Sarcomeric Ca²⁺ gradients during activation of frog skeletal muscle fibres imaged with confocal and two-photon microscopy

Abstract

1. Intra-sarcomeric gradients of [Ca²⁺] during activation of action potential stimulated frog single fibres were investigated with the Ca²⁺ indicator fluo-3 and confocal and two-photon microscopy. The object of these experiments was to look for evidence of extra-junctional Ca²⁺ release and examine the microscopic diffusion of Ca²⁺ within the sarcomere.

2. By exploiting the spatial periodicity of sarcomeres within the fibre, we could achieve a high effective line-scanning rate (∼8000 lines s⁻¹), although the laser scanning microscope was limited to < 1000 lines s⁻¹. At this high time resolution, the time course of fluorescence changes was very different at the z- and m-lines, with a significant delay (∼1 ms; 22 °C) between the rise of fluorescence at the z-line and the m-line.

3. To calculate the expected fluorescence changes, we used a multi-compartment model of Ca²⁺ movements in the half-sarcomere in which Ca²⁺ release was restricted to triadic junctions (located at z-lines). Optical blurring by the microscope was simulated to generate fluorescence signals which could be compared directly to experimental data. The model which reproduced our experimental findings most accurately included Ca²⁺ binding by ATP, as well as indicator binding to immobile sarcomeric proteins. After taking sarcomeric misregistration within the fibre into account, there was very good agreement between the model and experimental results.

4. We conclude that there is no experimental evidence for Ca²⁺ release at locations other than at z-lines. In addition, our calculations support the conclusion that rapidly diffusing Ca²⁺ buffers (such as ATP) are important in shaping the Ca²⁺ transient and that the details of intracellular indicator binding need to be considered to explain correctly the time course of fluorescence change in the fibre.

In striated muscle, Ca²⁺ release from the sarcoplasmic reticulum (SR) is initiated by t-tubular system depolarization which is sensed by a dihydropyridine receptor (for reviews see Rios & Stern, 1997; Leong & MacLennan, 1998). In frog skeletal muscle, the site of excitation-contraction (E-C) coupling is generally accepted to be at specialized junctions (‘triads’) between the terminal cisterns of the SR and the t-tubule membrane at the z-line (for review see Franzini-Armstrong & Jorgensen, 1994). The spatially discrete localization of the triad should therefore give rise to intra-sarcomeric gradients of free [Ca²⁺] during SR release (Cannell & Allen, 1984; Escobar et al. 1994; Monck et al. 1994; Zoghbi et al. 2000).

The amplitude and time course of such gradients were first estimated by Cannell & Allen (1984), who developed a computer model of the diffusion and binding of Ca²⁺ within a frog myofibril. Following the release of Ca²⁺ at the z-line, the model predicted significant [Ca²⁺] gradients the time course of which was dominated by the binding of Ca²⁺ to various Ca²⁺ buffers and a concomitant slowing in diffusive Ca²⁺ transport. The reduced rate of Ca²⁺ transport resulted in the Ca²⁺ gradients persisting for ∼20 ms which is much longer than the time taken for similar gradient dissipation in free solution (Cannell & Allen, 1984). More recently, Baylor & Hollingworth (1998) improved the model of Cannell & Allen (1984) by incorporating more accurate descriptions of Ca²⁺ buffers, as well as new information about the time course of SR Ca²⁺ release. This model also predicts large intra-sarcomeric [Ca²⁺] gradients.

The ability to measure such intra-sarcomeric [Ca²⁺] gradients has become possible with the advent of confocal fluorescence microscopy and suitable fluorescent Ca²⁺ indicators. Using a stationary confocal spot positioned near the z-lines or the m-lines of frog fibres containing a fluorescent Ca²⁺ indicator, Escobar et al. (1994) reported that the initial increase in the m-line Ca²⁺ signal was not significantly delayed relative to that of the z-line signal. This result was clearly inconsistent with the expected diffusive delays predicted by computer models of intra-sarcomeric Ca²⁺ movements (see above). Escobar et al. (1994) therefore proposed that the lack of a delay in the m-line signal might be explained by SR Ca²⁺ release occurring along the entire length of the sarcoplasmic reticulum, rather than just at z-lines (where triads occur). If correct, this proposal would require a major revision of currently accepted ideas regarding SR Ca²⁺ release in response to t-tubular depolarization. In contrast, the data of Monck et al. (1994), obtained by a pulsed-laser imaging technique and use of a digital filter to correct for out-of-focus light, suggested that a significant delay might exist between the rise of z- and m-line fluorescence in frog fibres. These authors, however, noted that the signal-to-noise ratio in their experiments made it difficult to exclude the proposal of Escobar et al. (1994).

We have therefore re-examined the question of whether there is any experimental evidence for extra-junctional SR Ca²⁺ release. Using the fluorescent Ca²⁺ indicator fluo-3 and confocal and 2-photon fluorescence imaging, we have imaged the development of intra-sarcomeric Ca²⁺ gradients following the action potential in frog skeletal muscle fibres. In contrast to Escobar et al. (1994) our measured time courses of fluorescence changes at the z- and m-lines were very different, with m-line fluorescence increasing significantly later than z-line fluorescence. We were able to reproduce the experimental signals by using a sophisticated multi-compartment model of the sarcomere in which release was restricted to the z-line and by accounting for the expected optical blurring by the microscope and sarcomere misregistration. It follows that there is no reason to suppose that Ca²⁺ release occurs at any other site within the sarcomere except the z-line (triad). In addition, our calculations emphasize the importance of diffusive Ca²⁺ buffers and indicator binding within the sarcomere and that blurring of the fluorescence image, even in ‘confocal’ microscopes, can be a problem when axially extended objects are examined.

METHODS

Preparation

All experiments were carried out in accordance with guidelines laid down by the Animal Welfare Committee. Frogs were killed by decapitation and pithed and intact single fibres were dissected from the semi-tendinosus and ileofibularis muscles from Rana temporaria. Single fibres were mounted in a chamber on the stage of a Zeiss LSM 410 confocal microscope (Zeiss, Oberkochem) and were pressure injected with the penta-potassium form of the Ca²⁺ indicator fluo-3 (Molecular Probes Inc., Eugene, OR, USA). The final myoplasmic concentrations achieved were estimated to be about 40-50 μm. The fibres were stretched to sarcomere lengths between 3.2 and 4.0 μm and single action potentials were evoked by point or field stimulation (as stated in the text). The bathing solution contained (mM): NaCl 120, KCl 2.5, CaCl₂ 1.8, Pipes 5, pH 7.1 and the temperature was 22°C.

Imaging

The fibre was mounted ∼20 μm above a no. 1.5 coverslip which formed the bottom of the experimental chamber. A Zeiss × 40 water immersion lens (NA 1.2) was used for both confocal and two-photon imaging. For confocal imaging, the 488 nm line of a 25 mW argon-ion laser was used while for two-photon imaging the output from a modelocked Ti:Sapphire laser at 850 nm with ∼100 fs pulse width was used (Soeller & Cannell, 1996). In both cases, fluorescence was measured between 510 and 550 nm (HQ filter, Chroma Technology, Brattleboro, VT, USA). To minimize possible photo-damage, the excitation light in both one- and two-photon experiments was attenuated during fly-back of the laser beam by an acousto-optical modulator.

Images were obtained at a pixel spacing of 0.132 μm and a time separation of 4.8 or 11.4 μs per pixel. At this speed, at a sarcomere length of 3.6 μm, a sarcomere would be completely scanned in 131 or 311 μs, respectively. Field stimulation resulted in synchronous activation of the sarcomeres (see Fig. 1). By examination of the fluorescence gradients in sequential sarcomeres as the laser spot moved along the fibre, it was possible to record intra-sarcomere signals with more than an order of magnitude improvement in time resolution (compared to normal line scanning) while preserving spatial information (see Fig. 2).

Figure 1. Line-scan images of the Ca²⁺ transient following point electrical stimulation.

A, line-scan image of the fluorescence transient evoked by electrical point stimulation of a single skeletal muscle fibre injected with fluo-3 using the maximum scan rate (1.4 ms line⁻¹) of the microscope. Fluorescence profiles along the fibre at different times following stimulation (see marks in A) are shown in B. Intra-sarcomeric gradients were apparent in one line at 1.4 ms but dissipated within ∼3 lines which was too fast to allow detailed analysis. Signals at locations on the z- and m-line are compared at this time scale in C. Note the slightly faster rate of rise of the z-line signal. D, time course of the fluorescence transient averaged over the extent of a whole sarcomere in two sarcomeres which are ∼30 μm apart. The signals suggest that stimulation of sarcomeres occurs synchronously over the observed length of fibre and propagation delays are negligible at this time scale.

Figure 2. Scanning scheme to track fast local calcium changes.

A illustrates how faster line scanning was achieved by exploiting the sarcomeric periodicity of the fibre (shown in the schematic diagram at the top). Using conventional line scanning the laser spot moves from one z-line to the next and then rapidly returns to the starting point before beginning another scan of that sarcomere (left side of diagram). On the right a number of sequential sarcomeres are scanned in a similar way. In this configuration, the end of the first scan line is aligned with the start of the scan line in the second sarcomere, etc. In this way a single long scan line tracing several sarcomeres (continuous black line) is equivalent to scanning one sarcomere repetitively at a much higher rate. In B a two-photon line-scan image obtained in this way is shown. The lowest four lines show the faint resting sarcomere pattern before stimulation. The fibre was stimulated between the fourth and fifth scan lines and the scan line at the top shows how the fluorescence increased as the laser spot moved along sarcomeres (scan speed ∼300 μs sarcomere⁻¹, sarcomere length 3.2 μm). The resting sarcomere pattern obtained from the first four scan lines is shown in C. In D the resting pattern (flatter trace) is compared to the rise in fluorescence extracted from the line at the top of the line-scan in B where peaks and troughs in the rising oscillatory curve correspond to the z- and m-line signals, respectively.

Fibre stimulation was synchronized to the microscope scan and 2-6 lines were acquired before the fibre was stimulated to allow determination of the resting fluo-3 fluorescence profile (F_R, see Fig. 2). Subsequent lines recorded the fluo-3 fluorescence in response to stimulation (F_A). The normalized change in fluo-3 fluorescence relative to the resting profile, ΔF(x,t)/F = (F_A(x,t)F_R(x))/F_R(x), was calculated on a pixel by pixel basis. At later times in some images, the sarcomeric pattern of F_A shifted relative to that of F_R as a result of fibre contraction. When such movement was detected, the periodic sarcomeric pattern evident in the fluorescence signals was used to align F_A with F_R. The radial position of the scan line was moved slightly after each scan to minimize any possibility of photo-damage.

Modelling

The multi-compartment model of Baylor & Hollingworth (1998) was used to compute sarcomeric Ca²⁺ gradients. The half-sarcomere was divided into 36 longitudinal compartments and 10 radial compartments. The sarcomere length of the model was 3.2 μm with a myofibrillar diameter of 1.05 μm. Model parameters were adjusted from those used by Baylor & Hollingworth (1998) to reflect the higher temperature used in the current experiments (22 vs. 16°C). A Q₁₀ of 1.35 was used for all diffusion coefficients, a Q₁₀ of 2.0 for all reaction rate constants and release fluxes, and a Q₁₀ of 3.0 for the maximum SR pump rate. In addition, the maximum SR pump rate at 16°C was doubled, a change which gave a better approximation to the complete time course of the measured fluo-3 signal and had only a small effect on the early time course (< 10 ms) of the transient.

Intracellular dye binding to immobile proteins is known to reduce the apparent diffusion coefficient of fluo-3 (Harkins et al. 1993). In some computations (referred to as Model 1) we took this into account by using the measured diffusion coefficient of fluo-3 in frog fibres (D_app= 0.2 × 10⁻⁶ cm² s⁻¹ at 16°C; Harkins et al. 1993). This value reflects the average behaviour of protein-bound and protein-free fluo-3 in a resting fibre (relative percentages approximately 87 and 13 %, respectively; Zhao et al. 1996). Model 1 also used the effective on- and off-rates for Ca²⁺ binding by fluo-3 as estimated by Baylor & Hollingworth (1998). All rates were scaled as described (above) to account for the higher temperature in our experiments. We also implemented a more complicated dye binding scheme (Model 2; Hollingworth et al. 1999) that treats protein-bound and protein-free indicator as separate species. This scheme has four reactions with the equilibrium constants (Harkins et al. 1993) and rate constants given in Table 1 (for 16°C). The diffusion constant of protein-free fluo-3 at 16°C, both Ca-bound and Ca-free, was assumed to be 1.54 × 10⁻⁶ cm² s⁻¹, while the protein-bound indicator was assumed to be immobile. Protein-bound and protein-free forms of the Ca-fluo-3 complex were assumed to contribute equally to emitted fluorescence. As will be shown later, the inclusion of this more complicated fluo-3 binding model significantly improved the match of model data to experimental results. In all simulations, resting free [Ca²⁺] was 100 nM and total [fluo-3] was 40 μm. The kinetics of the SR calcium release time course (J_rel) was given by the equation:

which is the same equation as used by Baylor & Hollingworth (1998) but with faster rising and falling phases (chosen to reflect the higher temperature used in this study). The delay between stimulation and the onset of release, as well as the amplitude of the release (K), were adjusted until the rising phase of the spatially averaged ΔF/F was similar to that measured experimentally. For the simulation shown in Fig. 4, the amplitude of release was 83 % of that given in Baylor & Hollingworth (1998). All models were implemented in FACSIMILE (AEA Technology, Bethel Park, PA, USA; cf. Cannell & Allen, 1984).

Table 1.

Reaction rates for the Ca²⁺, fluo-3, protein reaction scheme at 16°C

Reaction	On-rate (M−1s−1)	Off-rate (s−1)	Dissociation constant (μm)
Ca2+D ⇌ CaD	2·33 × 108	119	0·51
Ca2++ DP ⇌ CaDP	0·15 × 108	28·67	1·91
D + P ⇌ DP	0·1 × 108	3·67 × 103	367
CaD + P ⇌ CaDP	0·1 × 108	1·38 × 104	1380

In the reactions D refers to fluo-3, CaD to Ca-fluo-3 and P to protein. A protein concentration of 3 mM was used in the modelling, this concentration, coupled with a [fluo-3]_T of 40 μm and [Ca²⁺]_R of 100 nM gives 87% of fluo-3 bound to protein (cf. Zhao et al. 1996).

Figure 4. Comparison between model 1 and experimental data.

A, results from a simulation using our Model 1 (that assumed a simplified dye binding scheme) are compared with actual z-line (○), m-line (▵) and spatially averaged (□) signals obtained from a fibre stretched to a sarcomere length of 3.2 μm. The dashed lines show the z- and m-line signals which would be expected if optical blurring were negligible. The continuous lines are the result of taking optical blurring and the measured sarcomere misregistration into account. Note that the calculated m-line signal rises more slowly than the data even after such effects are included. The calculations shown in B were performed using Model 2 (which incorporates dye immobilization) and compared with the same set of data as in A. Although there is still some discrepancy between measured and calculated data when blurring is neglected (dotted lines) the simulated fluorescence data after blurring (continuous lines) agrees well with the experimental signals. Since our scanning scheme allows data to be obtained at other locations within the sarcomere, C shows a full spatio-temporal comparison of the experimental data (points) with the simulated fluorescence data (surface) from Model 2. Note the good superimposition of both data sets. From the simulation we can also obtain the spatio-temporal distribution of unblurred (‘ideal’) fluorescence changes (D). The underlying free [Ca²⁺] and pCa along the sarcomere in Model 2 is shown in E and F.

In order to account for the optical blurring of the fluorescence signal by the microscope, the Ca-fluo-3 signal calculated from the model was convolved with the microscope point spread function (PSF). The PSF was measured by recording the fluorescence from 0.2 μm diameter fluorescently labelled latex beads (Molecular Probes, Eugene, OR, USA) embedded in an aqueous solution containing 40 % glucose and 0.5 % agarose (refractive index of ∼1.38 to mimic the cytosol, see Huxley & Niedergerke, 1958). Beads 20 μm from the coverslip were imaged to define the microscope PSF within the fibre.

As a result of the refractive index mismatch, the full widths at half-maximum of the PSF in the radial and axial directions were relatively large (0.5 and 1.2 μm, respectively) and axial asymmetries indicative of spherical aberration were observed (Hell et al. 1993). A 3-D grid was constructed from the Ca-fluo-3 time course in a half-sarcomere. This corresponded to a grid of 6 × 4 × 6 (x-y-z) sarcomeres whose registration was obtained from volume images of the resting fibre sarcomere staining pattern (cf. Fig. 3). The calculated fluorescence changes in this ‘grid’ of sarcomeres were then convolved with the PSF to give a simulated fluo-3 time course which could be directly compared with experimental data.

Figure 3. Localized changes in fluorescence intensity following stimulation.

A, an average of the normalized fluorescence change from five measurements made in the same region of a fibre (stretched to a sarcomere length of 3.2 μm). The measurements were reproducible and used to extract the z- and m-line signals from the peaks and troughs of the signal, respectively. B, the time course of z- and m-line signals obtained in this way from the data shown in A and three other fibres using one- (confocal) and two-photon imaging. A delay between m- and z-line signals was observed in all fibres (see also Table 2). The amount of misregistration of sarcomeres in adjacent myofibrils along the optical axis was measured from images taken below and above the region in which we measured fluorescence transients. C, an x-y image of the region from which the data in A were obtained. The white line marks the position of the scan line. Note the varying degree of ‘tilt’ of the banding pattern in different areas of the image. An x-z image around the location of the scan line obtained from a sequence of such images shows that a similar tilt was also observed along the optical axis (D). The tilt corresponded to a shift of 0.2 μm longitudinally (along the direction of myofibrils) per micrometre in z.

RESULTS

Basic measurements

Figure 1 illustrates results obtained by confocal line scanning at the maximum scan rate of our microscope (1.4 ms line⁻¹). Panel A shows the line-scan image of the Ca-fluo-3 fluorescence evoked by electrical point stimulation of the fibre and the rapid increase in fluorescence everywhere along the scan line is apparent. The fluorescence along three line scans from this panel is shown in Fig. 1B. It is clear that fluorescence gradients are only discernible in the second line which implies that the gradients are very short lived. When the signals from a z- and m-line are compared at this time resolution (Fig. 1C), there is little difference detectable in the time of rise of the signals although there is a suggestion of a slightly lower rate of rise at the m-line. Figure 1D shows that the transient rises more or less synchronously along the length of the scan line (even though point stimulation was used). This result is not unexpected, with a longitudinal action potential propagation velocity of 3 m s⁻¹ the time taken to propagate over the 30 μm line-scan region would be ∼10 μs which is negligible compared with the line-scan speed (1.4 ms line⁻¹). From these data we conclude that the line-scan mode of the microscope is too slow to properly measure the time course of development of intra-sarcomere fluorescence gradients, although they can be clearly detected during one or two scan lines.

High resolution measurements of sarcomeric signals

Figure 2 shows how the limited time resolution of the confocal line scan can be overcome by using the periodic nature of sarcomeres along the fibre. The left of Fig. 2A shows how a line-scan image might be obtained from a single sarcomere. The laser spot moves steadily from z-line to z-line during the scan and then rapidly returns (dotted line) to the starting point before retracing the scan. These repeated scans would form a line-scan image (see Cannell et al. 1994), where the horizontal position represents distance along the sarcomere and the individual lines are separated by the scan speed of the instrument. On the right of Fig. 2A (illustrating the actual method used) a number of sequential sarcomeres are scanned. Since the end of the scan of the first sarcomere is aligned with the start of the scan of the second sarcomere, a single long scan line encompassing several sarcomeres is equivalent to scanning a single sarcomere at a much higher speed, if the behaviour of each sarcomere is identical. As shown by Fig. 1D, the sarcomere signals are highly synchronous (even for point stimulation), so by scanning more slowly over a number of sequential sarcomeres a higher time resolution can be achieved. Furthermore, the slight time delay expected from longitudinal action potential propagation was eliminated by using field stimulation in all subsequent experiments. Figure 2B shows a line-scan image that resulted from scanning the fibre more slowly. The bottom four lines are prior to stimulation and show the weak periodic fluorescence pattern present in the resting fibre (see below). The last scan line was started approximately at the time of electrical stimulation and as the scan progressed along the fibre the fluorescence increased. Periodicity in this signal is very clear at the middle of the scan line and then disappears by the end of the scan line. Figure 2C shows the resting fluorescence pattern (F_R) before stimulation. The periodicity of this signal was equal to the resting sarcomere length and was time invariant, being strongest at the m-line and weakest at the z-line.

Similar resting fluorescence patterns in frog skeletal muscle have been noted previously (Tsugorka et al. 1995; Klein et al. 1996; Hollingworth et al. 1997) and the simplest explanation for this pattern is that there are different levels of dye binding to internal components of the sarcomere. Figure 2D shows the fluorescence pattern observed in the first scan line after stimulation. At 2 ms (corresponding to ∼23 μm) the fluorescence starts to rise at the z-line and reverses the resting pattern. At 3 ms (∼35 μm) the fluorescence at the m-line starts to increase. Therefore there is a delay of about 1 ms between the onset of the z- and m-line signals. The difference between the z- and m-line signals is maximal at ∼4 ms (∼46 μm) and then declines until the periodic signal is lost (at about 80 μm or 7 ms). These data therefore indicate that there is a measurable delay (ca 1 ms) between the rise of fluorescence at the z- and m-lines.

The measurements shown in Fig. 2 could be reproducibly repeated and the normalized fluorescence change (ΔF/F, see Methods) averaged from five measurements made in the same region of the fibre is shown in Fig. 3A. The reproducibility of the active signal indicated that any possible photo-damage was not significant. The normalization corrects for the resting sarcomere pattern of fluorescence and results in an increase in the differences between the z- and m-line signals. Figure 3B plots the time courses of the successive z-line and m-line signals from the fibre of Fig. 3A (○) as well as three other fibres. It is clear that the delay between z- and m-line signals was observed in all fibres and that the rate of rise of the m-line signal is less than that of the z-line (see Table 2). While Escobar et al. (1994) found that z- and m-line signals had an identical time of onset, the data in Fig. 3 shows that the early time courses of the two signals are quite different. Not only is there a delay in the onset of the m-line signal but in addition, Δt_0.5 (the difference in half-rise time of the z- and m-line signals) is significantly larger (2.8 ± 0.3 ms) than that reported by Escobar et al. (1994) (1.84 ms for Rhod-2 and 2.1 ms for the lower affinity Calcium Green-5N; 15°C). Furthermore, at the times when the z-line signal is 0.5 or 0.75 of its maximum, the m-line signals reported here are 5.4 ± 2.3 and 9.4 ± 3.3 %, respectively, of the z-line signal. The corresponding percentages estimated from Fig. 2 of Escobar et al. (1994), would be 40-50 % and 40-60 %, respectively, at the times when the z-line signal is 0.5 and 0.75 of maximum. Thus in Fig. 3B, the initial slope of the m-line signal compared with the z-line signal is about one-eighth of that reported by Escobar et al. (1994). Qualitatively, our results appear to be consistent with the interpretation that most SR Ca²⁺ release sites are located at or near the z-line.

Table 2.

Comparison of z- and m-line fluorescence measurements at 22°C

Fibre	Sarcomere length (μm)	Spatially averaged peak (ΔF/F)	Δt0·5 (ms)	m/z at t0·5z (%)	m/z at t0·75z (%)
1	3·2	6·5	3·1	1·3	3·9
2	3·5	6·5	2·1	11·5	18·8
3	4·0	4·0	2·6	6·8	8·8
4	3·6	9·0	3·5	2·2	5·9
Mean	3·6	6·5	2·8	5·4	9·4
s.e.m.	0·2	1·0	0·3	2·3	3·3

Δt_0·5 is the difference between the times of half-rise of the z- and m-line signals. m/z is the amplitude of the m-line signal as a percentage of the z-line signal. This was measured at the half-rise time of z (t_0·5z) and at the 0·75-rise time of z (t_0·75z). The peak values of the z-line, m-line, and spatially averaged ΔF/F signals were estimated either from their values on the pixel row on which the active signal first occurred or from the subsequent row. The peak values of the spatially averaged ΔF/F are similar to those reported by Harkins et al. (1993); 5·5 (0·5, s.e.m.; N = 7). Fibres 1 and 3: two-photon; 2 and 4: one-photon (confocal).

Nevertheless, the onset of the m-line signal is faster than previously estimated for diffusion of Ca²⁺ over the distance of the half-sarcomere (∼2 ms, 20°C; Cannell & Allen, 1984). A complicating factor in interpretation of such data is the blurring of the z- and m-line signals by the microscope which is exacerbated by the possibility of misregistration of sarcomeres in adjacent myofibrils (whose diameter is comparable to the resolution of the microscope). An x-y image of resting fluo-3 fluorescence excited by two-photon illumination is shown in Fig. 3C. A series of such images separated by z-increments of 0.35 μm were taken at various positions above and below the plane of the measurement used in Fig. 2. It is notable that the banding pattern is tilted by varying degrees in the x-y plane (Fig. 3C). A slight misregistration of sarcomeres also occurs along the optical axis (Fig. 3D) where the image series indicates a small but significant shift in sarcomere registration of 0.2 μm longitudinally per micrometre in z (but with no large dislocations at the site of active recording). These data indicate that to correctly interpret our experimental data both microscope blurring and sarcomere misregistration must be accounted for.

Comparison with model data

Figure 4A shows computer model simulations of experimental data (obtained from a fibre stretched to sarcomere length of 3.2 μm) using simplified dye binding parameters (Model 1). The dashed lines show z- and m-line signals which would be expected if microscope blurring did not take place and it is clear that, compared with the data, the simulated z-line signal rises too rapidly and the m-line signal too slowly. When blurring and the sarcomere misregistration are included (continuous lines), the agreement with the early part of the experimental signals is improved, but at later times systematic deviations develop with the m-line signal being too small and the z-line signal too large. It was not possible to remove these systematic differences in the model calculation by simple adjustment of model parameters (not shown). The possibility was then considered that the treatment of the dye in Model 1, which assumes ‘effective’ properties for a homogeneous pool of fluo-3, is too simplistic and that a dynamic exchange between protein-bound and protein-free dye must be taken into account. Such a view is supported by measurements of dye behaviour in protein-containing solutions, which show that the Ca²⁺-bound form of the dye binds less strongly to protein than does the Ca²⁺-free form (Harkins et al. 1993) and therefore suggest that Ca²⁺-bound dye will diffuse more rapidly than Ca²⁺-free dye.

We therefore repeated the calculation of Fig. 4A using Model 2, which distinguishes between protein-bound and protein-free fluo-3 (see Methods and Table 1). With the revised model, the discrepancy between model and experimental data was reduced significantly (Fig. 4B). However, to reproduce accurately both z- and m-line signals as well as at all other points along the sarcomere microscope blurring and sarcomere registration still had to be included (continuous lines in Fig. 4B). Figure 4C illustrates the full data set (points) and the model calculation (surface) and at the centre of this figure the good superimposition of these data sets shows the remarkable accuracy of the simulated results. From this simulation we can extract the unblurred or ideal fluo-3 signal (Fig. 4D) and the underlying [Ca²⁺] levels along the sarcomere (Fig. 4E and F) as functions of time. It follows that we can quantitatively account for the spatially resolved time course of the fluo-3 signals within the fibre without having to invoke a broad band of Ca²⁺ release along the SR as proposed by Escobar et al. (1994).

DISCUSSION

This paper describes high resolution measurements of Ca-fluo-3 fluorescence within the sarcomere of frog skeletal muscle during action potential stimulation. The results are consistent with the existence of underlying gradients in free [Ca²⁺] that are large and brief, which were predicted by computer modelling over a decade ago (Cannell & Allen, 1984). The calculations presented here, which are based on the more recent models of Baylor & Hollingworth (1998) and Hollingworth et al. (1999), satisfactorily reproduce the time course of the measured Ca-fluo-3 signal. Escobar et al. (1994) reported that the onset of Ca²⁺-dependent fluorescence signals measured at the m-line was not delayed with respect to those at the z-line and suggested that a broad band of sarcoplasmic reticulum may participate in the release process. In contrast, our measurements detected a clear delay between the increase in fluorescence at the m- and z-lines (Fig. 3B and Table 2). Furthermore, since our model calculations assume that Ca²⁺ is released only at the z-line, the reasonable agreement reported here between the model predictions and the z-and m-line fluorescence signals (Fig. 4B) does not support the proposal of a broad band of calcium release. The reason why the gradients in fluorescence recorded here are steeper than those reported by Escobar et al. (1994), who used cut segments of frog fibres stretched to comparable sarcomere lengths, is unclear. Better confocality may have been achieved in the current experiments and/or misregistration of sarcomeres may have been greater in the experiments of Escobar et al. (1994).

Intra-sarcomeric gradients

It is expected that the level of activation of Ca²⁺-sensitive processes will depend critically on their subcellular location and on the spatial distribution of Ca²⁺ during activation. Our data show that during E-C coupling large Ca²⁺ gradients rapidly develop within the sarcomere and Ca²⁺ released at the z-line reaches the m-line with some delay. These gradients are shaped by a mix of mobile and immobile Ca²⁺ buffers. As recently suggested by Baylor & Hollingworth (1998), ATP appears to be a major determinant of mobile Ca²⁺ buffering in muscle cells and contributes significantly to the spread of Ca²⁺ throughout the sarcomere. In the present simulations, inclusion of ATP Ca²⁺ binding and diffusion was required to achieve the best possible agreement with the experimental data (not shown). Although the [ATP] is normally highly buffered within the cell, under some circumstances, such as fatigue, ATP levels may decline. If the ATP level is reduced, the Ca²⁺ buffering power of the cell will also decline and this would lead to an increase in the amplitude of the Ca²⁺ transient if SR release were unchanged (Baylor & Hollingworth, 1998). However, the amplitude of the Ca²⁺ transient does not appear to rise markedly during fatigue and even falls in late fatigue (Allen et al. 1989; Westerblad & Allen, 1991) which implies that the reduction in Ca²⁺ buffering due to ATP depletion is offset by a reduction in SR Ca²⁺ content or release. Note that most previous estimates of the extent of SR depletion in fatigue will have underestimated the change since they did not account for the reduction in Ca²⁺ buffering. In either case, the loss of mobile Ca²⁺ buffering power should lead to more extreme intra-sarcomeric Ca²⁺ gradients during twitches. This could lead to a change in the level of activity of Ca²⁺-dependent processes such as troponin activation, Ca²⁺ feedback on Ca²⁺ release, and ATP production. In connection with this point, the original calculations of Cannell & Allen (1984), which used a smaller and broader release function and did not include ATP, suggested that large gradients of Ca²⁺ bound to troponin might develop during twitches. It therefore seems possible that, in fatigue, gradients in thin filament activation might contribute to the decline in force production. With the methods presented here, it should be possible to directly test such hypotheses about changes in Ca²⁺ gradients in the future.

Models of fluo-3 behaviour in myoplasm

Two models of fluo-3 in the myoplasm were used to explain the observed fluorescence signals. In Model 1, fluo-3 was considered to be a single population of indicator with a diffusion coefficient given by that measured for fluo-3 in resting fibres. In the more complex scheme of Model 2, Ca-fluo-3 is less tightly bound to myoplasmic proteins than Ca-free fluo-3 and, in consequence, Ca-fluo-3 can diffuse more rapidly than Ca-free fluo-3. Close to the z-line, most of the fluo-3 binds Ca²⁺ following an action potential and the effective diffusion coefficient in Model 2 is transiently increased at the z-line about 2.5-fold above that used in Model 1. The gradients of Ca-fluo-3 predicted with Model 2 are consequently smaller and dissipate more rapidly than those predicted by Model 1 (Fig. 4). Since the gradients calculated with Model 1 are generally steeper than those measured, the use of Model 2 helps remove the differences between the calculated and measured signals (Fig. 4A and B).

Model 2 was based on the in vitro calibrations of Harkins et al. (1993) in which aldolase was used to mimic the myoplasmic environment. A more complex model is undoubtedly required for a complete description of the myoplasm, where fluo-3 probably binds to several different proteins with differing affinities. For instance, the resting banding pattern of fluo-3 in the myoplasm (Fig. 3C) suggests that fluo-3 binds to structural as well as soluble proteins. However, in vitro calibrations generally show a reduced affinity of indicator for Ca²⁺ in the presence of protein (e.g. Zhao et al. 1996) with the likely corollary that indicators have a reduced affinity for protein and, therefore, faster apparent diffusion in the presence of Ca²⁺. For these effects to influence the response to an action potential, the redistribution between protein-bound and protein-free indicator has to occur rapidly. The rates governing this redistribution have not been measured and those used were obtained from modelling the amplitude and time course of the spatially averaged Ca²⁺ and Ca-fluo-3 signals (not shown). Interestingly however, a small spatially averaged fluorescence polarization signal can be measured from fluo-3 in response to an action potential (Hollingworth & Baylor, unpublished observations). This signal relaxes with a rapid (in the order of milliseconds) time course and suggests that some population of fluo-3 molecules might redistribute rapidly, as hypothesized above. Calculations with Model 2 (not shown) suggest that the applicability of our model to the myoplasm might be tested by looking for the changes in the fluo-3 distribution along the sarcomere after stimulation. Unfortunately, these 10-20 % changes would be difficult to measure with fluo-3 because the indicator has no isosbestic wavelength for fluorescence and because Ca-fluo-3 fluoresces much more strongly than Ca-free fluo-3.

Conclusions

Using the Ca²⁺ indicator fluo-3 and confocal and two-photon microscopy, we have been able to resolve steep intra-sarcomeric gradients of Ca²⁺-related fluorescence during activation of frog skeletal muscle. The fluorescence signal is well explained by a computer model of Ca²⁺ movements that takes into account indicator behaviour and inherent limitations in the Ca²⁺ imaging process. We have shown that the peak Ca²⁺ level within 0.1 μm of the z-line probably rises to almost 0.1 mM in 2 ms whereas the rise in [Ca²⁺] at the m-line is nearly 2 orders of magnitude smaller and occurs with a significant delay. The observed rate of transport requires the presence of a rapidly diffusible Ca²⁺ buffer which can be explained by the presence of ATP. In the future, extension of our results and methods should enable examination of how non-linear signal transduction processes are affected by these calcium gradients. Finally, this paper reinforces the general idea that we can no longer consider the cytoplasm as a well stirred volume but must incorporate the spatial distribution of intracellular messengers and cellular processes to achieve a clearer understanding of cellular signal transduction.