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:
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.
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).
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:
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).
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:
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.
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.
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+.