Abstract
Skeletal muscle unloaded shortening has been indirectly determined in the past. Here, we present a novel high-speed optical tracking technique that allows recording of unloaded shortening in single intact, voltage-clamped mammalian skeletal muscle fibers with 2-ms time resolution. L-type Ca2+ currents were simultaneously recorded. The time course of shortening was biexponential: a fast initial phase, τ1, and a slower successive phase, τ2, with activation energies of 59 kJ/mol and 47 kJ/mol. Maximum unloaded shortening speed, vu,max, was faster than that derived using other techniques, e.g., ∼14.0 L0 s−1 at 30°C. Our technique also allowed direct determination of shortening acceleration. We applied our technique to single fibers from C57 wild-type, dystrophic mdx, and minidystrophin-expressing mice to test whether unloaded shortening was affected in the pathophysiological mechanism of Duchenne muscular dystrophy. vu,max and au,max values were not significantly different in the three strains, whereas τ1 and τ2 were increased in mdx fibers. The results were complemented by myosin heavy and light chain (MLC) determinations that showed the same myosin heavy chain IIA profiles in the interossei muscles from the different strains. In mdx muscle, MLC-1f was significantly increased and MLC-2f and MLC-3f somewhat reduced. Fast initial active shortening seems almost unaffected in mdx muscle.
INTRODUCTION
Skeletal muscle contraction is the mechanical result of a complex cascade of signaling events (e.g., (1–3)) that finally triggers actomyosin cross-bridge cycles (4–6). Force production and fiber shortening are primarily determined by external load conditions with purely isometric and isotonic contractions at both ends of the spectrum (7). The maximum rate of shortening in single fibers occurs under unloaded conditions and correlates with motility assay data from isolated motorproteins (8,9). During unloaded shortening, weakly attached cross-bridges are preferentially recruited, with strongly attached ones being as low as 1–5%, whereas strongly attached cross-bridges are formed when the external load increases (10). Maximum unloaded speed of shortening (vu,max) highly depends on distributions of myosin heavy chain (MHC), light chain (MLC), and myosin ATPase activity (11–13). The myosin composition is particularly variable in different muscle types, and even within the same muscle, under different developmental, neural, hormonal, aging, or disease states, fiber type changes may occur (14–16). Likewise, MLC phosphorylation is known to modulate shortening velocity (17).
Previous studies of unloaded speed of shortening in skeletal muscle primarily relied on two experimental approaches: force-velocity relationships and “slack-test” methods. The first uses the fact that speed of shortening critically depends on external load. After isometric contraction against an external load, shortening velocity is measured in the ensuing isovelocity phase and vu,max is usually indirectly extrapolated from the hyperbolic force-velocity relation toward zero loads (e.g., (18–20)). However, this value is not unproblematic, as vu,max may be underestimated by deviations of the force-velocity data from the hyperbolic Hill function for very heavy and light loads (20,21). The “slack-test” method assumes a phase of constant velocity during unloaded shortening while taking up a slack length (22,23). There have been considerable deviations of vu,max obtained from both methods (22,24), in both intact and skinned fibers, that may be due to experimental uncertainties in resolving slack times from the force traces or using different fitting procedures (20,25). Also, the concept of isovelocity phases in intact muscle fibers under conditions of maximum Ca2+-induced shortening might be questionable. Instead, velocity can be expected to change in a nonlinear fashion by the underlying cross-bridge kinetics and opposing forces from elasticity elements or friction from external environments. A more direct experimental approach to visualize depolarization-induced shortening in intact fibers would provide useful insights into single-fiber mechanics under more physiological conditions or to explore pathophysiological mechanisms of muscle diseases that may affect contractility.
In Duchenne muscular dystrophy (DMD), the 427-kDa protein dystrophin is absent due to different deletions in the dystrophin gene (e.g., (26)). Dystrophin mechanically links the cytoskeleton to the extracellular matrix and provides mechanical stability and positioning of single fibers within the matrix (27,28). The mechanism leading to progressive weakness is not understood in detail but involves aberrant mechanotransduction (29), altered Ca2+ homeostasis (30–32), or ion channels (33,34). As is the case in DMD patients, muscles from mdx mice, the animal model for DMD (35,36), show increased contraction-induced damage (37,38) and significantly decreased isometric force (39–41). In diaphragm muscle strips of 6-month-old mdx mice, an additional marked reduction in vu,max from force-velocity relationships, a decrease in slow myosin isoforms, and an increase in IIA MHC isoforms were found, and it was hypothesized that lack of dystrophin might additionally result in molecular motor dysfunction, at least in diaphragm muscle (41). However, there are still no data about unloaded speed of shortening in mdx hindlimb muscle fibers (36). Mechanical parameters, i.e., isometric force and power output, have been a sensitive diagnostic tool to test the efficiency of gene therapy strategies, e.g., using mini- or microdystrophin expression in mdx mice (42,43) that can potently restore force (44). Their effects on unloaded speed of shortening have not been assessed yet.
In this study, we introduce what to our knowledge is a new high-speed line-scan technique to monitor the time course of fiber length, l(t), during unloaded shortening under defined intracellular voltage-clamp conditions in single intact muscle fibers with a time resolution of 2 ms. Simultaneously, slowly-activating Ca2+ currents (iCa) during maintained depolarizations were recorded. vu,max seems to be considerably faster than that estimated using previous methods, described above. We show that unloaded speed of shortening is unaltered in mdx fibers.
Preliminary results were presented at the European Muscle Conference 2005 in Debrecen, Hungary (45).
METHODS
Preparation
Adult male BALB/c mice 12–14 weeks old were sacrificed by exposure to an overdose of CO2 atmosphere. All experiments were carried out according to the guidelines laid down by the local Animal Care Committee. Interossei muscles were dissected in isotonic Ringer's solution (see below) and enzymatically isolated as previously described (33,46). The BALB/c strain was initially used to establish the fast-fiber-length tracking system and to investigate the temperature dependence of the contraction kinetics under voltage-clamp conditions. In a subsequent setting of experiments, the influence of dystrophin on the contraction kinetics under the same conditions was studied. For this, fast-fiber-length recording was applied to single fibers from adult wt C57/SV129, dystrophic mdx, and transgenic minidystrophin (MinD)-expressing, middle-aged mice (8–12 months). MinD mice are a transgenic strain with the mdx background (CVBA3′, 43) that express the Δexon17–48 mouse minidystrophin construct with a molecular mass of 228 kDa (43,43).
Solutions
Ringer's solution contained (in mM) 136 NaCl, 4 KCl, 2 CaCl2, 1 Mg acetate, 5 glucose, and 10 HEPES, pH 7.4. For maximum mechanical activation of single muscle fibers under voltage-clamp conditions, a 10-mM free-Ca2+-containing isotonic solution for simultaneous recordings of slow L-type calcium currents (iCa) was used (mM): 10 Ca-acetate, 1 Mg acetate, 146 TEA-Br, 10 HEPES, 5 CsBr, 5 4-aminopyridine, 5 3,4-di-aminopyridine, and 5 glucose. The ionic strength (Γ/2 values) of this solution was calculated to 184 mM and had a measured osmolarity of 338 mOsm l−1. Protein extraction buffer contained (in mM) 300 NaCl, 100 NaH2PO4, 50 Na2HPO4, 10 Na4P2O7, 1 MgCl2, 10 EDTA, and 1.4 β-mercaptoethanol, pH 6.5.
Electrophysiology
For mechanical activation of single intact interossei fibers and recording of iCa, the two-microelectrode voltage-clamp technique was applied as previously described (33,46–48). To maximally activate both fiber shortening and iCa, step pulses to 0 mV were applied for 1 s from a holding potential of −70 mV under isotonic external conditions. Linear currents were subtracted using an analog leak subtraction procedure (33,47,48). A pulse to 0 mV was chosen because the iCa-V curve usually has its maximum close to 0 mV (e.g., (33,46,47)). In some fibers, a second pulse could be applied to +10 mV after having recovered from the 0-mV pulse, with no apparent further change in shortening parameters such as maximum shortening velocity or shortening length (not shown). Therefore, a pulse to 0 mV was well considered to maximally activate fiber shortening. For better comparison between different fibers, the current density, ICa, was calculated by normalizing iCa to the membrane surface assuming cylindrical fiber geometry, as described previously (e.g., (33,46)). The fiber dimensions were taken from optical measurements in isotonic Ringer's solution. From ICa recorded during the maintained 1-s depolarizing pulse, the ICa-induced rise in myoplasmic [Ca2+]i (i.e., additional to the Ca2+ release from the sarcoplasmic reticulum (SR)) was calculated by integration with respect to time. Note that the SR Ca2+ release itself could not be resolved using the current technique.
High-speed line-scan recording of fiber length during shortening
A b/w linear charge-coupled device (CCD) line (ILX26A, Sony, San Diego, CA) was integrated into a custom-built line-scan unit and connected to the optical side port of an inverse microscope (IMT-2, Olympus, Melville, NY). The maximum internal pixel sampling rate of the CCD line was 1 MHz, with a sensitivity of 300 Vlux−1 s−1. The line-scan recording could be started by an external TTL trigger pulse. Maximum sampling rate was 2 ms/line. This maximum scan frequency (500 Hz/line) was a compromise between the sampling rate of the acquisition board and the aim to trace the whole fiber length within a 512-pixel cycle at the given objective magnification (A10 PL 0.25 or ULWD CDPlan20 0.4, Olympus). Thus, a recording cycle of the actual fiber length was accomplished every 2 ms. The TTL trigger unit was further connected to the A/D-board (DigiData 1200 B, Axon Instruments, Foster City, CA) of the two-microelectrode voltage-clamp setup to start the step-pulse depolarization and iCa recording simultaneously with the fiber-length recording by application of a 100-μs TTL pulse (Fig. 1). To further validate the accuracy of our high-speed line-scan recordings, in some experiments fiber shortening was simultaneously recorded with a 25-Hz CCD camera (DXC-107P, Sony). Fig. 1 shows a schematic diagram of the experimental setup.
FIGURE 1.
Schematic diagram of the experimental setting for simultaneous recordings of ICa and fiber length l(t) during unloaded shortening. A manually elicited TTL trigger pulse is sent to the voltage clamp unit that starts intracellular stimulation (a 1-s depolarizing pulse to 0 mV) and recording of ICa. At the same time, a repetitive 500-Hz TTL pulse is applied to drive the CCD line. The line-scan signal is acquired via the A/D board and stored on the hard disk. In some experiments, a commercial 25-Hz CCD camera was used to simultaneously record the video sequence of fiber shortening.
Temperature control unit
The temperature of the experimental chamber was controlled by four liquid-cooled DC-driven Peltier elements. Temperature was adjusted by an analog feedback loop, including a thermosensor placed in the metal block containing the recording chamber. The thermosensor and the Peltier elements were electrically uncoupled to reduce noise to the voltage-clamp recording. Temperature was controlled with an accuracy of ±0.1°C and experiments were performed at different temperatures between 10°C and 30°C.
Experimental procedure
Single fibers were transferred to the recording chamber and inserted into the thermoblock. The desired temperature was set and ∼5 min allowed for temperature equilibration. Microelectrodes were filled with 3 M KCl and positioned close to the fiber ends. The CCD-line axis was then adjusted until it matched the fiber axis. The correct position of the CCD line was verified by the appearance of a sharp voltage spike on an external oscilloscope (HM205-3, Hameg, Frankfurt, Germany) that reflected the position of the microelectrodes close to the fiber ends. The microelectrodes were then repositioned and inserted in the middle of the fiber, perpendicular to the fiber axis. This configuration allows shortening of the fiber and eliminated contraction-induced damage to the membrane (33,46,47). The holding potential was quickly adjusted to −70 mV and the fiber was depolarized by manually eliciting a TTL trigger pulse that started simultaneous recording of membrane currents and fiber length by the CCD line via two acquisition PCs (see Fig. 1).
Data acquisition and analysis
Fiber-length traces l(t) were recorded and analyzed using AxoTape 2.0 (Axon Instruments). iCa were recorded using pClamp6 and pClamp8 software (Axon Instruments). The signal from the CCD-line output represents a voltage signal over a time period of 2 ms/frame (512 pixels, see Fig. 2 A). The apparent fiber length in a frame was manually evaluated by following the sharp voltage peaks (i.e., representing the change in contrast of transmitted light at the fiber ends) at the margin of successive frames. Using this method, the fiber edges could be reliably detected in each frame. The change in fiber length was calculated between successive frames, resulting in the time course of fiber length l(t) with a 2-ms resolution (l(t + 2 ms)). The peak-to-peak interval in each frame was converted to apparent fiber length using a calibration grate. Usually, l(t) was expressed as a percentage of the initial fiber length, L0, to compare data between different fibers. The time course of the shortening velocity v(t) and shortening acceleration a(t) were obtained by differentiating l(t). To preserve the resolution of the l(t) data, a single-step-forward differential was built between each time point ti and ti+1 (with ti+1 − ti = 2 ms). It should be noted that due to the discrete digitization of the line-scan intervals, the v(t) and a(t) data are also discrete (see, e.g., Figs. 5 and 6) and the error of their extracted maximum values is represented by the smallest discrete step. This error has been acknowledged in the statistics of mean values of v(t) and a(t). Other attempts to reduce the discrete step values included the use of a symmetrical forward backward differential (ti−1 and ti+1) and a five-point environment (ti and ti±2, not shown). However, all these approaches resulted in discrete averaging and a marked reduction in apparent v(t) and a(t), as would be expected by a smoothing procedure of the data. Therefore, the l(t) data were processed unfiltered and the values for maximum shortening velocities, vu,max, and acceleration, au,max, can be regarded as an upper limit at the given acquisition rate.
FIGURE 2.
Line-scan recordings of the fiber length, l(t), during contraction and shortening under maintained depolarization in single fibers. (A) The selection shown is from the shortening sequence of a representative single BALB/c fiber recorded with the CCD line at 500 Hz during a maintained 1-s depolarization to 0 mV from a holding potential of −70 mV at 30°C (identifier D27020.dat). Arrows mark the area between the fiber edges within the actual frame, given as elapsed scan time in the raw data and converted to absolute fiber length as described in Methods. The resting fiber length of L0 = 566 ± 6 μm at t = 0 ms from the line-scan data corresponded well with the value of L0 = 560 ± 10 μm optically measured using a microscope scale. (B) A selection of the shortening sequence recorded with the video camera after separation of half-frames (50 Hz) from another single fiber under the same conditions as in A. The fast initial shortening can only be resolved at 40-ms intervals (full frames) in B, whereas temporal resolution is 20 times faster in A.
FIGURE 5.
Unloaded speed of shortening vu(t) recorded at 500 Hz and compared to 50-Hz video data in single interossei fibers. (A) Time course of vu(t) in a single adult BALB/c fiber at 30°C derived from l(t) recorded with the line scan at 500 Hz, as shown in the upper inset for this fiber. Data are given as relative fiber lengths, l(t)/L0. vu(t) already has its maximum, vu,max, of ∼16 L0 s−1 after 28 ms. The two lower insets show vu(t) on an extended timescale for the first 50 ms, as well as the simultaneously recorded ICa trace and the calculated ICa-induced rise in [Ca2+]i for this fiber. Note that the hump in the Ica trace at 20 ms is an artifact. (B) Statistics for vu,max in several fibers for the temperatures indicated (white bars). Results from BALB/c and C57 wt interossei fibers available at ∼24°C were not significantly different and are lumped together here. In some experiments, simultaneous video sequences (recorded at 50 Hz) were also available, from which vu,max was also calculated (dark-hatched bars). When applying a 50-Hz low-pass filter to the line-scan data, vu,max from the video sequences was accurately predicted (diagionally hatched bars, 50 Hz average). vu,max was significantly larger for temperatures of 20°C and above compared to 10°C (P < 0.001). Temperature dependence of TTvu,max (C), calculated ICa-induced rise in [Ca2+]i at TTvu,max (D), and correlation of both parameters at the different temperatures (E) show weak linear correlations for lower temperatures but a strong linear correlation for larger temperatures. See text for details.
FIGURE 6.
Unloaded shortening acceleration, au(t), recorded at 500 Hz in single interossei fibers. (A) Time course of au(t) in the single fiber shown in Fig. 4 A at 30°C. Also shown is the 50-Hz filtered version of the signal (gray line) that markedly reduces maximum amplitude. In this fiber, au,max is ∼3000 L0 s−2 at 16 ms, followed by a quick deceleration to −1350 L0 s−2 at ∼40 ms. (B) Statistics of au,max from a number of fibers. Note that due to the very coarse time resolution, au,max could not accurately be obtained from video sequences.
Fig. 2 A shows the CCD line-scan data for a single BALB/c fiber bathed in isotonic 10 mM Ca2+ solution at 30°C that was activated by a step pulse to 0 mV. From the 500 frames of the 1-s lasting pulse, only a few are shown at the times indicated. The peak-to-peak times were measured (arrow lengths) and the resulting fiber lengths calculated as described above. To minimize errors in resting fiber lengths determined from the line-scan signal with respect to optically measured resting lengths from the same fiber, care was taken to select fibers with almost no curvature for the current experiments (see Appendix). Fig. 3 shows an example of such a single fiber (see Appendix for details).
FIGURE 3.
Single-fiber geometry and relative CCD line orientation used to estimate the error of fiber shortening recorded with the 500-Hz line-scan device. Example of a single fiber with a curvature. The trajectory of the fiber axis deviates from the linear CCD array at the fiber endings. The arc of the imposed fiber radius is used to estimate the error introduced in obtaining vu,max from the CCD-line data. As derived in the Appendix, vu,max is even underestimated in curved fibers. Care was taken to select fibers with a minimum curvature introducing <5% errors.
Video data from the CCD camera were stored on a PC using a frame grabber card (Matrox Meteor). To increase the time resolution of the 25-Hz video signal to 50 Hz, a Pascal-routine was written to split half-frames by selecting odd and even lines of the full-frame image. Fig. 2 B shows a selection of video frames from another shortening fiber at 30°C depolarized to 0 mV for 1 s. Fiber length was measured using the imaging software Scion Image (Scion Corporation, Frederick, MD) and Image J (National Institutes of Health software). Data were analyzed using SigmaPlot 9 (Systat Software, San Jose, CA) and Origin 6 (Microcal, Northampton, MA). Data are presented as mean ± SE, with the number of observations, n. A Grubbs test was performed on data sets to identify outliers at the P = 0.05 level. Temperature dependence of shortening kinetics was either expressed as Q10 values or calculating the activation energy Ea (where applicable) from the slope of the Arrhenius plots of the kinetics parameters. Statistical differences between temperature groups within one strain or differences between strains at a given temperature were detected by one-way ANOVA or pairwise multiple comparison procedures (Holm-Sidak method), where appropriate. P < 0.05 was considered significant.
Sodium dodecyl sulfate MHC and MLC protein quantification in wt, mdx, and MinD interossei muscles
To quantify the protein contents and distribution of MHC and MLC in interossei muscles from wt, mdx, and MinD mice, sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) was performed (49). Extensor digitorum longus (EDL) and soleus muscle from wt mice were also used for comparison. After dissection of small fiber bundles containing ∼15 fibers, myosin was extracted at room temperature for 30 min in protein extraction buffer (see Solutions), centrifuged, mixed 1:2 with standard protein buffer, and added (∼10 μl) to the running gel (49). The total protein content added to the gels was estimated to be ∼100–200 μg. MLC and MHC gels were run from the same supernatant each. The separating and stacking gels, as well as the separating and running buffer, were composed according to Agbulut et al. (50). MHCs were separated on 8% polyacrylamide gels (50) and MLCs on 12% gels (49). A standard Coomassie blue staining was performed. Broad-range protein standards were from BioRad Laboratories (Munich, Germany). Protein gels were scanned and analyzed using AIDA software (Raytest, Straubenhardt, Germany). For evaluation of the fast myosin light chain isoform (MLC-1f, MLC-2f, and MLC-3f) mean protein densities in the three genotypes (wt, MinD, and mdx), the area under the corresponding peaks in density profiles of the background normalized bands from up to nine gels were measured and the relative percentage calculated (MLC-1f + MLC-2f + MLC-3f adding up to 100%).
RESULTS
Simultaneous recording of l(t) and ICa under maintained depolarization to 0 mV at different temperatures
Fig. 4 A shows the time course of shortening l(t) normalized to the resting fiber length L0 during a 1-s depolarizing pulse to 0 mV in a representative single BALB/c muscle fiber recorded with the CCD line (500 Hz) at 30°C. A latency of ∼16 ms for the onset of shortening can be seen at the beginning of the recording that was similar in several fibers and not temperature-dependent (P > 0.1, Table 1). This latency represents the time required for excitation-contraction coupling (i.e., SR Ca2+ release and myoplasmic diffusion) and is ∼20 ms (51). It is followed by a fast contractile activation phase and a slow relaxation phase. The first 50 ms of the contractile activation are shown on an extended timescale in the inset of Fig. 4 A. In the example shown, shortening is complete after ∼400 ms at ∼50% of L0. The shortening phase was best described by a double exponential fit:
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(1) |
with a fast time constant τ1 and a slow component τ2, measuring 13.6 ms and 133 ms, respectively. The much slower relaxation phase was best described by a single exponential with a time constant τ3 of 678 ms. As the relaxation phase was very variable between fibers, even at the same temperature, we focused on the more interesting fast activation phase where both shortening velocity and acceleration had their maximum. Therefore, τ3 values are not further analyzed here. Note that the relaxation phase of the fiber took place while the fiber was still being depolarized by the 1-s pulse to 0 mV. At lower temperatures, relaxation was not yet fully present during the recording interval (e.g., Fig. 4, B and C). Table 1 summarizes the mean values for the onset latency: minimum fiber length lmin/L0; the time to minimum (TTM); maximum unloaded speed of shortening, vu,max; and time to vu,max, TTvu,max (see below) in several single BALB/c fibers at four different temperatures. Note that at 24°C, values from BALB/c and C57 wt single fibers were lumped together, as they were similar. The mean amplitudes of the exponential fits showed a tendency to increase with temperature for A1 (0.26 ± 0.06 at 10°C, 0.12 ± 0.02 at 20°C, 0.46 ± 0.08 at 24°C, and 0.90 ± 0.42 at 30°C) that was, however, not statistically significant (P = 0.1). For A2, values ranged from 0.03 to 0.52 and were only significantly smaller at 10°C compared to larger temperatures (P < 0.01).
FIGURE 4.
Kinetics of unloaded shortening l(t) during maintained depolarizations in single fibers. (A) Representative recording of l(t) with the line scan (500 Hz) in a single BALB/c fiber at 30°C. A biexponential shortening phase with time constants τ1 and τ2 and a single-exponential relaxation phase can be distinguished during the 1-s lasting depolarizing pulse from −70 mV to 0 mV. The early transient of l(t) is shown on an extended timescale (0–50 ms) in the inset. Shortening starts after an onset latency of ∼16 ms in the fiber shown. (B) Sample recording of l(t) in another BALB/c fiber at 24°C. The time course of the simultaneously recorded ICa and the calculated ICa-induced rise in intracellular [Ca2+]i is shown in the inset. (C) l(t) recorded with the line scan in a representative adult single wt, mdx, and MinD fiber at 25°C. The first 50 ms of shortening are shown in the inset on an extended timescale. (D and E) Exponential temperature dependence of both τ1 and τ2 (D) and Arrhenius plot of both shortening rate constants with the calculated activation energy as indicated (E).
TABLE 1.
Temperature dependence of the onset latency, lmin/L0, TTM, νu,max, and TT νu,max recorded at 500 Hz in single BALB/c (and C57 wt at 24°C) interossei fibers
| Temperature (°C) | Onset latency (ms) | lmin/L0 | TTM (ms) | vu,max (L0 s−1) | TTvu,max (ms) | n |
|---|---|---|---|---|---|---|
| 10 | 30.5 ± 6.1 | 0.67 ± 0.06 | 923 ± 78 | 5.75 ± 0.99 | 51.0 ± 9.3 | 4 |
| 20 | 19.0 ± 0.6 | 0.52 ± 0.03 | 832 ± 37 | 13.25 ± 2.02 | 28.5 ± 7.4 | 4 |
| 24 | 23.5 ± 1.2 | 0.57 ± 0.04 | 506 ± 77 | 12.54 ± 2.54 | 41.3 ± 3.6 | 11 |
| 30 | 19.5 ± 1.7 | 0.55 ± 0.02 | 395 ± 23 | 13.94 ± 1.37 | 35.0 ± 7.0 | 4 |
In some experiments, in addition to the line scan, l(t) was also recorded with an untriggered video camera. The minimum fiber length during shortening and its time course were very similar with both techniques (data not shown). Therefore, like the video sequence, the CCD line faithfully tracks l(t), but with at least 10-fold higher time resolution.
Simultaneous with the fast l(t) recordings, L-type iCa were recorded. Fig. 4 B shows l(t) in another single BALB/c fiber recorded at 24°C together with the time course of iCa, given as surface normalized ICa (Fig. 4 B, inset, solid line). Also shown is the calculated ICa-induced rise in intracellular [Ca2+]i during the maintained depolarizing pulse, [Ca2+]i (ICa), that results in an increase in [Ca2+]i of ∼70 μM by the end of the pulse. It should be noted that [Ca2+]i (ICa) reflects the contribution from Ca2+ influx through dihydropyridine receptors (DHPRs) under this maintained depolarization condition and not the contribution from sarcoplasmic reticulum (SR) Ca2+ release. Therefore, the increase in [Ca2+]i under voltage-clamp conditions is much larger than under single-twitch conditions (∼20 μM (52)), where only SR Ca2+ release contributes and DHPRs in skeletal muscle do not reach a fully conducting state (53). On the other hand, this increase, in addition to the Ca2+ release from the SR during activation, ensures Ca2+-saturated conditions of the contractile apparatus and, therefore, maximum mechanical activation (see also below). In the example shown, peak ICa was −51.9 μA/cm2 and time to peak (TTP) was 47.5 ms. The peak ICa, TTP, and [Ca2+]i (ICa) values at the end of the pulse (1 s) and at the time of maximum unloaded speed of shortening, TTvu,max (see below), for several single BALB/c fibers at 10°C, 20°C, 24°C, and 30°C are summarized in Table 2. The ICa data confirm our previous data carried out at room temperature under isotonic conditions (33,46). At 30°C, an early outward component of ICa was occasionally seen during the current decay after the ICa peak (46). This component obviously reduces [Ca2+]i (ICa) so that the corresponding values in Table 2 at 30°C might be somewhat underestimated. Q10 values for peak ICa were close to unity between 10°C and 20°C and ∼2 between 20°C and 30°C. ICa activation was most prominently affected by an almost fourfold decrease of TTP between 20°C and 30°C.
TABLE 2.
Temperature dependence of peak ICa, TTP during maintained depolarizations, and [Ca2+]i (ICa) at the TTνu,max and at the end of the 1-s lasting pulse in single BALB/c interossei fibers
| Temperature (°C) | Peak ICa (μA/cm2) | TTP (ms) | [Ca2+]i (ICa) at TTvu,max (μM) | [Ca2+]i (ICa) at 1 s (μM) | n |
|---|---|---|---|---|---|
| 10 | −31.47 ± 5.90 | 185 ± 64 | 2.76 ± 1.18 | 75.6 ± 17.9 | 4 |
| 20 | −31.68 ± 7.12 | 76 ± 9 | 1.70 ± 0.76 | 58.9 ± 13.8 | 4 |
| 24 | −54.51 ± 3.20 | 53 ± 8 | 6.55 ± 1.74 | 72.5 ± 20.0 | 4 |
| 30 | −51.81 ± 0.93 | 19 ± 3 | 11.87 ± 3.66 | 61.4 ± 16.1 | 4 |
Fig. 4 C shows representative examples of l(t) traces from adult single C57 wt, mdx, and MinD fibers of similar aged animals (8–12 months), each recorded during a maintained depolarization to 0 mV at 24°C. The more interesting fast-activation phase is again shown on an extended timescale in the inset. Shortening was very similar in all three genotypes. A more detailed analysis is given in the sections below.
The temperature dependence of the time constants of the shortening phase, τ1 and τ2, are evaluated for all BALB/C fibers (including some wt fibers at 24°C) in Fig. 4 D. The temperature dependence was exponential for both time constants. From the Arrhenius plot of τ1 and τ2, the activation energy Ea was calculated at 59 kJ/mol and 47 kJ/mol, respectively (Fig. 4 E).
Unloaded speed of shortening, vu(t), and fiber acceleration, au(t)
With the line-scan recording, the time course of shortening can be reliably measured at a 10-fold faster time resolution compared to the video acquisition (half-frames). The advantage of this increased resolution can be impressively demonstrated by the evaluation of the maximum unloaded speed of shortening, vu,max, and acceleration, au,max. Fig. 5 A shows the whole time course of vu(t) in another single BALB/C interossei fiber at 30°C with its corresponding l(t) recording, as shown in the upper inset. The more interesting initial 50 ms are shown on an extended timescale along with the corresponding ICa trace and the Ica-induced [Ca2+]i rise in the lower two insets. The maximum speed of shortening, vu,max, was close to 16 fiber lengths/s (L0 s−1) in this recording. In several fibers at four different temperatures, vu,max measured 5.7 ± 1.0 (10°C, n = 4), 13.2 ± 2.0 (20°C, n = 4), 12.5 ± 2.5 (24°C, n = 11), and 14.0 ± 1.4 (30°C, n = 4) L0 s−1 (Fig. 5 B). Note that values from both BALB/c and C57 wt mice were not significantly different (P = 0.27), and are lumped together here (∼24°C). In those experiments where simultaneous video recordings were available, vu,max was also calculated from the image sequences. Those values were substantially smaller than those obtained from the 10-times-faster line-scan recordings (Fig. 5 B, black hatched bars). To test whether the video image resolution (50 Hz) could be predicted from the 500-Hz line-scan recording, a 50-Hz low-pass filter was applied to the line-scan data. The corresponding data are shown as hatched bars in Fig. 5 B (50 Hz average). As can be clearly seen, the video data are well reproduced from the filtering procedure of l(t). Those data underestimate vu,max from the 500-Hz line-scan recordings by ∼65%.
In the previous section, it was suggested that shortening occurs at saturating myoplasmic Ca2+ concentrations sufficient to give maximum force when one calculates the ICa-induced rise in [Ca2+]i by the end of the pulse (Table 2). However, this might be less clear if the time soon after the depolarization (when shortening velocity reaches its maximum) is regarded. This time to vu,max (TTvu,max) was evaluated and its temperature dependence is shown in Fig. 5 C. With increasing temperature, TTvu,max decreased, and an exponential fit was drawn through the data (solid line). The corresponding ICa-induced [Ca2+]i rise at this time point of maximum unloaded shortening was then calculated and its temperature dependence is shown in Fig. 5 D with an exponential fit to the data. Note that at 24°C, ICa traces in three fibers were distorted during the shortening phase and excluded from the analysis. The data show that at TTvu,max, the ICa-induced rise in [Ca2+]i was at least 5 μM for temperatures >20°C, which is due mainly to the faster activation of ICa at these temperatures (Table 2). Therefore, maximum initial shortening can be assumed to occur at saturating myoplasmic Ca2+ concentrations, at least for larger temperatures. Fig. 5 E finally shows the correlations between TTvu,max and ICa-induced rise in [Ca2+]i at TTvu,max for the different temperatures in all individual fibers from which both data sets were available. A linear correlation was most pronounced for larger temperatures. At lower temperatures, the ICa-induced rise in [Ca2+]i was very small and eventually even zero in the 10°C case, simply because TTP of ICa greatly exceeded TTvu,max (Table 2).
Fig. 6 A shows the time course of the complete unloaded acceleration transient, au(t), of the fiber shown in Fig. 4 A. The corresponding vu(t) is shown in the upper inset. The more interesting initial phase of au(t) is again shown on an extended timescale in the lower inset along with the corresponding ICa and ICa-induced [Ca2+]i-rise transients. Also shown in the au(t) panel is the 50-Hz filtered version of the data (gray line). It is obvious that the very fast maximum of fiber acceleration is substantially underestimated by a 10-times-slower recording that could not be adequately analyzed from the video data due to the lack of data points in the first 50 ms of shortening (two points only in the video data). Between 10°C and 20°C, au,max almost doubled and remained relatively stable around ∼3000 L0 s−2 for higher temperatures (Fig. 6 B).
Shortening kinetics in single fibers from adult wt, mdx, and MinD mice
This section deals with the application of the high-speed shortening acquisition to single fibers related to the pathophysiology of Duchenne muscular dystrophy. Examples of representative l(t) traces in single fibers from wt, mdx, and MinD mice at 25°C were shown in Fig. 4 B. Fig. 7 shows the analysis from several recordings of l(t) in these strains at both 15°C and 25°C. Similar to the BALB/c strain, the degree of shortening was more complete and accelerated at the higher temperature, as reflected by a decrease in lmin/L0 (Fig. 7 A), TTM (Fig. 7 B), τ1 (Fig. 7 C), and τ2 (Fig. 7 D). In mdx fibers, compared to wt fibers, TTM and time constants of shortening seemed to be consistently larger, but only significantly so for τ1 and τ2 at 15°C. Although this suggests a somewhat slower unloaded shortening kinetics, the maximum degree of shortening was larger in these fibers compared to controls at 25°C (lmin/L0∼43% vs. ∼50%). At 15°C, however, it seems there was no difference in minimum fiber length, although there was an even more pronounced prolongation of kinetics. vu,max was very similar in all strains, measuring ∼9 L0 s−1 at 15°C and ∼15 L0 s−1 at 25°C (Fig. 7 E). Similarly, there was no statistically significant difference between the genotypes for au,max at either temperature (P > 0.44 at 15°C, P > 0.19 at 25°C, Fig. 7 F). Note that the number of observations was smaller for some parameters either after elimination of an outlier or due to fitting failure in cases where l(t) traces were distorted.
FIGURE 7.
Unloaded shortening kinetics and parameters from line-scan recordings at 500 Hz in single adult wt, mdx, and MinD fibers. Unloaded shortening was recorded with the 500-Hz line-scan technique in several (n) single fibers from adult wt, mdx, and MinD mice of similar age (see Fig. 4 for age bins) at 15°C and 25°C. (A–F) lmin/L0, TTM, τ1, τ2, vu,max, and au,max are shown. Some n values in the figure are smaller, either due to outlier detection and removal or to l(t) traces being somewhat distorted, and these could not be reliably fitted (particularly for τ1 or τ2). For details, see text. *P < 0.05.
Analysis of MHC and MLC protein contents in interossei muscle fiber bundles from wt, mdx, and MinD mice
To validate our robust findings of unaltered vu,max in wt, mdx, and MinD fibers, we performed SDS-PAGE analysis of MHC and MLC protein contents in interossei muscles of the three genotypes. Fig. 8 A shows representative gels to separate MHC isoforms from muscle extracts of soleus, EDL, and interossei C57 wt muscle. The MHC protein bands in soleus and EDL muscle are typically referred to as MHC I, MHC IIA, MHC IIB, and MHC IIX, according to their molecular weight from literature data, and using MHC standards (50,54,55). Soleus muscle shows the typical predominance of MHC I and MHC IIA, whereas in EDL muscle MHC IIX and MHC IIB distributions prevail. Interossei muscle homogenates show a single band reflecting MHC IIA for all three genotypes. This is also demonstrated in the protein density profile of the lanes that shows perfect matching of the curves with the MHC IIA peak from soleus muscle (Fig. 8 B). Fig. 8 C shows corresponding SDS gels for the MLC distributions. In mdx interossei muscles, some reduction in the MLC-2f and MLC-3f protein bands might be anticipated compared to both wt and MinD muscles, which is also suggested from the protein density profile (Fig. 8 D). This trend could be confirmed when evaluating the relative protein contents of the fast MLC isoforms from up to nine gels of the three genotypes (Fig. 8 E). However, the decrease in mdx MLC-2f and MLC-3f did not reach statistical significance (P > 0.07). In addition, a statistically significant increase in the mdx MLC-1f content was seen (P < 0.01).
FIGURE 8.
SDS-PAGE analysis of MHC and MLC protein contents in interossei muscle fiber bundles from wt, mdx, and MinD mice. (A) Representative 8% SDS-PAGE gels from wt, MinD, and mdx interossei muscle homogenates to separate MHC. The corresponding gels from wt EDL and soleus muscle are shown in the right two lanes for comparison. Soleus and EDL muscles show the well-known MHC isoform distributions of IIA and I and IIX and IIB, respectively. There is no difference in the protein distributions from the three strains in interossei muscles, as confirmed by the densitometry (B). The single bands in those gels solely represent MHC-IIA, as confirmed by comparison with the bands from soleus muscle. (C) MLC profiles of 12% SDS-PAGE gels from the three genotypes and muscles shown in A. The fainter staining of the ∼16.5-kDa band in mdx interossei muscle, corresponding to MLC-3f, compared to wt and MinD interossei muscles, is also seen in the densitogram (D). The corresponding peaks from wt EDL and soleus muscles are shown as vertical dotted lines in D. (E) The somewhat reduced MLC-3f content is confirmed in the relative contents of fast MLC isoforms from several gels but is, however, not statistically significant. MLC-1f content is significantly larger in mdx muscle (*: P < 0.01).
DISCUSSION
L-type Ca2+ currents during unloaded shortening in single interossei fibers
In this work, we have introduced a what to our knowledge is a new technique to directly monitor unloaded shortening in intact isolated mammalian skeletal interossei muscle fibers that allows simultaneous recordings of L-type Ca2+ currents. Using this line-scan technique, the full time course of fiber length, velocity, and acceleration was monitored at a sampling rate of 500 Hz and time-correlated to the electrophysiological data. Maximum peak ICa values showed bimodal temperature dependence with similar values for 10°C and 20°C and about two-times-larger values between 20°C and 30°C. Similar Q10 values of 2–2.5 for an increase in ICa have been described in rat omohyoid (56) and human vastus lateralis muscle (57). Likewise, in the same studies, TTP, or rise time, as a measure for channel activation, decreased 2.5- to 3-fold. Under single-twitch conditions, where L-type Ca2+ channels mainly act as voltage sensors and not as conducting channels (53), myoplasmic [Ca2+]i rises primarily due to fast SR Ca2+ release. Using proper Ca2+ sensitive dyes, peak [Ca2+]i in single mouse EDL fibers during single twitches reached ∼22 μM within ∼2 ms at 28°C (52). In rat EDL fibers, the peak of the Ca2+ transient of ∼4.5 μM was reached after ∼4.5 ms in response to single action potentials (51). In skinned rat EDL fibers, maximum force occurred from myoplasmic [Ca2+] values of ∼7–10 μM at 35°C and force-Ca2+ relationships were shifted toward larger pCa values (i.e., lower myoplasmic [Ca2+]i) with decreasing temperature (58). Under our conditions of maintained depolarizations in voltage-clamped single interossei fibers, intracellular [Ca2+] is expected to remain at levels that fulfill maximum activation of the contractile apparatus for the whole recording period. The early phase of transient SR Ca2+ release that we cannot resolve with our electrophysiology technique is followed by ICa influx through the L-type channel that in turn results in an additional ICa-induced rise in [Ca2+]i. By the end of the pulse, this ICa-induced rise in [Ca2+]i obviously exceeds the ∼20 μM myoplasmic [Ca2+]i from SR release ∼3-fold. ICa-induced [Ca2+]i rise was temperature-dependent and linearly correlated with the time of maximum unloaded speed of shortening TTvu,max for larger temperatures (i.e., 30°C, Fig. 5 E). For lower temperatures, ICa-induced [Ca2+]i rise was still small at TTvu,max (<7 μM (Fig. 5 D)), but vu,max values themselves were quite similar between 20°C and 30°C (see below). Therefore, it seems that the first phase of shortening is not limited by the ICa-induced [Ca2+]i rise but rather by the SR-induced [Ca2+]i rise and myofilament-based mechanisms.
Temperature dependence of unloaded shortening kinetics in normal interossei fibers
During depolarization-induced shortening, fibers contracted to ∼55% of the initial resting length, L0. lmin/L0 was similar for temperatures from 20°C and somewhat larger for lower temperatures (∼65% at 10°C). l(t) showed a characteristic biexponential activation phase. The biexponential shortening of the whole fiber upon maintained depolarizations is also reflected on the sarcomere level. Recent results from video tracking of Ca2+-activated rabbit psoas myofibrils consisting of 10–20 individual sarcomeres also showed a biphasic shortening kinetics of half-sarcomere lengths upon Ca2+ activation at pCa of 4.5 (59). The time constants of half-sarcomere shortening were in the second range which can be explained by differences in muscle type used (slow in Telley et al (59) versus fast in this study), but more obviously by technical differences (solution-exchange-induced Ca2+ activation of isolated myofibrils versus intracellular depolarization of intact fibers in this study). The question arises, what are the underlying mechanisms reflected by the two exponentials during unloaded shortening? Telley et al. (59) did not further comment on their biexponential shortening on the sarcomere level, but from their and other studies, it seems clear that active shortening is not an instantaneous consequence of force during force development. Current cross-bridge models also propose that force-generating steps precede the step determining active shortening velocity (59). We postulate that shortening processes represented by both the fast- and slow-activation kinetics under our conditions might be related to an initial fast shortening phase that is entirely unloaded and related to the near-optimal overlap of the filaments at the start of contraction (sarcomere lengths ∼2.2–2.4 μm, O. Friedrich, unpublished observation), followed by a slower phase that contains shortening against an increasing “internal load” that might arise from interference with and bending of the filaments as the fiber shortens to less than two-thirds of its original length in most of our fibers. Series elastic elements and noncycling cross-bridges would also oppose shortening with decreasing sarcomere lengths. The importance of an “instantaneous elasticity element” with a velocity-dependent behavior has been emphasized by Podolsky and Nolan (60). It is also interesting to note that in most studies on mammalian muscle fibers, the tension decline during ramp shortening occurs in two phases (e.g., (61)). Whether this relates to the biexponential shortening phases during unloaded shortening is currently not known and would be an important question for future studies.
The temperature dependence of the time constants for the two shortening phases in normal fibers was used to calculate the activation energies, Ea (Fig. 4 D). To our knowledge, activation energies for the complete time course of unloaded shortening have not yet been given. With 59 kJ/mol for τ1 and 47 kJ/mol for τ2, our values are quite similar to activation energies for other shortening parameters that were calculated for mammalian muscle. For example, in intact rat EDL and soleus muscle fibers contracting isotonically after release from an isometric tetanus-induced contraction, Ea of vu,max derived from force-velocity relations were in the range of 40–45 kJ/mol for both muscles (62). For rates of tension development, Ea values were 48 kJ/mol for EDL and 56 kJ/mol for soleus muscle, respectively (62). This is a further indication that the second slower phase in our shortening fibers may be affected by build-up of retracting force in the tens of milliseconds range (see Fig. 3 in (62)).
Maximum unloaded speed of shortening and acceleration in normal interossei fibers
With this acquisition technique, calculated vu,max values were substantially larger compared to values derived from video acquisition experiments, as expected from the much lower time resolution of the latter (Fig. 5 B). This was, for example, correctly predicted from experiments where both video and CCD recordings were performed and the latter additionally subjected to a 50-Hz filter (simulates half-frame resolution at 20-ms repetition rate (Fig. 5 B)). As in previous studies using mammalian muscle fibers, vu,max was temperature-dependent (e.g., (25,63)). Between 10°C and 20°C, the Q10 value for vu,max was 2.3, whereas between 20°C and 30°C, Q10 values were close to unity. This parallels findings from rat EDL muscle fibers, where a much greater temperature dependence of vu,max was found below 25°C as compared to above 25°C (63). Nyitrai et al. (55) give a possible explanation from their cross-bridge dissociation experiments using ATP-induced acto-heavy-meromyosin dissociation (55). For mammalian fast skeletal muscles, the rate constant of ADP release that limits cross-bridge detachment and contraction velocity becomes rate-limiting for velocity above temperatures of ∼25°C, but only with a very small temperature dependence (55). Interestingly, when comparing our vu,max values to data from force-velocity and slack-test experiments in the literature, our direct observation of unloaded shortening suggests larger values than previously described. Some examples for vu,max values from force-velocity relations include: ∼4 L0 s−1 at 21–27°C in mouse flexor digitorum brevis fibers (64), 6–10 L0 s−1 at 30°C in rat EDL (62,63), ∼9 L0 s−1 at 26°C in mouse diaphragm (41), ∼6 L0 s−1 at 21°C in mouse EDL fibers (65), or ∼1 L0 s−1 at 12°C in human vastus lateralis (IIA, IIB) muscle fibers (66). On the other hand, vu,max values of ∼30–60 L0 s−1 have been found in ultrafast rabbit inferior oblique muscles for temperatures between 20°C and 35°C (67). Two examples of vu,max values obtained from slack tests are ∼12.5 L0 s−1 at 32°C in mouse flexor digitorum brevis fibers (25) or ∼3 L0 s−1 at 12°C in rat fast muscle fibers (12). Up to 30% larger values for vu,max obtained from slack-test experiments have been described compared to force-velocity relationships in intact and even up to 50% in skinned fibers (24). Basically, three explanations have been suggested for this phenomenon (20): 1), the slack test method suffers from inaccuracy in determining the exact time interval for taking up the slack; 2), the Hill curve deviates from the recorded force-velocity relation in the range of very low and very high loads, thus underestimating vu,max; and 3), there is a discontinuity in the force-velocity relation for truly unloaded conditions. The authors (20) have already pointed out the necessity to directly image fiber length during shortening to better correlate the different techniques. That has been successfully addressed by means of the one-dimensional recording array in this study. It seems that vu,max values from fast recordings of unloaded shortening in intact mammalian toe muscle fibers under voltage-clamp conditions indeed exceed vu,max values from slack-test recordings by an additional 40–50%.
Apart from myosin ATPase activity and myoplasmic Ca2+ concentrations, the main determinants of vu,max are given by the MHC and MLC distributions, which may differ substantially in different muscles and even in the same muscle under different physiological or pathophysiological conditions (12,16,55). To date, MHC and MLC distributions in mammalian interossei muscles have been very poorly described and, to the best of our knowledge, not at all in mouse. In our murine interossei muscle preparations, SDS PAGE analysis showed a single MHC IIA band. The corresponding MLC protein distribution (Fig. 8 B, wt) showed a very similar pattern compared to a variety of other mammalian fibers investigated (55). Therefore, we think that the larger vu,max values under our conditions are not a result of a different MHC/MLC fiber composition but rather reflect a high maximum shortening velocity during a very short time interval in the initial shortening phase, which may have been undetected from both slack tests and force-velocity relations due to the time resolution and other constraints mentioned above. A further advantage of our technique is that the acceleration of unloaded shortening can be directly obtained. Depending on temperature, au,max values of several thousand fiber lengths/s2 were obtained.
Unloaded shortening characteristics of voltage-clamped interossei fibers from wt, mdx, and MinD mice
Several studies have found altered contractile properties associated with the lack of dystrophin in mdx mice, although the exact molecular mechanisms remain elusive (36). For example, specific twitch and peak isometric tetanic force are consistently lower in mdx versus wt mice >5 months old, whereas absolute force values can be normal by reactive muscle hypertrophy for a long time during the lifespan of the mdx animal (40). Fatigue resistance in some mdx limb muscles and the diaphragm was found to be either at control levels or even increased, probably due to MHC fast-to-slow conversions with greater oxidative capacity (68). The shortening dynamics of mdx muscle has been addressed in a few studies only (summarized, e.g., in (36)). Force-velocity relations were downward-shifted in EDL mdx muscle (40). These findings were compatible with MHC shifts from fast to slow isoforms and reduced amounts of MLC-3f (16,69). In mdx diaphragm, impaired dynamics of shortening was explained by prolonged cross-bridge cycle durations and slower cross-bridge detachment rates, based on calculations from Huxley's equations (41). In our interosseus muscle preparation, we confirmed the changes seen in MLC isoform distributions in EDL muscle, with a tendency toward reduced MLC-3f and MLC-2f isoforms (Fig. 8 E). In addition, we found a significant increase in MLC-1f levels. In contrast to EDL muscle (16), MHC distributions were identical in wt, mdx, and MinD interossei muscles (Fig. 8 A). This may be also reflected in our vu,max values. At two temperatures (15°C and 25°C), vu,max and au,max were similar in mdx versus wt or MinD fibers (Fig. 7, E and F). There was a significant prolongation of both shortening time constants in mdx fibers, but only at 15°C, whereas for temperatures that are more physiological in toe muscles (∼25–30°C), our data suggest no differences in unloaded shortening kinetics per se. This is in agreement with recent findings in maturing EDL muscle from mdx mice, where no difference in passive mechanical and viscoelastic properties was found before or after the overt onset of the dystrophic process (14–35 days) (70). Nevertheless, the observed differences in shortening parameters may be, at least partly, also related to differences in the phosphorylation of MLC that are known to modulate shortening velocities (17). Further research will help to clarify whether there are substantial differences in MLC phosphorylation between these genotypes.
In summary, we have presented what to our knowledge is a new imaging technique that allows high-speed recording of unloaded shortening in single intact voltage-clamped muscle fibers. Maximum unloaded speed of shortening was faster than recorded with other, more indirect, methods. From our results, it is likely that the contractile kinetics contributing to initial unloaded shortening, i.e., weak binding states and detachment rates, are not affected in our animal model of DMD. It will be interesting to apply our technique to other classical fiber models that differ in MHC isoform composition (e.g., soleus and psoas muscle) to clarify which of the parameters depend on MHC isoform. For other pathophysiological conditions in muscle that might be associated with altered cross-bridge kinetics, e.g., critical illness myopathies, we think our technique will provide a valuable tool to elucidate some of the underlying pathological mechanisms.
APPENDIX: ERROR ESTIMATE OF SHORTENING DUE TO FIBER GEOMETRY
This section deals with the estimate of the error that could be introduced to vu,max with the line-scan technique when bending is present in single fibers. Fig. 3 shows an image of a bent single fiber and the relative position of the CCD line through the fiber middle. The latter will only trace the time course of the fiber ending projections on the CCD line. From the initial image, the fiber contour is described by an arc segment b = lopt.(t) with radius r(t) and angle α(t). The actual position of the CCD line is in parallel to the secant of the arc segment, a = lCCD(t) and linearly shifted into the fiber middle to cover most of the fiber length. a represents the actual fiber length l(t) recorded by the CCD line (lCCD(t)). The angle α(t = 0) was determined from the initial image to
This was also the maximum allowed initial angle for the use of bended fibers (see below). An estimate of the initial ratio a0/b0, i.e., at t = 0, yields the maximum error in fiber-length recordings using, for the radius, r(t), and the secant of the arc, the relations
![]() |
(A1) |
![]() |
(A2) |
With the expansion series
it follows that
![]() |
(A3) |
The maximum deviation of the projected initial fiber length on the CCD line from the apparent fiber length is supposed to be <6% for maximum curvatures of
This error is expected to quickly decrease within the first tens of milliseconds of shortening, because fibers are fixed by the microelectrodes in their centre of mass, and therefore the curvature will rapidly decrease during shortening as the fiber endings move along the arc to the fiber middle (Fig 3, black arrows). The fiber endings, therefore, initially perform a translational as well as a small rotational trajectory. The CCD line, however, keeps tracking the projected fiber lengths, i.e. a translational movement (Fig. 3, gray arrows) that is smaller than the apparent distance covered by the fiber endings during the same time interval. From a time
shortening will be almost completely translational for all
as 
![]() |
(A4) |
From video images, fiber bending was already completely absent after two to three successive images, i.e., 20–40 ms. It may be that bending is already removed earlier but cannot be detected due to the too-slow video acquisition. As vu,max is reached in a time interval that lies within the window where
(h(t) > 0), the shortening velocity recorded by the CCD line still somewhat underestimates the apparent fiber shortening velocity because the projected fiber endings cover smaller distances during the sampling intervals than do the still bent fiber endings (see above). Therefore, our vu,max values given in Results may represent a lower limit for unloaded shortening velocities in voltage-clamped single fibers.
O. Friedrich is both first and senior author.
Editor: K. W. Ranatunga.
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