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Cardiovascular Research 2000 48(3):375-392; doi:10.1016/S0008-6363(00)00182-6
© 2000 by European Society of Cardiology
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Copyright © 2000, European Society of Cardiology

Facilitation of the L-type calcium current in rabbit sino-atrial cells: effect on cardiac automaticity

Matteo E. Mangonia, Pierre Fontanaudb, Penelope J. Noblec, Denis Noblec, Henri Benkemouna, Joël Nargeota and Sylvain Richarda,*

aUPR 1142 CNRS, Institut de Génétique Humaine, 141 rue de la Cardonille, Montpellier Cedex 5, France
bUMR 5101 CNRS, 141 rue de la Cardonille, Montpellier Cedex 5, France
cUniversity Laboratory of Physiology, Parks Road OX1 3 PT, UK

* Corresponding author. Tel.: +33-499-619-939; fax: +33-499-619-901 srichard{at}igh.cnrs.fr

Received 22 March 2000; accepted 12 July 2000


   Abstract
Top
 Abstract
1 Introduction
 2 Methods
 3 Results
 4 Discussion
 Appendix A
 References
 
Objective: The L-type Ca2+ current (ICa,L) contributes to the generation and modulation of the pacemaker action potential (AP). We investigated facilitation of ICa,L in sino-atrial cells. Methods: Facilitation was studied in regularly-beating cells isolated enzymatically from young albino rabbits (0.8–1 kg). We used the whole-cell patch-clamp technique to vary the frequency of the test depolarizations evoked at –10 mV or the conditioning diastolic membrane potential prior to the test pulse. Results: High frequencies (range 0.2–3.5 Hz) slowed the decay kinetics of ICa,L evoked from a holding potential (HP) of –80 mV in 68% of cells resulting in a larger Ca2+ influx during the test pulse. The amount of facilitation increased progressively between 0.2 and 3.0 Hz. When the frequency was changed from 0.1 to 1 Hz, the averaged increase in the time integral of ICa,L was 27±7% (n = 22). Application of conditioning voltages between –80 and –50 mV induced similar facilitation of ICa,L in 73% of cells. The maximal increase of Ca2+ entry occurred between –60 and –50 mV, and was on average 38±14% for conditioning prepulses of 5 s in duration (n = 15). Numerical simulations of the pacemaker activity showed that facilitation of ICa,L promotes stability of sino-atrial rate by enhancing Ca2+ entry, thus establishing a negative feedback control against excessive heart rate slowing. Conclusion: Facilitation of ICa,L is present in rabbit sino-atrial cells. The underlying mechanism reflects modulation of ICa,L decay kinetics by diastolic membrane potential and frequency of depolarization. This phenomenon may provide an important regulatory mechanism of sino-atrial automaticity.

KEYWORDS Ca-channel; Impulse formation; Sinus node


   1 Introduction
Top
 Abstract
 1 Introduction
2 Methods
 3 Results
 4 Discussion
 Appendix A
 References
 
The spontaneous activity of sino-atrial ‘pacemaker’ myocytes underlies cardiac autorhythmicity [1]. Several ionic currents, with complex reciprocal interaction, contribute to the sino-atrial automaticity. Their electrophysiological description has allowed the development of numerical models of the electrical activity of pacemaker cells [2,3]. Two types of Ca2+ current (ICa) have been identified in single sino-atrial myocytes. One is activated by moderate depolarization and is referred to as a low-voltage-activated T-type ICa (ICa,T) [4,5]. Stronger depolarization leads to the activation of a high-voltage-activated L-type ICa (ICa,L) [4–6]. ICa,L is highly sensitive to dihydropyridines (DHPs) and is upregulated by catecholamines and other neurotransmitters that increase intracellular cAMP [7,8]. Finally, sino-atrial cells are characterized by the presence of a sustained component (Ist) described recently [9]. Ist is activated early upon depolarization (about –70 mV), and shows sensitivity to β-adrenergic agonists like ICa,L. Together with the hyperpolarization-activated ‘pacemaker’ current If, ICa,L and Ist account for most of the β-adrenergic stimulation of the mammalian heart rate [9,10].

ICa,L is widely expressed throughout the whole myocardium, where it plays a major role in the modulation of the AP duration, and in the excitation–contraction (E–C) coupling [7,8,11]. However, several of its properties are also consistent with an important role in the generation and modulation of the pacemaker AP [12]. For example, ICa,L is rapidly activated and inactivated upon depolarization and is modulated in opposite ways by β-adrenergic and muscarinic receptor stimulations (increase and decrease in current amplitude, respectively) [8,13]. These basic regulatory mechanisms are involved in the control of sino-atrial cells automaticity and, thus, in the beat-to-beat modulation of cardiac activity. Although voltage is its primary effector, ICa,L is modulated by intracellular messengers, such as cAMP, cGMP and Ca2+, that activate various protein kinases [7,8]. Direct modulation via a membrane-delimited pathway mediated by G-proteins has also been proposed [14]. However, another interesting basic property of ICa,L is its regulation by the frequency of depolarization, a phenomenon described first in frog atrium, and then in rat, guinea-pig, dog and human cardiomyocytes [11,15–23]. In mammalian cardiomyocytes, an increase in the frequency of depolarization slows the decay kinetics of ICa,L. This mechanism induces larger Ca2+ influx during each depolarization. It may have critical effects on the AP amplitude and duration. Similar type of facilitation of ICa,L induced by a moderate depolarization of the diastolic membrane potential (in the range of –80 to –40 mV) has also been described in rat and human cardiomyocytes [24]. In the present work, we have addressed the question of whether facilitation of ICa,L is operant in spontaneously beating sino-atrial myocytes.


   2 Methods
Top
 Abstract
 1 Introduction
 2 Methods
3 Results
 4 Discussion
 Appendix A
 References
 
2.1 Rabbit sino-atrial cells isolation
Spontaneously-beating sino-atrial cells were isolated from young albino rabbits weighing 0.8–1 kg as described before [25,26]. The investigation conforms with the Guide for the Care and Use of Laboratory Animals published by the US national Institute of Health (NIH Publication No. 85-23, revised 1996). Briefly, beating hearts were removed under pentobarbital (3 ml/kg) and ketamine (1 ml/kg, Sanofi Veterinary) anesthesia. The sino-atrial region was excised in a normal Tyrode solution containing (mM): NaCl, 140; KCl, 5.4; CaCl2, 1.8; MgCl2, 1; Hepes–NaOH, 5; and D-glucose, 5.5; (pH 7.4). Strips of tissues were enzymatically digested in a low-Ca2+, low- Mg2+ solution containing (mM): NaCl, 140; KCl, 5.4; MgCl2, 0.5; CaCl2, 0.2; KH2PO4, 1.2; taurine, 50; D-glucose, 5.5; Hepes–NaOH, 5; pH 6.9. Collagenase type II (224 U/ml, Worthington), elastase (1.9 U/ml, Worthington), and bovine serum albumin (BSA) 1 mg/ml were added. The digestion step was carried out for about 15 min under gentle mechanical agitation at 36°C. Tissue strips were then washed out, and transferred into a modified ‘Kraftbrühe’ (KB) medium [27] containing (mM): L-glutamic acid, 70; KCl, 20; KOH, 80; D-β-OH-butyric acid, 10; KH2PO4, 10; taurine, 10; BSA, 1 mg/ml; and Hepes–KOH, 10; pH 7.4. Single sino-atrial myocytes were manually dissociated in KB solution by employing a flame-forged glass pipette. Finally, cell automaticity was recovered by gradually increasing the extracellular Ca2+ concentration up to 1.3 mM [25]. The final storage solution contained (mM): NaCl, 100; KCl, 50; CaCl2, 1.3; MgCl2, 0.7; BSA 1 mg/ml; pH 7.4, and gentamycin (50 µg/ml). Cells were then stored at 4°C until use.

2.2 Electrophysiological recordings
For electrophysiological recordings, cells were harvested in 35-mm Petri dishes, and mounted on the stage of an inverted microscope (Nikon). The whole-cell patch-clamp technique [28] was employed to record ICa in spontaneously beating cells at room temperature (22°C). The voltage-clamp circuit was provided by an Axopatch 200A (Axon Instruments) patch-clamp amplifier. Recording pipettes were fabricated from borosilicate glass. Final electrode resistances were 3 M{Omega}. The intracellular recording solution contained (mM): Cesium(Cs)-aspartate, 120; CsCl, 10; MgCl2, 2; ATP-Na+ salt, 2; GTP Na+ salt, 0.1: EGTA–CsOH, 10; Hepes–CsOH, 10; pCa=8, (pH 7.2) with CsOH. After seal formation the electrode capacitance was compensated electronically before patch rupture, and establishment of the whole-cell configuration. Seal resistances were in the range of 1–2 G{Omega}. Voltage errors resulting from the uncompensated series resistance were always ≤3 mV and were not corrected. Cell input resistances were in the range of 0.2–2 G{Omega}. Whole-cell membrane capacitance was calculated by integrating the capacitive currents recorded during +10 mV voltage steps from a HP of –80 mV. The standard extracellular solution was chosen to block inward Na+, and outward K+ currents, and contained (mM): tetraetylammonium chloride, 130; CaCl2, 2; MgCl2, 1; 4-aminopyridine, 4; Hepes, 25; (pH 7.4 with TEAOH).

ICa,L was routinely recorded by applying brief (60–100 ms) step depolarizations to a test potential which activated maximal current amplitude (usually –10 mV). To measure the current–voltage relationship (I–V), depolarizations were applied in 10 mV increments between –70 and +60 mV from HPs set between –100 and –50 mV at 0.1 Hz. To study the frequency-dependent facilitation of ICa,L, depolarizing steps were applied from an HP of –80 mV at variable frequency (0.1–5 Hz). Depolarization-dependent facilitation was assessed by applying conditioning voltage of variable duration (100 ms–5 s) and amplitude (–100 to –10 mV), prior to the test potential. For each type of facilitation, we measured ICa,L peak amplitude and the time integral between the zero current level after 40 ms depolarization. Although the zero current level does not correspond precisely to the zero ICa,L level (as measured ideally after specific ICa,L blockade) the offset is slight and was estimated to be less than 5% at –10 mV, by measuring the current I–V relation in the absence of extracellular Ca2+. Experimental parameters, such as HPs, test potentials, and sampling intervals were controlled with an IBM PC connected to a Digidata 1200 interface (Axon). Current signals were filtered at 3–5 kHz prior to digitization and storage. Data acquisition and analysis were performed using the PCLAMP software package (Axon), and the ORIGIN 6 data analysis software (Microcal).

2.3 Fittings
ICa,L current-to-voltage relation were fitted according to Eq. (1), which corresponds to the sum of two independent (2) and (3) Boltzmann equations


Formula (1)


Formula (2)


Formula (3)

where I is the current, f(V)1,2 are the two Boltzmann equations, V is the membrane voltage, ga and gb are normalized conductances, Erev is the current reversal potential, h1, and h2 are half-activation factors, and s1 and s2 are the slope factors.

ICa,L inactivation was best fitted by the sum of two exponential components according to the equation


Formula (4)

where ICa,L(fc) and ICa,L(sc) are the amplitudes, and {tau}fast and {tau}slow are the time constants of the fast and slow components of ICa,L, respectively. The zero time was set slightly before the peak of the current to determine ICa,L(fc) and ICa,L(sc) and, in all cases, the sum of ICa,L(fc) and ICa,L(sc) accounted for the peak current amplitude. Activation and inactivation time constants were also obtained from simultaneous multiexponential fitting of current activation, and inactivation. The time constants obtained from these two fitting methods were not significantly different.

ICa,L time integrals were calculated according to the trapezoidal rule (ORIGIN 6 built-in function). The voltage-dependency of the ratio ICa,L(fc)/ICa,L(sc) was fitted according to a two-parameters exponential function


Formula (5)

where Y is the ratio, a is a numerical coefficient, b is a quantity used to adjust the rate constants kf and kb in the model calculations and V is the membrane voltage.

Voltage-dependent facilitation curves were also fitted according to the Boltzmann formulation


Formula (6)


Formula (7)


Formula (8)

where Inorm is the normalized current, a1(V) is the Boltzmann equation corresponding to current facilitation, b1(V) corresponds to current steady-state inactivation, V is the membrane voltage, A1 and A2 are current values, V1/2f and V1/2i is the voltage for half-facilitation and inactivation, respectively, sl1 and sl2 are the slope factors. All fittings were performed by numerical iteration, employing a Levenberg–Marquart based algorithm (ORIGIN 6 built-in). To fit the experimental data shown in each figure, the calculated parameters were used to build a simulation curve for each function.

2.4 Model simulations
For numerical simulation of ICa,L, kinetics, we adapted a model described previously [21]. This model is based on a state diagram which describes the time-dependent changes in the probability of a channel being in each of two proposed kinetic states, referred to as ICa,L(fc) and ICa,L(sc), for the fast- and slow-inactivating component, respectively. The adaptation of this model to sino-atrial ICa,L, as well as the complete set of equations employed, is described in the Appendix section. ICa,L voltage-clamp simulations were accomplished using the XPPAUTO software [29] with the instantaneous probabilities over time obtained by numerical integration. For integrative calculations we have employed the CVODE numerical integration algorithm (software built-in). The integration step was 100 µs for simulations of the frequency-dependent facilitation, and 50 µs for depolarization-dependent facilitation. The calculated current waveforms were generated according to the equation


Formula (9)

where Of and Os are the open state probabilities, for the channel being open in the fast- and slow-inactivating pathway, g is the membrane conductance, V is the membrane potential, and Erev is the apparent reversal potential for Ca2+, which we have set to +50 mV. The voltage-dependent deactivation rate constants used in the numerical simulations were those used in our previous model [21]. The activation rate constants were measured after subtraction of the capacitative transient. obtained in the absence of extracellular Ca2+. The inactivation rate constants were measured in the presence of extracellular Ca2+, and Ba2+. The various rate constants were subsequently adjusted until the model generated currents with time- and voltage-dependent properties consistent with experimental recordings in sino-atrial myocytes. Finally, the model equations were incorporated into the OXSOFT HEART program [30]. The original equations for ICa in the Noble et al. [31] single cell model of sino-atrial automaticity were replaced by these equations to calculate change in cycle length, and AP duration. Intracellular Ca2+ buffering was calculated according to the equations in the Demir et al. model [3].


   3 Results
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
4 Discussion
 Appendix A
 References
 
3.1 Separation of T- and L-type Ca2+ currents
Only spontaneously-beating myocytes were used. The membrane capacitance of these cells was 28±2 pF (n = 25). Our recording conditions were optimized to isolate ICa,L from Na+ and K+ currents. In particular, we used intracellular Cs+ instead of K+ and extracellular TEA+ instead of Na+ in the presence of 4 mM 4-AP to block influx of TEA through Ca2+-independent Ito K+ channels [32]. Accordingly, a depolarizing ramp protocol applied to the cell evoked no inward current in the absence of extracellular Ca2+ (Fig. 1A). Step depolarizations from a HP of –100 mV led to the activation of two types of ICa exhibiting differential sensitivity to the membrane voltage. The first one, which was transient with fast decay kinetics, activated at a threshold of around –60 mV and reached maximal peak amplitude at –30 mV (Fig. 1Ba). This current, which was fully inactivated at a HP of –60 mV, corresponded to ICa,T described in pacemaker myocytes [4,5,33]. The other current had much slower decay kinetics, started to activate between –50 and –40 mV, and peaked at –10 mV (Fig. 1C). It was not inactivated at a HP of –50 mV (Fig. 1Bb). It corresponded to ICa,L. Its averaged density was 18±3 pA/pF (n = 24). In contrast to ICa,L, detected consistently (24/25 cells), ICa,T was recorded in only five cells and its amplitude was less than 20% of that of ICa,L (data not shown). Co-expression of ICa,L and ICa,T was observed in only one cell. However, to ensure that our recordings were representative of pure ICa,L, we routinely employed the differential sensitivity of ICa,T, and ICa,L to the HP as a test (Fig. 1B). This method appeared to be unequivocal, and did not require the use of pharmacological agents such as Ca2+ antagonists with use- and/or voltage-dependent effects that could alter the amplitude and kinetics of ICa,L. We obtained a satisfactory mathematical fit of the current–voltage relationship of ICa,L (Fig. 1C), by employing the expression (1) detailed in the Methods section. Since Ist is inhibited in Na+-free conditions [9], we did not need to separate ICa,L from Ist.


Figure 1
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  		Fig. 1 Voltage-dependent separation of ICa,L and ICa,T in rabbit sino-atrial myocytes. (A) Application of a voltage ramp between –100 and +100 mV, did not elicit inward current in the absence of extracellular Ca2+. Application of 2 mM Ca2+, evoked inward Ca2+ current. In (Ba), ICa,T is observed upon depolarization to the indicated test potentials from an HP of –100 mV (left). ICa,T is completely inactivated at HP –60 mV (right). (Bb) ICa,L was insensitive to depolarizing the HP from –100 (left) to –50 mV (right). (C) ICa,L current-to-voltage relation for traces shown in (Bb) at the HPs of –100 (filled circles), and –50 mV (open circles), respectively. The curve was fitted according to Eq. (1) in the Methods section.

 
3.2 Frequency-dependent facilitation of ICa,L
To study the modulation of ICa,L by the frequency of depolarization, we used test pulses activating maximal peak current (unless otherwise noted in Fig. 2). At the start of an experiment, the cells were stimulated for several min at 0.1 Hz to allow ICa,L to stabilize. At this rate, we observed no evidence for any change in terms of amplitude and kinetics. Then post-rest stimulations were applied at various rates. Rates lower than 0.2 Hz had no effect. Higher rates induced two types of effect: a slight augmentation of the peak current, and a slowing of the decay kinetics (Fig. 2Aa,b). These effects resulted into facilitation of ICa,L with steady-state achieved in four stimulations (Fig. 2Ba). Therefore, the trace corresponding to the fourth stimulation (t4) was taken as the reference in all experiments. In addition, steady-state facilitation was reached independently from the frequency of depolarisation, and therefore length of diastolic interval, per se (Fig. 2Bb). This was highly consistent among cells. There was no further change with additional stimulations, even for several min after the start of an experiment. When changes eventually occurred, they involved only a decrease in peak current amplitude (with no change in decay kinetics) due to either a time-dependent accumulation of the channels in the inactivated state at the highest frequencies (<3.5 Hz) or, sometimes, an irreversible rundown process.


Figure 2
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  		Fig. 2 Frequency-dependent facilitation of ICa,L. (A) Facilitation of ICa,L induced with the protocol shown in inset. (Aa) ICa,L was evoked by a train of stimulations at –10 mV from an HP of –80 mV. In (a) current facilitation is assessed by comparing the first trace at 0.1 Hz, with the fourth trace at 1 Hz. In (b) facilitation of ICa,L as measured on peak, and time integral for trace 1 (open bars 100%, control value), and trace 4 (filled bars). (B) Equilibrium for steady-state frequency-dependent facilitation of ICa,L is reached after four stimulations (Ba), and is independent from the frequency of stimulation (Bb). (C) Facilitation of ICa,L evoked at its activation threshold (–40 mV) by a train of stimulations at 1 Hz. (D) Facilitation of ICa,L evoked at the positive test potential of +10 mV by a train of stimulations at 3 Hz.

 
We routinely measured both the current peak, and the current time integral, to better evaluate the total change in Ca2+ entry. These parameters were measured at the first and at the fourth depolarization after the start of a train. The histogram in Fig. 2Ab illustrates the typical net augmentation of ICa,L peak, and time integral measured for the experimental data shown in Fig. 2Aa. At 1 Hz the averaged increase in ICa,L time integral was 27±7% (n = 22). Facilitation was observed for different levels of depolarization throughout the I–V relationship. For example, step depolarizations at voltages corresponding to ICa,L threshold (–40 mV, Fig. 2C), and at positive potentials (+10 mV, Fig. 2D) induced facilitation of ICa,L. When the frequency of depolarization was >3.5 Hz, a negative effect on the peak current amplitude was observed which limited Ca2+ entry (Fig. 2Bb). This phenomenon reflected incomplete reactivation of Ca2+ channels (data not shown).

3.3 Depolarization-dependent facilitation of ICa,L
We investigated whether, as described in other types of cardiomyocytes [20,21,24], depolarization-induced facilitation of ICa,L is also present in sino-atrial cells. We applied various conditioning potentials from a HP of –80 mV, followed by 100-ms test pulses to –10 mV. The results of a representative experiment are shown in Fig. 3. Both short (100 ms in duration) and long (5 s) conditioning potentials were tested. When 100-ms duration prepulses were applied, both ICa,L peak amplitude and time integral increased gradually with increasing conditioning depolarizations between –80 and –50 mV (Fig. 3A,C and D). The resulting facilitation of ICa,L consisted of an augmentation of the current peak and a slowing of the inactivation kinetics (e.g. between –80 and –60 mV in Fig. 3A). At conditioning voltages positive to –50 mV, ICa,L started to decrease, due to the steady-state, voltage-dependent inactivation process (Fig. 3C and D). For conditioning depolarizations lasting 5 s, facilitation was markedly enhanced and its voltage-dependence to reach the maximal effect was shifted to the left for both peak amplitude and Ca2+ entry (with a peak of time integral at –50 mV instead of –40 mV; Fig. 3D). The part of the curve corresponding to steady-state inactivation (for depolarizations >–50 mV) was also shifted to the left as expected. Among 15 cells investigated, 11 showed facilitation. There was no change in current waveform for depolarisations between –80 and –50 mV in the four remaining cells. The averaged maximal increase of Ca2+ entry when the conditioning potential was depolarized from –80 to –60 mV was 38±14% (n = 15). On average, peak amplitude varied by less than 1% (0.99±0.06% of control) suggesting that the main effect occurs on current decay kinetics. In pilot experiments, we determined that no facilitation occurs in a voltage range between –100 and –80 mV.


Figure 3
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  		Fig. 3 Depolarization-dependent facilitation of ICa,L in sino-atrial myocytes. Representative traces of ICa,L recorded for a preconditioning pulse of 100 ms (A) and 5 s (B) at voltages ranging from –80 to –10 mV prior to the test pulse at –10 mV (the experimental protocols are shown in the upper part of the panels). (C) Normalized value of current peaks, and (D), the time integral of ICa,L. ICa,L was measured upon applying a 5-s (open circles), and a 100-ms (filled circles) conditioning depolarization. Arrows indicate their respective fittings according to Eq. (6) detailed in the Methods section.

 
3.4 Analysis of decay kinetics of ICa,L
When extracellular Ba2+ was used instead of Ca2+ as the permeating ion, the decay of ICa,L was dramatically slowed, indicating that the fast decay of the current is, in major part, related to Ca2+-dependent inactivation (Fig. 4Aa). Since facilitation was related to slowing of inactivation, we analyzed more closely the kinetics of ICa,L. In extracellular Ca2+, ICa,L had a biexponential decay, best-fitted by two time constants (Fig. 4Aa,b). The fast rate constant ({tau}fast) ranged between 2 and 5 ms, and showed no voltage dependence. The slow rate constant ({tau}slow) ranged between 10 and 40 ms. The inactivation rate constants measured in extracellular Ba2+ for depolarizations of 100 ms in duration were similar to {tau}slow (Fig. 4Ab) confirming that the fast decay of ICa,L is due to Ca2+-dependent inactivation. For each cell, therefore, we measured the amplitudes (in pAs) of the fast-inactivating component ICa,L(fc), and the slow-inactivating component ICa,L(sc). The current peak, and the relative amplitude of ICa,L(fc), and ICa,L(sc) at each voltage were used to construct their respective current–voltage relationships (Fig. 4Ba). The voltage-dependence of ICa,L(sc) is 20 mV more positive than that of ICa,L(fc). The voltage-dependence of the ratio between ICa,L(fc) and ICa,L(sc) throughout the ICa,L current-to-voltage relation obeyed to an exponential relation (Fig. 4Bb). Accordingly, the time integral of ICa,L had a voltage-dependence that matched that of ICa,L(sc) more closely than that of ICa,L(fc) (data not shown).


Figure 4
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  		Fig. 4 Kinetics of ICa,L in sino-atrial myocytes. (Aa) Kinetics of ICa,L decay, recorded in extracellular 2 mM Ca2+, and Ba2+, at the peak of their respective current-to-voltage relation. (Ab) Voltage-dependence of {tau}slow, and {tau}fast.in extracellular 2 mM Ca2+ and Ba2+. (Ba) Current-to-voltage relations for ICa,L(fc) (open circles), ICa,L(sc) (filled squares), and current peak (filled circles). (Bb) Voltage dependence of the ratio ICa,L(fc)/ICa,L(sc) for the current-to-voltage relation shown in (Ba). The curve was fitted according to Eq. (6) detailed in the Methods section. All the data are from the same cell.

 
Since the sino-atrial ICa,L is kinetically the sum of a fast and slow components, we investigated whether depolarization- and frequency-dependent facilitation enhanced the relative contribution of ICa,L(sc) to the total ICa,L (Fig. 5). To this aim we used spindle-shaped cells, in which frequency-, and depolarization-dependent facilitation are co-expressed on the same cell, and are directly comparable (n = 8, Fig. 5A and B). Here, ICa,L was up-regulated by rates of stimulation up to 3 Hz (Fig. 5Aa) which reflected a decrease in the ratio between ICa,L(fc), and ICa,L(sc) (Fig. 5Ab). Robust depolarization-induced facilitation was observed in the voltage window between –70, and –50 mV (Fig. 5Ba). In this case, facilitation of ICa,L reflected an increase of ICa,L(sc) (Fig. 5Bb).


Figure 5
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  		Fig. 5 Relative contribution of ICa,L(fc) and ICa,L(sc) during frequency- and depolarization-dependent facilitation. (Aa) ICa,L facilitation increases gradually with the frequency of stimulation. Representative traces for data points at 1, 2 and 3 Hz are shown in insets. Calibration bars correspond to 20 pA, and 10 ms. (Ab) Frequency dependence of the ratio ICa,L(fc)/ICa,L(sc), showing the higher contribution of ICa,L(sc) at high frequencies. Data points are from the cell shown in (Aa, insets). (B) Depolarization-dependent facilitation is associated with up-regulation of ICa,L(sc). (Ba) Facilitation in spindle-shaped sino-atrial cells. Representative traces evoked at –10 mV, upon preconditioning at –80 and –50 mV for 5 s are shown in the inset. Error bars represent mean±SEM. Calibration bars correspond to 40 pA and 30 ms. (Bb): ICa,L peak amplitude (filled circles), ICa,L(fc) (filled squares), and ICa,L(sc) (open circles) following application of conditioning prepulses as described in (Ba).

 
3.5 Model for simulation of ICa,L
We attempted to evaluate the potential influence of modulation of the decay kinetics of ICa,L by frequency of stimulation, and diastolic membrane potential on pacemaker activity. To do this, we performed numerical simulations of both ICa,L and AP waveforms. First, we used a mathematical model to simulate the voltage-, time- and Ca2+-dependent behavior of macroscopic ICa,L. This model takes into account the predicted fraction of Ca2+ channels inactivated by Ca2+, and the fraction inactivated independently of Ca2+ at any time and any voltage. This approach has the advantage of being independent from the exact mechanism of Ca2+-dependent inactivation, as well as to allow to calculate ICa,L behaviour in terms of a voltage-dependent evolution of the ratio ICa,L(fc)/ICa,L(sc) which follows an exponential relationship as experimentally observed (see Fig. 4Bb). This voltage-dependence is also observed for conditioning potentials applied prior to the test depolarisation in a range of voltages that are presumed too weak to activate significant macroscopic ICa,L (Fig. 3; Fig. 5Ba,b). The voltage- and time-dependent equilibrium governing the relative contribution of the two components has been included (see the Methods section). For simplicity, we have assumed that the rate constants governing the transitions between each of the corresponding closed states are identical (see the Appendix). Since {tau}fast is independent from the test potential we used an averaged rate constant. {tau}slow was calculated as an averaged Ca2+-independent time constant.

Numerical simulations of voltage-clamp experiments reliably reproduced peak current and decay kinetics of the experimental macroscopic ICa,L, as well as that of ICa,L(fc) and ICa,L(sc), throughout the voltage range tested (data not shown). The model also predicted the effects of changing the rate of depolarization (Fig. 6A). High frequency-induced ICa,L facilitation was maximal between 2 and 3 Hz (Fig. 6Aa), and the ratio between ICa,L(fc) and ICa,L(sc) decreased accordingly (see Fig. 6Ab and Ac) which was consistent with experimental observations (Fig. 2Bb, 5Aa,b). Moreover, at frequencies higher than 3 Hz, the model correctly predicted the negative effect on current peak, as expected when channel voltage-dependent reactivation becomes limiting. Numerical simulations also reproduced the effect of changing the voltage from which the step depolarization is evoked (Fig. 6B). Consistent with our experimental observations (Fig. 3), depolarization-induced facilitation was dependent upon the duration of the preconditioning pulse and was associated with a decrease of the ratio between ICa,L(fc) and ICa,L(sc) as expected from the time-dependent change in the distribution of ICa,L(fc) and ICa,L(sc) (Fig. 6B). Depolarization-dependent facilitation was maximal when the conditioning potential was changed from –80 to –50 mV, for 2 s, as experimentally verified.


Figure 6
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  		Fig. 6 Numerical simulations of facilitation of ICa,L. (A) Numerical simulations of frequency-dependent facilitation, and relative amplitudes of ICa,L(Aa), ICa,L(fc)(Ab), and ICa,L(sc)(Ac), observed between 1 and 5 Hz. Current waveforms were calculated by setting the HP to –80 mV, and applying a 100 ms long depolarizing step to –10 mV. In each panel, the dotted trace represents reference at 1 Hz. (B) Time-dependency of the depolarization-dependent facilitation. Currents were calculated by applying a 20 (Ba), 200 (Bb), and 2-s (Bc) long preconditioning voltages. In each panel, the dotted lines represent ICa,L(fc) and ICa,L(sc).Traces evoked upon preconditioning at –80 mV (reference), and –50 mV are indicated by arrows.

 
3.6 Model simulation of AP automaticity
We thus integrated our equations in the DiFrancesco–Noble model of sino-atrial automaticity (Fig. 7A). For consistency, we used the same parameters values as in voltage-clamp simulations, except for ICa,L conductance which was scaled to give consistent ICa,L current density (Fig. 7B and C). This simulation reproduced AP waveform, and diastolic depolarization (Fig. 7A). The Na+–Ca2+ exchanger time-dependent kinetics (Fig. 7D), and the intracellular Ca2+ transients amplitude and kinetics (data not shown), were similar to those calculated in Demir et al. model. Three voltage-dependent currents were present in the diastolic depolarization: a decaying outward delayed rectifier current component (Fig. 7E), the hyperpolarization-activated If current (Fig. 7G), and ICa,T (data not shown). Furthermore, two voltage-independent current components also contributed to the diastolic depolarization: the time-independent background conductances (Fig. 7F), and the Na+–Ca2+ exchanger current. Finally, ICa,L was also present as an inward current component in the vicinity of the AP threshold.


Figure 7
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  		Fig. 7 Basic properties of the sino-atrial action potential in our model. The main ionic currents are shown in different panels. In each panel, arrows indicate either the sense of time (t) run, or the position of the maximum diastolic potential (VMDP), and the AP threshold (VUP). The dotted lines indicate the zero voltage (A) or current level. (A) Action potential and (B), time course of ICa,L. (C) Instantaneous current-to-voltage relation of ICa,L. Note the sustained component of ICa,L during the AP plateau due to facilitation. This promotes Na–Ca exchanger activity (D). AP repolarization is mainly driven by IK (E), which also provides decaying outward current during the diastolic depolarization. The ionic currents present in the diastolic depolarization are the background Na+, and Ca2+ conductances (F), together with If (G), the Na–Ca exchange current and ICa,L.

 
Our first goal was to evaluate whether and how the complex kinetics of ICa,L, that had never been taken into account before in numerical simulations, would influence sino-atrial automaticity. Fig. 8 shows a comparison between the DiFrancesco–Noble model, which exhibits only mono-exponential decay of ICa,L, and our variant model. Simulation showed that inclusion of the biphasic decay of ICa,L and its modulation by rate of stimulation and diastolic membrane potential slowed the basal rhythm, and hyperpolarized the maximum diastolic potential. Both effects are due to enhanced contribution of ICa,L(sc) to the AP plateau (Fig. 8Ba). Since ICa,L(fc) and ICa,L(sc) have differential dependence upon frequency of stimulation, and diastolic membrane potential, it was interesting to test the relative contribution of the two current components to automaticity at different rhythms. Fig. 9A shows that a 30% reduction in the amplitude of ICa,L decreased the APs frequency from 4 to 2.8 Hz (Fig. 9A). The ratio ICa,L(fc)/ICa,L(sc) was increased, because ICa,L(sc) was diminished (Fig. 9B and C). The greater contribution of ICa,L(fc) at low APs frequencies was confirmed by comparing the influence of suppressing ICa,L(fc) on automaticity, at each of the two frequencies tested (Fig. 9D and E, respectively). These simulations suggested that the Ca2+-inactivating component of ICa,L contributes significantly to regulation of the basal rhythm but its role is, however, not determinant in supporting automaticity. In contrast, suppression of the Ca2+-independent component ICa,L(sc) arrested automaticity (Fig. 9F) suggesting that ICa,L(sc) has a major contribution. Our last attempt was to test how sino-atrial frequency, and diastolic depolarization would influence ICa,L kinetics, and thus Ca2+ entry, during pacemaker cycle in physiologically relevant conditions (Fig. 10A). A spectrum of steady-state frequencies ranging from 4.6 to 3.2 Hz was generated by progressive activation of background IK(ATP) current [34]. Slow rates resulted in a prolongation of the diastolic depolarization, together with a shift of the maximum diastolic potential (Fig. 10Aa). At 3.2 Hz, the simulation resulted into facilitation of ICa,L as observed on current waveforms during APs (Fig. 10Ab), and instantaneous I–V plots (Fig. 10Ac). The time integral ratio of ICa,L was augmented with prolongation of the diastolic interval (Fig. 10B) which, despite the slowing of APs frequency, was the predominant factor. During the diastole, intracellular Ca2+ was also increased which resulted in turn in an enhancement of the Na+–Ca2+ exchange current at 3.2 Hz (data not shown).


Figure 8
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  		Fig. 8 Modulation of ICa,L inactivation kinetics by facilitation regulates the AP duration, and slows the basal rhythm.(Aa). Time course of a monophasic ICa,L, which sustains spontaneous activity shown in (Ab). Facilitation enhanced Ca2+ entry (Ba), and promoted activation of IK (data not shown) which, in turn, hyperpolarized the maximum diastolic potential. ICa,L facilitation also prolonged the AP duration.

 

Figure 9
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  		Fig. 9 Differential contribution of ICa,L(fc) and ICa,L(sc) during sino-atrial automaticity in our model. (A) Changing ICa,L amplitudes generates two independent rhythms of 2.8 Hz (dotted line), and 4 Hz (solid line). Note that the hyperpolarization of the maximum diastolic potential is due to reduced INaCa activity (not shown). (B) Instantaneous I–V plots of the ratio ICa,L(fc) and ICa,L(sc) at 2.8 Hz (dotted line), and 4 Hz (solid line). (C) Corresponding instantaneous I–V plots for the two ICa,L components. In (B) and (C) note the increment of ICa,L(fc) contribution at lower frequency. (D) Computed change in sino-atrial rhythm at 4 Hz (solid line) when ICa,L(fc) was set to zero (dotted line). (E) ICa,L(fc) has been set to zero at 2.8 Hz. (F) ICa,L(sc) is essential to sustain sino-atrial automaticity: the spontaneous activity ceased when the slow-inactivating component was set to zero.

 

Figure 10
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  		Fig. 10 Prolongation of the duration of the diastolic depolarization induces ICa,L facilitation. (A) Sino-atrial spontaneous activity (a), and ionic currents (b–f) during rhythm slowing due to activation of background IK(ATP). The reduced AP amplitude observed at low frequency (a) is due to strong outward K+ current flowing through IK(ATP) channels. The prolongation of the duration of the diastolic depolarization induces augmentation of ICa,L time course (Ab), and instantaneous current-to-voltage relation (Ac). (B) ICa,L time integral at different frequencies.

 

   4 Discussion
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
Appendix A
 References
 
This study describes for the first time the regulation of the decay kinetics of ICa,L by frequency of depolarisation, and diastolic membrane potential in rabbit sino-atrial pacemaker cells. To summarize our results: (i) ICa,L has a biexponential decay best-fitted by two time constants with the fast one being Ca2+-dependent and the slow one Ca2+ independent; (ii) both higher frequencies of stimulation and depolarized diastolic membrane potential between –70 and –50 mV prevent fast inactivation of ICa,L; (iii) the resulting facilitation of ICa,L promotes larger Ca2+ influx; (iv) numerical simulations suggest that the Ca2+-independent slow-inactivating component of ICa,L (ICa,L(sc)) supports pacemaker activity whereas the Ca2+-dependent fast-inactivating component (ICa,L(fc)) is a secondary regulator and (v) the depolarisation-induced facilitation, which develops during prolongation of the diastolic interval, is expected to oppose excessive rhythm slowing.

The decay kinetics of ICa,L are under the control of both the rate of stimulation and the diastolic membrane potential in rabbit sino-atrial cells. This observation is new and worth considering when studying Ca2+ channels regulation in cardiac pacemaker cells. This modulation of Ca2+ channel activity underlies the mechanism widely referred to as facilitation. Indeed, spindle-shaped sino-atrial cells present robust frequency- and depolarization-dependent facilitation of Ca2+ channel-mediated Ca2+ entry which may provide them with an important regulation of automaticity for several reasons. First, facilitation is detected in the majority of cells. Second, the overall net increase of Ca2+ entry can be substantial. Third, the amount of facilitation is graded, being function of increasing frequencies, or depolarization of the diastolic potential (range between –70 and –50 mV) from which the Ca2+ channels are activated, suggesting that Ca2+ channel activity is finely modulated in a wide spectrum of pacemaker rates and diastolic membrane potentials. Fourth, frequency-dependent facilitation reaches equilibrium within three to four stimulations, which is consistent with a beat-to-beat regulation of cell automaticity.

In cardiac cells, there is a joint dependence of the inactivation of ICa,L on both voltage and intracellular Ca2+ [8,20,35,36]. The early fast decay of ICa,L (and its related component ICa,L(fc)) is determined by a Ca2+ release-induced inactivation in a microdomain hardly accessible to EGTA or even BAPTA [37–40]. A local Ca2+ signalling has been demonstrated, for example, by depleting the SR Ca2+ content using ryanodine, thapsigargin or yet using phospholamban deficient mice which resulted into slowed inactivation of ICa,L [19,24,38–42]. The Ca2+-dependent inactivation can be totally inhibited using Ba2+ as the charge carrier or, alternatively, using high BAPTA concentration allowing to isolate slow voltage-dependent inactivation [8,20,35–37; present results]. The slowing of ICa,L decay kinetics involved in facilitation is likely to reflect reduced Ca2+-dependent inactivation and of its fast-inactivating component (ICa,L(fc)). This occurs with a concomitant increase in the Ca2+-independent component ICa,L(sc), because the fraction of channels that are sensitive to Ca2+ then inactivate slowly. The precise mechanism may involve reduced SR-Ca2+ release inactivation of ICa,L as reported recently in myocardial cells [19,24,42]. However, this mechanism, which seems likely for repetitive activation of ICa,L at high frequencies, is less evident for the depolarisation-induced facilitation. For example, it seems unrelated to Ca2+ channel opening during conditioning depolarizations that are considered too negative (range –70 to –50 mV) to generate a significant macroscopic ICa,L. In addition, the amount of facilitation is proportional to the prepulse duration which is reminiscent of a voltage- and time-dependent mechanism. Therefore, two mechanisms could account for this intriguing phenomenon: a voltage-driven Ca2+ release from the SR as proposed in cardiomyocytes [43] or, alternatively, Ca2+ entry via very few activatable Ca2+ channels. Since such current is hardly detectable at the macroscopic level, it should be postulated that this latter mechanism generates localized Ca2+ influx with the gain coupling Ca2+ influx and Ca2+ release high enough to deplete the SR during the conditioning depolarisation. The high driving force for Ca2+ at hyperpolarized membrane voltages may play a crucial role. Finally, another possibility could be that, in addition to decreasing the driving force for Ca2+, high voltages render the Ca2+-binding site hardly accessible to Ca2+ ions and thus Ca2+-induced inactivation becomes less important with larger depolarizations. Indeed, when evoked from hyperpolarized holding potentials, currents in the left branch of the I–V curve (test pulses less than 0 mV), where the fast inactivating component is predominant, are much faster than the currents in the right branch (<0 mV).

The depolarization-dependent facilitation of ICa,L may be involved in different physiological situations associated with modulation of the diastolic membrane potential. In both cases, the increase in transmembrane Ca2+ entry generates an additional depolarizing current, which is expected to influence the AP waveform. Since the sino-atrial cells generate an electrical oscillation, we expected the decay kinetics of ICa,L to regulate the pacemaker activity and, in turn, to be regulated by the AP cycle length and/or diastolic membrane potential. Since both the pacemaker rate and the diastolic membrane potential contribute to shape the waveform of ICa,L, and are interdependent, it was difficult to predict their relative influence on the pacemaker activity based on an experimental approach. For example, one limitation of AP-clamp experiments is the need of a pharmacological subtraction of currents in order to define their time-course during the AP. Manipulation of pharmacological agents with potential use- and voltage-dependent effects (such as Ca2+ channel antagonists) is also critical. Here, we used simplified experimental conditions to allow precise measurements of ICa,L kinetics and to have access to the mechanistic details. We isolated ICa,L from the other major contaminating currents (INa, IK) and used intracellular EGTA (to protect cells from Ca2+ paradox during recordings) to study facilitation in good experimental conditions. However, the disadvantage of our approach was that was the impossibility to get an insight into the precise mechanism of facilitation by itself, thus rendering difficult to extrapolate directly the role of facilitation to in vivo conditions. For example, it was difficult to establish the contribution (or interference) of the various mechanisms regulating Ca2+ homeostasis (Na+–Ca2+ exchange, SR Ca2+) to facilitation.

To overcome some of these problems, the development of a DiFrancesco–Noble-based numerical model of sino-atrial electrical activity [31] helped us to evaluate the possible consequences of ICa,L facilitation on automaticity. Our simulations showed that enhanced Ca2+ entry due to facilitation prolongs the AP duration, hyperpolarizes the maximum diastolic potential, and slows the basal pacemaker rate (Fig. 8) which is consistent with some of the observations made previously in a numerical model of the toad sinus venosus [44]. Our simulations also showed that the two kinetically distinct current components of ICa,L have differential contribution in the regulation of cell automaticity. Indeed, the slow-inactivating Ca2+-independent component ICa,L(sc) is mandatory to maintain automaticity (Fig. 9). The properties of ICa,L(sc) suggest that it could play a role in the latter phase of diastolic depolarization [45], and in the regulation of the AP plateau [46], as proposed in the Demir et al. model [3] or by the biphasic waveform of the nifedipine-sensitive current recorded during AP-clamp experiments [47]. In contrast, the Ca2+-dependent fast-inactivating component ICa,L(fc) is not crucial to maintain automaticity but it regulates the basal rhythm, in particular by having a greater contribution at low APs frequencies.

Pacemaker rate and diastolic membrane potential provide a way to modulate ICa,L indirectly. This may occur in conditions where autonomous neurotransmitters and/or intracellular second messengers have no direct effect on ICa,Lper se. For example, pacemaker slowing at low parasympathetic tone involves muscarinic inhibition of If at agonist concentrations that have no effect on ICa,L [48]. Since ICa,L regulates the pacemaker rate, the time-dependent facilitation of voltage-gated Ca2+ entry induced by slow depolarization of the diastolic membrane potential could thus represent a protection mechanism against excessive sino-atrial frequency slowing (see for example, Fig. 10). Prolonged sino-atrial pauses are expected to enhance Ca2+ channel activity and, depending from the membrane diastolic potential during the pause, favor the recovery of the pace-maker cycle. Recovery from sino-atrial pauses often depends on reactivation by atria, a phenomenon which implies a role for cell depolarization [49]. Since ICa,L is up-regulated even at its threshold for activation (Fig. 2C), facilitation could enhance the contribution of ICa,L to the late diastolic depolarisation at low pacemaker rates. Interestingly, increased Ca2+ entry due to facilitation is also expected to activate Ca2+ sensitive ionic currents such as, for example, the Ca2+ -dependent K+ conductance (IK) [50] and/or If via a yet unidentified intracellular signaling cascade [51,52].

In summary, pacemaker cells display facilitation of ICa,L. Facilitation is based on regulation of the inactivation rate of ICa,L by the pacemaker frequency and the diastolic membrane potential. Numerical simulation demonstrate that, in turn, modulation of ICa,L decay kinetics is a potentially important physiological mechanism for normalizing and regulating cardiac automaticity. This mechanism may be involved in the neurohormonal modulation of pacemaker rate.

Time for primary review 27 days.


   Appendix A
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
 Appendix A
References
 
Standards units used in the following set of equations

Quantity Units
Membrane potential V
Membrane current nA
Membrane conductance nS
Time constant s
Rate constant s–1

ICa,L model equations
Our equations for solving ICa,L correspond to the parallel channel gating model state diagram [21] shown below. This is based on eight closed states named C11–C14 for the channel in the fast mode of inactivation (Cf), and C21–C24 for the channel in the slow mode of inactivation (Cs), respectively. Two open states, O1 and O2 correspond to the channel open in the fast (Of) or slow (Os) mode, respectively. Finally, two inactivated states I1 and I2 correspond to the channel inactivated in the fast (If) or slow (Is) mode

Formula

According to the model this yields the following equations


Formula (A.1)


Formula (A.2)


Formula (A.3)


Formula (A.4)


Formula (A.5)


Formula (A.6)


Formula (A.7)


Formula (A.8)


Formula (A.9)


Formula (A.10)


Formula (A.11)


Formula (A.12)


Formula (A.13)


Formula (A.14)

where g1 and g2 are the membrane conductances for ICa,L(fc) and ICa,L(sc), respectively. Given the total ICa,L being the sum of the fast- and slow-inactivating current component, and in the hypothesis that ICa,L(fc) and ICa,L(sc) have the same conductance we can write


Formula (A.15)


Parameter values
k14, k24=1000 s–1
k–14, k–24=300 e(–5 V)
k11–13,21–23=5000 e(40 V)
k–11–13,–21–23=1000 e(–30 V)
k15=260 s–1
k25=35 s–1
k–16,–26=0
k16=0.4 e(–54 V)
k26=0.8054 e(–26.5 V)
kf=30 e(70 V)
kb=0.1 e(–20 V)


Initial values
O1=8.8734993 e–7
O2=1.9716894 e–7
C11=0.8576811
C21=0.12937438
C12=0.0078748195
C22=0.0011878541
C13=7.2287337e–5
C23=1.090584 e–5
C14=6.4820296 e–7
C24=9.9668384 e–8
I1=4.4703534 e–6
I2=7.9400161 e–7


   Acknowledgements
 
We are grateful to Produits Roche S.A., for supporting the experimental work. M.E.M. wishes to acknowledge a postdoctoral fellowship from the italian Ministero dell' Università e della Ricerca Scientifica. P.J.N. and D.N. wish to thank the British Heart Foundation and the Physiome Science for supporting the modeling work.


   References
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
 Appendix A
 References
 

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V. A. Maltsev and E. G. Lakatta
Synergism of coupled subsarcolemmal Ca2+ clocks and sarcolemmal voltage clocks confers robust and flexible pacemaker function in a novel pacemaker cell model
Am J Physiol Heart Circ Physiol, March 1, 2009; 296(3): H594 - H615.
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 Physiol. Rev.Home page
M. E. Mangoni and J. Nargeot
Genesis and Regulation of the Heart Automaticity
Physiol Rev, July 1, 2008; 88(3): 919 - 982.
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 J. Physiol.Home page
J Guo and H J Duff
Inactivation of ICa-L is the major determinant of use-dependent facilitation in rat cardiomyocytes
J. Physiol., March 15, 2003; 547(3): 797 - 805.
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