INTRODUCTION

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IN THE HEART Ca²⁺ plays a crucial role in transducing electrical excitation into muscle contraction. The depolarization causes a rise in intracellular Ca²⁺ concentration ([Ca²⁺]_i) and results in muscle contraction. In addition, [Ca²⁺]_i affects diverse cellular processes, including gating of numerous ion channels. Because Ca²⁺ is an extremely important ion in cellular physiology, considerable effort has been spent to understand the many factors that influence [Ca²⁺]_i dynamics (4).

Experiments using fluorescent [Ca²⁺]_i indicators (e.g., fura 2, indo-1, and fluo-3) and pharmacological interventions have revealed a great deal about the [Ca²⁺]_i dynamics in a uniformly polarized cell membrane. Depolarization-induced influx of Ca²⁺ occurs predominantly via sarcolemmal L-type Ca²⁺ channels and induces rapid and synchronous release of Ca²⁺ from the sarcoplasmic reticulum (SR) via the mechanism of calcium-induced calcium release (CICR) (14). As a result, [Ca²⁺]_i increases uniformly over the entire cell length (28). For example, in the guinea pig, [Ca²⁺]_i increases from a resting value of ~120 nM to a peak value of ~1,100 nM during an action potential (7). The Ca²⁺ released from the SR contributes the majority of [Ca²⁺]_i (10, 26), and in the guinea pig the SR contribution is ~70-80% (5, 13, 15). The [Ca²⁺]_i transient reaches its peak value within ~35 ms from the onset and declines thereafter with the majority of Ca²⁺ returned to the SR by SR Ca²⁺ ATPase (SERCA) (6, 26). The sarcolemmal Na⁺/Ca²⁺ exchanger also extrudes a small amount of Ca²⁺ from the cell, which is equivalent to the amount of Ca²⁺ entered via L-type Ca²⁺ channels (5, 8).

Because the Ca²⁺ entry via L-type Ca²⁺ channels is membrane voltage dependent, it is possible that during field stimulation, when the cell is nonuniformly polarized and different regions of the cell experience very different transmembrane voltages (11, 24, 32), spatial differences in Ca²⁺ current and therefore [Ca²⁺]_i can exist. To date no experimental studies have addressed the above hypothesis. Thus the aim of this study was to characterize the [Ca²⁺]_i transients in adult guinea pig ventricular cells field stimulated at rest and during the plateau phase of the action potential by using the fluorescent indicator fluo-3 and a high resolution multisite optical mapping system. We show that external fields can indeed induce spatial inhomogeneities and gradients in [Ca²⁺]_i both during rest and the plateau.

	METHODS

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Single ventricular myocytes were enzymatically isolated from whole hearts of adult male guinea pigs (Hartley strain, weight 200-300 g) as follows. The animals were anesthetized with an intraperitoneal injection of pentobarbital sodium (0.1 ml/100 g, Abbott Laboratories; North Chicago, IL) combined with 0.1-0.3 ml of heparin to minimize clotting. Once the animal failed to respond to the paw pinch test, its chest was quickly opened via a radical medial thoracotomy. The heart was quickly excised, mounted on a Langendorff column, and perfused retrogradely through the aorta. The enzymatic dissociation was performed using the following sequence of solutions, all of which were oxygenated and maintained at 37°C: 1) 1.8 mM Ca²⁺ Tyrode's solution for 5 min; 2) Ca²⁺-free Tyrode's solution for 7 min; 3) 50 ml Ca²⁺-free Tyrode's solution with 0.25 mg/ml protease (type XIV, Sigma; St. Louis, MO), 0.3 mg/ml collagenase (Worthington Biochemical; Freehold, NJ), and 1 mg/ml bovine serum albumin (type V, Sigma) for 7 min; and 4) Ca²⁺-free Tyrode's solution for 5 min. After perfusion the ventricles were chopped, gently stirred, and filtered to obtain single cells.

Cells were loaded with the [Ca²⁺]_i-sensitive dye fluo-3 by exposure to a 3 µM solution of cell-permeable fluo-3 AM (Molecular Probes; Eugene, OR) for 30-50 min. Fluo-3 loading solution was prepared by a 1,000-fold dilution of a 3 mM stock solution in dimethyl sulfoxide containing 20% wt/wt of Pluronic 127 (Molecular). After dye loading was completed, the cells were allowed to deesterify for 20-30 min and thereafter used for experimentation immediately.

During all experiments the cells were continuously superfused with normal Tyrode's solution maintained at 34-36°C. The floor of the experimental chamber consisted of a 0.17-mm thick, 22-mm diameter glass coverslip, which was cleaned thoroughly with sulfuric acid before each session. This allowed a majority of the cells to adhere firmly to the coverslip, thus minimizing the motion artifact in the fluorescence recordings. The composition of the Tyrode's solution (in mM) was 135 NaCl, 5.4 KCl, 1 MgCl₂, 0.33 NaH₂PO₄, 5 HEPES, 1.8 CaCl₂, and 5 glucose (adjusted to pH 7.4 with NaOH). The longitudinal axis of the cell under investigation was aligned with the field direction, and the cell was paced at 1 Hz using 5-ms duration (S1) field pulses. The experiments were performed with an S1 pulse only or with a combination of S1 and S2 pulses in which the S2 pulse (20 ms in duration) was applied 50 ms after the onset of the S1 pulse. The S1 pulse caused the cell to elicit [Ca²⁺]_i transient so that S2 was applied during the plateau phase of the [Ca²⁺]_i transient. Reversing the polarity of field electrodes reversed the field direction. The field directed from left to right is defined as positive (e.g., Fig. 3).

The experimental setup was assembled around an inverted microscope (Diaphot-TMD, Nikon). The light from a 150-W Xenon arc lamp (Opti Quip; Highland Mills, NY) was coupled into the epiillumination pathway of the microscope to excite the dye. The exposure time was controlled using an electronic shutter (Vincent Associates; Rochester, NY). The specifications of the optical filters used for recording [Ca²⁺]_i signals were as follows: excitation filter (ExF): 450-490 nm, dichroic (D): 510 nm, and emission filter (EmF): 520-560 nm. The fluorescence image of the cell was projected onto a bundle of 149 hexagonally packed plastic optical fibers. At ×60 magnification used for this study, each 1-mm diameter optical fiber collected fluorescence from a 17-µm spot in the specimen plane. The fluorescence signals were mapped along the cell length using up to 12 fibers. The fluorescence signals from these fibers were fed into an equal number of signal detection and conditioning circuits. The recording duration had two different settings: 400 and 150 ms. The longer 400-ms duration (at a sampling rate of 5 kHz per channel) allowed recording of complete transients but restricted the total number of exposures to one to three because dye photobleaching rapidly deteriorated the quality of signals. The shorter 150-ms duration (at a sampling rate of 10 kHz per channel) enabled up to 12 exposures from a cell. The baseline fluorescence level with the shorter recording duration essentially remained the same for two consecutive recordings and facilitated their comparison. The [Ca²⁺]_i signals from various sites were normalized to the signal level ~30 ms after the onset of the transients. For all experiments, the S1 field amplitude ranged from 5 to 20 V/cm and S2 amplitude from 8 to 40 V/cm.

To allow comparison of results obtained from cells of varying lengths, the field amplitudes were scaled by L/120, where L was the length (in µm) of the cell being stimulated. The scaled amplitude represents an equivalent electric field for a nominal 120-µm long cell, which is the average length for a guinea pig ventricular cell (30).

The statistical correlation between any two parameters was determined by calculating Pearson's correlation coefficient (R) and conducting a two-tailed Student's t-test for rejecting the null hypothesis that the slope of the best fit line was zero, and that the parameters were not correlated. Whenever applicable a two-tailed, Student's paired t-test was used to compare the means of various data sets. Values of P < 0.05 were considered to be significant.

	RESULTS

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Typical [Ca²+]_i transients. Figure 1A shows the image of a cell for which [Ca²⁺]_i signals were recorded using longer (400 ms) exposure time. The [Ca²⁺]_i transients were recorded from eight sites on the cell in response to one of the S1 (~7 V/cm) pacing pulses and are shown superimposed in Fig. 1B. The S1 pulse is shown beneath the [Ca²⁺]_i transients. Because the cell was adhered firmly to the glass coverslip, the motion artifact during the initial ~100 ms of the transients was negligible. Thereafter, a slight motion artifact was present, and the [Ca²⁺]_i signals from the various sites showed some spread (Fig. 1B). The mean duration (computed by measuring the duration between the 10% values of the peak [Ca²⁺]_i for each site and taking the average) of the [Ca²⁺]_i transients shown in Fig. 1B was ~270 ms, and the time to reach the peak from the onset of the transient was ~40 ms. The duration of [Ca²⁺]_i transients were measured for 18 cells with 400-ms recording duration and was found to be 245 ± 42 (means ± SD) ms. The time to peak of the [Ca²⁺]_i transient was measured for 26 cells with both short (150 ms) and long (400 ms) recording durations and was found to be 34 ± 11 ms.

View larger version (74K): [in this window] [in a new window]   Fig. 1.   Typical complete intracellular Ca2+ ([Ca2+]i) transients. Cell shown in A was stimulated with an S1 field pulse of ~7 V/cm in the indicated direction, and [Ca2+]i transients were recorded for a duration of 400 ms from 8 sites on the cell. [Ca2+]i transients from all sites are shown superimposed in B and illustrate the recordings were motion-artifact free for at least the initial ~100 ms.

Effect of ryanodine and nifedipine. Figure 2 shows examples of the effect of 5 µM nifedipine (a sarcolemmal Ca²⁺ channel blocker) and 2 µM ryanodine (a blocker of SR Ca²⁺-release channel), respectively. Figure 2 also shows control recordings obtained before drug exposure (left) and recordings obtained ~5 min after perfusion with a solution containing the drug. Consistent with previously published reports (2), both of these interventions were able to strongly suppress the signals recorded from fluo-3-loaded cells, thus establishing that the recorded signals were indeed [Ca²⁺]_i sensitive. Similar results were obtained for two other cells (each for nifedipine and ryanodine). Small residual transients were observed in the presence of nifedipine, possible causes of which are mentioned in DISCUSSION. The amplitude of [Ca²⁺]_i transients in the presence of ryanodine was ~10-15% of the control (Fig. 2B), suggesting that L-type Ca²⁺ current constitutes for ~10-15% of the [Ca²⁺]_i transient in guinea pig.

View larger version (39K): [in this window] [in a new window]   Fig. 2.   Effect of nifedipine and ryanodine on [Ca2+]i transients. A: cell stimulated with an S1 field pulse in the indicated direction. [Ca2+]i transients recorded from 6 sites in normal Tyrode's solution (control, left) and in presence of 5 µM nifedipine (right) are shown below the cell. Nifedipine abolished [Ca2+]i transients. B: shows another cell for which [Ca2+]i transients were recorded in the absence (control, left) and presence of 2 µM ryanodine (right). Ryanodine suppressed [Ca2+]i transients, and amplitude of the residual transients was ~10% of control level.

Effect of S1 on [Ca²+]_i transients. The [Ca²⁺]_i transients were recorded from eight sites on the cell shown in Fig. 3A for positive (S1 = +10 V/cm) and negative (S1 = 11 V/cm) field directions and are shown in Fig. 3B. For both field directions, the [Ca²⁺]_i transients from the various sites were not completely synchronous. For the positive S1 pulse, the [Ca²⁺]_i signal from site 1 was the fastest to rise, and [Ca²⁺]_i signal from site 8 was the slowest (Fig. 3B, middle row). On field reversal this trend was reversed, and the signal from site 8 was the fastest to rise (Fig. 3B, bottom row). These asynchronous signals imply that the [Ca²⁺]_i was nonuniform along the cell length during the rising phase of the transients, and thus gradients in [Ca²⁺]_i ([Ca²⁺]_i) were developed. To estimate [Ca²⁺]_i the normalized change in [Ca²⁺]_i ([Ca²⁺]_iN) was measured for the various sites along the cell length at a single instant corresponding to ~50% activation point (thick vertical line in Fig. 3B). [Ca²⁺]_iN was obtained by normalizing the change in [Ca²⁺]_i from the resting value ([Ca²⁺]_i) to the peak change ([Ca²⁺]_io) (Fig. 3C, inset). From Fig. 3C it is clear that both [Ca²⁺]_iN and [Ca²⁺]_i were nonuniform along the cell length (apparent from nonconstancy of the relation) with large [Ca²⁺]_i gradients existing in the regions of the cell facing the anode. On field reversal, the trend in [Ca²⁺]_iN and [Ca²⁺]_i was reversed, thus establishing that these patterns indeed depended on field direction and were not the result of intrinsic heterogeneities in the cell. Assuming [Ca²⁺]_io to be ~980 nM for a typical guinea pig cell (7), [Ca²⁺]_i values in the anodal half of the cell shown in Fig. 3A were estimated to be 4.2 and 6.3 nM/µm for the positive and negative S1 pulses, respectively (refer to Fig. 3C, bottom, for method of computing [Ca²⁺]_i).

View larger version (58K): [in this window] [in a new window]   Fig. 3.   Effect of S1 pulse. A: cell that was stimulated with positive and negative S1 pulses; B: corresponding [Ca2+]i transients superimposed from all 8 sites. For both field pulses, [Ca2+]i transients from all sites were not completely synchronous. In B, top shows the positive S1 pulse; middle shows that for this S1 pulse of +10 V/cm, the [Ca2+]i signal from site 1 was the fastest to rise, and the signal from site 8 was the slowest; and bottom shows that on field reversal, this trend in the onset of [Ca2+]i signals was reversed. The pair of vertical dashed lines spanning the duration of the S1 pulse help to discern the temporal relationship between the S1 pulse and [Ca2+]i transients. Onset of [Ca2+]i transients from all sites as a group was delayed from the make of the S1 pulse by a time duration (td), which was ~7.5 ms for both positive and negative S1 pulses. Change in [Ca2+]i relative to the resting level ([Ca2+]i) was measured during rising phase of the transients at the time indicated by the thick line in B. [Ca2+]i was normalized to the peak value ([Ca2+]io) of [Ca2+]i (C, inset), and the resulting normalized change ([Ca2+]iN) is plotted in C for positive S1 (top) and negative S1 (bottom) pulses. Gradient in [Ca2+]i ([Ca2+]i = /) in the anodal half of the cell was computed as illustrated in C, bottom, and was estimated to be 4.2 and 6.3 nM/µm for the positive and negative S1 pulses, respectively (see text for additional details).

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Summary of S1 pulse results. A: [Ca2+]i versus scaled S1 amplitude for 26 cells (114 S1 stimuli). [Ca2+]i increased monotonically with the S1 pulse amplitude (R = 0.46, P < 0.001). Intersection of horizontal and vertical lines indicates that [Ca2+]i was ~3.4 nM/µm for a nominal 10 V/cm S1 pulse. B: td plotted against scaled S1 amplitude. The td decreased monotonically with an increase in S1 amplitude (R = 0.39, P < 0.001).

Effect of S2 on [Ca²+]_i transients. Figure 5 illustrates the effect of the S2 pulse on the [Ca²⁺]_i transients. The onset of the S2 pulse occurred 50 ms after the break of the S1 pulse. The recordings were obtained from eight sites on the cell shown in Fig. 5A, first in response to an S1 pulse (+8 V/cm) only, and then in response to a pair of S1-S2 pulses (S1 = +8 V/cm, S2 = +29 V/cm). The recordings from the various sites in the absence and presence of the S2 pulse are shown superimposed in Fig. 5B. The bottommost row in Fig. 5B shows superimposed recordings from all sites obtained in response to the S1-S2 pair. The nonoverlapping behavior of these recordings suggests that the S2 caused nonuniformities in [Ca²⁺]_i along the cell length and produced [Ca²⁺]_i gradients. The S2-induced change in the [Ca²⁺]_i ([Ca²⁺]_i) was measured at the end of S2 pulse relative to the [Ca²⁺]_i at the same time recorded with S1 pulse only (Fig. 5C, inset). Similar to the case of the S1 pulse described above, [Ca²⁺]_i was normalized to the peak of the [Ca²⁺]_i transient ([Ca²⁺]_io), and the result ([Ca²⁺]_iN) is shown in Fig. 5C, top. On field reversal of S1 and S2, a similar behavior of [Ca²⁺]_iN along the cell length was observed (Fig. 5C, bottom). These results suggest that during the S2 pulse, intracellular calcium gradients develop from the center to either end of the cell. In Fig. 5C the [Ca²⁺]_i values in the anodal and cathodal halves of the cell were found to be 5.6 and 5.2 nM/µm, respectively, for the positive fields, and 7.7 and 5.0 nM/µm, respectively, for the negative fields. Results similar to those described above were obtained for n = 12 cells (24 S1-S2 stimuli; S2 = 25 ± 6 V/cm). The [Ca²⁺]_i in the anodal half (4.2 ± 2.2 nM/µm) of the cell was found to be statistically higher than in the cathodal half (2.8 ± 1.6 nM/µm) (P < 0.03).

View larger version (43K): [in this window] [in a new window]   Fig. 5.   Effect of S2 pulse. A: cell that was first stimulated with an S1 pulse only and then with a pair of S1-S2 pulses. [Ca2+]i recordings obtained from 8 sites in response to the S1 pulse and S1-S2 pair are shown superimposed for each site in B. B: bottommost row shows the [Ca2+]i transients superimposed from all sites in response to the S1-S2 pair. The pair of vertical dashed lines represents duration of S2 pulse. Perturbation of the [Ca2+]i transients was measured at the end of S2 pulse with respect to the value of [Ca2+]i recorded with the S1 pulse only as illustrated in inset of C. Change was normalized to [Ca2+]io and is plotted against the site number in C, top. C, bottom shows [Ca2+]iN for the same cell in response to an S1-S2 pair applied in the negative direction (S2 = 27 V/cm). For both field directions [Ca2+]iN was smallest at the cell center and increased in either direction implying that [Ca2+]i developed directed from the cell center to both cell ends. For +29 V/cm S2 pulse (C, top) [Ca2+]i values were found to be 5.6 and 5.2 nM/µm for the anodal and cathodal halves of the cell, respectively. For 27 V/cm S2 pulse (C, bottom) [Ca2+]i values were found to be 7.7 and 5.0 nM/µm, respectively.

	DISCUSSION

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In this study we used a multisite optical mapping system to record [Ca²⁺]_i transients along the lengths of isolated guinea pig ventricular myocytes and characterized the effects of uniform electric fields on [Ca²⁺]_i transients. We show that consistent with our hypothesis, an externally applied electric field can induce spatial heterogeneities in an isolated cardiac cell during both rest and the action potential plateau. To the best of our knowledge this is the first study showing subcellular scale calcium gradients in a nonuniformly polarized cardiac cell during field stimulation. Specifically, we show that a 5-ms duration S1 field pulse applied at rest results in an asynchronous rise in [Ca²⁺]_i along the cell length and induces spatial [Ca²⁺]_i. [Ca²⁺]_i estimated during the midpoint of the rising phase of the [Ca²⁺]_i transients is large in the anodal half of the cell (Fig. 3C), increases monotonically with the S1 amplitude (Fig. 4A), and has a value of ~3.4 nM/µm for a nominal 10 V/cm field. The S2 field pulse applied during the plateau also perturbs [Ca²⁺]_i and results in [Ca²⁺]_i gradients along the cell length (Fig. 5B). [Ca²⁺]_i during the plateau is directed from the center to either end of the cell (Fig. 5C) and on average is greater in the anodal half than in the cathodal half (4.2 and 2.8 nM/µm, respectively, for an S2 pulse of ~25 V/cm). As we discuss below, this is consistent with the notion that the diffusion of intracellular Ca²⁺ is a relatively slow process.

The field-induced change in [Ca²⁺]_i can be >20% (Fig. 5C). The change in [Ca²⁺]_i and its relatively large magnitude are likely the result of: 1) field modulation of the L-type Ca²⁺ current, which directly contributes about 20-30% of the Ca²⁺ transient in guinea pig (5, 15), and 2) further amplification of the modulated Ca²⁺ current in the form of CICR from the SR (9). Consistent with the latter hypothesis, [Ca²⁺]_i transients were suppressed by the interventions that blocked either the sarcolemmal Ca²⁺ current or SR Ca²⁺ release (Fig. 2). The small residual transients in the presence of nifedipine (Fig. 2A) are probably because of one or more of the following: 1) incomplete block of L-type Ca²⁺ current, 2) T-type Ca²⁺ current that is not blocked by nifedipine, 3) reverse mode Na⁺/Ca²⁺ exchanger acting to produce a small transient or serving as a weak trigger for Ca²⁺ release from the SR in the depolarized regions of the cell (25).

The pattern of S1- and S2-induced gradients can be explained in terms of what is known about voltage gating and the current-voltage (I-V) relation of the L-type Ca²⁺ channel and the relationship between Ca²⁺ current and Ca²⁺ release from the SR. The I-V relation of the L-type Ca²⁺ channel has a characteristic bell shape with peak inward current occurring at ~10 mV that declines to near-zero values at +60 and 60 mV (18, 22, 23, 29). Some studies have found SR Ca²⁺ release to vary linearly with Ca²⁺ current (9), although others have found more complicated relations (10, 23). However, irrespective of the details of this relation, it is clear that the qualitative changes in [Ca²⁺]_i in response to changes in the transmembrane potential will be governed by the I-V relation of the Ca²⁺ current.

It has been well established experimentally that single cardiac cells undergo nonuniform polarization in response to a uniform electric field stimulus (11, 24). Thus the S1 field pulse applied at rest hyperpolarizes the end of the cell facing the anode and depolarizes the end facing the cathode. Furthermore, our experiments reveal that [Ca²⁺]_i rises faster at the anodal end (Fig. 3B). Because the resting potential (approximately 90 mV) is situated at the leftmost extreme of the bell-shaped I-V relation of the L-type Ca²⁺ current, the S1 pulse will activate a large inward Ca²⁺ current at the cell end facing the cathode but a negligible current at the end facing the anode. This should result in a large [Ca²⁺]_i transient at the cathodal, but not the anodal, end. However, because activation of the cell likely occurs during the S1 pulse, the nonuniform membrane polarization becomes superimposed on the upstroke of the action potential. Hence, the hyperpolarization at the anodal end could significantly increase the driving force for influx of Ca²⁺ and compensate for the smaller activation of the Ca²⁺ channel, producing a larger and faster [Ca²⁺]_i transient at the anodal end. Another explanation for our experimental results could involve voltage-dependent inactivation of the L-type Ca²⁺ channels, which exists to some extent in guinea pig ventricular cells (16, 31). Assuming that the action potential is elicited during the S1 pulse, the hyperpolarization at the anodal end could diminish the inactivation of the Ca²⁺ channels compared with the cathodal end, so that upon S1 termination a larger influx of Ca²⁺ occurs at the anodal end. A third possibility involves Ca²⁺-dependent inactivation of the L-type Ca²⁺ channels (12). During the S1 pulse, calcium could be brought into the cell in the depolarized regions and extruded from the hyperpolarized regions of the cell via the electrogenic Na⁺/Ca²⁺ exchanger. This would result in a graded calcium concentration along the cell length in the restricted subspace and at the inner face of the cell membrane. The net effect would be to accentuate inactivation in the depolarized regions, and if Ca²⁺ conductance were partially inactivated at rest via calcium-dependent inactivation, to relieve inactivation in the hyperpolarized regions of the cell. Thus there would exist a spatially varying Ca²⁺ conductance along the cell length that could explain the observed S1-induced pattern of calcium transients.

Similar to the S1 pulse, the S2 pulse also causes hyperpolarization of the anodal-facing end and depolarization of the cathodal-facing end of the cell. However, unlike S1, this perturbation occurs from about the center (~10 mV) of the I-V relation for Ca²⁺ current when the S1-S2 delay is 50 ms. Thus Ca²⁺ current and [Ca²⁺]_i are expected to decrease at both ends of the cell compared with the center, as is the case experimentally (Fig. 5B). Upon S2 termination, the transmembrane potential returns close to the prepulse plateau level, resulting in a large inward Ca²⁺ current and surge in [Ca²⁺]_i at both ends of the cell (Fig. 5B, sites 1, 2, 7, and 8). The deactivation of Ca²⁺ channels at the anodal end and associated reduction in the channel conductance may explain the smaller amplitude of [Ca²⁺]_i surge in the anodal regions. We found the S2-induced [Ca²⁺]_i in the anodal regions of the cell to be greater than in the cathodal regions (Fig. 5C). Such differences are possible if the I-V relation of the Ca²⁺ current is not symmetric about the peak of the bell. Indeed, several different investigators have reported I-V relations that are slightly asymmetric with a larger slope for the negative potentials (15, 22, 29). Such an asymmetry will produce a larger spatial gradient in Ca²⁺ current and therefore in [Ca²⁺]_i in the anodal half of the cell. Another possibility is that an enhanced activity of the Na⁺/Ca²⁺ exchanger at the negative transmembrane potentials results in greater extrusion of Ca²⁺ from the hyperpolarized regions of the cell. This would result in greater depression of [Ca²⁺]_i and accentuation of [Ca²⁺]_i in the hyperpolarized regions compared with the depolarized regions.

It is worthwhile mentioning that the pattern of [Ca²⁺]_i would most likely be altered if the S2 pulse were to be applied during a later phase of the action potential, e.g., during the early repolarizing phase. Now the field-induced perturbation in transmembrane potential (V_m) would occur about a prepulse potential that is more negative than the early plateau value of ~10 mV. Thus the pattern of field-induced change in inward Ca²⁺ current, and therefore that of [Ca²⁺]_i, should be different. For example, if the prepulse potential is at the midpoint of the left half of the bell-shaped I-V relation of the Ca²⁺ current, then the field-induced changes in [Ca²⁺]_i are expected to vary monotonically along the cell length with hyperpolarized regions undergoing a decrease in [Ca²⁺]_i and depolarized regions undergoing an increase in [Ca²⁺]_i.

The existence of field-induced gradients in [Ca²⁺]_i is consistent with the notion that the diffusion of intracellular Ca²⁺ is a relatively slow process. If the Ca²⁺ diffusion were rapid, we should have observed smoothing of calcium gradients with time (e.g., during the S2 pulse). Indeed, several other studies directly or indirectly suggest that Ca²⁺ diffusion in cardiac tissue is severely retarded (3, 17, 27), although accurate quantitative estimates of diffusion constant (D) are unavailable. However, the value of D has been measured for skeletal muscle and is estimated to be 14 µm²/s (20). Allbritton et al. (1) measured a similar value of D (~38 µm²/s) in the cytosol extract from Xenopus oocytes and attributed the slow diffusion to abundance of Ca²⁺-buffering proteins in their extract. Because cardiac muscle, too, has plentiful Ca²⁺ buffers (e.g., inner sarcolemma, outer SR, troponin C, mitochondria, calmodulin), a slow diffusion of Ca²⁺ is not surprising. Assuming a conservatively high value for intracellular Ca²⁺ D to be ~370 µm²/s, which is the D for free Ca²⁺ in a medium with twice the viscosity of water (approximate viscosity of the cytosol) (1), the thickness of the diffusion layer s is estimated to be ~6 µm [s = (2Dt)^0.5, where t = 50 ms is the S2 duration]. Considering that our intersite distance (17 µm) was much larger than s, the effect of diffusion in smoothing the [Ca²⁺]_i gradients is expected to be small.

Because we were primarily interested in the field-induced changes in [Ca²⁺]_i, we used essentially single wavelength measurements of fluo-3 to record relative changes in [Ca²⁺]_i, and for technical reasons, we did not use the more complex ratiometric method that potentially could have yielded absolute measurements of [Ca²⁺]_i. Thus our estimates of the field-induced gradients in [Ca²⁺]_i rely on an assumed value for peak [Ca²⁺]_i, which was assigned a typical value reported in the literature. However, the peak [Ca²⁺]_i may vary somewhat from the assumed value and also from one cell to another, and thus produce an uncertainty in the reported field-induced [Ca²⁺]_i changes and gradients.

Finally, our field amplitudes were limited to ~40 V/cm. It has been reported that for higher field amplitudes when the induced V_m exceeds the electroporation threshold, the cells undergo preferential hypercontracture at the anodal end, which is hypothesized to be the result of an electroosmosis-driven Ca²⁺ influx at the anodal end (19). Under such conditions, the field-induced [Ca²⁺]_i gradients may have a different pattern than those reported in this study.

In summary, we have shown that uniform electric fields can induce spatial inhomogeneities in [Ca²⁺]_i in single cells. Because [Ca²⁺]_i regulates several sarcolemmal currents (21), an accounting for nonuniformities in [Ca²⁺]_i might be important for accurately predicting the field-induced membrane responses of single cardiac cells and presumably of cardiac tissue.