Calculation of muscle maximal shortening velocity by extrapolation of the force-velocity relationship: afterloaded versus isotonic release contractions

The maximal shortening velocity of a muscle (V(max)) provides a link between its macroscopic properties and the underlying biochemical reactions and is altered in some diseases. Two methods that are widely used for determining V(max) are afterloaded and isotonic release contractions. To determine whether these two methods give equivalent results, we calculated V(max) in 9 intact single fibres from the lumbrical muscles of the frog Xenopus laevis (9.5-15.5 °C, stimulation frequency 35-70 Hz). The data were modelled using a 3-state cross-bridge model in which the states were inactive, detached, and attached. Afterloaded contractions gave lower predictions of Vmax than did isotonic release contractions in all 9 fibres (3.20 ± 0.84 versus 4.11 ± 1.08 lengths per second, respectively; means ± SD, p = 0.001) and underestimated unloaded shortening velocity measured with the slack test by an average of 29% (p = 0.001, n = 6). Excellent model predictions could be obtained by assuming that activation is inhibited by shortening. We conclude that under the experimental conditions used in this study, afterloaded and isotonic release contractions do not give equivalent results. When a change in the V(max) measured with afterloaded contractions is observed in diseased muscle, it is important to consider that this may reflect differences in either activation kinetics or cross-bridge cycling rates.     

Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods

In using pharmacologic stimuli, force-velocity (FV) curves are usually obtained by the method of quick release (QR) and redevelopment of shortening at peak tetanic tension; the advantage of the method being that the active state is at maximum. However, the QR may itself reduce the intensity of the active state and result in reduced values of FV constants. We tested this by delineating FV curves in canine tracheal smooth muscle using both conventional afterloaded isotonic contractions (ALI), and redevelopment of shortening after QR methods. For both these studies a supramaximal tetanizing electrical stimulus was used. The analysis of 11 experiments revealed that the latter method resulted in statistically significant reductions of all FV constants except for Po (maximum isometric tetanic tension). The means and standard errors for the sets of constants for the ALI and QR, respectively, are as follows: Vmax (maximum velocity of shortening) = 0.275 lo (optimal muscle length)/s +/- 0.024 (SE), and 0.216 lo/s + 0.023; a (hyperbolic constant with units of force) = 294 g/cm2 +/- 35 and 236 g/cm2 +/- 32; b (hyperbolic constant with units of velocity) = 0.059 lo +/- 0.004 and 0.039 lo/s +/- 0.005; a/Po = 0.214 +/- 0.028 and 0.182 +/- 0.026; and Po = 1.362 kg/cm2 +/- 0.106 and 1.294 kg/cm2 +/- 0.097. These data clearly show that the quick-release method for measuring force-velocity relationships in canine smooth muscle results in significant underestimates of muscle shortening properties.     

A method for isolating adult and neonatal airway smooth muscle cells and measuring shortening velocity

Methods are described for isolating smooth muscle cells from thetracheae of adult and neonatal sheep and measuring the single-cell shortening velocity. Isolated cells were elongated,Ca²⁺ tolerant, and contractedrapidly and substantially when exposed to cholinergic agonists, KCl,serotonin, or caffeine. Adult cells were longer and widerthan preterm cells. Mean cell length in 1.6 mMCaCl₂ was 194 ± 57 (SD) µm(n = 66) for adult cells and 93 ± 32 µm (n = 20) for preterm cells(P < 0.05). Mean cell width at thewidest point of the adult cells was 8.2 ± 1.8 µm(n = 66) and 5.2 ± 1.5 µm(n = 20) for preterm cells(P < 0.05). Cells were loaded into aperfusion dish maintained at 35°C and exposed to agonists, andcontractions were videotaped. Cell lengths were measured from 30 videoframes and plotted as a function of time. Nonlinear fitting of celllength to an exponential model gave shortening velocities faster thanmost of those reported for airway smooth muscle tissues. For a sampleof 10 adult and 10 preterm cells stimulated with 100 µM carbachol,mean (± SD) shortening velocity of the preterm cells was notdifferent from that of the adult cells (0.64 ± 0.30 vs. 0.54 ± 0.27 s¹, respectively), butpreterm cells shortened more than adult cells (68 ± 12 vs. 55 ± 11% of starting length, respectively;P < 0.05). The preparative andanalytic methods described here are widely applicable to other smoothmuscles and will allow contraction to be studied quantitatively at thesingle-cell level.

     

Single rabbit stomach smooth muscle cell myosin heavy chain SMB expression and shortening velocity

Isolated single smoothmuscle cells (SMCs) from different regions of the rabbit stomach wereused to determine a possible correlation between unloaded shorteningvelocity and smooth muscle (SM) myosin heavy chain (MHC) S1 headisoform composition (SMA, no head insert; SMB, with head insert).-Toxin-permeabilized isolated single cells were maximally activatedto measure unloaded shortening velocity and subsequently used in anRT-PCR reaction to determine the SMA/SMB content of the same cell. SMMHC SMA and SMB isoforms are uniquely distributed in the stomach with cells from the fundic region expressing little SMB (38.1 ± 7.3% SMB; n = 16); cells from the antrum express primarilySMB (94.9 ± 1.0% SMB; n = 16). Mean fundic cellunloaded shortening velocity was 0.014 ± 0.002 cell lengths/scompared with 0.036 ± 0.002 for the antrum cells. Unloadedshortening velocity in these cells was significantly correlated withtheir percent SMB expression (r² = 0.58).Resting cell length does not correlate with the percent SMB expression(n = 32 cells). Previously published assays of purifiedor expressed SMA and SMB heavy meromyosin show a twofold difference inactin filament sliding speed in in vitro motility assays. Extrapolationof our data to 0-100% SMB would give a 10-fold range ofshortening velocity, which is closer to the ~20-fold range reportedfrom various SM tissues. This suggests that mechanisms in addition tothe MHC S1 head isoforms regulate shortening velocity.

     

Slowing of velocity during isotonic shortening in single isolated smooth muscle cells. Evidence for an internal load

In single smooth muscle cells, shortening velocity slows continuously during the course of an isotonic (fixed force) contraction (Warshaw, D.M. 1987. J. Gen. Physiol. 89:771-789). To distinguish among several possible explanations for this slowing, single smooth muscle cells were isolated from the gastric muscularis of the toad (Bufo marinus) and attached to an ultrasensitive force transducer and a length displacement device. Cells were stimulated electrically and produced maximum stress of 144 mN/mm2. Cell force was then reduced to and maintained at preset fractions of maximum, and cell shortening was allowed to occur. Cell stiffness, a measure of relative numbers of attached crossbridges, was measured during isotonic shortening by imposing 50-Hz sinusoidal force oscillations. Continuous slowing of shortening velocity was observed during isotonic shortening at all force levels. This slowing was not related to the time after the onset of stimulation or due to reduced isometric force generating capacity. Stiffness did not change significantly over the course of an isotonic shortening response, suggesting that the observed slowing was not the result of reduced numbers of cycling crossbridges. Furthermore, isotonic shortening velocity was better described as a function of the extent of shortening than as a function of the time after the onset of the release. Therefore, we propose that slowing during isotonic shortening in single isolated smooth muscle cells is the result of an internal load that opposes shortening and increases as cell length decreases.     

The maximum shortening velocity of muscle should be scaled with activation.

The purpose of this study was to determine whether the maximum shortening velocity (Vmax) in Hill's mechanical model (A. V. Hill. Proc. R. Soc. London Ser. B. 126: 136-195, 1938) should be scaled with activation, measured as a fraction of the maximum isometric force (Fmax). By using the quick-release method, force-velocity (F-V) relationships of the wrist flexors were gathered at five different activation levels (20-100% of maximum at intervals of 20%) from four subjects. The F-V data at different activation levels can be fitted remarkably well with Hill's characteristic equation. In general, the shortening velocity decreases with activation. With the assumption of nonlinear relationships between Hill constants and activation level, a scaled Vmax model was developed. When the F-V curves for submaximal activation were forced to converge at the Vmax obtained with maximum activation (constant Vmax model), there were drastic changes in the shape of the curves. The differences in Vmax values generated by the scaled and constant Vmax models were statistically significant. These results suggest that, when a Hill-type model is used in musculoskeletal modeling, the Vmax should be scaled with activation.     

Expression of smooth muscle myosin light chain 17 and unloaded shortening in single smooth muscle cells

These experiments were performed totest the hypotheses that myosin light chain 17 (MLC₁₇) aand b isoform expression varies between individual vascular smoothmuscle (SM) cells and that their expression correlates with cellunloaded shortening velocity. Single SM cells isolated from rabbitaorta and carotid arteries were used to measure unloaded shorteningvelocity and subsequently were analyzed via RT-PCR forMLC₁₇ a and b mRNA ratio. The MLC_17b/a mRNA andprotein ratios from adjacent tissue sections correlate very well(R² = 0.68), allowing use of the mRNA ratio topredict the protein ratio. The rabbit MLC₁₇ isoform proteinsequence was found to be similar to, but unique from, the swine, mouse,and chicken sequences. Isolated single SM cells from the aorta andcarotid have resting lengths of 70-280 µm and shorten to33-88 µm after contraction. Isolated cell maximum unloadedshortening velocity is highly variable (0.5-7.5 µm/s) butbecomes more uniform when normalized to initial cell length(0.01-0.05 cell lengths/s). Carotid cells activated in thepresence of okadaic acid (1 µm) have mean maximal unloaded shorteningvelocities not significantly different from carotid cells activatedwithout okadaic acid (0.016 vs. 0.019 cell lengths/s). Resting celllength before activation is significantly correlated with final celllength after unloaded shortening. Neither initial cell length, finalcell length, total cell length change, nor maximum unloaded shorteningvelocity (absolute or normalized) was significantly correlated withsingle-cell MLC_17b/a mRNA ratio. These studies wereperformed in isolated single SM cells where unloaded shorteningvelocity and MLC_17b/a mRNA ratios were measured in the samecell. In this preparation, the three-dimensional organization andmilieu of the cell is kept intact, but without the intercellularheterogeneity concerns of multicellular preparations. These resultssuggest the MLC_17b/a ratio is variable between individual SM cells from the same tissue, but it is not a determinant of unloadedshortening velocity in single SM cells.

     

Effect of theophylline on the velocity of diaphragmatic muscle shortening

The present study examined the effect of theophylline on the shortening velocity of submaximally activated diaphragmatic muscle (i.e., muscles were activated by the use of a level of stimulation, 50 Hz, within the range of phrenic neural firing frequencies achieved during breathing, whereas maximum activation is achieved at 300 Hz). Experiments were performed in vitro on strips of diaphragmatic muscle obtained from 21 Syrian hamsters. Muscle shortening velocity was assessed during isotonic contractions against a range of afterloads, and Hill's characteristic equation was used to calculate velocity at zero load. In addition, unloaded shortening velocity was also measured by the slack test, i.e., from the time required for muscles to take up slack after a sudden reduction in muscle length. Theophylline (160 mg/l) increased the velocity of muscle shortening against a wide range of external loads (0-14 N/cm2) and increased the extrapolated unloaded velocity of shortening from 6.4 +/- 0.9 to 7.9 +/- 1.1 (SE) lengths/s (P less than 0.01). Theophylline reduced the time required to take up slack for any given step change in muscle length, increasing the unloaded velocity of shortening assessed by the slack test from 7.6 +/- 0.9 to 9.3 +/- 1.1 lengths/s (P less than 0.002). The effect of theophylline on diaphragmatic shortening velocity was evident at concentrations as low as 40 mg/l and increased progressively as theophylline concentrations were increased to 320 mg/l. Theophylline increased the shortening velocity of fatigued as well as fresh muscles.(ABSTRACT TRUNCATED AT 250 WORDS)