ms) is determined solely by LSM. The concept of multi-mode composition for I_NaL provides a new rationale for I_NaL modulation by factors such as voltage, temperature, pharmacological agents, and pathological conditions.

KEYWORDS Ion channels; Single-channel currents; Na⁺ channel; Myocytes

	1. Introduction

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
We reported an ultraslow inactivating and reactivating late Na⁺ current (I_NaL) in human ventricular myocytes (VM) from both normal and failing hearts that has been implicated in the action potential (AP) plateau [1]. In VM of failing human and dog hearts, whole-cell I_NaL was augmented and I_NaL decay was slower as reported by our group and others [2–4]. Partially blocking this current with toxins or lidocaine returned AP to its normal duration and halted early afterdepolarizations [1,3]. Recently I_NaL has been recognized as one of the major factors contributing to abnormal repolarization in heart failure [5].

In spite of its importance, to our knowledge the complete I_Na decay time course, including I_NaL, has never been examined in humans or approximated numerically. Until recently such an examination has been hampered by technical difficulties related to simultaneous recording and analysis of relatively large fast/transient currents (I_NaT, 10 nA and 1 ms, respectively) and small slow/late currents (I_NaL, 10 pA and 1 s). Also, because the difficulty in working with human cardiac tissues in general, and recording the late Na⁺ channel (NaCh) [6] in particular, a statistically significant difference in late NaCh gating has not been demonstrated.

Based on a detailed patch-clamp examination of late NaCh activity, we believe the present study shows for the first time that both bursts (BM) and late scattered openings (LSM), the gating modes comprising I_NaL [6], are significantly slower in failing human VM compared to normal VM or the heterologously expressed NaCh -subunit, Na_v1.5. Channel gating was approximated numerically and included in a new model of a complete "multi-modal" I_NaL decay. Based on this model, we were able to clarify the origin of the exponential components of the whole-cell recordings, allowing us to assess the importance of specific NaCh gating modes for different phases of the I_NaL time course in normal and failing hearts. The model also predicted I_NaL modulation by voltage, temperature, and pharmacological interventions, such as amiodarone.

	2. Materials and methods

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
2.1 Cardiomyocyte isolation and heterologous Na_v1.5 expression
Single NaCh were examined in mid-myocardial VM isolated from three normal donor hearts which for technical reasons were not suitable for transplantation, and from three explanted hearts from patients with end-stage heart failure [1]. Whole-cell I_Na was studied in VM of four additional human failing hearts. The use of human tissues conforms with the principles outlined in Declaration of Helsinki and was approved by the Henry Ford Health System Human Rights Committee (Institutional Review Board). Human cardiac Na_v1.5 was heterologously expressed in a HEK293 cell line as reported previously [6].

2.2 Patch-clamp technique
Whole-cell and single-NaCh I_Na were recorded at room temperature (24 °C) by the whole-cell patch-clamp technique (pClamp 8.0, Axon Instruments) and analyzed as described previously [1,6]. Currents were low-pass filtered (–3 dB, 5 kHz) and digitized at a sampling rate of 20 kHz (Digidata 1200, Axon Instruments).

Whole-cell I_Na was recorded with low-resistance (0.6–0.8 M) fire-polished glass pipettes and elicited by 2 s membrane depolarizations from a holding potential of –140 mV applied at a rate of 0.1 Hz. Series resistance compensation was adjusted to provide optimum voltage control. The entire time course of I_Na (I_Na=I_NaT+I_NaL) was measured with, [Na⁺]_bath=5 mM and experimental traces were averaged (50). Average "zero" current (I₀) was obtained after applying tetrodotoxin (25 µM) and subtracted from total average current (I), so that I_Na=I–I₀. The bath contained (in mM): 5 NaCl, 133 CsCl, 1.8 CaCl₂, 2 MgCl₂, 5 glucose, 0.002 nifedipine, and 5 HEPES-CsOH (pH 7.3). The pipette solution contained (in mM): 5 NaCl, 133 CsCl, 2 MgATP, 20 TEA-Cl, 10 EGTA, and 5 HEPES-CsOH (pH 7.3). I_NaL was also measured without averaging in a bath solution containing a physiological concentration of Na⁺ (in mM): 140 NaCl, 5 CsCl, 1.8 CaCl₂, 2 MgCl₂, 5 glucose, 0.002 nifedipine, and 5 HEPES–CsOH buffer (pH 7.3). I_NaT was inactivated by a short voltage pre-pulse of 5 ms to +50 mV Multi-exponential function was fit to I_Na decays by Clampfit 9 program (Axon Instruments) with the Levenberg–Marquardt method, utilizing the sum of squared errors.

Single-channel cell-attached recordings were obtained with low-resistance pipettes (1.8–2.4 M) to increase the number of low-probability late NaCh in the patch (up to 25) and thereby improve the success rate. Depolarizations of 816 ms were applied at a stimulation rate of 0.2 Hz, so that late channel activity would recover completely. The composition of the pipette solution was (in mM): 280 NaCl, 1.8 CaCl₂, 2.0 MgCl₂, 10 tetraethylammonium, 0.002 nifedipine, and 10 HEPES–NaOH buffer (pH 7.3). The depolarizing bath solution contained (in mM): 150 KCl aspartate, 2 MgCl₂, 10 TEA-Cl, 5 glucose, and 10 HEPES–KOH buffer (pH 7.2).

Custom-made software was used for primary single-channel analysis. The channel opening threshold was set to half the amplitude of the single-channel current as evaluated from Gaussian fit to amplitude histograms. Only non-overlapping events were considered, omitting the last closure within the depolarization step. Distributions for single-channel events were analyzed using custom-made software and logarithmic histograms. When analyzing burst activity, we considered any period of inactivity as a gap when its length (_gap) was greater than 4._close1 (gap criterion). Changing the gap criterion from _gap>3._close1 to _gap>6._close1 resulted in only minor changes in envelope distribution (13.4 vs. 12.6 ms), supporting our contention.

2.3 Computer simulations
Single-channel openings were simulated employing a previously described algorithm [7]. The numerical model of I_Na decay was developed using Delphi-7 software (Borland).

2.4 Statistical analysis
Data are expressed as mean ± SEM. NaCh latency was compared between three groups: clone, normal and failing heart. There were 5–6 samples in each group. We found no evidence of an obvious deviation from normality for any of the groups, and therefore standard analysis of variance (ANOVA) was employed. Tukey's Studentized Range was used to adjust for multiple comparisons. Differences were considered significant at a value of P<0.05.

	3. Results

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
3.1 Three modes of NaCh activity, experimental data
Three major gating modes of NaCh activity were found in all cell-attached patches of heterologously expressed Nav1.5 (n=9 patches), normal VM (n=8) and failing VM (n=9) (Fig. 1A–C): a transient mode (TM), a late scattered mode (LSM), and "bursts" (BM). Statistical analysis of the LSM openings revealed significantly slower latency in failing VM compared to normal VM and clone (Fig. 1E).

View larger version (38K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 1 Single-channel data from human ventricular myocytes. (A)–(C) Three major types of single Na+ channel modal activity: transient (A), late scattered openings (B) and bursts (C), including total burst length and envelopes. (D) Ensemble-averaged current was from 160 original traces containing no bursts. A double-exponential function (solid line) was fit to the current decay (dots). (E) Time constant of the latency of the late scattered openings in heterologously expressed Nav1.5 in HEK293 cells and human normal and failing ventricular myocytes at –30 mV: m ± SEM, n=number of patches, *P<0.05 failing cells, vs. normal or Nav1.5. (F) The total burst length evaluated at different membrane potentials. Data were collected from 5–8 patches; m ± SEM, *P<0.05, heart failure vs. normal heart or clone. Cell-attached configuration: Vh=–140 mV, 24 °C.

 
We previously found that bursts had two close states characterized by _close1 and _close2 [6]. Burst activity was manifested by periods of rapid switching between the open state and the first close state, separated by long gaps without channel activity (second close state). Fig. 1C shows one such burst, indicating periods of rapid channel switching activity ("envelopes") and total burst length determined from single-channel measurements. Total burst length was potential-dependent (decreased with depolarization) and was largest in VM of failing hearts (Fig. 1F).

3.2 Simulations of single-NaCh currents
3.2.1 Transient mode (TM)
We employed a simplified non-unique model for early NaCh gating of heterologously expressed Na_v1.5 [8]. Based on our patch-clamp data (Fig. 1 and [6]), we made the following modifications (Fig. 2A):

1) The transition I₆I₅ was prohibited, thereby eliminating the steady-state current produced by channel re-openings.

2) c and e were slightly changed to c=1/0.4=2.5 ms^–1 and e=1/4.21=0.2375 ms^–1, where 0.4 and 4.21 ms are the time constants for open times and latency distributions of early openings at –30 mV [6].

3) Transitions C₃I₅ and I₅C₃ were omitted, as they were originally introduced only for scaling purposes.

4) We made d=0.1 ms^–1 to bring the contribution of ₂ in line with our estimate of 9% for ensemble current (Fig. 1D) and other reports [9].

View larger version (35K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 2 Kinetic models describing the three major modes of NaCh gating: transient mode (A), late scattered openings (B) and bursts (C), together with simulated traces and transition rates in ms–1. Rates a and b () for the activation process were taken from [8]. All other rates were calculated from single-channel data obtained at –30 mV (see text for details). Traces in (A), (B), and (C) were generated from 3, 5, and 1 channel(s), respectively. Total simulation times are indicated above the traces. Simulated traces had a noise amplitude and bandwidth similar to actual single-channel recordings.

 
3.2.2 Late scattered mode (LSM).
While the TM model describes early openings and re-openings in cardiomyocytes very well it does not reproduce the slowly inactivating late currents generated by late scattered openings and bursts [6]. Accordingly, we added two more channel populations operating in LSM and BM (Fig. 2). For LSM, e=1/474 ms=0.00211 ms^–1, where 474 ms is the time constant for latency of scattered openings at –30 mV (Fig. 1E). Note that we used the value measured for myocytes in heart failure for further comparison of model predictions with whole-cell recordings obtained in failing hearts (below). Early openings/re-openings and LSM have the same distribution for open times [6], indicating that fast inactivation (O₄I₅) has the same rate, c=2.5 ms^–1. In single-channel recordings, late scattered openings occurred in clusters (2 openings on average) seen approximately once in 10 traces within 200 to 800 ms after membrane depolarization. LSM traces simulated with d=0.01 ms^–1 showed this experimentally observed pattern. Alternatively, simulation with d=0.3 ms^–1 as in [8] displayed a pattern of several hundred re-openings that we never observed in human VM or Na_v1.5-expressing cells (not shown).

3.2.3 Burst mode (BM)
The burst mode was described by a kinetic scheme with one close state (C₁), one open state (O₂), and two inactivated states (I₃, I₄) (Fig. 2C), yielding two close states observed in NaCh bursts in human VM [6]. Rapid switching between C₁ and O₂ forms the burst itself, whereas transitions to the inactivated state I₃ result in gaps (Fig. 1C) corresponding to the second close time found in bursts [6]. Return from the "deep" inactivated state I₄ back to I₃ was not included, as we observed no burst reappearance once initial burst activity ceased. Rate constants were estimated based on single-channel data (Table 1) and confirmed backward and forward compatibility of simulated currents with experimental single-channel distributions (not shown) and whole-cell currents (see below), respectively.

View this table: [in this window] [in a new window]   Table 1 Estimated rate constants for the burst mode (BM) kinetic scheme shown in Fig. 2C

 
3.3 Model predicts whole-cell Na⁺ current
On average, we observed 4 late scattered openings in 10 traces in an average 5-channel patch; this opening rate could be simulated with one LSM channel, suggesting LSM % population 20%. The number of bursts per trace per channel in each patch was (1.93 ± 0.38).10^–3 as defined from 1,951 traces recorded in 6 patches; this estimates BM % population 0.193%. Simulations of total I_Na (Fig. 3) were performed with a total of 100,000 NaCh satisfying the previously reported density of 0.35 pA/pF for I_NaL measured at 200 ms depolarization in human VM [1]. Thus an average human VM with a membrane capacitance of 150 pF yields I_NaL50 pA (Fig. 3B). The predicted peak of I_NaT was 50 nA (Fig. 3A) with a ratio I_NaL/I_NaT10^–3, close to the experimentally measured ratio of 0.7.10^–3 for Na_v1.5 [10]. We then calculated the percent contribution of each gating mode to I_Na during its time course (Fig. 3D). The experimental and simulated currents appear almost identical in two time scales, 20 and 2000 ms (see insets in Fig. 3A and C).

View larger version (38K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 3 Simulated total Na+ current (Itotal) from 100,000 channels described by a composite multi-modal stochastic model (Fig. 2): 79,807 channels were operating in transient mode (TM), 20,000 in late scattered mode (LSM) and 193 in burst mode (BM). Itotal and the contributions of the different gating modes (Itotal=ITM+ILSM+IBM) are shown at different time scales increasing from (A) to (C). The early phase (A) is derived mainly from TM, the intermediate phase (B) from BM+LSM, and the late phase (C) entirely from LSM. Note that in (C), Itotal and ILSM almost overlap. Simulated Itotal and experimental whole-cell currents appear identical in time frames 20 and 2000 ms (patch-clamp recording insets in (A) and (C), respectively). (D) Instantaneous percent contributions to total INa predicted by the model for the three different gating modes during 300 ms of membrane depolarization to –30 mV.

 
The multi-mode model of complete I_Na decay (Fig. 2), by definition, manifests an apparent decay composed of four exponentials with the following time constants: ₁=1/c=1/2.5=0.4 ms (NaCh inactivation in TM and LSM), ₂=1/e=1/0.2375=4.2 ms (inactivation of re-openings in TM), ₃=54.6 ms (apparent time constant for burst inactivation), and ₄=1/e=1/0.00211=474 ms (inactivation of re-openings in LSM). To validate this prediction (and thus the model itself), we performed a four-exponential fit of the entire average I_Na decay measured in a low [Na⁺] bath (5 mM). Indeed, all four predicted I_Na decay components were found in the whole-cell recordings (Fig. 4A and B). The slight difference in percent contributions and values for the exponentials predicted by the model and those measured experimentally (Table 2) could be related to the difference in experimental conditions, particularly extracellular [Na⁺], 5 compared with 280 mM (whole-cell compared with cell-attached configuration from which the model was derived).

View larger version (24K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 4 Multi-exponential decay function closely fits whole-cell INa recordings in human ventricular myocytes. (A) and (B) Four-exponential fit for a total INa (in gray) recorded at a low bath Na+(5 mM) and shown as transient (INaT) and late (INaL) currents, respectively, at two different time scales. (C) Simplified two-exponential fit for INaL decay recorded with 140 mM Na+ in the bath. The respective fitting functions are shown as solid black lines, with a boxed numerical representation indicated by the arrows.

 

View this table: [in this window] [in a new window]   Table 2 Four-exponential fit of total whole-cell INa decay measured in 4 cells from 3 hearts ("patch clamp", mean ± SEM) or simulated with the stochastic model ("model simulation", n=107 channels)

 
To minimize differences related to the experimental conditions, we also performed whole-cell experiments with bath [Na⁺]=140 mM. Since the first and second decay components (₁ and ₂; Table 2) representing the transient Na⁺ current (Fig. 1F) are well known [11], we focused on the two new slow exponents with time constants ₃ and ₄, mainly comprising I_NaL. I_NaT surge was eliminated with a short voltage pre-pulse of 5 ms to +50 mV [1] and I_NaL decay (Fig. 4C) was fit to a two-exponential function beginning at 40 ms membrane depolarization, when any remaining TM activity is ceased (Fig. 3D). The average % contributions and time constants for the two slow exponential determined from the whole-cell recordings in 24 cells from 3 hearts were: 48.0 ± 4.7 ms and 42.5 ± 1.6%; 563 ± 32 ms and 57.5 ± 1.6%, in line the with predicted time constants of 54.6 and 474 ms, respectively, for BM and LSM (see above). The nearly equal percent contribution by the two identified exponentials also fits very well with the predicted BM and LSM contributions at 40 ms membrane depolarization (48% and 52%, respectively; Fig. 3D).

3.4 Voltage dependence of I_NaL
We previously identified three voltage-dependent parameters in single-NaCh inactivation in human VM [6]. One was the second ("slow") voltage-dependent inactivation component of early openings, represented by the constant e in the kinetic scheme for the transient mode (Fig. 2A). This component was not examined further in the present study, as it relates to I_NaT and has already been characterized extensively in a variety of species including human cardiomyocytes [9]. The other two voltage-dependent parameters are related to the burst mode: the open time (_o) and the slow component of distribution of close times (_C2) within bursts [6]. We used a linear approximation of _o and _C2 voltage dependency based on their respective linear regression lines from our previous data [6], as follows (in ms and mV): _o(V)=0.062*V+3.78 and _C2(V)=0.21*V+12.5. These voltage dependencies were incorporated into the model (Fig. 2C) with b=1/_o(V) and d=_C2(V), respectively. This modified model reproduces experimentally observed voltage dependence of NaCh bursts (Figs. 1F and 5A) and predicts that both P_open and average current decay accelerate with membrane depolarization (Fig. 5B and C), so that increasing gaps between envelopes (reflected by _C2) have a greater effect on P_open than longer openings within the envelope. The faster burst inactivation at higher voltages can readily be explained: by staying longer in a gap, the channel can more easily fall into the stable inactivated state I₄.

View larger version (30K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 5 Voltage dependence of Na+ channel bursts. (A) Experimentally measured activity reproduced by the model simulations. (B) and (C) Model predictions for time course of Popen (B) and average current of a single channel operating in burst mode at various membrane voltages (C). Predictions were obtained by averaging the activity from 1000 simulations of the bursting channel. Calibration bars are 1 pA and 10 ms.

 
3.5 Temperature dependence of I_NaL
Increasing temperature from 23 to 33 °C reportedly accelerated I_NaL decay from 143 to 65 ms (Q₁₀ 2.2), but did not change the ratio of I_NaL to peak I_NaT [12], indicating that human NaCh clone conductance had the same Q₁₀ for both currents. Assuming Q₁₀=2.2 for late NaCh gating and Q₁₀=1.5 [13,14] for NaCh conductance, I_NaL simulations at 37 °C (Fig. 6) closely reproduced the I_NaL decay acceleration observed in NaCh clone [12] and in our studies of canine ventricular myocytes ("gating" Q₁₀2; unpublished data).

View larger version (33K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 6 Model predicts acceleration of INaL decay and increase in INaL amplitude as temperature increases from 24 °C (A, B) to 37 °C (C, D). The figure shows simulated cumulative activity of 20,000 late scattered mode channels (LSM, Panels A and C) and 193 burst mode channels (BM, panels B and D) at different voltages indicated at the traces. All channels were available and activated upon depolarization. Channel numbers were chosen to correspond to a human ventricular myocyte (same as in Fig. 3). Gating schemes for LSM and BM are shown in Fig. 2B and C, respectively. Temperature dependence was explored using Q10 factors as discussed in the text. Single-channel currents for 24 °C were calculated with a conductance of 11 pS. Equilibrium Na+ potential was calculated as ENa=(RT/F)*ln([Na]o/[Na]i). The LSM currents were low-pass (100 Hz) filtered.

 
3.6 I_NaL of Na_v1.5 and normal and failing hearts
Based on our single-channel data (Fig. 1E and F), we evaluated LSM and BM for Na_v1.5 expressed in HEK293 cells, normal VM, and failing VM. Simulated current decays for both modes: BM and LSM were significantly slower in failing VM compared to either normal VM or Na_v1.5 (Fig. 7) at –30 mV. An important new prediction of the model was that the slower LSM gating in failing VM resulted in a larger I_NaL amplitude (by 30%; 65 pA compared to 50 pA in normal VM) measured 200 ms after depolarization. Also, I_NaL transferred significantly more Na⁺ to failing cells (see inset in Fig. 7A). The total charge transferred by I_NaL from 10 to 2000 ms was predicted as 28.5 and 45 pC for normal and failing VM, respectively, or a 58% increase.

View larger version (28K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 7 Model predicts augmented and slower INaL at various membrane potentials in a human ventricular myocyte in heart failure vs. a normal myocyte and Nav1.5 expressed in HEK293 cells. (A) Late scattered mode (LSM). (B) Burst mode (BM). The model parameters were changed based on the single-channel data (Fig. 1 E and F) as follows: rate e in Fig. 2B (LSM) was 0.0043554, 0.00334, and 0.00211 ms–1 and rate e in Fig. 2C (BM) was 3, 0.2, and 0.086 ms–1 for Nav1.5, normal and heart failure VM, respectively. Activity is shown at –30 mV from 20,000 LSM channels and 193 BM channels with a conductance of 11 pS. LSM currents were low-pass (100 Hz) filtered. Inset shows a larger integral of the LSM current in a heart failure myocyte vs. a normal myocyte; the box size is 50 pC x 1990 ms.

 
3.7 Model predicts amiodarone effect on I_NaL
As we reported previously [15], amiodarone effectively and selectively reduced amplitude (I_NaL not I_NaT) and significantly accelerated decay of I_NaL (see example in Fig. 8A). Our I_NaL model (Fig. 2B) predicts that the only way I_NaL decay could accelerate so dramatically is by speeding up the transition I₅I₆ (controlled by constant e). However, when we adjusted constant e to yield the experimentally observed acceleration, it resulted in only a relatively small drop in I_NaL amplitude of 23% (not shown) comparing to 50% observed experimentally, indicating that amiodarone has a more complex effect on NaCh gating. One possibility that would explain remaining 27% to the total blocking effect is to assume that amiodarone stabilizes the inactivated state (I₅, Fig. 8B) controlled by the constant d. We have shown that amiodarone effectively interacts with the inactivated state of the late NaCh with the dissociation constant of 0.15 µM [15]. Thus, a combined change of e and d closely predicts the experimentally observed effect on and I_NaL amplitude (Fig. 8). Future single-channel experiments will test this prediction.

View larger version (23K): [in this window] [in a new window] [Download PowerPoint slide]   Fig. 8 Experimental effect of amiodarone (AMIO, 5 µM) on INaL (A) in human ventricular myocytes as predicted by the new Markov model of late Na+ channel gating (B). Model simulations using the kinetic schemes shown in Fig. 2 were performed for 170,000 Na+ channels, 34,000 operating in LSM mode and 328 in burst mode. Rate constants e and d for LSM mode were 0.00145 and 0.01 ms–1 in control cells and 0.0028 and 0.0062 ms–1 in the presence of AMIO.

 

	4. Discussion

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
We believe the present study represents the first report of significantly slower gating of late NaCh in human failing VM. Also, based on our single-channel data, we developed the first stochastic numerical model of complete I_Na decay during long-lasting membrane depolarizations (up to 2 s) that included I_NaL in adult human VM. The model permitted important predictions about instant contributions of various gating modes to I_NaL and their modulation by voltage, temperature, pharmacological factors (such as amiodarone) and heart failure.

4.1 Theoretical importance: comparison with previous models
Böhle et al. [16] used Hodgkin–Huxley formalism [17] to describe ensemble-averaged currents produced by five distinct NaCh gating modes that comprise the fast peak component of I_Na in human VM (late NaCh was not examined). Another approach describing channel gating as a Markov process provides a much better approximation, as it reproduces single-channel behavior. However, existing Markov models for the cardiac NaCh are incomplete as they only describe transient I_Na [18–21] and miss late NaCh activity lasting hundreds of milliseconds. The most recent Markov model for the human cardiac NaCh clone Na_v1.5 [8] included a late component that faithfully described a persistent current produced by long-QT-related NaCh mutants. With respect to wild-type NaCh, that model also generated a substantial non-inactivated current (50 pA for 100,000 channels, not shown) that is absent in whole-cell recordings of both human VM [1] and heterologously expressed Na_v1.5 (our unpublished data) and also conflicts with single-channel latency data for scattered openings that become inactivated with time [6]. Our new Markov model for human cardiac NaCh prohibits transition I₆I₅ (Fig. 2), ruling out persistent I_NaL produced by LQT3 NaCh mutants [8]. The major advantage of the new model is that it handily predicts both single-channel kinetics of late NaCh (Fig. 2) and the complex composition of I_Na decay (Fig. 3), which is governed by a four-exponential decay process. All four exponentials predicted by the model were confirmed in the whole-cell recordings (Fig. 4), thereby validating the model and providing mechanistic insight into gating mode origin.

4.2 Interplay of gating mode contributions: paradoxes and their mechanisms
We discovered an interesting interaction among the contributions of the various gating modes to I_Na (Fig. 3D). Early after the onset of membrane depolarization, TM provides most I_Na; however, its dominance is short-lived, as TM becomes completely inactivated after 40 ms. All three modes have an almost equal contribution at 16 ms when BM briefly takes the lead. After 33 ms BM progressively decreases so that I_Na is formed entirely by LSM after 300 ms. This is a paradoxical outcome, as it means most I_NaL is produced by relatively rare scattered openings (Fig. 1B) rather than bursts characterized by abundant channel activity (Fig. 1C). We believe this is because bursts occur in a much smaller fraction of the NaCh than LSM (0.193% compared to 20%, respectively) and they are inactivated much faster (with an apparent decay time constant of 50 vs. 500 ms). Furthermore, the contribution from the bursting channels is expected to decrease with depolarization (Figs. 5B, C, and 6B, D).

Another important and unexpected finding is that despite a much smaller channel population operating in LSM compared to TM (20% vs. 79.8%) and a much smaller scale of I_NaL compared to I_NaT, LSM and TM channels transfer almost the same amount of Na⁺ through the plasma membrane during 2 s depolarization. We integrated the respective simulated currents for a cell with 10⁵ NaCh (similar to Fig. 3) and found that TM, LSM, and BM transferred total electrical charges of 42, 45 and 7 pC, respectively. In other words, the I_NaT peak is about 3 orders of magnitude larger than I_NaL (50 nA compared to 50 pA), yet its span is about 3 orders of magnitude shorter (2 ms compared to 2 s), resulting in both modes transferring almost the same total charge.

4.3 Physiological importance
We have previously reported the effect of ion currents produced by NaCh operating in BM and LSM on the AP plateau in human VM, suggesting that these gating modes are important for both plateau support and prolonging AP [6]. The present study evaluated populations of NaCh operating in different gating modes and examined the time, voltage, and temperature dependence of Na⁺ currents originating from different gating modes. These results provide a new theoretical basis for future modeling of AP in human VM, with predicted contributions for the NaCh gating modes to various phases of AP.

Previous studies suggested that NaCh could reopen after activation and thus contribute to the AP plateau [22]. The present study shows that not all NaCh re-openings contribute to the AP plateau. Both TM and LSM are capable of generating re-openings (Fig. 2A and B), but only LSM re-openings are sustained during membrane depolarization (up to 1 s; Fig. 3C), thus contributing to the entire AP plateau. The current produced by BM might be important for the very early phase of the AP plateau, as its contribution to total I_Na (evaluated by the model) would be greatest 30 ms after membrane depolarization (Fig. 4) and fade away almost completely after 300 ms. In contrast to LSM, BM gating shows a strong voltage dependence (Fig. 1F). Since its P_open decreased with membrane depolarization (Fig. 5), the BM current could be expected to contribute to AP only at relatively low voltages. Thus, only those NaCh operating in LSM and BM, not TM, contribute to the AP plateau.

The model provides important predictions that I_NaL composed of LSM and BM has greater amplitude at 37 than at 24 °C (Fig. 6), and its duration is comparable with AP plateau (250 ms) [1] in human VM at the physiological temperatures. Accordingly, I_NaL is expected to be significantly larger at 37 °C, and may have an even greater impact on the AP plateau than at 24 °C as we suggested previously [6]. Our earlier reports of the profound effects of partial blockade of I_NaL by TTX, STX, and lidocaine on AP duration at 37 °C in human and canine VM indirectly support this concept [1,3].

4.4 Clinical and pharmacological importance
We found significantly different gating of late NaCh in VM of patients with heart failure as compared to normal individuals (Fig. 1E, F). Our numerical model of I_NaL, utilizing the experimentally determined changes in the gating modes, predicted the augmented and slower whole-cell I_NaL (Fig. 7) already reported for VM in human failing hearts and canine models of heart failure (both diffused infarction and pacing models) [2–4]. An important result of the numerical model is that it suggests a mechanism for the increased I_NaL (despite reduced peak I_NaT [23]) that could result from an increased fraction of NaCh operating in LSM with a slower transition (Figs. 1E and 7A) to the "deep" inactivated state I₆ (Fig. 2B), and/or an increased fraction of NaCh operating in BM with a slower transition (Fig. 1F) into state I₄ (Fig. 2C), increasing both the number of bursts per trace per channel and burst length [6].

The suggested changes in BM and LSM can indeed modulate the AP plateau, as the two gating modes are operable in failing human VM at a membrane potential of –10 mV, comparable to take-off voltages for the early afterdepolarization (from –18 to –2 mV) [6]. Furthermore, an 58% increase in Na⁺ influx via a larger and slower I_NaL in failing hearts (see I_NaL integral in Fig. 7A, inset) may alter [Na⁺]_i homeostasis, resulting in enhanced Ca²⁺ influx through the Na⁺/Ca²⁺ exchanger and support the positive role of the sarcoplasmic reticulum Ca²⁺ load in force development at slow heart rates. In contrary, at high heart rates, increased I_NaL can lead to diastolic Ca²⁺ overload and poor VM contraction [24]. These data indicate that our models of NaCh gating for LSM and BM could prove important for future computer simulations of AP remodeling and Ca²⁺ handling in heart failure.

We previously showed that amiodarone accelerated I_NaL and preferentially blocked I_NaL compared to I_NaT [15]. Our model predicts that this effect is due to a complex preferential interaction between amiodarone and NaCh in the LSM mode, both accelerating the transition into the second inactivation state (I₅I₆) and stabilizing the first inactivation state I₅ (Fig. 8). This effect of amiodarone suggests that different NaCh gating modes in human VM may represent separate new pharmacological targets. Our I_NaL model may provide a valuable tool to advance pharmacological interactions with NaCh operating in different gating modes.

4.5 Study limitations
Data were obtained from a limited number of normal human hearts (n=3), as donor hearts rarely become available for study. Data obtained from HEK293 cells expressing Na_v1.5 may only partially simulate the native channel. The difference between cardiomyocytes and HEK293 cells in the membrane environment (such as the membrane underlying cytoskeleton) as well as auxiliary subunit composition, cell signaling, and other factors may affect channel gating. Multi-channel patches allow us to describe some, but not all characteristics of the NaCh gating modes comprising I_NaL. Our analysis was performed on mid-myocardial VM to avoid possible deviations due to I_NaL dispersion through the wall of the left ventricle [25,26]. How and if the multi-mode composition of I_Na relates to the I_NaL transmural profile awaits further study.

Limitations of the model include the absence of NaCh reactivation and the failure to explain the transition mechanism underlying different gating modes. Böhle et al. [16] reported transitions between modes of high-probability NaCh underlying peak sodium current within one trace, but the time course of switching was not resolved. The problem with resolving mode switches is that there must be only one channel in the patch, making it almost impossible to assess the low-probability late NaCh.

	5. Conclusions

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
Sodium current decay in human ventricular myocytes is governed by a four-exponential decay process resulting from gradual termination of activity of Na⁺ channels operating in three gating modes: transient, burst and late scattered. Heart failure significantly slows late NaCh gating, both bursts and scattered openings, resulting in much greater Na⁺ influx during prolonged membrane depolarization. The concept of a multi-mode composition for I_NaL provides a new rationale for I_NaL modulation by factors such as voltage, temperature, pharmacological agents, and pathological conditions.

	Acknowledgments

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 
This study was supported in part by National Heart, Lung and Blood Institute grants HL-53819 and HL074328 and American Heart Association grant in-aid 0350472Z (A.I. Undrovinas).

	Notes

 
¹ Current address: Gerontology Research Center, National Institute on Aging, NIH, 5600 Nathan Shock Drive, Baltimore, MD 21224, United States.

Time for primary review 13 days

	References

Top Abstract 1. Introduction 2. Materials and methods 3. Results 4. Discussion 5. Conclusions Acknowledgments References

 

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