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* Julius Bernstein Institute of Physiology; Institute of Numerical Mathematics; and Institute of Pathology, Martin Luther University, Halle-Wittenberg, Germany
Correspondence: Address reprint requests to Professor Manfred H. P. Wussling, Martin Luther University, Julius Bernstein Institute of Physiology, Halle-Wittenberg, Magdeburger Strasse 6, D-06097 Halle/S, Germany. Tel.: 49-345-557-1392; E-mail: manfred.wussling{at}medizin.uni-halle.de.
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12 g/l and amounted to nearly 60 µm/s. The corresponding distance of neighboring calcium release units was calculated to be 4 µm. The results further show that calcium signaling in the described reaction-diffusion system is optimal in a relatively small range of diffusion lengths. A change by ±2 µm resulted in a reduction of the propagation velocity by 40%. It would appear that 1), the distance between calcium release units (clusters of ryanodine receptors in cells) is a sensitive parameter concerning propagation of Ca2+ signals; and 2), a dysfunction of the reaction-diffusion system in living cells, however, might have a negative effect on the spreading of intracellular calcium signals, thus on the cell's function. |
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). Concomitantly with such processes, calcium oscillations and/or calcium waves may occur (Wier et al., 1987; Wier and Blatter, 1991; Lipp and Niggli, 1993; Trafford et al., 1995; Clapham and Sneyd, 1995; Wussling and Salz, 1996; Ishida et al., 1999; Subramanian et al., 2001; Sell et al., 2002; Worth et al., 2003). The calcium wavespeed in cells of several species and at different temperatures has been observed to vary between 3 and 160 µm/s (Jaffe, 1993, 2002). Calcium waves in fertilizing eggs of Xenopus laevis, for instance, propagate with 20 µm/s (Camacho and Lechleiter, 1993). In neuronal cells of mammals, to the contrary, calcium waves travel with velocities beyond 100 µm/s, e.g., 160 µm/s in retinal cells of newborn ferrets (Stellwagen et al., 1999). Under the condition of calcium overload, in adult as well as embryonic stem cell-derived cardiac myocytes, spontaneous calcium waves may easily develop (Cheng et al., 1993; Haberland et al., 2000). They show steep increase and flat decay of the fluorescence intensity, propagate within 80–100 µm/s, and annihilate one another after collision due to refractoriness (Ishide et al., 1990; Wussling et al., 1997).
A presupposition for the development of spatiotemporal calcium patterns is not the integrity of a living cell but the presence of a reaction-diffusion system. The latter is given already when vesicles of the SR are embedded homogeneously or inhomogeneously in agarose gel with a composition similar to that of the cytosol. In such a system, with an apparent calcium diffusion coefficient of 215 µm2/s (gel with SR vesicles) or 150 µm2/s (gel with SR vesicles and mitochondria), calcium waves propagate with velocities of 40 µm/s or even more (Wussling et al., 1999, 2001). Isolated mitochondria were previously shown to be excitable organelles that can generate travelling depolarization and Ca2+ waves (Ichas et al., 1997). Whereas energized mitochondria accelerate calcium waves in clustered SR vesicles, thapsigargin, a specific inhibitor of the SR calcium pump (SR CaATPase), slows down the wavespeed (Wussling et al., 1999). Spatiotemporal calcium patterns in gels with isolated cell organelles underlie, similar to living cells, the general principles of self-organization in excitable media, which numerically can be simulated by a reaction-diffusion model (Podhaisky and Wussling, 2004). This model predicts a biphasic dependence of the calcium wavespeed on the distance between neighboring calcium release units. However, there are no corresponding experimental data yet.
In twitch fibers of frog skeletal muscle, calcium waves are reported to be involved in the excitation-contraction coupling including junctional and parajunctional clusters of ryanodine receptors (Zhou et al., 2003; Felder and Franzini-Armstrong, 2002). Calcium waves have been shown to play an important role in the normal physiological function of cardiac atrial myocytes, pacemaker cells, and Purkinje cells (Blatter et al., 2003). Cardiac atrial cells lack transverse tubuli (invaginations of the sarcolemma), so that calcium waves must spread over relatively long distances (Hüser et al., 1996). It may be supposed that in such cells, the distance between neighboring calcium release units critically influences the reaction-diffusion mechanism. In cat atrial cells, for instance, clusters of ryanodine receptors were found to be regularly disposed in the membranes of the SR with an average neighboring distance of 2 µm, similar to a 3D lattice (Kockskämper et al., 2001). An activation of subsarcolemmal junctional Ca2+ release sites, usually initiated by an action potential, results in a significant increase of the cytosolic calcium concentration in the periphery of the cell and subsequent spreading of a calcium wave to the central nonjunctional SR in a regenerative fashion (CICR) with an unusually high propagation velocity of 250 µm/s (Sheehan and Blatter, 2003). On the other hand, Ca2+ alternans-induced calcium waves have been shown to cause the development of atrial arrhythmias (Kockskämper and Blatter, 2002). Whatever the contribution of calcium waves to the cell's physiological or pathophysiological function is, the question arises, how does the distance of neighboring calcium release sites influence the mechanism of CICR?
In gels with homogeneously distributed SR vesicles, wave patterns depend on several parameters, e.g., total calcium concentration within the gel (Krannich, 2001). This work is aimed to systematically investigate 1), the range of the gel's SR vesicle protein concentration where calcium waves occur; 2), the relationship between the gel's SR vesicle protein concentration and the average distance between neighboring calcium release units; and 3), the dependence of the propagation velocity of calcium waves on that distance. One may expect, of course, that gel preparations with a SR vesicle protein concentration below a threshold do not propagate calcium waves. In other words, gel preparations are expected to be nonexcitable when the distance between neighboring calcium release units exceeds a critical value.
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METHODS |
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). The protein content of the SR vesicles which were stored at –80°C in a suspension containing 300 mM sucrose and 10 mM PIPES amounted to 29.3 g/l (suspension A).
Agarose gel system
We exclusively used the type VII agarose gel (low gelling temperature, Sigma, Heidelberg, Germany) and reagents of the purest grade commercially available. Agarose gel was dissolved in aqua bidest at 100°C for 5 min and cooled to a temperature of 37°C. After being mixed with buffer solution and the calcium indicator Fluo-4, a certain volume of the gel was transferred to an adequate volume of suspension A (SR vesicles) and stirred repeatedly to obtain SR vesicles homogeneously distributed in the agarose gel system (suspension B). Due to the replacement of SR vesicles by agarose gel, the total volume of suspension B was constant in all experiments and amounted to 24.7 µl, independent of the requested protein concentration. Suspension B was prepared immediately before each experiment. The composition of the final agarose gel system was (in mM) KCl 100, MgCl2 5, Na2ATP 4, phosphocreatine 10, EGTA 0.04, Pipes 20, and CaCl2 0.025....0.41 (dependent on SR vesicle protein concentration), Fluo-4 10, and 0.4% agarose gel. A set of four specimens (6 µl each) derived from suspension B was stored in darkness in humid chambers until needed for the investigation with the confocal laser scanning microscope at room temperature. The duration of measurement was restricted by the consistency of the agarose gel. Increasing protein concentrations resulted in a more rapid solidifying of the gel and an impairment of the reproducibility of repetitive calcium waves. Good patterns were usually observed in fresh preparations during the first 20 min.
To reach a nearly constant calcium loading of the SR vesicles in the agarose gel system, it was important to keep constant the ratio of protein concentration and total calcium concentration in suspension B. Most of the calcium is stored in the SR vesicles. Therefore, cCa-tot 
cCa-ves VA/VB, where cCa-tot is the total calcium concentration, cCa-ves is the vesicular calcium concentration, VA is the volume of suspension A, and VB is the volume of suspension B (24.7 µl in all experiments). On the other hand, cCa-tot = k x cProt, where cProt is the protein concentration and k is the constant. In our experiments, a proportional factor of k = 0.0253 mmol/g proved to be optimal (Krannich, 2001). The background Ca2+ in gels with varying protein concentrations was measured initially and found to be constant in the order of magnitude of 10–8 M (Krannich, 2001).
Confocal laser scanning microsopy and data processing
For the measurements, a confocal laser scanning microscope (INSIGHT-PLUS, Meridian Instruments, Okemos, MI) with the Brakenhoff scan system, enabling a 100/s sample rate, was used (images of 512 x 480 pixels). Due to the use of a CCD camera (CCD 72 cooled by two Peltier batteries; Dage-MTI, Michigan City, IN), the frequency of captured frames actually amounted to 25 Hz. The computer-controlled Z-drive accessory provided optical sectioning with a step size of 0.6 µm at minimum. All frames obtained with a LWD 40x and NA 0.55 objective (Olympus, Tokyo, Japan) were recorded on videotape. After digitization with a frame grabber board (QuickCapture 1.13, Data Translation, Marlboro, MA) data were processed using software for the Macintosh OS D2-9.1 and the Macintosh IIci computer (IPLab Spectrum QC, Signal Analytics, Vienna, VA; NIH Image 1.43, Microsoft, Redmond, WA).
Electron microscopy and data processing
Additional agarose gel preparations with SR vesicles of varying density (protein concentrations between 3 g/l and 16 g/l) were prepared, fixed (glutaraldehyde), stained (osmiumtetroxide) and embedded in epoxy. A series of semithin slices (35 µm in thickness) was manufactured suitable for the check in a light microscope at relatively low magnification. To store selected samples on the hard drive of a IIci Macintosh computer, a CCD camera (C 3077) with control unit (C 2400), an additional controller (II), and the Argus-10 image processor (Hamamatsu, Bridgewater, NJ) was used. Ultrathin slices (55 nm in thickness) were investigated using a 50–80 kV electron microscope (EM 902 A, Zeiss, Oberkochen, Germany). We used a semiautomatic approach to analyze the images obtained from the microscope: first, for each photo we marked the midpoints of SR vesicles (electron micrographs) or of clusters of SR vesicles (light micrographs) on a transparency. In a second step, we scanned the slides and applied simple image detection to the high-contrast pictures. That procedure gave us a list of coordinates of the midpoints. Finally, the nearest neighboring distance in that list has been evaluated using MATHEMATICA (Wolfram Research, Champaign, IL). The number of vesicles inside the images varied from 161 to 807. For the determination of the areas of clusters of SR vesicles the freeware ImageJ was used (Image Processing and Analysis in Java, http://rsb.info.nih.gov./ij/).
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5 x 10–8 M (Krannich, 2001) were demonstrated to propagate calcium waves with a velocity of 40 µm/s in the absence and 60 µm/s in the presence of mitochondria (Wussling et al., 1999). Fig. 1 shows a sequence of four phases (A–D) of a stimulated calcium wave spreading through a clustered area of 300 µm x 450 µm (see outline) in agarose gel with a vesicular protein concentration of 16.32 g/l and in the presence of mitochondria. The arrow in the left lower corner of each frame points to the edge of the gel. The time between sequential images amounted to 1 s and the wavespeed was 64 µm/s in average. Wavespeed is related to the direction of the spreading wave, i. e., orthogonally to the wavefront (cf. Fig. 3 in Wussling et al., 1999), and was determined from intensity profiles. Note that the wave's fluorescent intensity is relatively high so that the wavefront appears clearly visible. In an isotropic 3D medium, calcium waves are expected to occur as spherical waves (or circular waves in the confocal plane). Fig. 1 shows deviations from circular wavefronts. This is surely due to inhomogeneities concerning either the distribution of the SR vesicles or of the fluorescent calcium indicator, possibly both. The observed calcium waves, however, were found to be stable at relatively high protein concentration (e.g., 16.32 g/l). They appeared repetitively and spread throughout the cluster with nearly constant velocity within a few minutes (not shown in Fig. 1).
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70 µm/s in Fig. 2 compared to 64 µm/s in Fig. 1). We later will show that the protein concentration of 11–12 g/l is optimal for propagating calcium waves in the agarose gel system.
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14 s (cf. frames A and O or B and P). A total of nine oscillations with a period of 15 ± 3.1 s (mean ± SD) were observed in the preparation corresponding to Fig. 3. Two points are worth mentioning:
Local and global distribution of SR vesicles
To reveal the dependence of the propagation velocity of calcium waves on the distribution of SR vesicles in the gel, we investigated electron micrographs of gels with protein concentrations varying between c = 3 g/l and c = 16 g/l and determined the mean inter-SR vesicle distance, d, as described above (Methods). The highest protein concentration in agarose gel was 16.32 g/l. Fig. 4 A shows a representative ultrathin slice (55 nm in thickness) of SR vesicles in agarose gel at c = 9 g/l. The mean inter-SR vesicle distance was d = 193 ± 53 nm (mean ± SD; n = 100). The microsome's mean diameter resulted in 
= 172 ± 37 nm (mean ± SD; n = 100 vesicles). The points shown in Fig. 4 B mark the SR vesicle's centers, which were used for the determination of the mean inter-SR vesicle distance.
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(1/c)1/3, then
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25 µm2 within the corresponding range of protein concentrations (see inset of Fig. 8; data are mean ± SD, number in parentheses underneath are the number of preparations).
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30 µm in diameter) or rather local oscillations than waves (cf. Fig. 3). Corresponding data (within outline in Fig. 9 A) are different from those of stable calcium waves which propagate throughout a relatively large area (a few hundreds of µm in distance; see Fig. 1). Therefore, we exclude the calcium signals which were (occasionally) detected at protein concentrations <7 g/l. At protein concentrations between 7 and 16.32 g/l stable calcium waves with velocities between 28 and 63 µm/s were observed. The velocity was maximum at 12 g/l (see asterisk). The decrease of the wavespeed beyond the protein concentration of 12 g/l was originally unexpected (i.e., before corresponding model simulations). We supposed that shorter diffusion distances improved the generation and propagation of calcium waves. Though, as later shown, the decay of wavespeed at higher protein concentrations (i.e., shorter distances between neighboring clusters of SR vesicles) is possibly due to a prevailing effect of calcium pumps (SR Ca-ATPases). Fig. 9 B shows propagation velocity relative to the maximum, marked by an asterisk (see Fig. 9 A), in dependence on the mean distance between neighboring SR vesicle clusters. Estimates of distances were based on the data shown in Fig. 8 (regression line). Note that the points of Fig. 9 B (means ± SD) correspond to those of Fig. 9 A with the exception of the data within the outlined area. Fig. 9 B shows that the calcium signaling seems to be optimal in a relatively small range of distance. A deviation of ±2 µm (see horizontal dashed line in Fig. 9 B) from the optimal distance of 4 µm (i.e., where wavespeed is maximum) results in a reduction of the propagation velocity by 40% (see vertical dashed line in Fig. 9 B).
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DISCUSSION |
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, 1997). This ubiquitous element undergoes spatial and temporal transients of cytosolic concentration both in periodically active cells (e.g., cardiocytes) and in those responding to random stimuli (e.g., cochlear hair cells, fertilizing oocytes). In cardiac cells, calcium sparks are considered to be the origin of calcium waves (Cheng et al., 1993, 1996), which propagate due to regenerative calcium release (Wussling and Salz, 1996; Wussling et al., 1997). A model proposed by Izu et al. (2001) predicts the velocity of calcium waves in cardiac cells to depend on kinetic parameters (rate of Ca2+ release, total amount of Ca2+ released, Ca2+ sensitivity of calcium release units (CRUs)) and on the disposition of neighboring CRUs.
Disposition of CRUs in agarose gel
If SR vesicles (see electron micrograph, Fig. 4) are considered as spheres with a diameter of 172 ± 37 nm (mean ± SD), the microsomes' surface area is calculated to vary between 85,000 nm2 and 205,000 nm2. Based on morphometric data concerning CRUs of the junctional sarcoplasmic reticulum of skeletal muscle fibers (Franzini-Armstrong et al., 1999), the area of a cluster of functionally cooperating ryanodine receptors (RyRs) may be estimated. If the number of RyRs (feet) per CRU amounts to 30 ± 11 (mean ± SD, determined from the data of 11 skeletal muscle types according to Table 1 of Franzini-Armstrong et al., 1999) and the feet-to-feet distance is 29 nm, then an area of 17,000 nm2....36,000 nm2 per CRU results. Thus, the number of CRUs per SR vesicle might vary between 2 (large area of CRU, small surface area of microsome) and 12 (small area of CRU, large surface area of microsome), theoretically. Unfortunately, we don't have corresponding immunofluorescence data. The SR vesicles that we used in the experiments described above stem from heavy protein fractions. It is assumed, therefore, that vesicles with at least one or rather more CRUs form the majority of the microsomes.
Clusters of SR vesicles and calcium signals in agarose gel
In gels, spontaneous or stimulated calcium waves were observed to propagate throughout clusters of SR vesicles (Wussling et al., 1999). To investigate how wave propagation depends on the disposition of neighboring CRUs, the protein concentration of SR vesicles was varied. The relationship between mean inter-SR vesicle distance and protein concentration was supposed to be nonlinear. Despite several efforts toward a homogeneous distribution similar to a lattice with hexagonal disposition of the microsomes (see Fig. 5), we failed to confirm the expected relationship (Fig. 6). Actually, SR vesicles appear homogeneously distributed within a single cluster, i.e., locally (Fig. 4) but not globally in the whole agarose gel. The light micrograph of Fig. 7 clearly shows SR vesicles distributed in clusters. This might be due to electrostatic forces that prevent the separation of the microsomes. Clusters of SR vesicles, to the contrary, were distributed nearly homogeneously with monotoneously decreasing center-to-center distance as SR vesicle protein concentration increases (Fig. 8). The inset of Fig. 8 shows an enhancement of the cluster's size with increasing protein concentration from 3 to 9 g/l. This might be due to electrostatic and/or unavoidable stirring effects. However, since the mean area of the clusters is not constant in the range of protein concentrations where clusters may be distinguished (see inset of Fig. 8), we cannot exclude a certain influence of its size on the mean distance of neighboring clusters. Supposing a constant cluster size, that distance is expected to decay with increasing protein concentration, too, but not basically differently than the regression line of Fig. 8 does. Since the SR vesicle cluster's size is relatively constant at protein concentrations >7 g/l, the optimum intercluster distance (see Fig. 9 B) is likely not too far from being exact.
At relatively small protein concentrations (e.g., 1 g/l) local calcium oscillations (occasionally abortive waves) instead of globally spreading calcium waves were observed (Fig. 3). Local oscillations may be considered as proof of the excitability of the reaction-diffusion system, at least of isles of the gel preparation (or clusters of SR vesicles) scanned confocally. At SR vesicle protein concentrations <7 g/l (i.e., center-to-center distance between neighboring calcium release sites >8.3 µm), however, stable calcium waves did not occur. The reason is that the distance between potential calcium "sources" (or the diffusion length between CRUs) is too large to sustain the regenerative calcium release mechanism in the gel. The wavespeed was shown to be optimum at a protein concentration of 12 g/l or a center-to-center distance of nearly 4 µm and to significantly decay at smaller as well as greater distances between neighboring calcium "sources" (Fig. 9 B). This is an interesting result inasmuch as calcium "sources" and "sinks" would be expected to remain at a fixed ratio independent of the concentration of SR vesicles in the gel. According to Spiro and Othmer (1999), the calcium reuptake through pumps is considered to follow a Michaelis-Menten kinetics, i. e., the actual rate is a simple function of the local calcium concentration only. This is in contrast to the calcium release channels that are supposed to work autocatalytically and hence with a time delay. This can be modeled with an additional state variable describing the nonrefractory fraction of the channels and an additional ordinary differential equation for this state. Numerical calculations of a corresponding model basically resulted in biphasic characteristics of wavespeed versus the vesicle's density, as shown previously (Podhaisky and Wussling, 2004).
Comparison of gels with cells
In our artificial gel system we experimentally could vary the distance between clusters of CRUs. An optimum (with respect to the propagation velocity of calcium waves) of 4 µm is similar but not identical, with average distances between individual calcium release sites of living cells as reported previously (cardiac cells: Kockskämper et al., 2001; Sobie et al., 2002; Xenopus oocytes: Shuai and Jung, 2003). A quantitative comparison of the optimum intercluster distance of gels with living cells is a problem inasmuch as the function of calcium release sites and pumps in the membranes of SR vesicles embedded in agarose gel is likely impaired, in general, compared to the intact SR/ER of living cells. An impairment of the SR function, however, might require shorter distances between neighboring clusters of CRUs to enable regenerative calcium release. It should be emphasized that SR vesicles are the result of a stressful procedure that may interfere with distinct properties of the SR membranes. A second concern is that we embedded SR vesicles in an artificial gel with features that are similar to but not necessarily identical with the cytoplasm of living cells (Pollack, 2001). This opinion is supported by different apparent calcium diffusion coefficients measured by the same method both in cardiac myocytes (120 µm2/s) and agarose gels with embedded SR vesicles (215 µm2/s) (Wussling et al., 1997, 2001).
The calcium signaling is more stable and faster in the neighborhood of mitochondria (Hajnóczky et al., 2000). As previously shown, well-energized mitochondria accelerate the propagation of calcium waves in cells (Jouaville et al., 1995) and gels (Wussling et al., 1999) by 50%, which is most likely due to the cooperation of both SR and mitochondria (Duchen, 1999). It would appear that an improvement of the SR vesicle's function, however, not only increases the velocity of spreading calcium waves but also may change the critical distance between neighboring clusters of CRUs. To avoid additional clustering, we did not add mitochondria to the gels with embedded SR vesicles with the exception of only one preparation (see Fig. 1).
In summary, an artificial gel system which allows us to vary the distance between calcium "sources" on the one hand and calcium "sinks," on the other hand, was investigated. We have shown that the disposition of calcium release units in agarose gels with embedded vesicles of the sarcoplasmic reticulum critically influences the regenerative mechanism of calcium release underlying the spreading of calcium waves. The relationship of mean distance between neighboring calcium release units (SR vesicles and clusters of SR vesicles) versus protein concentration was determined from electron micrographs and light micrographs using a home-made software (see Methods). The main result of the experiments is that stable calcium waves exclusively occurred in a range of the distance between either single SR vesicles or clusters of SR vesicles from nearly 200 nm to 8.3 µm. Calcium wavespeed peaked at a distance of 4 µm between neighboring clusters of SR vesicles. This qualitatively agrees with the reaction-diffusion model of Podhaisky and Wussling (2004). Because of the dependence of the calcium signaling on the inter-SR vesicle cluster distance within the artificial system presented here, we would think that a dysfunction of calcium "sources" and "sinks" in living cells, which is expected to increase the distance of neighboring release sites, however, might have a negative effect on the intracellular spreading of calcium signals, and thus on the cell's function.
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Submitted on October 7, 2003; accepted for publication September 7, 2004.
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