INTRODUCTION

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AFTERCONTRACTIONS ARISE in damaged regions of cardiac muscle and propagate into the neighboring myocardium. Propagating contractions, which can be measured as waves of sarcomere shortening, have been denoted as triggered propagated contractions (TPCs) and have been observed in both rat ventricular (10, 19) and human atrial trabeculae (9).

Similar to the mechanism proposed for Ca²⁺ waves in a single isolated myocyte (17), the propagation mechanism of a TPC is thought to be consistent with a model of Ca²⁺-induced Ca²⁺ release (CICR) from sarcoplasmic reticulum (SR) mediated by Ca²⁺ diffusion to adjacent SR for the following reasons. First, TPCs do not require an intact sarcolemma (8). In addition, Gd³⁺, a stretch-activated channel blocker, affects neither initiation nor propagation velocity of a TPC in intact trabeculae, suggesting that stretch activation of ion fluxes are not involved in TPC propagation (32). Second, TPCs are abolished by agents that interfere with SR Ca²⁺ loading or release, such as ryanodine and caffeine (11), similar to findings with Ca²⁺ waves in single myocytes (17). Third, TPCs propagate along the undamaged parts of the trabeculae at constant velocities that vary from 0.1 to 15 mm/s depending on SR Ca²⁺ loading (10, 19). These propagation velocities are too fast for simple diffusion of Ca²⁺ alone (see Ref. 2, discussion) and slower than conduction velocities of electrical signals reported for normal ventricular muscle (1 m/s). Finally, computer simulation studies using a model of CICR and Ca²⁺ diffusion predict propagation velocities of TPCs that are in agreement with the observed experimental data (2).

Therefore, if we assume that a CICR model describes the propagation mechanism of TPCs, it is important to know how fast Ca²⁺ diffuses through cells as well as from cell to cell within trabeculae. The equivalent diffusion coefficient (D_eq) in water (D_sol) for Ca²⁺ is 750 × 10⁸ cm²/s (30); D_eq in myoplasm (D_myop) for Ca²⁺ is unknown but should be lower than that in pure water because of the intracellular milieu, which has an ionic strength of 0.15-0.20 M, and the presence of large protein moieties (22). In a multicellular preparation, Ca²⁺ must diffuse from cell to cell through gap junctions (GJs), which respond dynamically to a variety of regulatory factors (24), such that D_eq in trabecula (D_trab) for Ca²⁺ should be affected by the agents that alter the permeability of gap junctions (P_GJ). Recently, we demonstrated that octanol and heptanol, which decrease open probability of GJ channels in a nonselective manner (26), reduce the propagation velocity, triggering rate, and force of TPCs (31). These observations are consistent with the idea that Ca²⁺ diffuses from cell to cell through GJs for the propagation of a TPC. However, the direct effects of octanol or heptanol on P_GJ in intact cardiac muscle have not yet been evaluated.

With regard to Ca²⁺ dynamics within trabeculae during TPCs, regional increases in intracellular Ca²⁺ concentration ([Ca²⁺]_i) are thought to underlie the TPCs and are assumed to be similar to the Ca²⁺ waves in single myocytes (16-18). Furthermore, Ca²⁺ sparks and waves occur at a subcellular level (20) and Ca²⁺ sparks precede or lead to Ca²⁺ waves in myocytes (6). In contrast, little is known about the spatial and temporal changes in [Ca²⁺]_i in multicellular cardiac trabeculae.

Therefore, in this study we have tested 1) whether a regional increase in [Ca²⁺]_i propagates along trabeculae during a TPC in multicellular preparations (>1 mm). Furthermore, we determined 2) the diffusion properties for fura 2 to evaluate how Ca²⁺ ions diffuse through cells as well as from cell to cell within trabeculae and 3) the effects of octanol on fura 2 diffusion properties. Subsequently, we could then evaluate to what extent Ca²⁺ diffusion through the myoplasm and the GJs is affected by octanol under our experimental conditions. Preliminary data have recently been published (31).

	METHODS

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Dissection and Mounting of Rat Ventricular Trabeculae

Experimental Equipment

View larger version (33K): [in this window] [in a new window]   Fig. 1.   A: simplified diagram shows experimental setup used for measurement of fluorescence signals, force (F), and sarcomere length (SL). Xe, xenon arc lamp; PMT, photomultiplier tube; IIC, charge-coupled device (CCD) camera coupled to 2-stage image intensifier; PC, personal computer, VCR, video cassette recorder. B: original SL and stress tracings of last stimulated twitch of a train of 15 twitches at 2 Hz and a subsequent triggered propagated contraction (TPC). SL was measured at 2 sites (A and B) 270 µm apart. During TPC, sarcomere shortening transient (arrowheads) occurred earlier at site A than site B. Experiment was performed at 20.8°C and 1.5 mM extracellular Ca2+ concentration ([Ca2+]o). C: in vitro calibration curve. Applied [Ca2+] was plotted against ratio of fluorescence at 340 and 380 nm (340/380) calculated from signal of PMT after subtraction of autofluorescence. Kd, effective dissociation constant; Rmin, ratio at zero [Ca2+]; Rmax, ratio at a saturating [Ca2+].

Fura 2 Loading and Analysis of [Ca^2+]_i

Fura 2 loading. The free acid form of fura 2 was microinjected electrophoretically into trabeculae, as described previously (1). In brief, the tip of the microelectrode was filled with 2 mM fura 2 pentapotassium salt (Molecular Probes, Eugene, OR) and the remainder of the electrode was back filled with 4 mM KCl. With this microelectrode solution, the tip resistances ranged from 180 to 250 M when measured using the standard KH solution. Intracellular membrane potentials were measured using an intracellular amplifier (Intra 767, World Precision Instruments, Sarasota, FL) and were between 40 and 80 mV under standard conditions [SL = 2.1 µm, extracellular Ca²⁺ concn ([Ca²⁺]_o) = 0.7 mM, 26°C]. After stability was achieved, 5-10 nA of negative current was passed for 10-20 min. During the injection period, the fura 2 diffused from the impalement site into the adjacent cells via GJs as previously described (1). On completion of injection and removal of the microelectrode, the trabecula was stimulated at 1 Hz for 30-60 min until uniform loading with fura 2 was obtained. Under such conditions, changes in the fluorescence ratio of fura 2 determined using the IIC or PMT were superimposable, as shown in Fig. 2A, even when the trabecula was moved over several hundred micrometers, showing that fura 2 loading was uniform.

View larger version (22K): [in this window] [in a new window]   Fig. 2.   A: superimposed ratio transients (360/380 or 340/380) measured at 3 positions along trabecula (at 0-, 210-, and 650-µm displacement) calculated either from signal of PMT (top) or from signals at central 20 × 20 pixels of IIC (bottom) during same electrically stimulated twitch (0.5-Hz stimulation rate, [Ca2+]o 0.7 mM, and 26°C). B: relationships of ratios determined by IIC vs. PMT at the 3 different positions on trabeculae (0 µm, top; 210 µm, middle; 650 µm, bottom) calculated from A. Note that at each position along trabecula, ratios determined by the 2 methods were correlated linearly. r, Correlation coefficient.

Analysis of signal from PMT. [Ca²⁺] was determined using the following equation (13) (after subtraction of the autofluorescence of the muscle)

(1)

where K_d is the effective dissociation constant, R is the ratio of the fluorescence at 340-nm excitation to that at 380-nm excitation (340/380), R_min is R at zero [Ca²⁺], R_max is R at a saturating [Ca²⁺], and  is the ratio of fluorescence value for Ca²⁺-free dye to fluorescence value for Ca²⁺-bound dye at 380-nm excitation. Values for K_d, R_min, R_max, and  were determined using in vitro calibrations (Fig. 1C) as previously described (1). Previously, we reported that there is a good correlation between in vitro and in vivo calibrations when free Mg²⁺ is 1 mM in the solutions, mimicking the intracellular milieu (1). Solutions for calibration were prepared using a calcium calibration buffer kit (Molecular Probes) and contained different known free [Ca²⁺], 1 mM free Mg²⁺, 10 mM ethylene glycol-bis(-aminoethyl ether)-N,N,N',N'-tetraacetic acid, 100 mM KCl, 10 mM 3-(N-morpholino)propanesulfonic acid, and 1 µM fura 2 (pH 7.2). Calibration was performed by placing 100 µl of solutions of different known free [Ca²⁺] into chambers on the microscope stage. Each solution was illuminated with 340-, 360-, and 380-nm excitation light, and fluorescence was collected onto the PMT and then stored in the computer for later analysis. The background fluorescence was determined by illumination of a solution with zero free Ca²⁺ in the absence of fura 2. Values for K_d, R_min, R_max, and  were calculated from the curve describing the relationship between the ratio and pCa. For these experiments the R_min and R_max were 0.152 and 4.60, respectively, and K_d and  were 361 nM and 9.18, respectively. This is in agreement with previous data from this laboratory (1).

Analysis of image from IIC. The fluorescence data of each video frame were digitized with a 8-bit analog-to-digital converter and stored in a frame buffer memory of 512 × 480 pixels (Coreco). Therefore, in our optical system, 1 pixel of memory corresponded to 2.87 × 2.87 µm of the image. For analysis of the image, a sampling region of interest (ROI) was set horizontally along the long axis of the fluorescence image of trabeculae. The horizontal length of the ROI was always 512 pixels (1,470 µm), and its vertical width was 20 pixels (57.4 µm). To obtain intensity profiles of the fluorescence (F_s) along the long axes of trabeculae, we calculated an average intensity value from each vertical line of pixels within the ROI. To eliminate high-frequency noise from the intensity profile, we used the low-pass finite impulse response filter of MATLAB (Math Works, Natick, MA), which was a Hamming-windowed, linear-phase filter, and set the cutoff frequency of the filter at 5 pixels (14.4 µm). After subtraction of the autofluorescence of the muscle, we calculated the ratio of the fluorescence at 360-nm to that at 380-nm excitation (360/380) at each point on the average intensity profiles obtained from the images at 360- and 380-nm excitation light.

Analysis of D_eq for Fura 2

Measurement of D_trab for fura 2. Fura 2 pentapotassium salt was microinjected electrophoretically into trabeculae (Table 1) using 10 nA of negative current for 10 min. To determine the effects of octanol on D_trab, fura 2 was injected after a 1- or 3-h superfusion of trabeculae with KH solution containing 100 µM 1-octanol (Table 1). Trabeculae were constantly stimulated at 0.5 Hz except for the fura 2 injection periods. Epifluorescence of the trabeculae obtained using the IIC (see Analysis of image from IIC) was recorded with the VCR at the completion of fura 2 injection and thereafter every 10 min for 60 min.

View larger version (24K): [in this window] [in a new window]   Fig. 3.   A: average intensity profiles of fluorescence (Fav) along long axis of trabecula after a 1-h superfusion with 100 µM 1-octanol (0, 10, and 50 min after injection of fura 2). After injection of fura 2, Fav exhibited a maximal value at injection site; fura 2 diffused evenly in both directions, whereas maximal value of Fav decreased. B: left half of normalized intensity profiles of fluorescence (Fnorm) obtained by dividing Fav of A by spatially corresponding values of intensity profiles of fluorescence image from solution containing 1 µM fura 2 (Fsol; not shown). Solid lines reflect regions of the 3 profiles in which intensity varied between 73 and 27% of maximal intensity. C: fit of intensity of profile (27-73% of maximal intensity) shown in B to diffusion equation (Ref. 7). Abscissa shows square of distance (X2) from region in which fura 2 had been injected; ordinate shows natural log of Fnorm. These relationships were fitted by linear regression (r = 0.99-1); slope coefficients equal 1/(4 · Dtrab · t). Dtrab · t was calculated from fit data. D: relationship between time after fura 2 injection vs. Dtrab · t. Dtrab was calculated from slope of relationship.

(2)

Measurement of D_myop for fura 2. Fura 2 was microinjected 11 times into three trabeculae (Table 1) using 7 nA of negative current for 10-20 s. To study the effects of octanol on D_myop, fura 2 was microinjected 6 times into trabeculae after 1 h of superfusion of the muscle with 100 µM 1-octanol and 11 times into the same trabeculae (Table 1) after a 3-h superfusion with the same solution. The epifluorescence from the trabeculae was recorded, using the procedure described in Analysis of image from IIC, for 30 s immediately after the completion of each fura 2 injection.

View larger version (27K): [in this window] [in a new window]   Fig. 4.   A: Fav along long axis of trabecula at 5, 15, and 30 s after injection of fura 2 in absence of octanol. Intensity profile of Fav spread at almost comparable velocities in both directions. B: left half of Fnorm obtained by dividing Fav (A) by spatially corresponding values of Fsol from solution containing 1 µM fura 2. Solid lines reflect regions of the 3 profiles where intensity varied between 73 and 27% of maximal intensity. C: fit of intensity values of profile (27-73% of maximal intensity) shown in B to diffusion equation (7). Abscissa shows square of distance (<50 µm) from region in which fura 2 had been injected; ordinate shows natural log of Fnorm. These relationships were fitted by linear regression (r = 0.95-0.99); slope coefficients equal 1/(4 · Dmyop · t). Dmyop · t was calculated from fitted data. D: plots of time after fura 2 injection against Dmyop · t. Dmyop was calculated from slope of relationships. E: 3 examples of Fav relations that showed clear asymmetries after a 3-h superfusion with octanol. Fura 2 diffused slowly outside a limited region within muscle; edges of these regions are indicated by gray bars. Distance between edges of serial Fav at 5, 15, and 30 s after injection was 100-150 µm, i.e., similar to length of a single myocyte. We assumed that GJs were located at regions indicated by gray bars (see DISCUSSION). In these cases we calculated Dmyop using diffusion in direction indicated by arrows.

Measurement of D_sol for fura 2. A droplet of fura 2 solution (300-µm diameter) was placed in a stationary flow bath and image profiles of the droplet excited by 360-nm light were recorded for 30 s at room temperature (20°C). To determine D_sol for fura 2, an ROI of 512 × 20 pixels was set horizontally through the fura 2 droplet. The F_av was calculated from F_s obtained from eight sequential frames (0.27 s) every 5 s. With F_av, D_sol was then determined at every 5 s for 30 s using the procedure described above. The contribution of convective fluid motion caused by illumination of the fluid was ignored.

Calculation of P_GJ. P_GJ was calculated using the following equations (7, 12)

(3)

(4)

where L_myoc is the length of one myocyte, L_GJ is the dimension of GJs, and L is the total length of L_myoc and L_GJ. For the calculation of P_GJ, we used 100 µm for L_myoc.

Statistics

	RESULTS

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Diffusion of Fura 2

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We are not aware of data to compare our D_GJ measures directly with those of previous studies. Therefore, we calculated the P_GJ from D_trab and D_myop using Eqs. 3 and 4 (see METHODS). It follows from Eqs. 3 and 4 that

(5)

where P_GJ does not require an assumption about the linear dimension of the GJs (L_GJ) and thus can directly be compared with results from studies on cell pairs. When we calculated P_GJ for fura 2 based on our average values of D_trab and D_myop, we found that P_GJ was reduced from 4.15 × 10⁵ cm/s in control to 2.10 × 10⁵ cm/s and 0.86 × 10⁵ cm/s after 1 and 3 h of superfusion with 100 µM 1-octanol, respectively (Table 1). Our control calculated P_GJ for fura 2 pentapotassium salt (mol wt 832) is in close agreement with data presented by Dr. Irisawa's group (15) depicting the relationship between the P_GJ of a solute and its molecular weight. They showed that there is an inverse linear relation between log(P_GJ) and molecular weight (see Fig. 8 in Ref. 15), where P_GJ values range from 7 × 10⁵ cm/s (mol wt 559, lissamine rhodamine B-200) to 770 × 10⁵ cm/s (mol wt 39, K⁺).

The conductance of GJs (g_GJ) at a voltage difference across the GJs of 0 mV can now be calculated using P_GJ and the following equation (12)

(6)

where F is the Faraday constant, C_out is the concentration of fura 2 within the cell in which fura 2 had been injected (M₀), C_in is the concentration of fura 2 within the neighboring cell (M₁) of M₀, A is the area of intercalated disk between M₀ and M₁, R is the molar gas constant, and T is absolute temperature. The calculated g_GJ is ~3.3 nS. When we calculate the conductance of a single GJ channel on the assumption that open probability of the GJ channel is 0.43% and that GJ channel density is 2.3 × 10⁴ µm² in rat ventricular muscle (15), the conductance of a single GJ channel for fura 2 is ~0.15 pS. Using the relationship between P_GJ and molecular weight of the solute, this value would predict a unitary conductance for K⁺ of ~28 pS in trabeculae, which is in the same order of magnitude as the reported unitary conductance of GJ channels for K⁺ (~50 pS) (24).

Ca²⁺ Waves During TPCs

Figure 5 shows a typical example of the global [Ca²⁺]_i and the force development during the last electrically stimulated twitch of a train and a subsequent TPC in one trabecula at 22.1°C and [Ca²⁺]_o of 0.7 mM. Figure 5A shows the change in [Ca²⁺]_i calculated from a PMT signal. When the muscle was stimulated at 2 Hz, the Ca²⁺ transient shortened progressively so that the total duration after 15 stimuli was ~0.37 s. Figure 5B shows the force records made while fluorescence was recorded, first using excitation with UV light at 340 nm followed by excitation at 380 nm. The arrows indicate an increase in [Ca²⁺]_i (Fig. 5A) and the occurrence of an aftercontraction (Fig. 5B) observed during a TPC. The global measurement obtained with the PMT shows that the amplitude of the Ca²⁺ transient during the TPC is small (10%) compared with that of the preceding stimulated twitch and lasts twice as long as the Ca²⁺ transient of the twitch. The force transient of the TPC is also small in amplitude (14%) and lasts longer (40%) than that of the preceding stimulated twitch. The force transient of the TPC lasts slightly longer than the concomitant Ca²⁺ transient. In this study, all imaging data were accepted for analysis when the stresses recorded at both excitation wavelengths were identical as shown in Fig. 5.

View larger version (14K): [in this window] [in a new window]   Fig. 5.   Global intracellular Ca2+ concentration ([Ca2+]i) calculated from fluorescence signals recorded by PMT (A) together with force records (normalized for cross-sectional area of muscle) recorded at 340- and 380-nm excitation wavelength (B) during last electrically stimulated twitch and a subsequent TPC. Arrows indicate an increase in [Ca2+]i and an aftercontraction during which a TPC was observed. s, Moment of electrical stimulation.

To determine the spatial and temporal changes in [Ca²⁺]_i during the TPC, we analyzed the images recorded by the IIC directly after a PMT recording. Figure 6 shows the last stimulated Ca²⁺ transient and a cytosolic Ca²⁺ wave during the TPC in the same trabeculae as presented in Fig. 5. In this three-dimensional representation the abscissa is time, the ordinate is [Ca²⁺]_i, and the z-axis is the position of each pixel along the long axis of the trabecula. After the end of a series of stimulated Ca²⁺ transients, a smaller Ca²⁺ transient was observed to move as a wave from position A (indicated by * in Fig. 6) toward position B. The Ca²⁺ waves appeared to travel at constant velocity along the trabeculae similar to properties of TPCs we have previously described (Refs. 10, 19; Fig. 1B).

View larger version (42K): [in this window] [in a new window]   Fig. 6.   Regional [Ca2+]i calculated from images by IIC during last electrically stimulated twitch and a TPC a few minutes after recording of PMT shown in Fig. 5. Abscissa, time; ordinate, [Ca2+]i; z-axis is position along long axis of trabecula. After end of clearly uniform stimulated Ca2+ transient, a smaller Ca2+ transient appeared to move from A (*) toward B (for explanation see text).

To calculate of the velocity of the Ca²⁺ wave in Fig. 6, we selected the peak of the Ca²⁺ transient during the Ca²⁺ wave at each pixel along the trabeculae and plotted the time of the peak point against the position of the peak (Fig. 7A). Regression analysis showed a linear relationship. The slope of the fitted line was taken as the velocity of the Ca²⁺ wave occurring during the TPC. This analysis shows that the Ca²⁺ wave propagates along the trabecula at a constant velocity, and the calculated velocity of the Ca²⁺ wave was 2.27 mm/s (Fig. 7A). The analysis of 10 reproducible Ca²⁺ waves in 8 trabeculae shows that the velocity of the traveling Ca²⁺ waves was 1.69 ± 1.48 mm/s (range 0.34-5.47 mm/s, n = 10) at [Ca²⁺]_o of 0.73 ± 0.30 mM and a temperature of 21.5 ± 0.9°C. Figure 7B shows that the [Ca²⁺]_i at the peak of the Ca²⁺ wave and the diastolic [Ca²⁺]_i between the last stimulated Ca²⁺ transient and the Ca²⁺ wave at each pixel position along the trabeculae were almost constant.

View larger version (18K): [in this window] [in a new window]   Fig. 7.   A: relationship between moment at which [Ca2+]i during Ca2+ wave (Fig. 6) was maximal against position of maximal point along trabecula. Relationship was fitted by linear regression (r = 0.971); slope of fitted line was taken as velocity of Ca2+ wave. B: peak [Ca2+]i during Ca2+ wave (solid line) and diastolic [Ca2+]i between last stimulated Ca2+ transient and Ca2+ wave (dotted line) as a function of position along trabecula. C: average [Ca2+]i in a 600-µm-long region of interest (ROI) along trabecula (calculated from Fig. 6). Solid line shows average of stimulated Ca2+ transients during twitch and average of Ca2+ transient during Ca2+ wave (TPC) after correction for time required for Ca2+ wave to move from pixel to pixel as calculated from Fig. 6. Dotted line shows same trace of global change in [Ca2+]i as presented in Fig. 5, recorded with PMT from a region of ~1.00 µm that overlapped with ROI of IIC.

The average time course of Ca²⁺ transients during the Ca²⁺ wave was obtained by using our observation that Ca²⁺ waves traveled at constant velocity. Therefore, we could shift the time axis of the Ca²⁺ transient of every pixel according to the time required for the Ca²⁺ wave to move from pixel to pixel. After this correction, the Ca²⁺ transients of all corresponding pixels (n = 250) were averaged. The solid line in Fig. 7C shows the average of the stimulated Ca²⁺ transients in all pixels during the twitch as well as the average of regional Ca²⁺ transients during the Ca²⁺ wave after the shift of the time axis calculated from the imaging data of Fig. 6. The peak of the averaged regional Ca²⁺ wave reached 40% of that of the stimulated Ca²⁺ transient, whereas its duration was slightly longer than that of the stimulated Ca²⁺ transient itself. The time course of decline of the "regional" Ca²⁺ wave was identical to that of the electrically induced transient, although the time constant of decline of Ca²⁺ was shorter in the stimulated Ca²⁺ transient (144 ms) than in the regional Ca²⁺ wave (235 ms) because of the difference in their peak Ca²⁺ levels (4). The rise of the regional Ca²⁺ wave lasted ~0.15 s longer than that of the electrically induced transient, accounting for the difference in duration of the two transients. The dotted line in Fig. 7C shows the same record of the global Ca²⁺ transient, measured with the PMT, as presented in Fig. 5A. The twofold longer duration of the global Ca²⁺ transient (dotted line) during the TPC is presumably caused by the displacement of the Ca²⁺ wave during the TPC along the segment of muscle, which was observed by the PMT.

It follows from Figs. 5 and 6 that when the Ca²⁺ wave started during the late relaxation of the twitch [as we have shown previously (19)], the site of origin of the wave must have been located ~700 µm from position A toward the tricuspid valve, as was indeed the distance between position A and the insertion of this trabecula in the AV ring.

In summary, a sequential, spatial, and temporal change in [Ca²⁺]_i (a traveling Ca²⁺ wave) underlies a TPC in thin right ventricular trabeculae. These waves start at one of the damaged ends of the trabeculae.

	DISCUSSION

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To our knowledge, this is the first study to provide a quantitative assessment of propagating Ca²⁺ waves in multicellular cardiac preparations. As we discuss here, both the presence and properties of Ca²⁺ waves during TPCs are consistent with a previously proposed model of propagation, i.e., CICR from the SR mediated by diffusion of Ca²⁺ along the cell. Our previous observation that TPCs are delayed by octanol is consistent with the conclusion from this study that the permeability of GJs is drastically reduced by octanol, such that the propagation process for TPCs is delayed because of slower diffusion of Ca²⁺ from cell to cell.

Diffusion of Fura 2 Within Trabeculae

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Diffusion of fura 2 (D_trab) calculated for 1 h after the injection of the probe into trabeculae illustrates that an additional diffusion barrier was present along trabeculae, because D_trab was nearly one-half of D_myop. We assume that this barrier is formed by the GJs. Several lines of evidence support this assumption. First, the diffusion coefficient of the GJs (D_GJ) can be calculated from D_myop and D_trab, treating the trabeculae as a planar diffusion sheet. The permeability of GJs follows from D_GJ and is similar to P_GJ determined for molecules of a similar size (15). Second, our calculated g_GJ, based on reasonable assumptions regarding GJ density and open probability, was similar to g_GJ measured in lipid bilayers (24). Third, when we observed fura 2 diffusion directly after injection of fura 2 into a cell, cell diffusion was clearly rapid and unaffected by octanol (see RESULTS).

The asymmetry of short-term diffusion of fura 2 shown in Fig. 4E is also consistent with our interpretation of an effect of octanol on GJs for the following reason. In these cases fura 2 diffused faster in one direction than another (see RESULTS). We propose a simple explanation for this observation, i.e., impalement with a microelectrode occurs at a random position within the impaled cell. Obviously, the microelectrode is more likely to impale the cell near one of the two ends than in the center. Hence, we assume that fura 2 diffusion was slow on the side of the fluorescence profile when it had been injected near the edge of a cell. Asymmetrical diffusion was visible in muscles that had not been treated with octanol (data not shown) but became pronounced after exposure to octanol (Fig. 4E). Calculation of the diffusion coefficient for the three cases shown in Fig. 4E suggests that diffusion across the regions including the gray bars reflects a barrier with diffusion properties similar to those of the barrier that exists during diffusion along the whole trabecula. In addition, the distance between the gray bars was similar to the length of a single myocyte. Thus we assume that GJs were located at the regions indicated by the gray bars and that the inhibitory effect of octanol on diffusion of fura 2 is caused by the effect of octanol on GJs. It is reasonable to assume that the reduction of P_GJ by octanol is caused by the reduction of the open probability of GJ channels, as has been described by others (26).

The formation of an oval spot of fluorescence after injection of fura 2 with the long axis parallel to the muscle axis means that diffusion of fura 2 is faster longitudinal than transverse to myocardial fiber orientation, suggesting anisotropy of the GJ distribution. This nonuniform distribution of fura 2 is consistent with the report that velocity of electrical conduction is greater longitudinal than transverse to myocardial fiber orientation (23). This report also shows that heptanol slows the conduction velocity transverse to fiber orientation to a greater degree than longitudinal. However, in this study we did not compare the effect of octanol on P_GJ in the longitudinal direction with that in the transverse direction quantitatively, because we did not measure the effect of octanol on P_GJ calculated from the transverse diffusion of fura 2.

In summary, by using diffusion characteristics of fura 2, we conclude that octanol, in a concentration known to affect TPC propagation velocity (31), reduces P_GJ, thus supporting the concept that calcium ions need to diffuse from cell to cell through GJs for propagation of a TPC through normal myocardium.

Ca²⁺ Waves

Comparison between global and regional measurement. The global Ca²⁺ transient (Figs. 5 and 7) during the TPC showed a smaller maximal amplitude and longer duration than the regional Ca²⁺ transients (Figs. 6 and 7). This difference can be explained in a straightforward manner because the PMT averages the fluorescence intensity from an area of the muscle that is ~1 mm long. The Ca²⁺ wave travels at 2.27 mm/s and lasts ~0.40 s. Therefore, the PMT is expected to "see" a Ca²⁺ wave that lasts ~0.84 s (1/2.27 s + the duration of the wave itself), as is indeed the case. For the same reason, the maximal amplitude of the global Ca²⁺ wave seen by the PMT is expected to be almost one-half of that of the regional Ca²⁺ wave, as is the case.

Comparison with Ca²⁺ waves in single myocytes. The Ca²⁺ waves during TPCs in trabeculae propagate faster (0.34-5.47 mm/s) than the reported Ca²⁺ waves in isolated single myocytes (~0.1 mm/s; Refs. 16-18). In our previous studies, the velocity of the TPCs varied depending on the [Ca²⁺]_o, the number and frequency of the electrical stimuli (10, 19), and the presence or absence of Ca²⁺ channel agonists and antagonists (11). These observations are consistent with the assumption that Ca²⁺ loading of the cell is the main determinant of the velocity of the TPCs. Thus we assume that the Ca²⁺ waves during TPCs propagate along trabeculae faster than the Ca²⁺ waves in single myocytes, because both the myoplasm and the SR are probably more loaded with Ca²⁺ in trabeculae than in myocytes because of the preceding repetitive stimulation and thereby CICR is probably facilitated.

Comparison with TPCs. Similar to the TPCs (10, 19), the propagation velocity of the Ca²⁺ waves was constant along the trabeculae (Fig. 7A) and varied under the conditions in this study from 0.34 to 5.47 mm/s (mean 1.69 ± 1.48 mm/s). We were unable to measure Ca²⁺ waves with a velocity >7 mm/s in our experimental setup (see METHODS). The duration of the Ca²⁺ transients seen in this study during Ca²⁺ waves was ~0.40 s (Fig. 7C), which is similar to the duration of the SL shortening waves observed during TPCs (10, 19). Furthermore, our results are consistent with the observation that TPCs are initiated at or near the (damaged) ends of the trabeculae (19). These similarities in behavior suggest that Ca²⁺ waves underlie TPCs in trabeculae.

Comparison with CICR computer model of Ca²⁺ wave propagation. Propagation of the Ca²⁺ waves was clearly faster than the expected maximal rate of displacement of a diffusion front of Ca²⁺ (20 µm/s, see above). The presence of Ca²⁺ waves during TPCs is consistent with the hypothesis that TPCs propagate along the trabeculae by CICR mediated by Ca²⁺ diffusion to adjacent SR. This hypothesis is supported by the observation that the time course of the Ca²⁺ wave is similar to that of the electrically evoked transient, suggesting that the Ca²⁺ wave and twitch transient share underlying mechanisms. In particular, our observation is consistent with the report that the decline of Ca²⁺ during both the Ca²⁺ transients is mainly caused by uptake by SR and that the rate of uptake depends on the [Ca²⁺]_i (4).

Limitation of resolution of fluorescence measurement. Injection of fura 2 into single cells for the measurement of D_myop probably allowed resolution within a few micrometers, such that transport from cell to cell (via GJs) could be monitored. In contrast, we cannot expect to resolve events at this level when Ca²⁺ waves pass through the trabeculae. Trabeculae were ~90-µm thick, so that Ca²⁺ waves passing through the four cells above and below the plane of focus contributed to the wave observed by the IIC. This would blur the observed image in such a way as to make it impossible to resolve events at the level of the cell edges. The above "averaging" effect may also explain why we have not observed local variations in the velocity of Ca²⁺ waves as one would expect based on simple Ca²⁺ diffusion characteristics through GJs versus the adjacent cytosol. On the other hand, this error may be small because in one study of Ca²⁺ waves and cell-cell coupling (25), no delay in propagation at the GJs was detected even using confocal microscopy. (Note, however, that in this latter study propagation occurred at lower velocity than that in our study.)

Summary