Length-dependent Ca²⁺ activation in skeletal muscle fibers from mammalians

Abstract

We tested the hypotheses that 1) a decrease in activation of skeletal muscles at short sarcomere lengths (SLs) is caused by an inhibition of Ca²⁺ release from the sarcoplasmic reticulum (SR), and 2) the decrease in Ca²⁺ would be caused by an inhibition of action potential conduction from the periphery to the core of the fibers. Intact, single fibers dissected from the flexor digitorum brevis from mice were activated at different SLs, and intracellular Ca²⁺ was imaged with confocal microscopy. Force decreased at SLs shorter than 2.1 μm, while Ca²⁺ concentration decreased at SLs below 1.9 μm. The concentration of Ca²⁺ at short SL was lower at the core than at the peripheries of the fiber. When the external concentration of Na⁺ was decreased in the experimental media, impairing action potential conduction, Ca²⁺ gradients were observed in all SLs. When caffeine was used in the experimental media, the gradients of Ca²⁺ were abolished. We concluded that there is an inhibition of Ca²⁺ release from the sarcoplasmic reticulum (SR) at short SLs, which results from a decreased conduction of action potential from the periphery to the core of the fibers.

the force-sarcomere length (SL) relation, a prominent feature of skeletal muscles, is commonly described by three regions: a plateau, in which the degree of overlap between myosin and actin filaments is optimal, an ascending limb at lengths shorter than the plateau, and a descending limb at lengths longer than the plateau (11, 20). While the descending limb of the force-SL relation is readily explained by a decrease in filament overlap, the mechanisms behind the ascending limb have generated debate in the literature. Experiments with intact fibers isolated from frog muscles showed that the intracellular concentration of Ca²⁺ ([Ca²⁺]_i) was lowered during activation at short lengths (26, 37), and studies with permeabilized fibers maximally activated with Ca²⁺ showed forces that are significantly higher than those predicted by the degree of filament overlap (33, 35).

Studies revealing a wavy appearance in the core of the muscle fibers suggest that a deactivation at short lengths results from a failure in the spread of the action potential from the periphery to the core of the fibers (19, 32). The failure could occur if the electrochemical gradient for Na⁺ is reduced, either by a decrease in external Na⁺ ([Na⁺]_e), similar to what occurs during intense muscle stimulation (6, 9), or by an increase in internal Na⁺ ([Na⁺]_i) (28). In both cases, a failure of action potential conduction along the T-tubule would reduce the amount of [Ca²⁺]_i release in the center of the fibers. Furthermore, even a slight depolarization and a reduction in the amplitude of the action potential would result in fewer number of sarcolemma dihydropyridine receptor (DHPR) units undergoing a conformational change that results in opening of the ryanodine receptor (RyR) channels in the sarcoplasmic reticulum.

Subsequent studies with intact frog fibers activated with Ca²⁺ potentiating agents (23) and skinned fibers activated with high Ca²⁺ concentration (1, 27) failed to show a length dependence of activation at short SLs. The authors of these studies related the decrease in force uniquely to a constraint in filament geometry: an increased overlap of thin filaments from opposite ends and a compression of the thick filaments against the sarcomere Z-lines. Furthermore, Balnave and Allen (5) used intact fibers isolated from the mouse and also did not observe a difference between [Ca²⁺]_i in contractions produced at the plateau of the force-fiber length relation and at a length 10% shorter than the plateau. The study of Balnave and Allen (5) was the first to use intact fibers dissected from mice, adding important information regarding the length dependence of Ca²⁺ activation in mammalian muscles. However, it is difficult to compare their study with others that used amphibian muscle fibers or permeabilized muscle fibers. The authors used force measurements to estimate the plateau in the force-SL relation (and relative changes in lengths below and above the plateau). Such method of estimating the force-SL relation may lead to large discrepancies when compared with studies that measure the SLs, as the plateau of the force-SL relation may extend to SLs as long as 3.0–3.2 μm during fixed-end contractions (21, 38). Balnave and Allen (5) have not investigated the possibility of a decrease in [Ca²⁺]_i at SLs shorter than 10–15% below the plateau of the force-SL relation where force decreases significantly. Finally, they have not investigated the possibility of a reduction in [Ca²⁺]_i release in the center of the fibers as a potential mechanism for the length dependence of activation.

The mechanism behind the length dependence of muscle activation of skeletal muscles along the ascending limb of the force-SL relation remains elusive. In the present study, we used single fibers isolated from mammalian muscles activated at a variety of SLs, and measured [Ca²⁺]_i during contractions using confocal microscopy. Such a technique allows for the evaluation of the spatial distribution of [Ca²⁺]_i within well-defined regions of the fibers, while avoiding confounding effects arising from out-of-focus light. We observed that [Ca²⁺]_i was significantly lower at shorter lengths (≤15% below the plateau), and that [Ca²⁺]_i decrease was more prominent at the core of the fibers than at the periphery of the fibers. The results suggest that muscles are only partially activated at short SLs, a phenomenon potentially caused by a failure of the action potential spread inside the muscle fibers.

MATERIALS AND METHODS

Preparation of muscle fibers.

Single fibers (n = 16) were dissected from the flexor digitorum brevis (FDB) muscle from mice using fine forceps and scissors, and the tendons were gripped with two T-shaped, aluminum foil clips that were hooked between a force transducer and a motor arm. The fibers were loaded with the membrane permeant acetoxymethyl esters (AM) of fluo-3 (Molecular Probes) for measurements of [Ca²⁺]_i. Fluo-3 was dissolved in dimethyl sulfoxide and prepared in 1 mM stock solutions. The fibers were incubated in 0.5 ml of the dissection solution containing 5 μM of Fluo-3 for 20–30 min at room temperature and were transferred to a chamber perfused with an experimental solution (137 mM NaCl, 5 mM KCl, 1 mM MgCl_2, 1 mM NaH₂PO_4, 16 mM NaHCO₃, 11 mM glucose, 2 mM CaCl₂) and a mixture of 95% O₂ and 5% CO₂ (pH 7.4; temperature: 21–23°C) for 30–40 min to allow for the hydrolysis of Fluo-3. Two additional sets of experiments were performed, in which we either used caffeine (5 mM) or decreased the concentration of [Na⁺]_e by replacing half the Na⁺ in the solution by N-methylglucamine (40). In this case, the fibers were first activated with regular solution, and after solution exchange, a rest period of 20 min was allowed before stimulation.

Measurement of sarcomere length.

When the fibers were ready for mechanical experimentation, their length and diameter were measured (fiber diameter: 40–50 μm in the current experiments). The average SL was measured using images collected through a CCD camera (Imperx; pixel size: 7.4 × 7.4 μm) with a 40× dry objective lens. The striation spacing produced by myosin and actin bands creates contrasting light peaks, and the distance between the peaks was calculated using Fast Fourier Transform (FFT) using an automated software (Aurora Scientific, Canada); a quadratic curve was fitted to the spectrum around the peaks to provide the average SL. This system allows the calculation of striation spacing and SL even when only small sections of the fibers are clear. It is recognized that measuring the SL during activation of mammalian fibers is not always possible, as the striation pattern becomes unclear due to remaining pieces of fibers that were cut during dissection, and due to lateral movements of the fibers (5, 13). Therefore, the force-SL relation in our study was derived using the SL measured before activation in each contraction. When we were able to measure the SL during contractions we observed an amount of shortening of 6.5 ± 0.2% of initial length, in the same range as that reported previously (∼4%) for a similar preparation (13). This amount of shortening should not affect our results significantly. While the inability of measuring SLs during contractions represents a limitation in this study, imaging only the fluorescence signals during fiber activation optimizes measurements of [Ca²⁺]_i during the experiments.

Confocal imaging of [Ca^2±]_i.

The experimental chamber was placed on the stage of an inverted, confocal microscope (Nikon Eclipse TE2000-U, C1 confocal head, Japan). The fiber was positioned ∼100–150 μm above a glass cover slip (thickness: 150 μm) that formed the base of the chamber. During the experiments, the fiber was studied with a dry objective lens (×60 magnification; NA 0.7), using a 488-nm illumination laser at 25–35% of maximum power. The fluorescence signals were recorded at wavelengths of 510–560 nm. We avoided signals arising from damaged/dead fibers, and tried to use the same region in all images during any given experiment.

At the beginning of the experiments, before activation, and during tetanic contractions performed at different SLs, line scan images (X-axis: 20–60 μm) were collected transversally, at the midsection of the fiber in xt mode, i.e., repeated scanning of the same line over time. The scans taken before the contractions were used for measuring fluorescence at rest (F_r), which was used to normalize fluorescence signals during the experiments. Although this self-ratio method introduced in experiments evaluating excitation-contraction coupling in cardiac myocytes (10) does allow a precise calibration across the fiber diameter, it allows for comparisons between experiments and conditions. Fibers often moved a small distance laterally and/or vertically during contractions, and a few times the signals were lost; in this case, the experiments were discarded from analysis.

It is reportedly difficult to calibrate fluo-3 signals for obtaining absolute values of [Ca²⁺]_i, a common limitation encountered by investigators who use nonratiometric dyes for the measurement of spatial, cross-sectional images (39, 40). We therefore present all fluorescence data as the ratio between the fluorescence signals obtained in a given condition and the resting fluorescence signal (F/F_r) collected during the same experiment. Fluo-3 signals were analyzed with image software (NIKON NIS Elements).

We have not calculated experimentally the point-spread function of the microscope under the experimental conditions that we used. The point-spread function should not interfere with our results, as it is invariably observed within a few nanometers of distance (depending on the experimental condition) during sample imaging, and we focused in changes that happens on the micrometer (μm) scale.

Protocol.

Stimulation (Grass S88, Grass Instruments) was given through two platinum wire electrodes placed inside the experimental chamber 4 mm apart on each side of the fiber. Square wave pulses (0.4 ms duration) were delivered at amplitude of 25% above the voltage that provided maximal force production. The frequency of stimulation to provide a tetanic contraction (in this case between 55 and 75 Hz) was set individually for each fiber using contractions of 1-s duration. After the optimal voltage and frequency of stimulation were defined, the fibers were paced for 60 min with twitch contractions (90 s intervals) elicited at SLs between 2.2 and 2.3 μm. For the main set of experiments, contractions of 3–4 s were produced at SLs varying between 1.4 and 2.8 μm in random fashion. If there were small effects of bleaching on the fluorescence signals collected during the experiments, they would not affect the main results of this study, as the variation would be taken into account in our statistical analysis. A period of 3 min was always allowed between contractions to avoid fatigue during the experiments.

During all experiments, the fibers were inspected visually for potential damage. The fibers were also constantly activated at SLs between 2.2 and 2.4 μm to evaluate if the force did not decrease over the course of the experiments. If the force decreased >3% from the beginning of the experiment, the data would be discarded from further analysis.

Data analysis.

[Ca²⁺]_i concentrations were analyzed during contractions for 1) the total amount of [Ca²⁺]_i, and 2) the spatial distribution of [Ca²⁺]_i in cross-sectional areas of the fibers. The total [Ca²⁺]_i concentration was measured by taking all the images in xt mode and averaging over time. The spatial distribution of [Ca²⁺]_i, of special interest for this study, was analyzed for gradient concentrations, according to an established procedure (12). For data analysis over the whole contraction, fluorescent signals were determined in rectangular regions (15 μm, 100 μm) at both edges (E1 and E2) and in the central region (C) of each fiber image. Thus the inner box measures [Ca²⁺]_i in the central one-third section of the fiber, while the two outer boxes measure [Ca²⁺]_i in the outer two-thirds of the fiber. The signals in E1 and E2 were averaged (E) for comparisons with the signals from C. For statistical purposes, the signal values for E and C were binned into discrete SLs and compared in each length using analysis of variance (ANOVA) for repeated measures. A significance value of P < 0.05 was used for the comparisons.

RESULTS

Figure 1A shows typical contractions produced by an activated fiber at three different SLs. Forces decreased when the fiber was activated at SLs corresponding to the ascending and descending limbs of the force-SL relation; in this example the forces produced at 1.88 and 3.0 μm were 81.0% and 62.8% of the force produced at 2.34 μm, comparable to previous observations (13). When fibers were activated at SLs between 2.1 and 2.4 μm, which corresponds to the plateau of the force-SL relation for mammalian muscles (13, 16, 29), they produced a stress of 330 ± 32 mN/mm². While the value is slightly different from another study that used intact fiber from the mouse reporting 312 ± 20 kN/m² in SLs between 2.28 and 2.52 μm (11), which corresponds to the plateau of the force-SL relation, it is within the range observed with single fibers from the FBD (5, 13). When fibers were stimulated in the same SL range before treatment with Fluo-3, they produced similar levels of force (349 ± 69 mN/mm²), suggesting that Fluo-3 does not change the contractile properties of the fibers that we investigated.

Fig. 1.

A: contractions produced by an activated fiber at sarcomere lengths of 1.88 μm (red), 2.34 μm (black), and 3.0 μm (green). Force decreases at lengths below and above the optimal length for force production. B: spatially averaged time course of changes in fluorescence signals (ΔF/F_r) of [Ca²⁺]_i corresponding to the contractions shown in A. The stimulations frequency in this experiment was set at 68 Hz.

The SLs corresponding to the plateau of the force-SL relation in the study by Balnave and Allen (5) ranged between 2.6 and 3.1 μm (mean: 2.85 μm), which is longer than the plateau observed in our study. Their values are also larger than those reported in other studies performed with intact fibers (11, 40) and isolated sarcomeres (20) from mammalians. While the reason for such difference is unknown, our results and others (11, 16, 40) are on line with theoretical predictions based on the force-SL relation originally derived by Gordon et al. (20). In mammalians, the myosin and actin filament lengths are ∼1.63 and ∼1.12 μm, respectively (34). The widths of the Z-line and the bare zone in the middle of myosin are ∼0.10 and ∼0.15 μm, respectively (22). Therefore, the plateau of the force-SL relation should span from 2.24 to 2.39 μm. The ascending limb should cover SLs below 2.24 μm, and the descending limb should cover SLs between 2.39 and 3.87 μm.

Figure 1B shows the spatially averaged time course of fluorescence signals of [Ca²⁺]_i corresponding to the contractions shown in Fig. 1A. The [Ca²⁺]_i signal increased rapidly during the contraction, and decreased quickly after activation was finished. Although the absolute level of [Ca²⁺]_i was not measured, the fluorescence signal increased by ∼6–8 times during the tetanic contraction. Note that the [Ca²⁺]_i trace is lower at the short SL, following the same pattern as that observed with force.

Length dependence of Ca²⁺ gradients.

Figure 2 shows xt plots of [Ca²⁺]_i fluorescence signals collected at rest (Fig. 2A), and during the activation of a fiber contracting at SLs of 3.00 μm (Fig. 2B) and 2.34 μm (Fig. 2C) in a regular, experimental solution. At rest, there was a small increase in the fluorescence signals collected over time. There was not a visible gradient in the Ca²⁺ concentration across the fiber. When the contractions were produced at SLs of 2.34 or 3.00 μm, [Ca²⁺]_i was increased upon activation and homogeneously distributed across the fibers. The numerical values representing the fluorescence intensity of [Ca²⁺]_i signal during the contractions shown in the right panels were taken from a cross-sectional section (represented by the X-axis) between 0–15 and 35–50, representing the edges of the fiber, and values between 15 and 35 μm, representing the center of the fibers.

Fig. 2.

Images taken during contractions in an experiment conducted with a single muscle fiber using confocal microscopy. The images were taken at SLs of 3.00 μm (A and B) and 2.34 μm (C), and represent three-dimensional plots using values for time (Y-axis), distance across the fiber (X-axis), and pixel intensity (Z-axis), which corresponds to [Ca²⁺]_i. The pixel intensity was transformed in color images for better visualization; a simplified scheme for the coloring scale is shown in the small bars on the top-right of each panel. At rest (A) and during activation (B and C), [Ca²⁺]_i was homogeneously distributed. The right panels show quantitative measurements of [Ca²⁺]_i distribution across the fiber during the same contractions as in the left panels, collected at the beginning (black), half the way through the contraction (red), and at the end of the contraction, just before relaxation (green). The values were averaged over 1 s in each of the measured periods during the contraction. The y-axis is shown as changes in fluorescence signal (ΔF/F_r), and the x-axis shows the distance across the fiber. In this case, values close to 0 and 50 μm are at the peripheries, and values between 15 and 35 μm are at the central core of the fibers. The stimulation frequency in this experiment was set at 68 Hz.

Figure 3 shows xt plots of [Ca²⁺]_i fluorescence signals collected at rest at a SL of 1.88 μm (Fig. 3A), and during the activation of the fiber contracting at SLs of 1.88 μm (Fig. 3B) and 1.62 μm (Fig. 3C). At rest, there was a small increase in the fluorescence signals collected over time. There was a slight reduction in [Ca²⁺]_i resting signal in the core of the fibers, but not a visible, large gradient developed across the cell. Such result was confirmed statistically (see below in Fig. 7C), and its implications for the interpretation of results is elaborated further in discussion. When the contraction was produced at a SL of 1.88 μm, [Ca²⁺]_i was lower at the central core of the fiber, as indicated by a darker pattern of fluorescence. In most fibers, gradients of Ca²⁺ started to show at lengths below 1.9 μm, although it became more repeatable and pronounced at shorter lengths. Figure 3C shows a contraction produced at a length of 1.62 μm, in which a Ca²⁺ gradient was also pronounced. The three-dimensional plots provide a clear visualization of the gradient patterns of activation that develops over time in Fig. 3, B and C, as the pixels clearly show less intensity in the core regions of the fibers, reflecting a lower [Ca²⁺]_i. A decrease in fluorescent intensity was observed in the central regions compared with the two edges. Note that there is a lack of time dependence for the development of the gradients—the fluorescence signals are similar when three different times during the contractions are chosen for analysis. The result suggests that the gradient concentrations form almost instantaneously with activation of the fibers and do not disappear within the time scale that we worked.

Fig. 3.

Images taken at SLs of 1.88 μm (A and B) and 1.62 μm (C). At rest, there is a small increase in fluorescent signals, which is homogeneously distributed across the fiber. During activation, [Ca²⁺]_i was lower at the core of the fiber, as indicated by a darker pattern of fluorescence. The three-dimensional plots give a clear visualization of the gradient pattern of activation in B and C; the pixels show less intensity in the core regions of the fibers, reflecting a lower [Ca²⁺]_i concentration. The right panels (A–C) show quantitative measurements of the [Ca²⁺]_i distribution across the fiber collected at the beginning (black), half the way through the contraction (red), and at the end of the contraction (green). The y-axis is shown as changes in fluorescence signal (ΔF/F_r), and the x-axis shows the distance across the fiber. The stimulation frequency in this experiment was set at 68 Hz.

Fig. 7.

A: relation between the average SL, force, average [Ca²⁺]_i concentration, [Ca²⁺]_i at the peripheries, and [Ca²⁺]_i at the core of the fibers. Data were binned in discrete SLs for statistical comparisons. The [Ca²⁺]_i at the periphery was different from the [Ca²⁺]_i at the core of the fibers at SLs ≤ 1.9 μm (shown with asterisks). Statistical parameters: SL 1.51 ± 0.01 μm, n = 14, P < 0.001; SL 1.71 ± 0.02 μm, n = 11, P < 0.001; SL 1.91 ± 0.02 μm, n = 10, P = 0.042; SL 2.18 ± 0.03 μm, n = 12, P = 0.94; 2.50 ± 0.02 μm, n = 11, P = 0.97; SL 2.74 μm, n = 10, P = 0.95. B: relation between average SL, average [Ca²⁺]_i concentration, [Ca²⁺]_i at the peripheries, and [Ca²⁺]_i at the core of the fibers. All parameters we measured at rest, before activation. The [Ca²⁺]_i concentration at the periphery was not different from the [Ca²⁺]_i at the core of the fibers, in all SLs investigated

To evaluate if the Ca²⁺ decrease observed at short SL was caused by a decreased Ca²⁺ release from the sarcoplasmic reticulum during activation, we used caffeine, a drug known to increase Ca²⁺ release from the sarcoplasmic reticulum. Figure 4A shows xt plots of [Ca²⁺]_i fluorescence signals during activation of a fiber treated with 5 mM caffeine while contracting at a SL of 1.92 μm. This fiber presented [Ca²⁺]_i gradients in SLs below 1.95 μm. After caffeine administration, [Ca²⁺]_i was homogeneously distributed even at the short SL. The contraction resembles one produced at a longer SL, and the fluorescence signal at the center of the fiber is relatively similar to that observed at the edges, and [Ca²⁺]_i gradients were abolished. Figure 4B shows a contraction produced by the same fiber after caffeine treatment activated at 1.58 μm. Even when activated at this very short SL, gradients of [Ca²⁺]_i were not observed.

Fig. 4.

Images depicting experiments conducted at SLs of 1.92 μm (A) and 1.58 μm (B) in the presence of 5 mM caffeine. During contractions, [Ca²⁺]_i was homogeneously distributed across the fiber in both cases. The right panels show quantitative measurements of [Ca²⁺]_i distribution across the fiber collected at the beginning (black), half the way through the contraction (red), and at the end of the contraction (green). The y-axis is shown as changes in fluorescence fluorescence signal (ΔF/F_r), and the x-axis shows the distance across the fiber. The stimulation frequency in this experiment was set at 68 Hz.

To investigate if the decrease in [Ca²⁺]_i, and more importantly the gradient concentrations of [Ca²⁺]_i, may be caused by a failure in the spread of action potential, fibers were activated with a decreased concentration of [Na⁺]_e in the experimental media. Decreasing the concentration of [Na⁺]_e inhibits the conduction of action potential from the periphery to the inner myofibrils. Figure 5, A and B, shows contractions produced at SLs of 2.41 and 1.85 μm, after lowering the concentration of [Na⁺]_e. The concentration of [Ca²⁺]_i was lower at the central core of the fiber than at the edges in both lengths, as indicated by a darker pattern of fluorescence. Of special interest is the contraction produced at 2.41 μm, in which gradients are observed similarly to that observed in fibers activated in regular solutions but at shorter SLs. The three-dimensional plots (right panels) provide a clear visualization of the gradient patterns of activation in B and C; the pixels show less intensity in the core regions of the fibers, reflecting a lower Ca²⁺ contraction.

Fig. 5.

Images depicting experiments conducted at SLs of 2.41 μm (A) and 1.85 μm (B) when the [Na⁺]_e concentration was reduced by replacing half the Na⁺ by N-methylglucamine. In both cases, [Ca²⁺]_i is lower at the core of the fiber than at the peripheries, as indicated by a darker pattern of fluorescence. The two-dimensional plots provide visualization of the gradient patterns of activation, showing quantitative measurements of [Ca²⁺]_i distribution across the fiber collected at the beginning (black), half the way through the contraction (red), and at the end of the contraction (green). The y-axis is shown as changes in fluorescence signal (ΔF/F_r) and the x-axis shows the distance across the fiber. The stimulations frequency in this experiment was set at 71 Hz.

The relation between SL, force and [Ca²⁺]_i.

Figure 6A shows the relation between force, [Ca²⁺]_i and SL measured in our experiments. The shape of the force-SL length relation resembles that obtained previously in studies that measured the fiber length (5), average SL (13), or individual SL (30) in mammalian muscles. It also resembles the classic force-SL relation obtained in studies performed with fibers dissected from amphibian muscles (e.g., 14, 20). Novel is the relation between SL and [Ca²⁺]_i concentration. We used values averaged over 3 s of full force development during the contractions. The average [Ca²⁺]_i is similar in SLs between 1.9 and 2.9 μm, representing a large area of the force-SL relation. The [Ca²⁺]_i concentration decreases significantly at SLs below 1.8 μm, which represents a length ∼15% below the plateau of the force-SL relation.

Fig. 6.

A: relation between the average SL measured before activation, force (black circles), and [Ca²⁺]_i concentrations (empty squares). Since the fibers shortened slightly during contractions (∼6%), the SL during full activation may have been slightly shorter than the SL depicted in the graph. Force was normalized using the maximum force produced in each contraction, and [Ca²⁺]_i was averaged over 2–3 s of full force development during the contractions. B: similar relation between average SL and [Ca²⁺]_i concentrations, showing the average values (empty squares), the values collected at the peripheries (red) and at the core of the fibers (green).

Figure 6B shows the relation between SL and [Ca²⁺]_i values extracted at the peripheries of the fibers during the contractions [(E1+E2)/2] and in the central section of the fiber (C). The total average concentration of [Ca²⁺]_i is also shown (data similar to Fig. 6A) for comparisons. In SLs in which the total concentration of [Ca²⁺]_i starts to decrease, the difference between the [Ca²⁺]_i values at the peripheries and at the core of the fibers increases. There is a significant decrease in [Ca²⁺]_i at the peripheries of the fibers at short SLs.

In Fig. 7A we binned the data shown in Fig. 6 into discrete SLs between 1.5 and 2.7 μm. After comparing the data using ANOVA for repeated measures, we observed that [Ca²⁺]_i concentrations in the periphery of the fibers were significantly different from the core region of the fiber at SLs ≤ 1.9 μm. We performed a similar analysis for the fluorescence signals collected at rest in these fibers. The results are shown in Fig. 7B, and depict no statistical differences for [Ca²⁺]_i between the different regions of the fibers. [Ca²⁺]_i gradients were not present before the fibers were activated in any of the SLs investigated.

The results shown in experiments using caffeine (Fig. 4) were confirmed statistically when we compared experiments performed at short SLs (Table 1). The [Ca²⁺]_i concentration at the edges and central core of the fibers was not different in any of the SLs used in this study when experiments were conducted in the presence of caffeine.

Table 1.

Force, total [Ca²⁺]_i, [Ca²⁺]_i at the edges (E) of the fiber, and [Ca²⁺]_i at the core (C) of the fiber in experiments conducted in the presence of caffeine (5 mM)

SL, μm	Force	[Ca2+]i Total	[Ca2+]i E	[Ca2+]i C
1.57 ± 0.21	85.21 ± 5.89	82.94 ± 3.24	83.34 ± 1.77	80.94 ± 2.57
1.66 ± 0.19	88.90 ± 4.14	93.90 ± 0.89	91.91 ± 0.93	90.05 ± 3.17
1.92 ± 0.09	98.23 ± 6.10	97.40 ± 1/06	95.25 ± 1.06	93.23 ± 5.83

Values are means ± SE. All values are normalized per the maximum value obtained in sarcomere lengths (SLs) ranging between 2.1 and 2.4 μm. There was not a statistical difference between [Ca²⁺]_i, [Ca²⁺]_i E, and [Ca²⁺]_i C in all SLs investigated.

Since differences in [Ca²⁺]_i concentrations were observed in SLs ≤ 1.9 μm, we evaluated the time course for the development of [Ca²⁺]_i gradients. We measured the values extracted at the peripheries [(E1+E2)/2] and in the core section of the fibers (C) in intervals of 100 ms, the limit imposed by the time resolution in our system. Figure 8 shows the time dependence for the development of gradients, which is also length dependent. The [Ca²⁺]_i gradients started to develop after 800 ms in a SL of 1.5 μm, after 1,000 ms in a SL of 1.7 μm, and after 1,300 ms in a SL of 1.9 μm.

Fig. 8.

Time course for the development of [Ca²⁺]_i gradients in fibers during the contractions. Measurements were made in 100-ms intervals, using the same fiber areas used in the previous figures: periphery (filled symbols) and core (empty symbols) of the fibers. The [Ca²⁺]_i concentrations in the periphery of the fibers remained relatively constant throughout the contractions, but at the core of fibers they start to decrease significantly at 800, 1,000, and 1,300 ms when activation was induced in SLs of 1.5 μm (P < 0.001), 1.7 μm (P = 0.01), and 1.9 μm (P < 0.001), respectively.

The steady-state [Ca²⁺]_i during tetanus is determined by the relative magnitudes of Ca²⁺ release and uptake by the sarcoplasmic reticulum. To have an indication of the length dependence of such kinetics, we evaluated the time course of [Ca²⁺]_i during twitch contractions recorded at different sarcomere lengths. Figure 9, A and B, shows examples of [Ca²⁺]_i transients during twitch contractions recorded in SLs of 2.24 and 1.62 μm. The time measured from the start of the Ca²⁺ rise to the peak (rise time: R_t) (Fig. 9C) was similar in these lengths (average of twitches = 2.3 and 2.1 ms in these examples). The same is true for the decay times, measured from the peak signal to the halfway point during signal decay (4.1 and 4.3 ms in these examples). Mean values measured across all lengths investigated also show no difference in R_t (P = 0.89) and D_t (P = 0.67) among these lengths.

Fig. 9.

Fluorescence signals (ΔF/F_r) recorded during twitch contractions performed at SLs of 2.24 μm (A) and 1.62 μm (B). The signals have similar amplitudes. Measurements of rise time (R_t) and relaxation time (1/2R_t) as shown in C suggest that the time course for [Ca²⁺]_i release and [Ca²⁺]_i uptake by the sarcoplasmic reticulum are not dependent on SL during the twitch contractions.

DISCUSSION

The main results of this study were 1) when muscle fibers are activated at SLs ≤ 15% of the plateau of the force-SL relation, the [Ca²⁺]_i was lowered; and 2) the decrease in [Ca²⁺]_i was lower at the central core than at the peripheries of the muscle fibers. Fibers activated in the presence of caffeine did not show [Ca²⁺]_i gradients, but when fibers were activated with a low [Na⁺]_e, a gradient in [Ca²⁺]_i similar to that observed during contractions produced at short lengths was observed at all lengths. Altogether, the results suggest a length dependence of muscle activation, likely caused by an electrochemical Na⁺ gradient that induces a failure in the spread of the action potential.

The force-length relation and [Ca²⁺]_i concentrations.

The force-SL relation measured in this study was similar to that observed previously in fibers isolated from mammalian muscles. The plateau of the force-SL relation—the region where maximal force is obtained—was extended from 2.1 and 2.4 μm, and force decreased substantially below a SL of 2.0 μm, similar to results from another laboratory that used intact fibers from the mouse (16) and consistent with a recent study performed in our laboratory with individual sarcomeres isolated from mammalians (29). The plateau of the force-SL relation is moderately different from that reported by Colombini et al. (11) who reported values between 2.28 and 2.52 μm, but the general shape with three distinct regions (ascending limb, plateau, and descending limb of the force-SL relation) is similar.

The ascending limb of the force-SL relation has been the focus of research in the past but the mechanism behind the decrease in force is still unclear. Gordon et al. (20) used intact muscle fibers from the frog and observed that, at SLs below 2.0 μm, the force declined linearly to 1.7 μm, producing the shallow part of the ascending limb. At lengths below 1.7 μm, the slope of the force-SL relation increased sharply—the steep part of the ascending limb—and tension declined linearly to zero at 1.3 μm. Gordon et al. (20) originally interpreted the decrease in force at short lengths as resultant from structural constraints. The shallow part would be caused by an interference of thin filaments with cross-bridges in the opposite half of the sarcomere and thin filaments meeting in the middle of the sarcomere. The steep part would be caused by a progressive compression of the ends of the thick filaments against the Z-lines. The interpretation was strengthened by subsequent studies in which permeabilized fibers were activated at high Ca²⁺ concentration and observed a similar force-SL relation (1, 23, 27), suggesting that the ascending limb of the force-SL relation is not influenced by the degree of muscle activation.

However, other studies performed with seemingly similar methods observed different results; permeabilized fibers activated with high Ca²⁺ concentration produced forces that were significantly greater than those produced at lower activation levels (33). In fact, one study showed a total absence of an ascending limb with full activation, and force was not changed between sarcomere lengths of 1.2 and 2.5 μm (35). Consistent with these studies, experiments performed with intact frog fibers showed that the [Ca²⁺]_i was lowered during activation at short lengths (26, 37), and that potentiating agents (caffeine, Zn²⁺) that induce an increase in Ca²⁺ release from the sarcoplasmic reticulum increased the force significantly at short SLs (26, 32, 36, 37). These results were interpreted as a length-dependent failure of muscle activation. Our results support these findings and show a decrease in [Ca²⁺]_i concentration at short muscle lengths, similar to what was observed in previous studies with frog fibers (26, 37).

Comparisons between fiber preparations from different species are always complex and demand caution. In the current study, comparisons are particularly challenging, as measurements with intact fibers from mammalian muscles are not commonly performed. Another study that evaluated [Ca²⁺]_i concentrations in intact fibers from mammalians was performed by Balnave and Allen (5), a laboratory with large experience and high reproducibility in such measures. The authors did not observe a length dependence of [Ca²⁺]_i concentration, but the results do not necessarily lead to an interpretation different from ours. Balnave and Allen (5) observed an optimal length (L_o) for force production (i.e., the plateau of the force-length relation in their study) in SLs ranging from 2.6 to 3.1 μm (mean: 2.85 μm), and compared force and [Ca²⁺]_i between L_o and L_o − 100 μm, which corresponds to ∼0.4 μm change in the average SL. Therefore, comparisons would have been made between ∼2.85 and ∼2.45 μm, a length in which force decreased by ∼10%. In the current study, the plateau was observed between 2.1 and 2.4 μm, and [Ca²⁺]_i concentration only decreased at SL ≤ 1.9 μm, when force was 80% of maximum. Thus our study and that by Balnave and Allen (5) still show similar results in the range of lengths that were investigated in both studies.

Activation gradients.

The mechanism behind the decrease in muscle activation at short SLs is unclear. Studies showing a wavy appearance in the core of fibers during activation suggest it may result from a failure in the spread of the action potential from the periphery to the core of the fibers (19, 32, 36). In this case, a failure of action potential conduction along the T-tubule would lead to a reduced Ca²⁺ release in the center of the fibers. The idea of intracellular gradients of [Ca²⁺]_i has been evaluated successfully when muscle fibers are fatigued with high-frequency electrical stimulation (12, 40). In this situation a gradient of [Ca²⁺]_i, similar to what was observed in the current study, was observed and an overall decrease in [Ca²⁺]_i caused by fatigue was associated with a more prominent decrease at the center of the fibers.

Failure in the spread of action potential could occur if the electrochemical gradient for Na⁺ is reduced, either by a decrease in [Na⁺]_e, as it occurs in the T-system during intense muscle stimulation (6, 9), or by an increased [Na⁺]_i (28). Our results suggest this may be the case when muscle fibers are activated at short SLs. We observed that when [Ca²⁺]_i concentration was decreased at short SLs, the decrease was accompanied by significant gradients of [Ca²⁺]_i, such that [Ca²⁺]_i was lower at the center of the fiber than at the edges. The conclusion was strengthened by the findings that caffeine abolished the length dependence of Ca²⁺ activation, and the gradients in the fibers stimulated at short SLs. More tellingly, a decrease in the concentration of [Na⁺]_e concentration, which leads to hyperpolarization and a failure in action potential conduction, led to the same result as that observed in short SLs: a significant gradient of [Ca²⁺]_i concentration across the cross-sectional area of the fiber in all lengths investigated. Our working hypothesis is also supported by the time course for the development of [Ca²⁺]_i gradients at short SLs. A reduction in [Na⁺]_e or an increase in [Na⁺]_i should develop over time. We observed that, although [Ca²⁺]_i gradients were formed rapidly, they presented a time dependence. The gradients started to develop between 800 and 1,300 ms. More tellingly, the delay for the gradient formation was correlated with the SLs in which [Ca²⁺]_i measures were taken; the shorter the SL, the faster the development of gradients.

Although invoking hyperpolarization by lowering the Na⁺ has been used in the evaluation of muscle fatigue, and the authors also observed gradient concentrations of Ca²⁺ as a result (40), future research will be needed to fully elucidate the involvement of [Na⁺]_e in the t-tubule action potential. While small changes in resting membrane potential are unlikely to affect action potential amplitude and propagation, a large decrease in [Na⁺]_e affects propagation on the surface membrane for a train of muscle stimulation (9), and it likely affects the t-tubules propagation. Furthermore, movements of fluids between interstitial and t-tubule space may contribute to our findings. It is known that, when skeletal muscles contract, t-tubules decrease in diameter and force some of the content out in the interstitial fluid. Accordingly, in contractions produced at low SLs, the t-tubules may be squeezed and contain less fluid than at long SLs. During a prolonged isometric contraction, the depletion of Na⁺ can be even more severe and eventually affect action potential propagation.

The changes in [Ca²⁺]_i at the core of the fibers, which ultimately leads to a decrease in the total amount of [Ca²⁺]_i, must contribute to the decrease in force, but it is difficult to ascertain its precise contribution. We would need an analysis of precise fractions of the fibers that were submaximally activated, not feasible in this study. Since the overall [Ca²⁺]_i concentrations were decreased by 65% in SLs of 1.5 μm (Fig. 7A), based on force-Ca²⁺ relation reported for FDB muscle fibers (2), the force would decrease to ∼60–70% of maximal force. Most importantly, the results obtained with the experiments with caffeine strengthen the importance of [Ca²⁺]_i in the force outcome at short SLs. After caffeine administration, the force increased to values that were close to the maximal force obtained at the plateau of the force-SL relation, supporting our interpretation that a decrease in [Ca²⁺]_i concentration is a major factor causing the decrease in force at short SLs.

The mouse FDB expresses predominantly MHC-IIX and MHC-IIA (∼83–94%), with small amounts (∼3–17%) of MHC-I isoform (18, 31). Therefore, differences in MHC did not likely influence Ca²⁺ kinetics in our study, specially taking into account the following: 1) Ca²⁺ ATPase isoform SERCA 1A is predominant in fast adult fibers while SERCA 2A is predominant in slow fibers (7, 8), 2) parvalbumin is present almost exclusively in fast fibers (25, 31), 3) calsequestrin isoform CSQ1 is predominant in fast fibers, while a mixture of CSQ1 and CSQ2 is present in slow fibers, and 4) a higher density of ryanodine receptors is present in fast fibers than in slow fibers (3, 17).

An advantage of this study was the use of confocal microscopy to evaluate the gradient activation of [Ca²⁺]_i. Images obtained from thick objects such as muscle fibers might contain contributions from peripheral parts above and below the plane of focus, which reduce significantly their spatial resolution. The net effect of this distortion would be a reduction in the apparent size of gradient concentrations present within the fibers (40). Thus the likelihood of detecting [Ca²⁺]_i gradients might have been diminished if we had used regular bright field microscopy.

Limitations.

Although a statistical difference was not detected in fluorescence signals across the fibers at rest, there is still the possibility that a nonuniform [Ca²⁺]_i distribution exists before activation. The fluorescence signals from the interior of the fiber will inevitably suffer from spherical aberrations, potentially leading to dimming of the signal across the fiber diameter, depending of the degree of confocality (24). This situation is especially complex at the edges, due to the curvature of the fiber surface (24), which could have influenced our results and interpretation. If the signals collected at the edges of the fibers at rest would have been underestimated compared with the signals measured at the core of the fibers, a [Ca²⁺]_i gradient, although existing, might not be detected. Since we normalized the fluorescence signals by the line scans taken at rest, the baseline for normalizing the edge signals would be underestimated. In fact, a very small difference was seen in some fibers at rest (e.g., Fig. 3A, right panel). However, during activation such underestimation at the edge signals would likely also play a role in the gradients that we detected; in that case the difference in signals could have been even more pronounced. Most importantly, statistical analysis of the resting fluorescence signals (Fig. 7B) strongly suggests that significant Ca²⁺ gradients were not preset at rest, not accounting for the main results obtained during activation.

Most tellingly, the [Ca²⁺]_i gradients that we observed during activation presented a time course of development which is slow and length-dependent (Fig. 8), a pattern that is not consistent solely with potential artifacts caused by fiber movements during high-speed tetanic stimulation. The profiles observed during the tetanic contractions do not simply fit with a simple resting fluorescence gradient profile.

Finally, there is the possibility that the fiber diameter increased during shortening induced by contractions at different SLs. It has been shown that the fiber volume is kept constant in a large range of SLs (4, 15), and thus the fiber diameter would be larger in short SLs. In that case, the confocal plane for [Ca²⁺]_i measurements could move into different depths within the fiber, and calculations of the total [Ca²⁺]_i signals could be confounded. Although data on fiber diameter changes at the ascending limb of the force-SL relation is not readily available, we can calculate the expected changes during fiber shortening. The fibers investigated in this study were ∼1,mm (1,000 μm) long and the fiber diameter was ∼50 μm. Assuming circular circumference, the cross-sectional area of the fiber would be 1.96E+03 μm², and the fiber volume would be 1.96E+06 μm³. During contractions, the fibers shortened on average ∼6.5%, and thus the cross-sectional area would be increased by 1.36E+02 μm² (2.10E+03 − 1.96E+03) to maintain the same volume, or the equivalent to a 6.95% increase in cross-sectional area. This change corresponds to a very small increase in diameter: 1.71 μm (∼3.4%). Since we used averaged signals from larger areas of the fibers (two edges and core, each representing ∼15 μm in fiber diameter) when making comparisons, the overall effects of fiber shortening in the results would be negligible.

A related issue is the length-dependent changes in fiber diameter and lattice spacing as a result of changes in sarcomere lengths. Such change would cause a large spacing between the t-tubule and sarcoplasmic reticulum systems on opposite sides of a muscle fiber at short sarcomere lengths, and it could lead to a lower [Ca²⁺]_i concentration in the center of the fiber. We did not detect large changes in fiber diameter in our study. The difference in diameter between sarcomere lengths of 2.2 and 1.5 μm (shortest length that we used in this study) was 8.63 μm. Even if larger changes in diameter were present and could not be detected, they would not exceed an increase of ∼10.5 μm (assuming a linear relation between sarcomere length and fiber diameter). Approximate changes between 8.63 and 10.5 μm are significantly smaller than the area in which gradients were observed in our fibers (e.g., Figs. 2 and 3).

Conclusions.

The results of this study suggest that the decrease in force along the ascending limb of the force-SL relation is caused, at least partially, by a length-dependent decrease in muscle activation. The decrease in activation is likely caused by a failure in the spread of action potentials from the periphery to the core of the fibers, which causes smaller concentrations of Ca²⁺ release from the sarcoplasmic reticulum. A lower level of activation at the center of the fiber induces a decrease in force produced by the fibers at short lengths.

GRANTS

This study was supported by the Canadian Institutes of Health Research (CIHR) and The Natural Science and Engineering Research Council (NSERC) of Canada.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

D.E.R. conception and design of research; D.E.R. performed experiments; D.E.R. analyzed data; D.E.R. and F.C.M. interpreted results of experiments; D.E.R. and F.C.M. prepared figures; D.E.R. drafted manuscript; D.E.R. edited and revised manuscript; D.E.R. and F.C.M. approved final version of manuscript.