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Key points

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  • • 
    Calcium-dependent Na+–Ca2+ exchange (NCX) activation undergoes bidirectional up/down control in intact rabbit cardiomyocytes.
  • • 
    In rested cells with normal [Na+]i, NCX was initially inactive, but activated after field stimulation causing Ca2+ entry.
  • • 
    Increased [Na+]i strongly promoted Ca2+-dependent activation.
  • • 
    A fully co-operative fourth-order dynamic NCX activation model, incorporated into a ventricular cell model, predicted our observations.
  • • 
    The model further predicted that activation increased with increasing pacing frequency.

Abstract  Cardiac Na+–Ca2+ exchange (NCX) activity is regulated by [Ca2+]i. The physiological role and dynamics of this process in intact cardiomyocytes are largely unknown. We examined NCX Ca2+ activation in intact rabbit and mouse cardiomyocytes at 37°C. Sarcoplasmic reticulum (SR) function was blocked, and cells were bathed in 2 mm Ca2+. We probed Ca2+ activation without voltage clamp by applying Na+-free (0 Na+) solution for 5 s bouts, repeated each 10 s, which should evoke [Ca2+]i transients due to Ca2+ influx via NCX. In rested rabbit myocytes, Ca2+ influx was undetectable even after 0 Na+ applications were repeated for 2–5 min or more, suggesting that NCX was inactive. After external electric field stimulation pulses were applied, to admit Ca2+ via L-type Ca2+ channels, 0 Na+ bouts activated Ca2+ influx efficaciously, indicating that NCX had become active. Calcium activation increased with more field pulses, reaching a maximum typically after 15–20 pulses (1 Hz). At rest, NCX deactivated with a time constant typically of 20–40 s. An increase in [Na+]i, either in rabbit cardiomyocytes as a result of inhibition of Na+–K+ pumping, or in mouse cardiomyocytes where normal [Na+]i is higher vs. rabbit, sensitized NCX to self-activation by 0 Na+ bouts. In experiments with the SR functional but initially empty, the activation time course was slowed. It is possible that the SR initially accumulated Ca2+ that would otherwise cause activation. We modelled Ca2+ activation as a fourth-order highly co-operative process ([Ca]i required for half-activation K0.5act = 375 nm), with dynamics severalfold slower than the cardiac cycle. We incorporated this NCX model into an established ventricular myocyte model, which allowed us to predict responses to twitch stimulation in physiological conditions with the SR intact. Model NCX fractional activation increased from 0.1 to 1.0 as the frequency was increased from 0.2 to 2 Hz. By adjusting Ca2+ activation on a multibeat time scale, NCX might better maintain a stable long-term Ca2+ balance while contributing to the ability of myocytes to produce Ca2+ transients over a wide range of intensity.

Abbreviations 
[Ca2+]jct

junctional [Ca2+]

[Ca2+]sm

subsarcolemmal [Ca2+]

E–C coupling

excitation–contraction coupling

I Ca(L)

L-type Ca2+ current

I K1

inward rectifier K+ current

I NCX

NCX current

K 0.5act

[Ca2+]i required for half-fractional activation

0 Na+

Na+ free

NCX

Na+–Ca2+ exchange

NKA

Na+,K+ pumping

SR

sarcoplasmic reticulum

τ

time constant

Introduction

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix

Allosteric regulation of Na+–Ca2+ exchange (NCX) by cytosolic-side Ca2+ was first demonstrated in invertebrate preparations (DiPolo, 1979) and was soon verified in mammalian cells (Kimura et al. 1986; diPolo & Beauge, 2006). Regulatory sites, separated from transport sites (Hilge et al. 2007), were first reported to bind two Ca2+ ions with high co-operativity (Levitsky et al. 1996); however, two interacting domains binding as many as six Ca2+ ions are now known to be involved (Hilge et al. 2006, 2007; Besserer et al. 2007; Boyman et al. 2009). Dynamic Ca2+-dependent NCX regulation with order >2 greater than two and strong co-operativity (which would impart a steep Ca2+ dependence) is not accounted for in current functional models.

To date, the physiological role of allosteric NCX regulation in cardiac myocytes by Ca2+ (hereafter called Ca2+ activation), or by Na+, remains unclear. Viewed as an instantaneous (static) process, Ca2+ activation showed half-effective affinities below (Miura & Kimura, 1989; Condrescu et al. 1997; Fang et al. 1998), near (Weber et al. 2001) or above physiological resting free [Ca2+]i (Collins et al. 1992; Matsuoka et al. 1995; Trac et al. 1997; Fujioka et al. 2000; Maack et al. 2005), depending on the species and type of preparation.

We (Weber et al. 2001) and others (Maack et al. 2005) demonstrated Ca2+ activation in intact cardiomyocytes directly using simultaneous measurement of NCX current (INCX) and [Ca2+]i. We used a rapidly alternating Ca2+ influx–efflux protocol to trace out the steady-state envelope of Ca2+ activation and described it with a static Michaelis–Menten (hyperbolic) model, recently also used by Boyman et al. (2011). A large fast Ca2+ release via caffeine (Weber et al. 2001) or photolysis (Kappl & Hartung, 1996) led to nearly instantaneous Ca2+ activation by mass action.

In intact rat myocytes at rest, NCX activity was low but accelerated strongly during cytosolic Na+ loading (Haworth & Goknur, 1991), depolarization or field stimulation (Haworth et al. 1991). These outcomes suggest that Ca2+ activation has a sharp threshold-like dependence on cytosolic Ca2+.

Dynamic NCX Ca2+ activation was first shown in excised patches (Hilgemann, 1990; Hilgemann et al. 1992) or macropatches (Fujioka et al. 2000). Time constants of inactivation/recovery in the range of 0.1–6 s were measured on step addition/removal of cytosolic-side Ca2+ (Hilgemann, 1990; Matsuoka et al. 1995). Using fluorescence resonant energy transfer, Ottolia et al. (2004) followed conformational changes in an NCX Ca2+-binding domain expressed in HEK or cardiac cells on a beat-to-beat time scale.

Both Ca2+ influx and Ca2+ efflux via NCX transport activate dynamically, dependent on [Ca2+]i. In NCX expressed in Chinese hamster ovary cells, Ca2+ influx activated from a low-[Ca2+]i state on removal of external Na+ with a delayed sigmoidal time course, persisting for some seconds after [Ca2+]i was reduced (Reeves & Poronnik, 1987; Reeves & Condrescu, 2003). These features indicate positive feedback of inwardly transported Ca2+ to augment and promote further activation. Calcium efflux to remove Ca2+ released from stores also activated slowly, with threshold-like behaviour (Chernaya et al. 1996; Chernysh et al. 2004).

Here, we show that Ca2+ activation of NCX in intact cardiomyocytes is severalfold slower than the beat-to-beat interval in the heart. We have by intention not applied voltage clamp. While voltage clamp allows NCX flux to be isolated and measured directly, the clamp unavoidably interferes with physiological self-control of Ca2+ and Na+ fluxes by NCX in combination with other Ca2+ and Na+ flux sources. Remarkably, in rested rabbit myocytes with sarcoplasmic reticulum (SR) function suppressed, NCX did not self-activate when pulses of sodium-free (0 Na+) solution were applied (which should force Ca2+ influx). Upon external field stimulation, Ca2+ brought in via the L-type Ca2+ current (ICa(L)) efficaciously promoted NCX Ca2+ activation. Deactivation occurred on return to resting conditions, showing bidirectional on–off behaviour. When Na+,K+ pumping (NKA) was inhibited in order to elevate [Na+]i, and in mouse cardiomyocytes, where [Na+]i is higher than in rabbit cardiomyocytes, NCX Ca2+ activation was strongly promoted. In cells with SR function intact, the time course of 0 Na+-mediated Ca2+ influx appeared to be affected by SR Ca2+ uptake and release as well as Ca2+ activation. To describe Ca2+ activation, we incorporated a fourth-order dynamic NCX model inside a comprehensive ventricular cell model (Shannon et al. 2004). The model predicts for twitch stimulation that fractional Ca2+ activation increases from 0.1 to 1 as frequency is increased from 0.2 to 2 Hz. Control of Ca2+ activation involves positive feedback, as also recognized by Kuratomi et al. (2003), and may help NCX maintain both incremental sensitivity to Ca2+ transients and reserve capacity to stabilize long-term Ca2+ balance. Some preliminary results were presented in abstract form (Ginsburg & Bers, 2010).

Methods

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix

Ethical approval

All animal procedures were approved by the Institutional Animal Care and Use Committee at University of California, Davis, which operates under United States Public Health Service Animal Welfare Assurance guidelines.

Experiments

All experiments were done on freshly isolated adult rabbit or mouse ventricular myocytes at 37°C. For cell isolation, hearts were excised under deep surgical anaesthesia (for rabbits, pentobarbital, 100 mg kg−1i.v.; and for mice, 2–5% isoflurane, inhaled, in 100% O2). Animals died of exsanguination while insensate. To ensure that NCX was initialized to low activity, cells were bathed in solutions with [Ca2+] < 200 μm for the entire time until the start of experiments. Cells were plated on laminin-coated glass coverslips and loaded in low-Ca2+ normal Tyrode solution (mm: CaCl2, <0.2; KCl, 4; NaCl, 140; and MgCl2, 1; pH was adjusted to 7.4 at room temperature by apportioning HEPES (2-[4-(2-hydroxyethyl)piperazin-1-yl]ethanesulfonic acid) acid and Na+ salt to total [HEPES] = 10 mM), with Fluo-Lojo AM (acetoxymethyl ester; Teflabs, Austin, TX, USA), a low-leakage version of typical Fluo dyes, for 30–35 min, followed by washing/de-esterification (45 min minimum). Except for experiments such as the one shown in Fig. 8, thapsigargin (1 μm) was applied to deplete the SR and prevent any Ca2+ reuptake. In adult ventricular myocytes, thapsigargin depletes SR Ca2+ without elevating [Ca2+]i, unlike the situation in pacemakers and some non-cardiac cell types (Bassani et al. 1997).

image

Figure 8. With SR initially functional but unloaded, NCX-mediated Ca2+ influx was initially reduced; the fourth-order model preducted delayed but ultimately greater Ca2+-dependent NCX activation  In an initially rested cell with SR function intact, the first Ca2+ increases in response to 0 Na+ were snubbed, suggesting that Ca2+ uptake into the SR occurred. Fast transients then developed, presumably because SR released Ca2+ once it had sufficiently loaded (A, left panel; filled bars mark 0 Na+ bouts). In A, middle panel, ryanodine (30 μm) was added to suppress SR function. The first Ca2+ increases after 0 Na+ pulses were stronger, and no fast transients developed. A, right panel shows left and middle traces superimposed. B, smoothed [Ca2+]i during the entire experiment. Gaps in the record are interepisode periods. Numbers of field stimuli are shown. Grey indicates that ryanodine was present. With the SR intact, the model predicts progressive SR loading from the initial rested, unloaded state (C), with onset of [Ca2+]i transients (E, top panel) and sudden increase of INCX (F, top panel) after the fifth field pulse. D, activation time course with (black line) or without SR function (grey line). E and F, bottom panels show that [Ca2+]i and INCX increased in a graded fashion during field pulses.

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For experiments, initially rested cells were switched to Tyrode solution as above but with 2 mm CaCl2. We attempted to activate NCX as shown in Fig. 1B. After a 2.5 s baseline period, we applied five repetitions of a 5 s switch from 140 to 0 mm Na+ (Li+-substituted) solution, each followed by a 5 s return to 140 mm Na+ (period 10 s), followed by a final return to 140 mm Na+ for 12.5 s. We repeated the five-bout 60 s protocol at appropriate intervals to observe and control NCX activation. As appropriate to each experiment, one or more 0 mm Na+ repetitions within a protocol instance was either omitted (rest) or substituted by a series of 1 to 60 or more depolarizing external field stimulation pulses at 1 Hz (in 140 mm Na+; see examples in Fig. 1Bii and iii).

image

Figure 1. Initially rested rabbit cells showed no self-activation of Na+–Ca2+ exchange (NCX) Ca2+ influx even after 40 applications of Na+-free (0 Na+) solution (5 s each), but influx was progressively activated by increasing numbers of depolarizing field stimuli (1 Hz)  A, time line of the experiment; each filled circle represents one 0 Na+ bout, with numbers of field stimulation pulses shown. Bi–Biv, [Ca2+]i traces at time points marked in A. Filled bars mark 0 Na+ bouts and ticks mark stimuli. C (mouse) and D (rabbit), [Ca2+]i stabilized at its existing level whenever 10 mm Ni2+ was present (hatched bars), indicating that Ca2+ influx or efflux due to removal or restoration of Na+ was nearly abolished. Sodium–calcium exchange was fully pre-activated by field pulses. E, example response to a single 0 Na+ bout, showing curve fit and analysis as described in the Results.

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Our fast solution switcher had minimal lag (Fig. 1E), after which the best-fit 10–90% and 90–10% concentration transition time was 862 ms (τ≈ 300 ms; not shown). We measured this as block/unblock of inward rectifier K+ current IK1 in a voltage-clamped cell in place, using the above protocol to apply and remove 100 μm BaCl2, instead of 0 Na+.

The [Ca2+]i was detected using standard epifluorescence microscopy with excitation at 480 ± 4 nm and detection at 530 ± 20 nm full width at half maximum intensity. Detector output was converted after subtraction of background and system fluorescence to [Ca2+]i using the following equation:

  • image(1)

where F is observed fluorescence, Kd= 1100 nm and Fmax the maximal fluorescence, obtained while damaging the cell under study with a patch pipette (Trafford et al. 1999). Alternatively, and where an Fmax datum was lacking, we used a standard pseudoratio method (assuming resting [Ca2+]i= 100 nm in 2 mm[Ca2+]o bathing solution).

In experiments such as those of Figs 5 and 6, we measured [Na+]i with membrane-permeant esterified SBFI (1,3-Benzenedicarboxylic acid, 4,4′-[1,4,10-trioxa-7,13-diazacyclopentadecane-7,13-diylbis(5-methoxy-6,12-benzofurandiyl)]bis-, tetrakis[(acetyloxy)methyl] ester; Life Technologies, Grand Island, NY USA) in addition to Fluo. Excitation wavelength was switched among 340, 380 and 480 nm (full width at half maximum intensity 5–8 nm; dwell 10–30 ms per wavelength) with a fast-switching monochromator (Cairn Research, Faversham, UK). Emitted light at 530 nm was integrated and demultiplexed according to the excitation wavelength. We represented [Na+]i as SBFI fluorescence ratio and calibrated it using a linear nomogram. The nomogram was established on gramicidin-permeabilized (10 μm) cells (where possible the same cell was used in each experiment; compare Despa et al. 2002), with Ca2+-free solutions containing 140 mm KCl and 0, 10 or 20 mm NaCl, applied successively.

image

Figure 5. Calcium activation was promoted and sustained during block of Na+,K+ pumping (NKA) in the rabbit  A, left panels, [Na+]i (above) and [Ca2+]i responses (below) to 0 Na+ before application of strophanthidin (100 μm) first appeared upon 20 pulse field stimulation. A, middle panels, during NKA block, Ca2+ influx self-activated in response to 0 Na+ without the need for field stimulation. A, right panels, on washout, field stimulation was again required to evoke Ca2+ influx (20 pulses). B and C show time lines of [Ca2+]i and [Na+]i, respectively, during the entire experiment. Straight segments in the record are interepisode non-recording periods. Black arrows mark 0 Na+ applications which evoked no Ca2+ influx. Thick grey arrows mark where 0 Na+ was sufficient to evoke influx. The time line for 0 Na+ applications is at the bottom of the figure.

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image

Figure 6. In mouse myocytes, where [Na+]i is higher than in rabbit myocytes, NCX showed self-activation of Ca2+ influx in response to 0 Na+ bouts, before initial application of field stimuli  A, [Ca2+]i during intervals marked by the arrows on the experimental time line (B). As [Na+]i increased in the cell (C), the propensity of Ca2+ influx to self-activate due to 0 Na+ increased (Ai, Aii and Av). After 20 pulses, strong, possibly maximal activation was evident (Aiii and Aiv). In C, the asterisk indicates that the [Na+]i calibration used averaged parameters from four other mouse cells. The time line for 0 Na+ bouts appears at the bottom of the figure.

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Analysis and modelling

Previously (Weber et al. 2001), we measured Ca2+ activation using our rapidly alternating voltage-clamp protocol. We defined NCX current using the following equation:

  • image(2)

in which inline image is a thermodynamic relation governing transport [eqn (4), below], A is an instantaneous (static) fractional allosteric activation factor (0 ≤A≤ 1), and K0.5act is the [Ca2+]i required for half-fractional activation, which we found by fitting:

  • image(3)

NCX ion flux depended on Em, [Ca2+]i, [Ca2+]o, [Na+]i and [Na+]o as follows:

  • image(4)

In this equation, Kmci, Kmno, Kmco and Kmni are respective transport affinities for external Ca2+, external Ni2+, internal Ni2+ and internal Ca2+. These are constrained by the equilibrium condition:

  • image(4a)

Equation (4) and parameters are as in Weber et al. (2001), except that we have included in the denominator a second saturation factor, which serves only to limit maximal NCX turnover to a finite rate under the formally infinite electrical driving force which would exist if [Na+]o were strictly zero. We set ksat2= 0.0005 and ηsat2= 0.5, and ENCX was defined from respective Na+ and Ca2+ equilibrium potentials as:

  • image(4b)

The NCX exchange ratio n was set at 3.14:1 (unpublished observations, Ginsburg KS and Weber CR; also Kang & Hilgemann, 2004). The first saturation factor in the denominator, from Luo & Rudy (1994), limits inward INCX at negative Vm.

Here, we use eqn (2) but redefine A as a dynamic fractional activation factor, as follows:

  • image(5)

where h is order of reaction (not larger than the number of Ca2+ binding sites) and the kact are respective on- and off-rate constants, related by K0.5act, as follows:

  • image(5a)

Equation (5) represents fully co-operative binding (Hill equation), in which the probability of NCX states other than completely Ca2+ free and fully Ca2+ bound (h Ca2+ ions) is zero. This and other rate or transport equations we considered are described by Segal (1993). We chose h= 4 because models with lower order and/or lacking co-operativity did not describe our results. In evaluating models, we adjusted kact(on) and K0.5act, with kact(off) constrained by eqn (5a) to 0.05 s−1.

In eqns (3) and (5), activation appears formally to be separable from transport eqn (2). This is not true in cells, because activating and cytosolic-side transported Ca2+ ions belong to the same pool and participate in feedback.

We simulated and predicted NCX behaviour in myocytes using the ventricular cell model of Shannon et al. (2004; for further details see Grandi et al. 2007). We retained key features of Shannon et al. (2004), including the distribution of NCX, ICa(L), INa and other moieties by compartment. Thus, we implemented separate instances of eqns (2)(5) for junctional and subsarcolemmal compartments. Sodium–calcium exchange does not communicate directly with bulk cytosol. Further details appear in Fig. 3.

image

Figure 3. Proposed Ca2+ activation model  A, Matsuoka et al. (1995) model (shown in D) is expanded to show possible details around the I2 inactivated state (E + S: E, enzyme and S, substrate). Possibly conductive states are shown with bold outlines and asterisk [(SE)*, (ES)*, with the predicted conductive state in grey (SES)*]. Unshaded boxes are substates within the non-transporting I2 state. A second-order framework is shown for clarity, but we used a fully co-operative fourth-order structure, where the only likely states are non-conductive/fully unbound, E + 4S and conductive/fully bound, (ESSSS)*. B, transport is assumed to occur only once all relevant regulatory sites are fully Ca2+ bound. C, steady-state relative [ligand] dependence of activation probability for fourth-order [co-operative and non-co-operative, (ESSSS)*] and second-order models [(SES)*]. Only the fourth-order fully co-operative (Hill) model (thick black line) shows on–off switching for small [Ca2+] variations near the physiological value (reference lines refer to submembrane [Ca2+] seen by NCX and assume K0.5act = 375 nm). Left panel, linear concentration scale; right panel, logarithmic scale. E, relevant features of compartment myocyte model of Shannon et al. (2004), used here as modified (see main text). Feedback between Ca2+ binding/activation and Ca2+ transport is essential to control of NCX activation in situ.

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We decreased Ca2+ background leak to 10% of the value in Shannon et al. (2004) to preserve the decay of Ca2+ loading on rest, which is characteristic of rabbit cells (Bassani & Bers, 1994). We increased Na+ background leak 5-fold, to improve stability of [Na+]i at rest. Model-predicted Na+ leak flux was comparable with observation (Despa et al. 2002). Calcium ion diffusion coefficients were changed (junctional to subsarcolemmal doubled and subsarcolemmal to bulk cytosol increased 5-fold; Fig. 3E), allowing the model to match better the observed relationship between bulk [Ca2+]i and subsarcolemmal [Ca2+] ([Ca2+]sm; Trafford et al. 1995; Weber et al. 2002). To eliminate SR function (all experiments except Fig. 8), we reduced initial SR Ca2+ loading, both free and calsequestrin bound, and maximal SR Ca2+ uptake (SERCA2) rate to 0.1% of normal. To simulate the Na+ loading observed in experiments with strophanthidin (Fig. 5), we reduced Na+,K+-ATPase (NKA) maximal current to 10% of normal.

Commanded changes in [Ca2+]o or [Na+]o caused the bath concentrations to change as described by the following equation:

  • image(6)

where [X]CMD is the commanded value and [X]o the attained value of either Na+ or Ca2+ concentration, and the solution switching rate constant ax was 3 s−1 (consistent with observed 10–90% rise time ≤0.9 s).

We analysed experiments using home-written routines in Microsoft Excel with Visual Basic for Applications. Curve fitting was performed using the Excel Solver. Modelling was done using Matlab (MathWorks, Natick, MA, USA).

Results

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix

Kinetics of Ca2+ activation and deactivation in intact myocytes

Given the relative strength of NCX in rabbit myocytes (Bassani et al. 1994), we were surprised that repeated 0 Na+ bouts (black bars in Fig. 1B) failed to induce NCX-mediated Ca2+ influx in an initially rested cell (Fig. 1A). However, after 1 Hz field stimulation (ticks in Fig. 1Bii), which brought in Ca2+ via L-type Ca2+ channels (ICa), 0 Na+ bouts became effective. Figure 1A shows shows the overall time course of Ca2+ activation in a representative experiment. We first applied our 60 s protocol eight times (40 bouts of 0 Na+) with no effect to increase [Ca2+]i (Fig. 1Bi). In subsequent trials, we replaced one or more of the 0 Na+ bouts with field pulses at 1 Hz. More field pulses (marked by ticks) led to larger NCX-mediated influx (Fig 1Bii–iv). The results in Fig. 1 and subsequent figures are representative of >40 cells from 14 preparations.

Figure 1C and D shows that Ca2+ influx was Ni2+ sensitive and thus mediated by NCX. At the time of Ni2+ application, [Ca2+]i stabilized and remained constant as long as bath Ni2+ (10 mm NiCl2) remained present. In Fig. 1C (mouse cell), Ni2+ and 0 Na+ were applied simultaneously (hatched bar) while in Fig. 1D (rabbit cell), Ni2+ was applied during a transition of [Na+]o from 0 to 140 and then to 0 mm. In both cases, NCX had previously been fully activated by field pulses (ticks in Fig. 1D).

Figure 1E shows how we measured activation from fluorescent [Ca2+]i data during each 0 Na+ bout to produce time series as in Fig. 1A. We applied the following conditional fit:

  • image(7a)
  • image(7b)
  • image(7c)

where t is time, td is the delay for solution switching, Δ[Ca2+]i is the Ca2+ transient amplitude as a difference from [Ca2+]i,rest, and τ1 and τ2 are respective onset and offset time constants. All parameters were fitted apart from D, the 0 Na+ duration (always 5 s). Parameter td was included to improve the sensitivity of the fit to the cell-related parameters. To follow the time course of activation as in Fig. 1A, we used the maximal value reached by eqn (7b) during each 0 Na+ bout.

Figure 2 shows that the activated state reverted on return to rest. Reversion was slower after NCX was activated more strongly by more field pulses with (in this example) τ= 33.7 (10 pulses), 44.4 (20 pulses) and 89.2 s (>60 pulses). The influx driven by 0 Na+ and the time constant for reversion on rest both increased significantly with the increasing number of field pulses (P < 0.05, n= 14 cells). Repeated probing with 0 Na+ also tended to sustain activation (Fig. 1Biv). This suggests that NCX self-activation is sustained by positive feedback.

image

Figure 2. In a rested rabbit cell, Ca2+ influx was initially unresponsive to 0 Na+ pulses, was activated by increasing numbers of field stimuli, and reliably reverted to an unresponsive state during periods without field stimulation; decay was slower after stronger activation  A, time line of experiment. Each filled circle represents one 0 Na+ application. Underbars mark times and numbers of field stimulation pulses. B, smoothed representation of [Ca2+]i during the entire experiment. Gaps in the record are due to use of episodic rather than continuous recording. Two millimolar Ca2+ was present continuously, starting at the arrow in B.

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Model simulation of Ca2+ activation in intact myocytes

Figure 3A–D shows our proposed model for Ca2+ activation. The formal structure in Fig. 3A covers several possibilities. A fourth-order Ca2+ dependence was required to describe our results, but we show here only a second-order scheme for ease of reading. State (E + S) is Ca2+ free, while states (ES) and (SE) are singly bound and state (SES) has two Ca2+ ions bound. States (ES)*, (SE)* and (SES)* are conductive (transporting). Formally, all states are interconvertible, with diverse rate constants and probabilities 0 ≤P≤ 1 as observed (Boyman et al. 2009), constrained only by the total probability over all states being 1. Scale factors α and β[0 ≤ (α or β) ≤ 1] adjust off-rate constants koff3 and koff4 to allow for co-operative binding of a second Ca2+ ion (SES), given that a single Ca2+ ion was already bound [state (ES) or (SE), respectively]. If α and β= 1, this would indicate no co-operativity (the two sites act independently), while α and β= 0 represents full co-operativity (Hill model). Rate constants kact and kdeact govern transitions between non-conductive and conductive Ca2+-bound states.

For tractability, we have simplified this structure (Fig. 3B). We subsumed all on-rate constants (kon in Fig. 3A) into the single forward rate constant kact(on) of eqn (5). We assumed that NCX transports ions only when all relevant sites are fully Ca2+ bound, eliminating states (SE)* and (ES)*. That is, in Fig. 3A, kact1→ 0 and kact2→ 0. We also assumed that activation ensues instantaneously, once all required Ca2+ ions bind; in Fig. 3A, kact3 →∞. We subsumed all rate constants for deactivating transitions into kact(off) in eqn (5). Finally, we restricted co-operativity to either 0 or 1 for all states where intermediate numbers of Ca2+ ions are bound (α=β= either 0 or 1 in Fig. 3A).

We tested three dynamic models, for which we show the submembrane [Ca2+] dependence of steady-state fractional activation in Fig. 3C. Calcium ion dependence is shown relative to K0.5act = 375 nm, with a logarithmic scale in the left panel and linear in the right panel. Setting 375 nm[Ca2+]sm for K0.5act preserves responsiveness in a physiological [Ca2+]i range (see Fig. 10 below).

image

Figure 10. Model parameter K0.5act (the [Ca2+]i required for half-fractional activation) set to 375 nm matched experimental behaviour well, while 33% increased or 50% decreased K0.5act did not  Predicted decay of fractional Ca2+ activation (A) and [Ca2+]i (B) after maximal activation by a sequence of 60 field pulses with K0.5act set to 250 (left), 375 (middle) or 500 nm (right). For each K0.5act, the on-rate constant was adjusted to maintain the intrinsic activation decay rate constant at 0.05 s−1. The simulation was as in Fig. 4, with the period 340–500 s shown. Thick lines show monoexponential fits starting at the end of pacing (345 s). The final value was constrained to 0 for fractional Ca2+ activation (A) or 100 nm for [Ca2+]i (B). The 0 Na+ bouts are marked below the traces.

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Our proposed fourth-order Hill model (thick black line) predicted near-complete deactivation at rest, with A= 0.005 when [Ca2+]sm was 100 nm. The [Ca2+]sm is likely to decline to this value or below during rest; that is, [Ca2+]sm should approach bulk cytosolic [Ca2+]i. As alternatives, a second-order Hill model, similar to that of Weber et al. (2001) but using eqn (5) with h= 2 (grey line), predicted A= 0.066 at 100 nm, while a non-co-operative model requiring four Ca2+ ions bound for activation predicted A= 0.116 at the same resting [Ca2+]sm (dashed line). Dynamic activation in this model is described using a joint probability, as follows:

  • image(5b)

In the NCX transport scheme (Fig. 3D) of Reeves (1998) and Matsuoka et al. (1995, 1996), the model of Fig. 3B is subsumed within I2 activation. We did not consider I1 (Na+-dependent) inactivation (not shown in Fig. 3D), which is unlikely to be relevant at physiological levels of [Na+]i..

In Fig. 3E, we show relevant features of the Shannon et al. (2004) compartmental ventricular myocyte model. The NCX, NKA, Ca2+ and Na+ leak channels and the plasma membrane Ca2+ pump (not shown) are uniformly distributed over the sarcolemmal surface, with 11% junctional (JCT in the figure), and the rest subsarcolemmal (SM in the figure). The L-type Ca2+ channels are non-uniformly distributed, with 90% being junctional, as are 100% of the SR Ca2+ release units.

The cell model confers positive feedback on the NCX activation model eqns (5) and (5a), wherein subsarcolemmal [Ca2+]sm and junctional [Ca2+] ([Ca2+]jct) each affect both transport and regulation in their respective compartments.

In Fig. 4, we simulate the time-dependent activation and deactivation seen in experiments such as those of Figs 1 and 2. Sodium–calcium exchange was initially inactive and resisted activation by 0 Na+ bouts (time line at bottom of Fig. 4), but responded after Ca2+ influx first by 12, then more strongly after 60 field pulses (black bars in Fig. 4A).

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Figure 4. Myocyte model with fourth-order Hill Ca2+ dependence for NCX Ca2+ activation (Fig. 3) predicts experiments like Figs 1 and 2 Sarcoplasmic reticulum (SR) function was blocked. Activation, initially minimal, was initiated by 12 field pulses, relaxed, and was then further enhanced by 60 field pulses. A, observable NCX activation (composite with 0.89 subsarcolemmal + 0.11 junctional). B, corresponding [Ca2+]i prediction. C, predicted NCX current (INCX). Increasing outward current with increasing [Ca2+]i, opposing the thermodynamic driving force, demonstrates increased activation. Calcium-dependent inactivation of ICa(L) increased (D) and action potential duration increased (E); the first 9 pulses are shown. F, detail of increased INCX envelope, both inward and outward components, during activation; the first 37 pulses are shown.

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We defined observable Ca2+ activation in a cell (Fig. 4A) as follows:

  • image(8)

where Fjunct is 0.11 and Fsl is 0.89, while Ajunct and Asl are the respective predicted fractional activations. When L-type Ca2+ channels, concentrated in junctional space, are active, high [Ca2+]jct can promote very strong activation of junctional NCX, but their relatively low density limits their contribution to Aobs (not shown).

Predicted cytosolic [Ca2+]i and INCX appear in Fig. 4B and C, respectively. The [Na+]i countervaried with [Ca2+]i during 0 Na+ bouts but increased during field stimulation (not shown). Subsarcolemmal, junctional and bulk [Na+] were very similar. During field stimulation, ICa(L), shown in Fig. 4D for the first nine pulses in the 60 pulse sequence (from 285 s), declined progressively due to Ca2+-dependent inactivation. Action potentials predicted over a corresponding time lengthened (Fig. 4E). Figure 4F (first 37 pulses) shows that INCX increased in amplitude and shifted outward, opposing the inward thermodynamic drive expected from increased [Ca2+]i during field stimulation. The outward shift is a hallmark of increasing NCX Ca2+ activation (Weber et al. 2001).

We tested the second-order fully co-operative (Hill) model and the fourth-order non-co-operative model, requiring binding of all four Ca2+ ions to produce activation, whose steady-state Ca2+ binding/activation are shown in Fig. 3C. These models (not shown) could not reproduce the the key features of Figs 1 and 2; namely, low activation and lack of response to 0 Na+ at rest, sharp increase in activation upon field stimulation, and gradual decay on return to rest.

Increased [Na+]i enhanced Ca2+ activation

In Fig. 5, we examine how increasing cytosolic [Na+]i influenced Ca2+ activation. Both [Na+]i and [Ca2+]i were recorded, and NKA was inhibited with strophanthidin (100 μm; hatched bar on time line in Fig. 5C). Inhibiting NKA raises [Na+]i, especially local to NCX, limiting the drive for NCX to extrude Ca2+, and thus favouring potential Ca2+ entry during 0 Na+ bouts. Figure 5A shows [Na+]i (top panels) and [Ca2+]i details (bottom panels) before, during and after strophanthidin, on the [Ca2+]i time series (Fig. 5B, grey arrows). Initially unresponsive to 0 Na+ (black arrows below Fig. 5B), this cell responded to field pulses. Activation reverted gradually (τ= 51.8 s), even while 0 Na+ bouts were applied. After applying strophanthidin, we rested the cell for 10 min. By this time, [Na+]i had increased to >10 mm, and 0 Na+ bouts activated Ca2+ influx without need for field stimulation (thick grey arrows below Fig. 5B). With further elevation of [Na+]i, a single 0 Na+ bout activated Ca2+ influx, even after >200 s rest (at 1800 s). On removing strophanthidin, [Na+]i decreased towards its initial value, and 0 Na+ bouts after rest were again ineffective (black arrows). Sodium–calcium exchange was again activatable by field pulses (near 2400 s), and this reverted as before (τ= 89.9 s).

In Fig. 6, we further tested the role of increased [Na+]i, by recording both [Na+]i and [Ca2+]i from a mouse myocyte. Figure 6A shows expanded [Ca2+]i traces at relevant times indicated on the Ca2+ time series (Fig. 6B) and the Na+ time series (Fig. 6C). The [Na+]i, initially higher than in rabbit cardiomyocytes, increased during the experiment in this cell. Self-activating 0 Na+ responses became evident around 200 s (Fig. 6Ai). The 0 Na+ evoked a response even after 550 s rest, severalfold longer than the time constant (<80 s) for deactivation in rabbit myocytes (Fig. 6Aii). Field pulses led to activation of Ca2+ influx, strongly enhancing and augmenting the 0 Na+ responses afterwards (Fig. 6Aiii and iv). After 150 s further rest, 0 Na+ still evoked self-activation without prior field stimuli (Fig. 6Av). This contrasts with rabbit cells (Fig. 2), in which rest led affirmatively to reversion, and self-activation without field stimuli was not evident with normal [Na+]i.

Figure 7 shows that our model predicted increased self-activation by 0 Na+ bouts in rested cells when [Na+]i was increased, without the need for prior field stimulation (Figs 5 and 6). Figure 7A shows observable Ca2+ activation [eqn (7)] and Fig. 7B shows [Ca2+]i. Starting from rest, 0 Na+ bouts (Fig. 7C) were applied, interrupted after 200 s by 10 field pulses. In control conditions (thick black line; model parameters the same as in Fig. 4), NCX did not activate beyond 0.007 within 200 s ([Ca2+]i= 109 nm), and was activated only transiently by the 10 field pulses (ticks in Fig. 7A). With NKA Vmax reduced to 10% and initial [Na+]i set to 10 mm (grey line), a value expected in mouse and also expected in rabbit cardiomyocytes within several minutes of NKA inhibition, fractional activation reached only 0.018 by 200 s ([Ca2+]i= 137 nm), yet 10 field pulses forced sustained maximal activation, a clear demonstration of on–off switch behaviour. Finally, we increased initial [Na+]i to 15 mm, simulating rabbit cells after longer NKA inhibition (thin black line). With [Na+]i initially at 15 mm, 0 Na+ bouts activated NCX progressively (0.297 by 200 s, with [Ca2+]i at 197 nm), and the following pulses forced sustained maximal Ca2+ activation.

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Figure 7. The model predicts increased net Na+ influx (NKA Vmax reduced to 10% of normal) to promote Ca2+ influx strongly  A, observable NCX activation (composite with 0.89 subsarcolemmal + 0.11 junctional). B, cytosolic [Ca2+]. With normal NKA (thick black lines), NCX activates only transiently and only after 10 field pulses (ticks in A). The initial [Na+]i was 7.0 mm, as in Fig. 4. With reduced NKA and initial [Na+]i at 10 mm, field pulses were still required for activation after 200 s of 0 Na+ applications, but activation was sustained by further 0 Na+ bouts (thick grey traces). With [Na+]i initially at 15 mm, 200 s of 0 Na+ bouts were sufficient to activate NCX partly, and [Ca2+]i control destabilized after the field pulses. Dual time scale.

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Sarcoplasmic reticulum affected the predicted time course of Ca2+ activation

The experiments in Figs 1–7 were done with SR Ca2+ transport blocked. Given that the SR normally acts to amplify Ca2+ influx, we investigated the interaction between NCX and SR, as shown in Fig. 8. The cell in Fig. 8 was not thapsigargin treated. The overall time course of Δ[Ca2+]i responses appears in Fig. 8B, and details of the 0 Na+ response at relevant times are in Fig. 8A. The initially small Δ[Ca2+]i in response to 0 Na+ bouts was boosted after 10 field pulses, and then further towards maximal activation by >60 pulses. The 0 Na+ responses after maximal activation were initially snubbed (flat topped), but after the second, third and fourth 0 Na+ bouts, large sharp Δ[Ca2+]i transients developed (Fig. 8A, left panel). Once more, Δ[Ca2+]i responses reverted to minimal upon rest. We next applied ryanodine (30 μm) to block SR Ca2+ release, and again strongly activated NCX with >60 field pulses. Ensuing 0 Na+ responses (Fig. 8A, middle panel and grey traces throughout the figure) were no longer flat topped, but rather looked like those in Figs 1 and 2 where SR was blocked. Also, no sharp transients appeared. Figure 8A, right panel, superimposes traces with and without ryanodine.

Thus, the SR, initially unloaded or lightly loaded, could take up Ca2+ from cytosol during 0 Na+ bouts, snubbing Ca2+ activation. Once filled sufficiently, the SR could limit further Ca2+ entry and support Ca2+ release, both factors promoting Ca2+ activation. We could not measure Ca2+ activation directly via Δ[Ca2+]i in this experiment, because Δ[Ca2+]i was due to both NCX- and SR-mediated fluxes.

Modelling in Fig. 8C–F allowed us to infer SR function and Ca2+ activation, and supports this interpretation. Ten field pulses were applied to an initially rested cell, with or without intact SR. As the intact SR loaded progressively (Fig. 8C), Ca2+ activation was first delayed (Fig. 8D, black trace) and was less than without SR (grey trace), but then quickly increased to a final value near 1, larger than the final value attained gradually without SR. At the fifth pulse, when NCX activation increased suddenly, full [Ca2+]i transients with decay to a typical diastolic level appeared (Fig. 8E), and INCX increased and shifted inwards (Fig. 8F).

Calcium activation is predicted to increase with pacing frequency

As shown in Fig. 9, our model predicts that Ca2+ activation varies in physiological conditions (same model as Fig. 4, but with SR function intact). After initializing the model at rest for 100 s, we evoked twitch responses at 0.2, 0.5, 1 and 2 Hz. Figure 9 shows SR free [Ca2+] (Fig. 9B), cytosolic [Ca2+]i (Fig. 9C), INCX (Fig. 9D) and [Na+]i (Fig. 9E). As pacing frequency was increased, observable fractional Ca2+ activation (Fig. 9A) increased progressively to near maximum. These data are summarized in Fig. 9F. Sarcoplasmic reticulum Ca2+ loading and fractional Ca2+ release increased, and outward INCX increased, which indicates activation, because increased [Ca2+]i would thermodynamically drive INCX inwards (Weber et al. 2001). Individual action potential-driven ICa(L) and INCX in quasi-steady state at 0.2 Hz (reference time 120 s) and 2.0 Hz (reference time 240 s) appear in Fig. 9G and H, respectively. At 2.0 Hz, Ca2+-dependent ICa(L) inactivation was more prominent, and both inward and outward INCX was larger.

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Figure 9. Predicted progressive NCX activation with increased pacing frequency, with SR intact  Model otherwise identical to Fig. 4. The initially rested cell was paced at 0.1 Hz (not shown), then starting at 100 s, it was paced at 0.2, 0.5, 1 and finally 2 Hz as marked. A, observable (composite, 0.11 junctional + 0.89 sarcolemmal) activation increased progressively. B–E, progressive increase of SR free [Ca2+], cytosolic [Ca2+]i, INCX and [Na+]I, respectively. The INCX clearly shifted outward, opposing the inward thermodynamic drive due to increased [Ca2+]i, and indicating activation. F, observable activation plotted vs. frequency. The L-type Ca2+ current (ICa(L)) showed increased Ca2+-dependent inactivation (G) and both outward and inward INCX (H) were larger at 2.0 than at 0.2 Hz in the quasi-steady state. In G and H, reference points for time = 0 were 120 and 240 s, respectively.

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Model prediction of K0.5act

Figure 10 shows how we chose 375 nm for the K0.5act of Ca2+ activation. We ran our model using the protocol in Fig. 4, and focused on the decay that ensued after NCX had been strongly activated by 60 field pulses, which was probed by 0 Na+ bouts, as in our experiments. Using monoexponential fits (thick lines), we compared the decay of observable activation (Fig. 10A) and cytosolic [Ca2+]i (Fig. 10B) for K0.5act = 375, 250 (33% higher) and 562 nm (50% lower). We maintained intrinsic kact(off) at 0.05 s−1 (τ= 20 s) by setting respective on-rate constants kact(on) to 1.25 × 1010, 2.53 × 109 and 5 × 108 mm−4 s−1. The final plateau was constrained to 0 for activation and 100 nm for [Ca2+]i. As shown in Figs 1, 2, 5, 6 and 8, we expect the activation decay time constant to be longer than the intrinsic 20 s due to application of probing 0 Na+ bouts. The decay time course at K0.5act = 375 nm matched our data well (τ= 33.2 ms), but with 250 nm the activation was sustained far longer than we ever observed with normal [Na+]i (τ= 149 ms). With 562 nm, decay τ was only 21.8 ms despite repeated probing with 0 Na+.

Discussion

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix

Summary of results

We have shown that Ca2+-dependent NCX activation undergoes bidirectional up/down control in intact rabbit cardiomyocytes not under voltage clamp. We repeatedly applied 5 s bouts of Na+-free external solution to myocytes, to induce and assay Ca2+ activation via Ca2+ transients representing Ca2+ influx (outward NCX current), with SR function disabled. Sodium–calcium exchange did not self-activate in response to 0 Na+ in rested cells with normal [Na+]i, but field stimulation causing Ca2+ to enter via L-type Ca2+ channels efficaciously promoted activation, which decayed upon rest (Figs 1 and 2). When NKA was inhibited and [Na+]i increased, or in mouse cardiomyocytes where [Na+]i is intrinsically higher, NCX activation was strongly promoted, so that 0 Na+ bouts produced Ca2+ influx responses even after rest and without extrinsic field stimulation (Figs 5 and 6). With the SR functional but initially unloaded, uptake appeared to compete for activating Ca2+ (Fig. 8), but eventually released Ca2+, promoting a fast increase in Ca2+ activation. An established ventricular cell model, incorporating a fully co-operative (Hill) fourth-order dynamic NCX model having K0.5act = 375 nm (Figs 3, 4, 7 and 10) and off-rate constant = 0.05 s−1 predicted our observations. When we included SR function in our model, with no other changes, we predicted that pacing frequency affected Ca2+ activation; fractional activation increased from 0.1 to 1 as frequency was increased from 0.2 to 2 Hz (Fig. 9).

Study of NCX Ca2+ activation without voltage clamp

We propose that maintaining near-physiological non-voltage-clamp conditions (except during 0 Na+ bouts) contributed to our ability to observe reversible bidirectional up/down modulation of Ca2+ activation, in contrast to previous reports (see below; Previous work: static and dynamic Ca2+ activation) and our own voltage-clamp data (Bers & Ginsburg, 2007) where complete deactivation was not observed. While the onset of Ca2+ activation depends on mass action and positive feedback, deactivation is more delicately controlled. With physiological [Na+]i, [Ca2+]i, [Na+]o and [Ca2+]o, the resting membrane potential of a metabolically healthy rabbit myocyte is negative of NCX equilibrium, based on a Na+–Ca2+ stoichiometry near or slightly above 3:1 (Kang & Hilgemann, 2004; Bers & Ginsburg, 2007). Therefore, during rest, active NCX should extrude Ca2+. Sodium–calcium exchange can potentially deactivate itself as it approaches equilibrium, establishing a delicate balance with the plasma membrane Ca2+ pump (Caroni & Carafoli, 1980, 1981) against non-specific Ca2+ leak into a cell.

Voltage clamping could constrain the time course of Ca2+ activation and deactivation. As a secondary active transporter, NCX translocates ions according to the Na+–Ca2+ stoichiometry towards establishing minimal electrochemical free energy (Mullins, 1979; Reeves & Hale, 1984; Noma et al. 1991; Baartscheer et al. 1998; Hilgemann, 2004). With Em imposed, and with NCX-selective conditions, as needed for voltage clamp, the equilibrium condition for NCX could be non-physiological.

Given that we could not measure INCX without voltage clamp, we have inferred it through [Ca2+]i changes and by modelling. However, the model also allowed us to refer Ca2+ activation to [Ca2+]sm and [Ca2+]jct, which cannot be measured experimentally, in addition to bulk [Ca2+]i. Our dynamic model can also predict Ca2+ activation in various protocols, in contrast to previous time constant values, which are particular to each protocol and situation.

Previous work: static and dynamic Ca2+ activation

Our model represents a more comprehensive description of Ca2+ activation dynamics in the physiological [Ca2+]i range than has so far been available. In previous studies, static affinity was estimated to be 22–47 nm in guinea-pig myocytes (Miura & Kimura, 1989) or Chinese hamster ovary cells (Condrescu et al. 1997; Fang et al. 1998), but at least 10-fold lower in guinea-pig myocyte excised patches (200–600 nm; Collins et al. 1992; Matsuoka et al. 1995; Trac et al. 1997; Fujioka et al. 2000) or expressed canine NCX (860 nm; John et al. 2011). We (Weber et al. 2001) found K0.5act = 125 nm in ferret myocytes (much higher in mouse myocytes) using a rapidly alternating Ca2+ influx–efflux voltage-clamp protocol. Others, using similar protocols, reported ∼340–500 nm (guinea-pig, Kuratomi et al. 2003; Maack et al. 2005; rat, Boyman et al. 2011). Our present K0.5act value of 375 nm, referred to [Ca2+]sm, is in the range of previous reports and also corresponds well with our previous global [Ca2+]i datum, 125 nm.

Dynamic Ca2+ activation was seen in excised patches (Hilgemann, 1990; Hilgemann et al. 1992), macropatches (Fujioka et al. 2000) or giant patches (Matsuoka et al. 1995). Sodium–calcium exchange deactivated with τ= 10.8 s on removal of cytosolic-side Ca2+. Activation τ was 7.5 s at 1 μm, but large increases of [Ca2+]i, e.g. by caffeine (Weber et al. 2001) or photolysis (Kappl & Hartung, 1996), would force faster activation by mass action (see also Matsuoka et al. 1995).

In sarcolemmal vesicles (Reeves & Porronik, 1987) and intact Chinese hamster ovary cells (Reeves & Condrescu, 2003), NCX Ca2+ influx activated slowly with a sigmoidal time course, and persisted many tens of seconds or more after [Ca2+]i was reduced, consistent with positive feedback (see next section and Figs 5A and 6A). Presaging our observations (Fig. 1), Matsuoka et al. (1995) showed that NCX transport does not occur under even a strong gradient unless [Ca2+]i is sufficient. Kuratomi et al. (2003) saw delayed but persistent activation in initially rested voltage-clamped guinea-pig myocytes with SR function blocked and proposed a second-order dynamic model that considered only activation. Dynamic Ca2+ activation also occurred during Ca2+ efflux, evident as an acceleration of NCX-mediated efflux at free [Ca2+]i >∼100 nm (Chernaya et al. 1996; Chernysh et al. 2004).

Structure of Ca2+ activation model

Positive feedback is intrinsic to control of NCX Ca2+ activation in intact cells, as was recognized by Kuratomi et al. (2003). Our NCX model cascades a formally separable scaling factor (Ca2+ activation, i.e. fraction of exchangers available) with a transport factor (eqns (4) and (5); Hilgemann et al. 1992). Activating and transported Ca2+ are not strictly separable in the model of Matsuoka et al. (1996; Fig. 3D). The I2 (Ca2+-inactivated) and I1 (Na+-inactivated; not shown) states are respectively accessible only when NCX is oriented on the cytosolic side (states E1, no ions bound, or E1–3Na, 3 Na+ ions bound), and not when external Na+ and Ca2+ are absent, in which case exchangers would orient extracellularly (E2 state; Matsuoka & Hilgemann, 1994). Furthermore, Na+-dependent I1 inactivation can interact with Ca2+ activation at high [Na+]i and/or [Ca2+]i (Hilgemann et al. 1992; Matsuoka & Hilgemann 1994; Matsuoka et al. 1995; Reeves, 1998). However, our separable formulation for NCX is appropriate, because we kept [Ca2+]o fixed, removing only [Na+]o, and did not allow [Na+]i near ∼100 mm (Reeves, 1998).

Once the NCX model is placed in the cell model of Shannon et al. (2004), positive feedback from transported Ca2+ becomes critical, underlying the on–off switch behaviour we observed for Ca2+ activation. It enhances activation and loading during 0 Na+ bouts and enhances deactivation during rest. Rest in 2 mm Ca2+ solution ultimately deactivated NCX in all rabbit cells we studied where [Na+]i was expected or measured to be normal.

Our fourth-order co-operative model recapitulated the observed on–off transitions. The NCX and cell model together preserve resting Ca2+ balance (Bassani et al. 1997; Lester et al. 2008) as well as physiological ‘rest decay’ of Ca2+ loading (Bassani & Bers, 1994). In both the models we rejected, namely our original second-order Hill NCX activation model [eqn (3); Weber et al. 2001] and the fourth-order non-co-operative model [eqn (5b)], NCX remained partly active during rests long enough for experimentally complete deactivation. The rejected alternatives also did not show switch-like behaviour. Experimental Hill coefficients for Ca2+ activation have typically been between 2 (e.g. Fang et al. 1998; Weber et al. 2001) and 4 (Miura & Kimura, 1989; Maack et al. 2005), although >8 was recently reported (Boyman et al. 2011).

We do not relate our model or parameters to NCX molecular structure. Two NCX cytosolic Ca2+ binding domains, CBD1 and CBD2 (Levitsky et al. 1994; Hilge et al. 2006, 2007), on the large hydrophilic loop of NCX (Nicoll et al. 1990) are known. These domains bind multiple Ca2+ ions co-operatively (Levitsky et al. 1994, 1996; Hilge et al. 2006; Besserer et al. 2007) and interactively (John et al. 2011; Boyman et al. 2011), and are both necessary for Ca2+ activation (Besserer et al. 2007). At least three Ca2+ sites are relevant for Ca2+ activation. This and the match with observation make our choice of a fourth-order model reasonable.

Parameterization and predictive power of the model

In our model, NCX will ultimately deactivate during long enough rest until it can remove no further Ca2+. In contrast, under sufficient driving force, Ca2+ influx will become maximal, for instance in priorly stimulated cells with longer (15 s) 0 Na+ bouts (Satoh et al. 2000), probably leading to maximal Ca2+ activation. Between these two extremes, our experiments suggest that NCX exists in a sensitive balance between influx and activation vs. efflux and deactivation, centred over a physiologically relevant range. We set relevant model parameters in order to be consonant with this outcome.

We set kact(off) = 0.05 s−1 (τ= 20 s) as the intrinsic deactivation rate during pure rest. Decay half-time on removing cytosolic Ca2+ was 12.6 s in excised patches (Matsuoka et al. 1995). Our 0 Na+ bouts prolonged decay somewhat in both experiment (Figs 1, 2, 5, 6 and 8) and modelling (Figs 4 and 7) due to positive feedback. Beat-to-beat changes in Ca2+ activation have been inferred from experiments (Haworth et al. 1991; Ottolia et al. 2004; Sobie et al. 2008). With our chosen kact(off), beat-to-beat variation is evident, although heavily smoothed (Figs 4, 7 and 10).

While a full sensitivity analysis matching data with parameters would be impractical, our explorations of kact(off), K0.5act and nHill showed that we could simulate experiments appropriately only when each parameter was kept <50% larger or smaller than we chose (as an example, see tests with K0.5act in Fig. 10).

We adjusted other parameters of the Shannon et al. (2004) model as follows. Background Ca2+ conductance was reduced to 10% of the original value, so that background Ca2+ influx was in the range of 0.25 instead of the 2.5 μmol l−1 s−1 reported by Choi et al. (2000) for rat myocytes. This preserved long-term Ca2+ stability and rest decay mentioned above. We increased the Ca2+ diffusion coefficient between junctional and subsarcolemmal compartments 2-fold and between subsarcolemma and bulk cytosol by 5-fold, so that Ca2+ transient amplitude prediction would vary reasonably with pacing frequency (Fig. 9), and to match the experimental inference that peak [Ca2+]sm is about triple [Ca2+]i in most conditions (Trafford et al. 1995; Weber et al. 2001).

Spatial distribution of NCX

Observable Ca2+ activation eqn (8) was nearly full during Ca2+ transients with the SR intact at 2 Hz (Fig. 9), while it attained only ∼50% with normal [Na+]i and without the SR (Fig. 4). As a step towards explaining this, in our model the relationship among junctional, subsarcolemmal and bulk [Ca2+] differs in the three situations we studied. During twitch stimulation with the SR blocked, Ca2+ influx on ICa(L) (concentrated in the junctional space) activated junctional NCX (not shown) almost fully (model of Fig. 4). The [Ca2+]sm increased up to a fewfold larger than bulk [Ca2+]i (not shown; see Methods). With the SR intact (model of Fig. 9), Ca2+ release was predicted to raise junctional [Ca2+] to ≥20 μm, strongly saturating junctional NCX activation and further increasing [Ca2+]sm relative to bulk [Ca2+]i. Thus, it is not surprising that field stimulation, even without the SR, was more efficacious than 0 Na+ bouts to activate NCX in our model and experiments, as supported by several previous studies (Haworth & Goknur, 1991; Haworth et al. 1991; Viatchenko-Karpinski et al. 2005; Sobie et al. 2008), nor is it unexpected that Ca2+ release with the SR intact could promote essentially maximal Ca2+ activation. During 0 Na+ bouts, the [Ca2+] gradients among the Ca2+ compartments were small, leading the observed Ca2+ activation with normal [Na+]i (see next section) to be smaller.

As in Shannon et al. (2004), we located NCX moieties 89% subsarcolemmal and 11% junctional, i.e. uniformly distributed over the sarcolemma, with the majority not being junctional, as reported for tissue (Thomas et al. 2003; Dan et al. 2007). In modelling our experiments with the SR blocked, the NCX spatial distribution did not strongly affect Ca2+ activation by 0 Na+ bouts (not shown), owing to the small differences between [Ca2+]jct and [Ca2+]sm.

The NCX spatial distribution would be more critical for physiological control of Ca2+ activation during excitation–contraction (E–C) coupling, where [Ca2+]jct depends on ICa(L) and SR Ca2+ release (Sher et al. 2008), and a junctional location for at least some NCX seems essential. During normal E–C coupling in intact cardiomyocytes, severalfold subsarcolemmal-to-cytosolic [Ca2+] gradients develop transiently near NCX (Trafford et al. 1995; Weber et al. 2002) and [Na+] (Weber et al. 2003; Barry, 2006). Our model indicates that the origin of [Ca2+]sm-to-[Ca2+]i gradients is junctional Ca2+, and we made the above minor adjustments of diffusion among the three compartments to match experiment. Recent critical examinations of the ability of NCX to sense local junctional Ca2+ during E–C coupling reinforce the idea that NCX are localized partly, but not dominantly, to t-tubular and junctional space (Acsai et al. 2011; Livshitz et al. 2012). Sodium–calcium exchange near junctions may help to ensure high-fidelity synchronous triggering during E–C coupling (Neco et al. 2010). The spatial distribution of NCX would also influence any possible role in direct triggering of E–C coupling (see below, NCX Ca2+ activation in excitation–contraction coupling).

Cytosolic Na+ modulates Ca2+ activation

It has long been recognized that cytosolic [Na+]i profoundly influences contractility (Bers, 1987), with third-power dependence (Eisner et al. 1984). Kuratomi et al. (2003) as well as Ramirez et al. (2011) recognized that NCX Ca2+ activation may figure in this [Na+]isensitivity.

Normal NKA helps to control and stabilize the thermodynamic operating point for NCX Ca2+ activation and transport. The NKA can limit or even deplete local [Na+], because NCX and NKA colocalize (Fujioka et al. 1998; Terracciano, 2001; Despa & Bers, 2003). During twitch Ca2+ transients, [Na+]i increases with increasing frequency (see simulation in Fig. 9). Aside from influx via Na+ channels, this must be due to increased Ca2+ extrusion via NCX that is driven by SR Ca2+ release. This [Na+]i increase would curtail the drive for Ca2+ efflux via NCX and so promote Ca2+ activation; however, NKA activity would also accelerate in a compensatory manner, limiting the rise of [Na+]i at any given frequency.

Inhibition of NKA severely limited control of [Na+]i by removing compensating fluxes. Elevated [Na+]i, possibly local to NCX, would limit the thermodynamic gradient driving NCX to extrude Ca2+, as predicted (Mullins, 1979) and observed (Bers & Ellis, 1982; Sheu & Fozzard, 1982). On return to 140 mm Na+ after a given 0 Na+ bout, Ca2+ extrusion would be limited by local [Na+]i depletion, favouring accumulation of Ca2+ that enters at subsequent bouts, and hence stronger and more persistent Ca2+ activation. This was supported by our observations (Figs 5 and 6) and model (Fig. 7). In our experiments with NKA block, [Na+]i increased to near 15 mm, the range we have seen in previous NCX-selective voltage-clamp experiments (14.8 ± 1.6 mm, n= 10; unpublished observations, Ginsburg KS and Weber CR; not shown) where Ca2+ activation was promoted and persistent (Bers & Ginsburg, 2007).

The SR also has an evident stabilizing role. In our model (Fig. 8), the initially unloaded SR took up Ca2+, temporarily restricting activation. Once a steady state was reached, the predicted activation was partial and regulated by pacing frequency (Fig. 9).

During 0 Na+ bouts with or without SR function, thermodynamic dissipation also limits the ability of NCX to self-activate via its own Ca2+ influx, because some loss of Na+ is forced during each bout.

In the experiment shown in Fig. 5, Ca2+ activation in the presence of NKA inhibition was not examined until 10 min. Other NKA-inhibited rabbit cells studied did not readily self-activate when probed with 0 Na+ bouts during the first ∼3 min but did later, once [Na+]i had increased enough (not shown). Our simulation (Fig. 7) reproduced this sharp [Na+]i dependence and highly co-operative switch-like behaviour. It is notable that increased [Na+]i accelerated the transition to instability.

Supraphysiological [Na+]i may abrogate or circumvent I2 Ca2+ inactivation, via an apparently separate regulatory pathway. Calcium activation was observed after Na+ loading (20–40 mm[Na+]i, higher than in our study but not high enough for I1 inactivation) in NCX mutants with desensitized Ca2+ activation (Urbanczyk et al. 2006). Like Ca2+ activation itself, this pathway may respond to Phosphatidylinositol 4,5-bisphosphate (PIP2), earlier identified as a regulator (Hilgemann & Ball, 1996).

Normal [Na+]i without NKA inhibition is higher in the mouse than in the rabbit, evidently contributing to the higher propensity to self-activation (data in Fig. 6; model in Fig. 7). An additional factor may be larger background Ca2+ or Na+ leaks.

NCX Ca2+ activation in excitation–contraction coupling

A major prediction of our model is that Ca2+ activation dramatically increases with pacing frequency, increasing 8-fold over the range from 0.2 to 2 Hz (Fig. 9A and F). Although below native in corpore rabbit heart rates, this pacing range is typical for E–C coupling studies in isolated myocytes and is appropriate to induce meaningful variation in E–C coupling gain and SR Ca2+ loading (not shown), as well as Ca2+-dependent ICa(L) inactivation (Fig. 9G) and INCX (Fig. 9H).

It was suggested that when the physiological operating points of all mechanisms regulating Na+ are considered, about half of NCX are active Hilgemann et al. (2006). It was also suggested that Ca2+ activation would enhance the dynamic range of regulation but that a preponderance of evidence, especially from intact cells, indicates that NCX is near fully activated in physiological conditions (Matsuoka & Hilgemann, 1994; Reeves, 1998).

We predict that NCX can freely activate and deactivate (Fig. 4). High-order, highly co-operative Ca2+ activation might vary over a wide range, adapting NCX to fine control of SR Ca2+ loading, which in turn controls E–C coupling gain or efficacy. Sodium–calcium exchange is well situated to stabilize SR Ca2+ loading and regulate it to demand (Eisner et al. 1998; Venetucci et al. 2007).

Kuratomi et al. (2003) also predicted a strong role for Ca2+ activation in regulating contraction, through positive feedback on Ca2+ influx. Their study, done under voltage clamp, has relevant quantitative and qualitative contrasts with ours. Sarcoplasmic reticulum Ca2+ release was blocked. They modelled only Ca2+ buffering and control, not Na+ or other ion fluxes, and Ca2+ activation was structured as a first-order process with an off-rate constant of 1.0 s−1, 20-fold faster than our value. During a 50 s staircase increase of contraction from rest due to pacing at 2 Hz, model-predicted fractional Ca2+ activation increased only to 5%. Steady-state pacing and return to rest were not studied.

Calcium activation appears to be biased higher in mice, where we (Weber et al. 2001) saw K0.5act well below physiological [Ca2+]i in intact cells. Also for mice, Hilgemann (2004) and others suggested that Ca2+ (de)activation might serve only to prevent severe diastolic loss of Ca2+. In future, it would be of value to incorporate our NCX Ca2+ activation model into a comprehensive mouse ventricular cell model, in order to test these predictions, considering the role of higher [Na+]i and/or background fluxes.

While NCX became essentially inactive after enough rest, it appears nonetheless to be important to maintaining flux balance at diastole. The slow off-rate for activation (predicted τ= 20 s) means that NCX does not fully deactivate at any physiological heart rate. Sodium–calcium exchange dominates over the plasma membrane Ca2+ pump in control of diastolic [Ca2+]i (Bassani & Bers, 1994; Bassani et al. 1994; Lamont & Eisner, 1996; Choi & Eisner, 1999).

Sodium–calcium exchange could have a direct role in triggering SR Ca2+ release, and this could be enhanced by dynamic Ca2+ activation. However, NCX triggering efficacy is low (Sipido et al. 1997). Calcium influx via ICa(L) and NCX can be superadditive during E–C coupling. Synergy may occur in baseline conditions (Sobie et al. 2008), but might require β-adrenergic stimulation (Viatchenko-Karpinski et al. 2005). Synergy between NCX and ICa(L) also appears to increase with increasing [Na+]i (Ramirez et al. 2011). Localization of NCX has been predicted to have dual antagonistic effects on E–C coupling; greater density in cleft spaces would enhance potential triggering but would also enhance diastolic Ca2+ removal (Sato et al. 2012). The efficacious activation of NCX by ICa(L) influx we have shown may contribute to potential direct triggering, but our data indicate that NCX Ca2+ activation dynamics are slower than the beat-to-beat dynamics necessary for a direct role. Sodium–calcium exchange seems more likely to act by modulating E–C coupling gain or threshold (Litwin et al. 1998; Goldhaber et al. 1999; Neco et al. 2010), and this control may be effective in the same multibeat time range as Ca2+ activation.

Calcium influx via NCX during E–C coupling could be enhanced by increased Ca2+ activation. Even in the maximal activation our model predicts, however, the Ca2+ influx would be curtailed promptly on the initiation of Ca2+ release. On release, local Ca2+ accumulation is predicted to dissipate the transport gradient and force early initiation of efflux (Weber et al. 2002). Once SR Ca2+ release ends and relaxation ensues, SR reuptake competitively retards efflux via NCX, but Ca2+ activation should increase the contribution of NCX.

Conclusion

We have demonstrated bidirectional dynamic changes of Ca2+-dependent NCX activation in rabbit cardiomyocytes in response to stimulation or rest, which we describe with a fourth-order co-operative model. Data and modelling predict that [Na+]i sets an effective operating point for Ca2+ activation. We further predict that Ca2+ activation is modulated by pacing frequency during physiological E–C coupling. Dynamic, time-dependent control of NCX activation, dependent on the full panoply of Ca2+ and Na+ flux sources and sinks, might enhance the range over which NCX can maintain long-term ion balances while also, as pointed out by Hilgemann (2004), minimally snubbing rapid E–C coupling-related changes.

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  6. Discussion
  7. References
  8. Appendix
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Appendix

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix

Author contributions

The experiments were designed, performed, analyzed and interpreted, and the ms. was written by KS Ginsburg. The other two authors provided substantial intellectual input which was resulted in critical improvements to the experimental design, data interpretation and exposition. All authors agree on the content.

Acknowledgements

This work was supported by NIH grant R37-HL030077 to DMB. We are grateful to Charles Wilkerson and Khanha Dao for their technical contributions.