Measurement and Modeling of Ca²⁺ Waves in Isolated Rabbit Ventricular Cardiomyocytes

Cell isolation and permeabilization

Ventricular myocytes were isolated from Langendorff perfused rabbit hearts by enzymatic digestion as previously described (16). Isolated cells were maintained in a modified Krebs solution buffered with 1 mM ethylene bis[oxyethylenenitrilo] tetraacetic acid (EGTA) at a concentration of ∼10⁴ cells/ml until use. The cells were allowed to settle onto the coverslip at the base of a small bath. β-escin (Sigma, St. Louis, MO) was added from a freshly prepared stock solution to the cell suspension to give a final concentration of 0.1 mg/ml for 0.5–1 min and the β-escin subsequently removed by perfusion with a mock intracellular solution (see below).

Solutions

Permeabilized cells were perfused with a mock intracellular solution with the following composition (mM): 100 KCl, 5 K₂ATP, 5Na₂CrP, 5.5 MgCl₂, 25 HEPES, 0.05 K₂EGTA, pH 7.0 (20–21°C). The [Ca²⁺] in the perfusing solution was varied by the addition of known amounts of 1 M CaCl₂ stock solution (BDH, UK). Fluorescent Ca²⁺ indicators Fluo-3 or Fluo-5F (Molecular Probes, Eugene, OR) were added to the solution to give a nominal final concentration of 10 μM. Myocyte contraction was minimized by the inclusion of 10 μM cytochalasin-D; separate measurements confirmed that this concentration of cytochalasin-D does not affect the SR Ca²⁺ release or uptake processes and had no effect on spontaneous Ca²⁺ wave frequency. Autocamtide-2-related inhibitory peptide(AIP) (CalBiochem, San Diego, CA) was used in the myristoylated form at a concentration of 300 nM. Intact cells were incubated for 30 mins with AIP before β-escin treatment. All solutions used subsequently contained 300 nM AIP.

Data recording and analysis

Confocal line-scan images were recorded using a BioRad (Cambridge, MA) Radiance 2000 confocal system. The Fluo-5F in the perfusing solution was excited at 488 nm and measured above 515 nm using epifluorescence optics of a Nikon (Tokyo, Japan) Eclipse inverted microscope with a Fluor 60× water objective lens (N.A. 1.2). Iris diameter was set at 1.9 providing an axial (z) resolution of ∼0.9 μm and X-Y resolution of ∼0.5 μm based on fullwidth half-maximal amplitude measurements of images of 0.1 μm fluorescent beads (Molecular Probes). Data were acquired in line-scan mode at 2 ms/line; pixel dimension was 0.3 μm (512 pixels/scan; zoom = 1.4). The scanning laser line was oriented parallel with the long axis of the cell and placed approximately equidistant between the outer edge of the cell and the nucleus/nuclei, to ensure the nuclear area was not included in the scan line. As illustrated in Fig. 1 A, the LaserScan (BioRad) software saved the data as a series of image files each containing 30,000 line scans (i.e., 1 min of continuous recording). An experimental record typically comprised four to five line-scan image files; these were reviewed offline and a single intracellular region (80 pixels wide) was selected close to the origin of the wave (indicated in Fig. 1 A). Every protocol was followed by a series of three Ca²⁺ calibration solutions, identical in composition to the experimental solutions apart from containing 10 mM EGTA and a free [Ca²⁺] of: i), 1 nM; ii), 380 nM; and iii), 60 μM. The subsequent intracellular and extracellular fluorescence signals were used to convert the previous fluorescence signals to intracellular [Ca²⁺] as described previously (11) and detailed in the online Supplementary Material. Conversion of fluorescence to [Ca²⁺] was accomplished assuming a Fluo5F K_d of 1.04 μM (17).

Wave detection and velocity correction

Measurements of Ca²⁺ wave velocity along the length of the myocyte were made using a cross-correlation method similar to that described previously (1). Briefly, a line-scan image of Fluo-5F fluorescence was divided into 10 pixel bands. Cross correlation of individual Ca²⁺ wave signals gave a measure of the time taken to propagate eight sequential 3-μm segments along the length of the cardiomyocyte. The mean velocity over an 80 pixel (24 μm) segment was calculated for eight sequential Ca²⁺ waves recorded in the steady state. The cross-correlation technique was also used to align the waveforms of the Ca²⁺ wave recorded in 8 × 10 pixel bands. The series of aligned signals were used to generate an average fluorescence signal of a Ca²⁺ wave in an 80-pixel region of the cardiomyocyte.

Three-compartment model of Ca²⁺ fluxes in a permeabilized cardiomyocyte

Cytoplasmic [Ca²⁺] in a subcompartment of a cardiac myocyte during a Ca²⁺ wave was reconstructed using a three-compartment model (Supplementary Fig. 1). Estimates of the magnitude and time course of the various Ca²⁺ flux pathways were derived from experimental measurements in permeabilized cardiac myocytes. Cytoplasmic [Ca²⁺] from a resolution limited volume of a cardiac myocyte during the Ca²⁺ wave was calculated from confocal Fluo-5F fluorescence signals. These values in conjunction with estimates for intracellular buffering and the diffusion rate constant were used to calculate the underlying Ca²⁺ fluxes. This approach was based on the assumption that once initiated, the Ca²⁺ wave in cardiac muscle is a one-dimensional wave; i.e., effectively the Ca²⁺ wave occurred simultaneously throughout the depth and width of the cell. Evidence for assumption comes from experimental measurements that indicated that the Ca²⁺ wave is essentially planar in both z axis (cell depth) and x axis (cell width) (4,15). The consequence of the planar wave is that the gradient of cytoplasmic [Ca²⁺] and therefore diffusion in the z and x axis is small. Behind the wave front (e.g., 2 μm) in the y axis, the cytoplasmic [Ca²⁺] is still high from the passing Ca²⁺ wave (having occurred ∼20 ms earlier). In advance of the wave front in the y axis is the only direction with a significant cytoplasmic [Ca²⁺] concentration gradient and the potential for diffusion. The sharp wave front observed (within the spatial resolution of the confocal (5)) suggests that over the timescale of the release event (<1 s) diffusion is minimal. The three-compartment model also assumes that diffusion of Ca²⁺ within the SR is minimal. Measured values of the luminal Ca²⁺ diffusion coefficient (50–60 μms⁻²) (18,19) indicate that intra-SR movement of Ca²⁺ during the time course of the wave is small.

The method by which the change in free cytoplasmic Ca²⁺ () under a range of conditions was used to calculate the Ca²⁺ fluxes and free intra-SR () within a resolution-limited volume of permeabilized cardiac myocyte using a three-compartment model is illustrated in Supplementary Fig. 1. Assuming the free [Ca²⁺] in the bath solution () was constant ( = 0), the differential equations describing the change of free [Ca²⁺] within the cytoplasm and SR were as follows:

(1)

(2)

SERCA-mediated Ca²⁺ flux (J_SERCA) was described using a previously published equation (20) (see Appendix, Eq. A1). The Ca²⁺ flux due to diffusion between the cytoplasm and the extracellular space (J_diff) was measured experimentally (Appendix, Eq. A2). The periodic changes in RyR2-mediated flux (J_RyR) was modeled using the following conditions:

is the calculated maximum value of based on experimental measurements of total SR Ca²⁺ content. J_leak is the background Ca²⁺ leak from the SR (see Appendix, Eq. A3) and is presumed to be mainly via spontaneous activity of RyR2. The magnitude of this flux pathway was measured experimentally (see Fig. 5). J(t)_wave is a time-dependant change in RyR2 permeability; the time course and extent was calculated from measurements made on permeabilized cells. The function transforms the net Ca²⁺ flux in the cytosol to a change in This function used previously published measurements of cytosolic Ca²⁺ binding in permeabilized rabbit cardiac myocytes (21) (see Appendix, Eq. A4).

Equation 2 is used to quantify the change whereas transforms the net Ca²⁺ flux in the SR a change in based on previously published estimates of the concentration and binding capacity of Ca²⁺ buffers in rabbit cardiomyocytes (20) (see Appendix, Eq. A5).

Measurement of Ca²⁺ waves in permeabilized single myocytes

Fig. 1 A shows a typical line-scan image from a permeabilized rabbit ventricular cardiomyocyte perfused with a solution containing 280 nM Ca²⁺. This solution caused regular Ca²⁺ waves (∼0.2 Hz) that propagated the full length of the cardiomyocyte. At the point indicated, 10 mM caffeine and 25 μM thapsigargin were rapidly applied to release Ca²⁺ from the SR and to inhibit reuptake. The horizontal dashed lines delineates an 80-pixel region (24 μm) along the scan line through the permeabilized myocyte. Fig. 1 A (ii) shows time course of (black line) and (gray line) derived from the average fluorescence signal from the 80-pixel band within the cell and a comparable region in the extracellular space adjacent to the cell, respectively. Note that after prolonged perfusion with caffeine/thapsigargin, the signal is equal to the indicating equilibration of the [Ca²⁺] within the two compartments. The same situation exists before addition of caffeine, despite the oscillating level of the mean over a period of 2–4 s is equal to the (11). Fig. 1 B (i) shows the line-scan image of the Ca²⁺ wave on a faster time base with an 80-pixel central region indicated. The sloping wave front represents the propagation of the Ca²⁺ wave from one end of the cell to the other at an approximately constant velocity (∼120 μm/s). The diagram in Fig. 1 B (ii) shows the time course of the in the 80-pixel section (black line). The gray line represents the time course after correction of the wave front for the smearing of the upstroke caused by the propagation of the Ca²⁺ wave over the ∼24 μm (80 pixels) within the cell (see Methods). Panels iii and iv are the corresponding line-scan image and from the cell during rapid application of caffeine/thapsigargin. On addition of caffeine, the rise of is approximately synchronous along the length of the cell, and the upstroke and amplitude of the signal is similar to that of the corrected Ca²⁺ wave. The decline of the signal in the presence of caffeine/thapsigargin is considerably slower than the Ca²⁺ wave due to the inability of the SR Ca²⁺ pump to sequester the Ca²⁺; this decline reflects the loss of Ca²⁺ from the cardiomyocyte by diffusion. In these measurements caffeine causes a small (∼10%) but significant quench of the Fluo-5F fluorescence. This was evident from the extracellular fluorescence signal. The time course and extent of caffeine-induced quench was quantified and used to correct the intracellular signal. This correction was minimal during the initial rise of

Ca²⁺ waves at a range of perfusing [Ca²⁺] values

Fig. 2 A shows records of recorded from 80-pixel regions of line scans recorded from cardiomyocytes exposed to solutions containing Fluo-5F and a range of (∼300 nM (i), ∼600 nM (ii), and ∼900 nM (iii)). The gray line in each panel indicates the in each experiment. As the was increased, Ca²⁺ wave frequency, and minimum and maximum all increased. Average values of these parameters are shown in Fig. 2 B (i). The gray line is the unity relationship between mean and The values of mean during a 30-s period of Ca²⁺ waves follows the unity relationship indicating that over the range of 300–900 nM there is no net diffusion of Ca²⁺ between the cytosol and the extracellular space despite the oscillation of The relationship between the maximum and was nonlinear, the increase observed from ∼600 to 900 nM was much greater than that seen between 300 and 600 nM. Fig. 2 B (ii) shows the mean values of Ca²⁺ wave frequency versus the relationship with respect to was also nonlinear. The increase in frequency observed between 600 and 900 nM was considerably less than that seen from 300 to 600 nM. The average Ca²⁺ wave velocities showed a similar nonlinear relationship to frequency. At a ∼ 300 nM, wave velocity was 130 ± 4 μm/s; at ∼900 nM the frequency of the Ca²⁺ waves had increased approximately fivefold whereas the velocity had increased to 180 ± 5 μm/s (P < 0.05).

Conversion to total cytoplasmic [Ca²⁺]

Fig. 3 A shows the process of conversion of signal to total cellular [Ca²⁺] () using the intracellular Ca²⁺-buffer characteristics measured for digitonin-treated rabbit ventricular myocytes in previous studies (21). The change in was derived from eight sequential velocity-corrected Ca²⁺ waves recorded in the steady state (Fig. 2 A). As shown in Fig. 3 A (ii), although the amplitude of the signals at 600 nM was larger than that at 300 nM; the amplitude of the two signals is similar. This is confirmed by the mean data shown in Fig. 3 C (i) and suggests that over a range of cellular Ca²⁺ loads, the total [Ca²⁺] released by the SR during a Ca²⁺ wave is constant irrespective of the mean and frequency. Furthermore, the similarity of the amplitude Ca²⁺ wave and caffeine-induced Ca²⁺ release indicates that the Ca²⁺ wave releases the majority of the available SR Ca²⁺ (Fig. 3 B). Therefore the increase in the of ∼150 μM during a Ca²⁺ wave or caffeine transient provides an estimate of the total Ca²⁺ content of the SR under these conditions. Using previously published estimates of SR volume, concentration of intra-SR Ca²⁺ buffer and the apparent K_d of Ca²⁺ (20), these values predict that maximum [Ca²⁺] in the SR () is ∼3 mM and the free intra-SR Ca²⁺ () is ∼1 mM. The average value of predicted at a mean of ∼300 nM was not significantly different from that calculated at 600 and 900 nM and supports the earlier contention that spontaneous SR Ca²⁺ release occurs at a fixed intraluminal [Ca²⁺] (7,10). An important additional conclusion is that locally, the Ca²⁺ released during a Ca²⁺ wave depletes the SR Ca²⁺ as effectively as caffeine-induced Ca²⁺ release. One source of error in this estimation is the variable timing of the caffeine-induced Ca²⁺ release relative to the preceding Ca²⁺ wave. Releasing Ca²⁺ with caffeine shortly after a Ca²⁺ wave may underestimate the maximum Ca²⁺ content of the SR since refilling may be incomplete. An estimation of the relationship between SR Ca²⁺ content and the time after the preceding wave can be gleaned from a plot between Ca²⁺ wave amplitude and the interwave interval. Fig. 3 C shows this relationship based on data from permeabilized cells at ∼300, ∼600, and 900 nM. This plot shows a shallow dependence of SR Ca²⁺ released during a Ca²⁺ wave and the interwave interval. The data suggest that Ca²⁺ release at periods >60% of the maximum interwave interval will release >90% of the Ca²⁺ released at the longest interwave interval. Therefore if the caffeine-induced Ca²⁺ release is in the latter 50% of the interwave interval it will not substantially underestimate maximum SR Ca²⁺ content. This time course of SR refilling is supported by the predictions from the computational model (see Fig. 8).

Estimation of rate of loss of Ca²⁺ from the myocytes by diffusion

The rate constant for the efflux of Ca²⁺ from permeabilized cardiomyocytes was estimated by examining the rate of decay of the Ca²⁺ signal after rapid application of caffeine/thapsigargin. Under these conditions, it was assumed that the rate of decay of the Ca²⁺ signal was dependant on the loss of Ca²⁺ from the permeabilized cell by diffusion. The method used to estimate the rate of diffusion is illustrated in Fig. 4, the decay of within the cell was converted to a signal as described in Fig. 3 A. The resultant signal was fitted a polynomial (fourth to eighth order) to obtain a smoothed decay curve. The polynomial fit of the decay time course was differentiated (to calculate Ca²⁺ flux) and plotted against the corresponding ΔZ signal (). As shown in Fig. 4 B, this relationship was approximately linear, the gradient of which reflected the value of the rate constant to describe the loss of Ca²⁺ from the cell. The average rate constant was 30.1 ± 2.1 s⁻¹ (n = 24 cells). Knowledge of this constant allowed the signal to be corrected for the Ca²⁺ loss and gain from the extracellular space during the Ca²⁺ wave. An example of the corrected transient is shown in Fig. 4 C and the signal represents the total Ca²⁺ released and taken up by the SR during a single Ca²⁺ wave. Despite the high during a wave, the loss of Ca²⁺ from the cell by diffusion is small, at the peak of the transient it is ∼3 μM, and by the end of the transient the value is ∼10 μM compared to the total released from the SR of ∼150 μM.

Estimation of the background leak of Ca²⁺ from the SR

Ca²⁺ efflux from the cardiac SR in the absence of Ca²⁺ waves is thought to be mainly due to spontaneous nonpropagating Ca²⁺ sparks that generate a background Ca²⁺ leak from the SR. The magnitude of the background flux can be quantified by monitoring the loss of Ca²⁺ from the SR in the absence of SERCA activity. These measurements were made in permeabilized cardiomyocytes as shown in Fig. 5 A. Cells were perfused with of 150 nM in the presence of 0.3 mM EGTA. Rapid and complete inhibition of SERCA was achieved by using a mixture of two SERCA inhibitors, 2′,5′-di(tert-butyl)-1,4-benzohydroquinone (TBQ) (25 μM) and thapsigargin (25 μM). The time course for the loss of SR Ca²⁺ was tracked by application of 10 mM caffeine at fixed times after SERCA inhibition. The amplitude of the signal at each time point was taken to reflect the SR Ca²⁺ content. Fig. 5 B shows the mean data from a number of experiments, the time course of the decay suggests an approximately exponential decay of SR Ca²⁺ content with a rate constant of 1.37 ± 0.01 min⁻¹ (n = 8 cells). The additional curve shown in Fig. 5 B is the predicted time course of the decrease in amplitude of caffeine-induced Ca²⁺ signals from the computational model described below.

Calculation of SERCA-mediated fluxes from the time course of the Ca²⁺ wave

Fig. 6 illustrates the approach used to estimate the SERCA-mediated flux and subsequently the time course and magnitude of RyR2-mediated Ca²⁺ flux during a Ca²⁺ wave. Fig. 6, A and B, show the time course of the change in and (corrected for diffusion), respectively, during a Ca²⁺ wave. A smoothed waveform of the signal was generated by a pair of fourth- to eighth-order polynomials fitted to the upstroke and decay phases of the waveform (gray line). The net Ca²⁺ flux associated with a Ca²⁺ wave was calculated by differentiating the signal to generate the waveforms shown in Fig. 6 C (back line). The differential of the polynomial fit generated a smooth time course (gray line), whereas the magnitude of the release phase (positive flux) could be resolved directly from the Ca²⁺ signal. But the differential of the original total Ca²⁺ signal was too noisy to extract the negative flux (uptake phase) of the signal. The time course of the negative phase was resolved from the differential of a polynomial fit (inset, Fig. 6 C). During the latter phase of these signals (the section highlighted by the gray area), the underlying Ca²⁺ fluxes were assumed to be: i), background SR Ca²⁺ leak (Fig. 4); ii), diffusional loss/gain of Ca²⁺ (Fig. 3); and iii), SERCA-mediated Ca²⁺ flux. The rate constants associated with fluxes i and ii were estimated from the measurements described above and used to calculate the magnitude of the associated fluxes during the decay phase of the Ca²⁺ wave. These fluxes were subtracted from the underlying Ca²⁺ signal to reveal the SERCA-mediated flux (black line, Fig. 6 D). As shown in Fig. 6 D, between 200 and 600 nM the relationship between the SERCA-mediated Ca²⁺ flux and the corresponding fitted well with a previously published model of SERCA function (gray line; Appendix, Eq. A1) (20) and this allowed the estimate of the maximum turnover rate (V_max) and the Ca²⁺ sensitivity (K_mf) and slope (H) of SERCA. Once established, these values were assumed to apply for the complete time period of the Ca²⁺ wave (Fig. 6 E). These calculations suggested that for the majority of the time course of the Ca²⁺ wave, SERCA was operating at, or close to, the V_max.

Calculation of RyR2-mediated fluxes from the time course of the Ca²⁺ wave

By assuming that the calculated SERCA parameters and the rate constants for both background SR Ca²⁺ leak and the Ca^2-diffusion apply equally to the initial phase of the Ca²⁺ wave, the time course and magnitude of transient increase in RyR2-mediated Ca²⁺ flux can be estimated (Fig. 6 F). This approach predicted an RyR2-mediated efflux that peaks at ∼4 mMs⁻¹ within 30 ms and decays to negligible values within 100 ms. The time course of the Ca²⁺ flux can be converted to a permeability by calculation of the corresponding changes in using previously published estimates of SR volume and intrinsic cellular buffering properties (22). This parameter is independent of the trans-SR Ca²⁺ concentration gradient and indicates the time course of the change in RyR2 activity. These calculations suggest that the Ca²⁺ efflux from the SR increases from a basal level of ∼1.2 μM/s to ∼3 mM/s during a Ca²⁺ wave as a result of a transient increase in the permeability of the SR to Ca²⁺.

Derivation of SERCA flux and RyR2 flux parameters from Ca²⁺ waves generated at a range of intracellular [Ca²⁺]

The analysis described in Fig. 6 was applied to Ca²⁺ waves recorded from cardiomyocytes exposed to solutions with a of ∼300, ∼600, or ∼900 nM Ca²⁺. As shown in Fig. 7, the mean values of SERCA V_max and K_mf were not constant across this range of both increased significantly, whereas the change in slope (H) was not significant. The corresponding changes in RyR2 flux parameters predicted by the analysis are shown in Fig. 7, A (iii) and C. The calculated peak RyR2-mediated flux and permeability progressively increased over the range of [Ca²⁺] studied but the duration at half-maximum (FWHM) was unchanged (Fig. 7 C (iii)).

Comparison of model and recorded Ca²⁺ wave parameters

The complete set of Ca²⁺ flux parameters for Ca²⁺ waves recorded in a typical permeabilized cell at of ∼300 nM (including the time course of RyR2-mediated Ca²⁺ flux) were used in a computational model to predict the time course and frequency of Ca²⁺ waves. The details of the model are given in the Methods section and in the Appendix, the only assumption used in the model is that RyR2-mediated Ca²⁺ release was triggered by the reaching a threshold value (). This value was taken as the maximum free intra-SR [Ca²⁺] calculated from the estimated total SR Ca²⁺ content. As shown in Fig. 8, the computational model predicted Ca²⁺ waves of similar time course (Fig. 8 A) and frequency to that observed experimentally. When run continuously to reach a steady state, the model generated Ca²⁺ transients at = 300 nM that had a frequency, maximum and minimum that was within 5% of the experimental data. The application of caffeine/thapsigargin was simulated by increasing background leak by a factor of 1000 and reducing V_max of SERCA by 1000. The resultant Ca²⁺ transient decayed with a similar time course to that observed experimentally due to loss of Ca²⁺ by diffusion. The calculated signal is shown to indicate the predicted time course of during release and loading to a threshold level during each wave. The third signal is the integral Ca²⁺ flux due to diffusion. This indicates that during each Ca²⁺ wave ∼10 μmol of Ca²⁺ leaves the cell during the Ca²⁺ wave. In the period between Ca²⁺ waves, the same amount of Ca²⁺ enters the permeabilized cell from the extracellular space. Thus, in the steady state, the amount of Ca²⁺ leaving and entering the cell is balanced. Fig. 8 B (i and ii) show model predictions of Ca²⁺ waves at 900 nM Ca²⁺ under two conditions: i), with the same values of V_max, K_mf, H, and peak RyR2 permeability used to simulated waves at 300 nM; and ii), with the values of V_max, K_mf, and RyR2 peak permeability appropriate for 900 nM derived from the relationships shown in Fig. 7. As shown, without changing the SERCA and RyR2 values, the model predicts a rise of Ca²⁺ wave frequency (to 372% of control) and amplitude (to 136% of control). However, adjusting of the SR parameters to those appropriate for 900 nM predicts waves of higher frequency (514% of control) and similar amplitude (138%). The predicted increase in wave frequency going from 300 to 900 nM (514%) is comparable to that observed experimentally (481 ± 12%, n = 10). The same result can be achieved by using the SR parameters at 900 nM as the starting conditions and predicting the Ca²⁺ waves at 300 nM, the decrease in frequency of Ca²⁺ waves predicted by uncorrected SR parameters is less than that seen experimentally (data not shown). In summary, the use of fixed SERCA and RyR2 parameters to predict Ca²⁺ wave characteristics does not mimic the experimental data over a range of Adjustment of SERCA K_mf and V_max and RyR2 maximum permeability is necessary to accurately predict changes Ca²⁺ wave frequency at different values of

The effects of CaM kinase inhibitor AIP on Ca²⁺ waves

One mechanism that may be responsible for the experimentally observed change in the characteristics of RyR2 and SERCA at different is modulation of the activity of these proteins by phosphorylation via the Ca²⁺ sensitive enzyme CaM kinase (23). To test this hypothesis, intact cells were incubated with the CaM kinase inhibitor AIP before exposure to solutions containing either ∼300 or ∼600 nM Ca²⁺. The data shown in Fig. 9 summarizes the Ca²⁺ wave characteristics and the derived SERCA and RyR2 parameters relative to those measured at Incubation with AIP reduced the degree to which the Ca²⁺ wave frequency increased at = 900 nM (from 481 ± 12%, n = 10 to 340 ± 10%, n = 15, P < 0.05; Fig. 9 A (iii)) but did not change any other aspect of the Ca²⁺ wave (Fig. 9 A (i and ii)). Analysis of Ca²⁺ fluxes indicated that AIP treatment prevented the apparent increase in SERCA V_max observed at 900 nM Ca²⁺ (P < 0.05; Fig. 9 B (iii)) but the effect of AIP on SERCA K_mf and H were not statistically different from the control values. Furthermore, the derived values of peak RyR2 flux and permeability after AIP treatment were significantly lower than control values at 900 nM (P < 0.05). Wave velocity in AIP was significantly lower after AIP treatment (130 ± 7 μm/s) compared to control (180 ± 5 μm/s), and was similar to that measured at = 300 nM (130 ± 4 μm/s). AIP treatment did not significantly affect any of the Ca²⁺ wave parameters or derived SERCA and RyR2 parameters at Plotted on the right-hand side of each on the panels in Fig. 9 are the relative changes in parameters on raising from 300 to 900 nM predicted by the computational model under two conditions: i), with values of SERCA and RyR2 values corrected for increased [Ca²⁺]; and ii), using values of SERCA and RyR2 parameters appropriate for The effects of removing Ca²⁺ correction on i), Ca²⁺ wave frequency; ii), SERCA turnover rate (V_max); and iii), RyR2 peak permeability is similar to that observed experimentally on addition AIP. This supports the view that AIP inhibits the Ca²⁺-dependent changes in SERCA and RyR2 function observed upon raising the from 300 to 900nM.

Comparison between Ca²⁺ wave and caffeine transient

Careful calibration of fluorescence signals allowed the accurate measurement of within a limited region of the cytosol of permeabilized cardiac cells (11). Previous studies have shown that both intact and permeabilized cells exhibit a threshold for Ca²⁺ wave generation of above ∼200 nM. Above this value, cycles of spontaneous SR Ca²⁺ release occur with increasing frequency as the cellular Ca²⁺ load is increased. At the whole cell level, spontaneous Ca²⁺ release was estimated to deplete the SR Ca²⁺ by ∼15% compared to that achieved during rapid application of caffeine (7). This study suggests that Ca²⁺ release during a fully propagating Ca²⁺ wave locally depletes the SR by ∼100% compared to that achieved by caffeine. This observation is not contrary to the measurements from intact cardiac myocytes; normally the complete Ca²⁺ wave takes ∼1 s to propagate along the length of the cell at room temperature. But at any one time over this period only ∼20% of the volume of the cardiomyocyte experiences an increased ∼80% of the volume is either awaiting the arrival of the Ca²⁺ wave or is recovering after the release phase. In contrast, caffeine releases Ca²⁺ synchronously throughout the cardiomyocyte; therefore local and whole cell signals are comparable. A similar principal applies to the published records of luminal Ca²⁺ using Fluo-5N fluorescence. These data suggest that a Ca²⁺ wave releases ∼60–70% of the total caffeine-accessible signal (24,25). These studies may have underestimated the amplitude of signal associated with a Ca²⁺ wave. The Fluo-5N line-scan signal of a Ca²⁺ wave was derived from the average fluorescence from the full length of the cell. The finite time (∼1 s) for the wave to propagate along the length of the cell will smear the time course and reduce the amplitude of the signal. A similar phenomenon is seen with the Fluo-5F cytoplasmic signals (see Supplementary Fig. 3). This averaging of the nonsynchronous Ca²⁺ wave signal may explain why the amplitude is lower than those observed with synchronous caffeine-induced signals.

The data described in this study are entirely derived from permeabilized cardiac myocytes, but the principles are thought to apply to Ca²⁺ waves in intact myocytes. Previous studies have compared intact and permeabilized cells; no significant differences were observed in time course, amplitude, or frequency of spontaneous Ca²⁺ waves recorded from these two preparations (10,26).

Raising the cellular Ca²⁺ load increased the minimum and maximum and apparently increased the amplitude of change during the Ca²⁺ wave. However, when the total Ca²⁺ released from the SR at various cellular Ca²⁺ loads was calculated the increase in within the cytosol during a Ca²⁺ wave was constant (∼0.15 mM) regardless of the cellular Ca²⁺ load (Fig. 3 C). This calculation and the subsequent analysis is based on the assumption that the only subcellular components contributing to the intracellular Ca²⁺ signals are: i), cytoplasmic Ca²⁺ buffers; ii), SR Ca²⁺ release and uptake processes; iii), intra-SR Ca²⁺ buffers. There is evidence that cardiac mitochondria contribute to Ca²⁺ homeostasis (27,28), but previous work indicates that under the conditions of this study, the activity of mitochondria does not influence the time course or frequency of the Ca²⁺ waves (11).

Measurement of background Ca²⁺ fluxes

The rate constant for Ca²⁺ loss from a permeabilized cardiomyocyte was calculated from the rate of decay of the caffeine-induced response. Assuming this value can be applied to Ca²⁺ movement both into and out of the myocyte, this was used to calculate the magnitude of Ca²⁺ fluxes across the permeabilized membrane during a Ca²⁺ wave. These calculations suggested that only a small amount of Ca²⁺ is lost and gained during a Ca²⁺ wave cycle (∼10 μM) compared to the total released from the SR (∼150 μM). Interestingly, these estimates are close to those published for intact cardiomyocytes where Ca²⁺ loss and gain from the cell is via sarcolemmal transport processes (mainly the Na⁺/Ca²⁺ exchange) (7).

In a separate set of experiments, the efflux of Ca²⁺ from the SR in the absence of Ca²⁺ waves was estimated by monitoring the decline in SR Ca²⁺ content at various times after rapid inhibition of SERCA. This time course was approximately exponential and could be adequately modeled with a single rate constant. This was used to estimate the rate of efflux of Ca²⁺ from the SR in the periods between Ca²⁺ waves; a flux that is normally countered by the activity of SERCA. Over the initial 30 s after inhibition of SERCA, the leak of Ca²⁺ from the SR was ∼1.2 μM/s. This value is lower than those measured in intact rabbit myocytes using rapid tetracaine application (4–15 μM/s) (22) but higher than estimates in earlier studies (20,29). One possibility for the range of values is the critical dependence of leak rate on SR luminal Ca²⁺, a variable that was not necessarily constant across studies.

Model derived values of SERCA and RyR2 fluxes

Assuming that the transient increase in SR Ca²⁺ permeability that caused the Ca²⁺ wave did not contribute significantly to the Ca²⁺ signal late on in the decay phase of the wave, then the Ca²⁺ fluxes determining the in the latter part of the wave are: i), exchange with the bath solution; ii), background efflux from the SR; and iii), uptake by SERCA. Since i and ii are known, iii was calculated using a previously published model of SERCA (20). The values of SERCA binding constant (200–300 nM), the slope of the relationship (3–4), and the maximum turnover rate (V_max) values (200–400 μM/s) are comparable to those values estimated for the intact cardiac myocyte (20,22,30). When these SERCA characteristics were used to predict SERCA activity early in the Ca²⁺ wave it was clear that, for the majority of the release phase, SERCA will be operating at maximal turnover rate. Assuming that SERCA activity can influence the Ca²⁺ signal immediately (∼5 ms) after the release of Ca²⁺ from the SR, the predicted SERCA fluxes during the Ca²⁺ wave were used to predict the corresponding SR Ca²⁺ release waveform required to generate the measured change in The transient rise of SR flux calculated by this approach peaked within 30 ms with a flux rate of ∼2–3 mM/s and was complete by ∼100 ms. These values are comparable to those measured during E-C coupling in cardiomyocytes at high SR Ca²⁺ loads (31–33). Throughout these calculations, equilibrium constants and not rate constants were used to calculate Ca²⁺ binding to cytosolic buffers and SERCA. This simplifying assumption has been made by several previous studies (20,34–36) and is justified in the current study by the relatively coarse spatial (∼5 μm) and temporal resolution (10 ms) of the measurements.

Changes in Ca²⁺ wave characteristics with cellular [Ca²⁺]

Examination of the characteristics of the Ca²⁺ waves at a range of cellular [Ca²⁺] revealed changes in the calculated underlying Ca²⁺ fluxes (Fig. 7, B and C). The analysis suggests that the time course of the Ca²⁺ wave at higher require changes in the parameters for both SERCA and the RyR2 activity. The most striking of these changes are the increase in SERCA V_max and the increased peak permeability of release waveform. This suggests that the increased frequency of the Ca²⁺ waves at higher cellular Ca²⁺ load cannot simply be explained by a fixed set of SR fluxes. This conclusion was confirmed using a computational model. Using the characteristics of the SR that apply at 300 nM to predict the changes in wave characteristics at 900 nM indicated an increase in Ca²⁺ wave frequency that was considerably lower than that observed (375 vs. 514%). Using the higher SERCA and RyR2 parameters measured at ∼ 900 nM reproduced the Ca²⁺ wave frequency to within 5% of the measured values (481 ± 12%).

Changes in Ca²⁺ wave velocity with cellular [Ca²⁺]

Ca²⁺ wave velocity was higher when the and therefore the mean was increased. A positive correlation between Ca²⁺ wave amplitude and velocity has been previously reported for propagated waves in intact (37) and permeabilized cardiomyocytes (10,11). Although the precise mechanism underlying the relationship has not been verified, propagation of a Ca²⁺ wave is thought to be mediated via a “fire-diffuse-fire” mechanism between discrete clusters of RyR (14,38,38). Simplistically, larger Ca²⁺ release would be expected to propagate faster because the threshold required to trigger release at adjacent sites would be attained earlier. A computational model of Ca²⁺ waves in the heart (14) indicated that over a limited range of wave amplitudes, an approximately linear relationship existed between Ca²⁺ wave propagation velocity (v) and the coefficient σ/dc* where d is the distance between release sites, c* is the threshold for Ca²⁺ release, and σ is the amount of Ca²⁺ released from the SR (14). Normally, the parameters d and c* are considered fixed, but modeling of Ca²⁺ waves has been extended to include an influence of luminal [Ca²⁺] () on c* (39). A considerable amount of data now supports the concept that increased SR luminal [Ca²⁺] () acts on luminal sensors to increase the open probability of RyR2 and hence lower the cytoplasmic threshold for Ca²⁺ release (c*) (39,40).

Recent work suggests that the SERCA activity between adjacent release sites may directly influence propagation velocity (41). In particular, rapid inhibition of SERCA instantaneously reduced conduction velocity (42). This suggests that SERCA mediated uptake has a role in the propagation of the Ca²⁺ wave. In particular, the high after release at one site may activate SERCA and increase in adjacent sites thereby lowering the cytoplasmic threshold for release (c*). If this mechanism acted as a modulatory influence then factors that increase SERCA V_max would be anticipated to increase propagation velocity by increasing the rate of rise of The data presented in this study are consistent with this theory; the increased propagation velocity observed at higher was paralleled by an apparent increase in SERCA V_max. After inhibition of CaM kinase, neither the calculated SERCA V_max nor the propagation velocity was significantly increased at the higher despite an increase in Ca²⁺ wave amplitude.

CaM kinase inhibition

CaM kinase II is the most obvious candidate for the Ca²⁺-dependent modulation of SERCA and RyR2 observed in this study. The enzyme exists both within the cytosol and bound to the SR membrane in cardiac muscle and has previously been reported to influence the activity of SERCA and RyR2 via phosphorylation (23). Support for this hypothesis was obtained by using the CaM kinase inhibitor AIP, which appeared to alter the Ca²⁺ wave characteristics at high (∼900 nM), but not at lower values (∼300 nM). Furthermore, flux analysis of Ca²⁺ waves suggests that the effects of CaM kinase inhibition could be explained by the preventing the increase in SERCA V_max and RyR2 peak permeability observed at = 900 nM (Fig. 9). The increased values of SERCA V_max at higher reversed by CaM kinase inhibitors, is entirely consistent with previous reports of the effects of CaM kinase phosphorylation on SERCA (43). This contrasts with A-kinase mediated effects that change in the Ca²⁺ affinity of the pump.

In intact myocardium, frequency-dependent acceleration (FDA) of relaxation is an important part of the physiological response to increased frequency of stimulation. The role of CaM kinase in this response is controversial (44,45). The data in this study would suggest that a similar FDA of Ca²⁺ uptake occurs in spontaneously active cardiac cells. As the mean is increased, the CaM kinase-mediated effect enhances SERCA activity and increases the frequency of spontaneous Ca²⁺ release.

Increasing also affected the Ca²⁺ efflux pathways. The marked increase in permeability observed at ∼ 900 nM was prevented by inhibition of CaM kinase by AIP treatment. Previous reports on the consequences of CaM kinase phosphorylation of RyR2 are controversial, with increases (46) and decreases (47) being reported. In mice overexpressing CaM kinase II, spark frequency approximately doubles (48), and the enhanced CaM kinase II activity in heart failure is linked to the increased leak via RyR2 in heart failure (49,50). The data in this study is consistent with CaM kinase mediated stimulation of RyR2 activity. These effects combined with CaM kinase mediated effects on SERCA increase the frequency of spontaneous Ca²⁺ waves in cardiac muscle. At the higher cellular [Ca²⁺] values that occur at high heart rates, the increased CaM kinase activation is unlikely to increase the probability of spontaneous Ca²⁺ release during diastole due to the corresponding shorter diastolic period. But the increased CaM kinase II expression and activity documented in failing hearts (49–52) may increase the probability of spontaneous Ca²⁺ release at normal heart rates, a potentially proarrhythmic event.