The Huxley crossbridge model as the basic mechanism for airway smooth muscle contraction

Abstract

The cyclic interaction between myosin crossbridges and actin filaments underlies smooth muscle contraction. Phosphorylation of the 20-kDa myosin light chain (MLC20) is a crucial step in activating the crossbridge cycle. Our current understanding of smooth muscle contraction is based on observed correlations among MLC20 phosphorylation, maximal shortening velocity (V_max), and isometric force over the time course of contraction. However, during contraction there are changes in the extent of phosphorylation of many additional proteins as well as changes in activation of enzymes associated with the signaling pathways. As a consequence, the mechanical manifestation of muscle contraction is likely to change with time. To simplify the study of these relationships, we measured the mechanical properties of airway smooth muscle at different levels of MLC20 phosphorylation at a fixed time during contraction. A simple correlation emerged when time-dependent variables were fixed. MLC20 phosphorylation was found to be directly and linearly correlated with the active stress, stiffness, and power of the muscle; the observed weak dependence of V_max on MLC20 phosphorylation could be explained by the presence of an internal load in the muscle preparation. These results can be entirely explained by the Huxley crossbridge model. We conclude that when the influence of time-dependent events during contraction is held constant, the basic crossbridge mechanism in smooth muscle is the same as that in striated muscle.

INTRODUCTION

Our current understanding of the molecular mechanism of contraction in striated muscle is based on a model of cyclic interactions between myosin crossbridges and actin filaments within the structural confines of a sarcomere (18). A similar mechanism is thought to be operative in smooth muscle (10). In striated muscle the maximal unloaded shortening velocity (V_max) is determined by the intrinsic actin-activated Mg²⁺-ATPase activity of the myosin (2). In smooth muscle a number of myosin isoforms with different intrinsic ATPase activities are associated with different V_max (22). Smooth muscle ATPase is activated by phosphorylation of the 20-kDa myosin light chain (MLC20) (19, 29), the extent of which also appears to influence V_max. In tonic smooth muscle V_max was found to be directly proportional to the degree of MLC20 phosphorylation (1). This has led to a theory (latch-bridge model) asserting that there are two types of crossbridges: phosphorylated normally cycling bridges and attached and nonphosphorylated slowly cycling latch-bridges (14). The latter are thought to be responsible for the observed decline in V_max during a sustained contraction. Although the theory explains the parallel decline in both V_max and MLC20 phosphorylation (1, 5), it has been found that the relationship between V_max and phosphorylation varies with different modes of stimulation (24), suggesting that factors other than MLC20 phosphorylation, e.g., the time-dependent chemical modification of other proteins and enzymes, may play a role in determining the velocity. In phasic or partially phasic smooth muscles like airway smooth muscle (ASM), consistent correlation between MLC20 phosphorylation and V_max has not always been found (21, 23). Some studies have shown a clear divergence between MLC20 phosphorylation and V_max in ASM, in that a decline in V_max was not accompanied by any decline in MLC20 phosphorylation (11, 13). With higher temporal resolution using a computer-controlled freezing apparatus, Mitchell et al. (25) found that during the early phase of ASM contraction, the decline of V_max occurred while MLC20 phosphorylation was increasing, a result opposite to what the latch-bridge model (14) would predict.

If the latch-bridge theory is inadequate to explain the behavior of smooth muscle, there is a need for a theory either to replace or complement it. In the present study we examined the dependence of V_max of ASM on MLC20 phosphorylation by applying isotonic quick releases at a fixed time after activation during isometric contractions. Applying Occam’s razor, the simpler crossbridge model of striated muscle (18) is adopted over the latch-bridge model (14) as the working model for the present study. The guiding hypothesis is that MLC20 phosphorylation acts as a switch (akin to calcium binding to troponin C in striated muscle) to turn on the actomyosin crossbridge cycle. Once turned on, the crossbridge cycling rate is a pure function of muscle load (18). A corollary of the hypothesis is that the degree of MLC20 phosphorylation is proportional to the number of activated crossbridges. We obtained force-velocity (F-V) curves of fully and partially activated muscles, which allowed us to examine, besides force and velocity, the maximal power output and stiffness of the muscle and their relationship with different levels of MLC20 phosphorylation. The F-V data thus obtained also allowed us to determine the internal load opposing shortening. We found that the results obtained at a fixed time during contraction can be explained by the striated muscle model (18).

MATERIALS AND METHODS

Airway smooth muscle preparation.

In this study we used sheep tracheal smooth muscle. Experimental procedures were approved by the Ethics Committee for Animal Care and the Biosafety Committee of the University of British Columbia and conformed to the guidelines set out by the Canadian Council on Animal Care.

Tracheas were obtained from a local abattoir and carried to our laboratory in ice-cold physiological saline solution (PSS) that had the following composition: 118 mM NaCl, 4 mM KC, 1.2 mM NaH₂PO₄, 22.5 mM NaHCO₃, 2 mM MgSO₄, 2 mM CaCl₂, and 2 g/l dextrose at pH 7.4. Tracheal tissues were either immediately used in experiments or stored in PSS at 4°C and used within the next 4 days. The in situ length of the muscle was measured in tracheal rings before cutting the C-shaped cartilage open. The opened trachea was then pinned on both ends on the dissection plate while maintaining the muscle length at its in situ length. Smooth muscle strips (8–9 mm long, 1.5–2 mm wide, and 0.2–0.3 mm thick) were dissected and attached to a force/length transducer (duo mode, Model 300C, Aurora Scientific Inc.) via aluminum foil clips affixed on both ends of the strips. Strips were mounted and equilibrated for 60 min at their in situ length in organ baths at 37°C in PSS aerated with carbogen (95% O₂-5% CO₂). Indomethacin (5 × 10⁻⁵ M) was added to the bath to reduce intrinsic tone without affecting contractile response. To verify muscle viability and ensure consistent force generation, the preparations were periodically activated isometrically (every 5 min for 10 s) by electric field stimulation (EFS) (60 Hz and a current density eliciting maximal muscle response) for ~1 h. The in situ length of the muscle was used as a reference length (L_ref) for normalization of length and velocity measurements.

Force-velocity experiments in fully and partially activated muscle.

After stable maximal isometric force was achieved, F-V properties of the muscle were assessed in each strip under conditions of full and partial activation. Partial activation in each strip was achieved by modifying the voltage setting to reduce isometric force to ~50% and 75% of that produced by full activation.

Isotonic quick releases (Fig. 1) were applied at the point of maximal force induced by EFS (9.5–10 s). The slope of the length trace at 0.1 s after the release was obtained by a linear fit to the length data points within the 0.08–0.12-s interval after the quick release (dL/dt in Fig. 1B) and used as a measurement of the shortening velocity. The 0.1-s delay was chosen to avoid distortion of velocity measurements by the recoil of the series of the viscoelastic element that occurs at early time points. Quick releases were performed seven times in seven separate contractions separated by 5-min intervals of resting period using a different isotonic load for each quick release. The loads were applied in random order and were 5%, 10%, 15%, 25%, 35%, 50%, and 75% of the maximal active force (F_max) produced by EFS.

Fig. 1.

An example of isotonic quick release. A: an isotonic force step (ΔF) is obtained by applying a force-clamp at the plateau of an isometric contraction; this instantly lowers the load on the muscle from maximal active force (F_max) to an isotonic load, which in this example was 10% of the tension at plateau. B: length response to the isotonic force step, which is made of two components, a quick elastic recoil (ΔL), because of viscoelastic recoil, and a slower shortening, because of active muscle shortening; the former dominates the early phase and the latter dominates the late phase of shortening. Active shortening velocity (dL/dt) is measured at 100 ms after the onset of quick release to avoid viscoelastic recoil. Stiffness of the series elastic component of the muscle is defined as ΔF/ΔL.

The F-V data were fitted using the Hill’s equation of the form: (F + a)(V + b) = c, where F is the isotonic force, V is the shortening velocity, and a, b, and c are constants (16). A nonlinear least-square fit to the data was performed using SigmaPlot 14.0 (Systat Software, Inc., San Jose, CA). Force-power (F-P) curves were obtained from the F-V curves by multiplying force and velocity values: P = F × V = F[c/(F + a) – b]. Fig. 2 shows typical F-V and F-P curves; the intersection of the F-V curve with the velocity axis is the maximal shortening velocity in the absence of any externally applied load (V_max), while P_max designates the maximal value of the power function. Note that in later analyses, when internal load is accounted for, the true maximal velocity is different from V_max and is designated as V_max.

Fig. 2.

An example of force-velocity (F-V) and force-power (F-P) curves. The F-V data (closed circles) were fitted with the Hill equation. By extrapolating the curve to zero external load, maximal shortening velocity (V_max) was obtained. The F-P curve was obtained from the F-V curve by setting power = force × velocity. The peak power is designated as P_max. L_ref, reference length; F_max, maximal active force.

From the quick release experiments, we also obtained an estimate of the stiffness of the series elastic component (SEC) of the muscle. The amount of the elastic recoil immediately after a quick release (shown as ΔL in Fig. 1) was taken as the change in the length of the SEC. Isotonic quick releases at 5% and 10% of F_max were used for the stiffness measurements (ΔF/ΔL).

Identification of internal load and rescaling of the isotonic load axis.

The method for determining the internal load has been described by Ford (7) and Wang et al. (31). Because a fixed internal load is a relatively larger load for partially activated muscle and reduces V_max to a greater extent than it does at full activation, F-V curves for fully and partially activated smooth muscles can be used to determine the value of the internal load. In the analysis, these curves were extrapolated to negative values on the load axis, and the crossing point of the two curves indicated both the absolute zero load and the true maximal shortening velocity in the absence of internal and external loads (31).

The values of internal load were then used to rescale the load axis so that it represented the sum of internal and external loads (and not just the external load). F-V data in these rescaled plots were refitted with the Hill equation and the true maximal shortening velocity and power output were recalculated.

Measurement of MLC20 phosphorylation.

To measure the level of MLC20 phosphorylation, three muscle strips from the same trachea were frozen under different conditions. Two strips were frozen at the time point when isotonic quick releases were applied (9.5–10 s) in fully and partially activated strips; a third strip was frozen at rest for the determination of baseline phosphorylation. The tissue strips were snap-frozen in prechilled acetone (at dry ice temperature, −78.5°C) while still attached to the transducer. A typical recording of the force produced by a strip snap-frozen at peak contraction is shown in Fig. 3. Frozen strips were quickly taken off the apparatus and placed in tubes of prechilled acetone containing 5% trichloroacetic acid (TCA) and 10 mM dithiothreitol (DTT) and stored at −80°C. Within a week the strips were processed to extract total protein. Immediately before the protein assay, the strips were brought to room temperature. TCA was removed from the strips by washing the strips twice (30 min each) in 1 ml acetone containing 10 mM DTT. At a proportion of 150 µl/mg wet tissue weight, the strip was then homogenized in lysis buffer containing 6.4 M urea, 5 mM DTT, 10 mM EGTA, 1 mM EDTA, 5 mM NaF, 1 mM phenylmethylsulfonyl fluoride, 26.4 mM tris base, and 29.3 mM glycine. Samples were incubated for 2 h and then centrifuged at 13,200 g for 30 min at 4°C. After centrifugation, the supernatant was obtained and the Bio-Rad QuickStart Bradford protein assay performed to obtain total protein concentration for each sample. An aliquot of each supernatant was then diluted further with additional lysis buffer containing 0.02% bromophenol blue and stored at −80°C.

Fig. 3.

An example of the time course of isometric contraction induced by a 10-s electrical field stimulation (EFS). At the plateau of contraction the muscle bath was quickly (within 0.75 ± 0.19 s, shown here as Δt) replaced by a container filled with dry ice-chilled acetone. The frozen sample was then processed to determine the level of 20-kDa myosin light chain phosphorylation.

Phosphorylated and nonphosphorylated MLC20 were separated on a 10% acrylamide, 40% glycerol mini gel with 3% acrylamide-urea stacking gel. Electrophoresis was performed at 200 V for 2.5 h at room temperature in running buffer containing 100 mM glycine, 50 mM Tris, and β-mercaptoethanol (1 ml/l buffer). An additional 0.5 ml of β-mercaptoethanol was added to the inner chamber. Proteins were then transferred to 0.2 µm nitrocellulose membrane at 25 V at 4°C overnight. Nonspecific binding sites were blocked with tris-base saline (TBS)-5% bovine serum albumin (BSA) for 1 h at room temperature. Western immunoblots were developed using, in sequence, a monoclonal mouse antibody to smooth muscle MLC (Sigma, clone MY-21) (1:5,000) and goat anti-mouse IRDye 800 conjugated antibody (1:10,000) in TBS with Tween (TBST)-5% BSA. The membranes were washed three times with TBST for 10 min each time during standard washing steps, i.e., after primary and secondary antibodies. The membrane was then scanned on a LI-COR Odyssey 2.1 Infrared Imaging System. The intensity of each band was analyzed using the software Odyssey 2.1 with background intensity subtracted from the total integrated optical intensity. Fractional phosphorylation in each sample was determined as the ratio of the optical density of the band stained for phosphorylated light chain to the sum of the density of the bands stained for phosphorylated and nonphosphorylated proteins (the lower and upper band, respectively) in the same lane. MLC20 phosphorylation in full or partial activation was then calculated by subtracting the value of fractional phosphorylation in a strip from the same trachea that was frozen in a resting state.

Data analysis.

Data are expressed as means and standard errors. Results in fully and partially activated conditions were compared using paired t-test. A P value of 0.05 or less was used to reject the null hypothesis. To evaluate the effect of partial activation, data from each set of experiments were expressed as the fraction of the values obtained in the same strip when repeated measurements were possible or a parallel strip from the same trachea when repeated measurements on the same strip were not possible (e.g., strips frozen for MLC20 measurements), under full activation. Data of stress, stiffness, V_max at zero external load, maximal power (P_max), and MLC20 phosphorylation obtained for the two sets of experiments with different degrees of partial activation were then compared by two-way ANOVA and with post hoc all pairwise multiple comparison procedures (Student-Newman-Keuls Method).

RESULTS

Stress as an index of full and partial ASM activation.

Muscle activation can manifest as three different mechanical outputs—active stress, stiffness, and power (7). When all other variables are held constant, these three outputs should all correlate linearly with the number of activated crossbridges (18). In the present study, the independent variable was the degree of muscle activation. Time-dependent variables were controlled for by measuring muscle properties at a fixed time point, 10 s after activation, when isometric force induced by EFS just reached its maximal or near maximal value.

Isometric stress (isometric force normalized by the cross-sectional area of the muscle preparation) was chosen as an index of muscle activation in the present study. This index was correlated with muscle stiffness and power output to verify the validity of the choice. Note that according to the Huxley model, isometric force, active stiffness, and power can all be used as indices of muscle activation; however, this is not true for the latch-bridge model. Using the values of isometric stresses obtained at different degrees of activation and the average value from full activation as 100%, the two groups of partially activated muscles had indices of activation of 57.5 ± 1.9% and 71.7 ± 1.8% (Fig. 4, C and D). These two groups are referred to as 58% and 72% activation for the rest of this article.

Fig. 4.

Active stress and stiffness of muscle at different degrees of activation. A: an example of force record showing time courses of isometric contractions from a fully and partially activated muscle. The partial activation in this example was 54% of the full activation. B: active stiffness of the muscle at different degrees of activation. Full activation, n = 12; 72% and 58% activation, n = 6. C and D: active stress at different degrees of activation, n = 6 for each group. Data are means ± SE. *P < 0.05, **P < 0.01.

Stiffness of the series elastic component in fully and partially activated ASM strips.

Active stiffness of the series elastic component (SEC) has been shown to be linearly correlated to isometric force and could be used to estimate the number of active crossbridges (32). The SEC stiffness measured in the present study at 58% and 72% activation (Fig. 4B) was respectively 57.9 ± 6.4% and 74.3 ± 1.8% of the fully activated stiffness, very close to the isometric force (relative to F_max at full activation, 100%) measured at the corresponding levels of activation; the results are consistent with previous studies (32).

F-V properties and power output in fully and partially activated ASM strips.

The F-V curves obtained in partially and fully activated muscles are plotted in Fig. 5. We present the data in two ways; first we fit F-V data from individual muscle strips and plotted the fitted curves in groups: fully activated (Fig. 5A) and partially activated (Fig. 5C). Table 1 shows the mean ± SE values of the Hill constants obtained during the curve fitting, while Table 2 shows mean ± SE values of V_max. We then plotted combined F-V data obtained under the same conditions and fitted a single Hill’s hyperbola through the combined data: fully activated (Fig. 5B) and partially activated (Fig. 5D). Single extrapolated V_max values are shown in Table 2. The fitted curves are plotted without data points in Fig. 5E. The mean V_max values obtained by extrapolating the F-V curves (Fig. 5, A and C) to zero external load at different degrees of activation are shown in Fig. 5F. It is well known that the extrapolated isometric force from an F-V curve is always greater than the experimentally measured F_max (27) because at the high-force region of the curve the Hill equation overestimates the velocity (i.e., the curve is slightly above the F-V points leading to an intersecting point with the force axis beyond the measured maximal isometric force values. The theoretical basis for this discrepancy has been explained by Seow (27). For this reason, the extrapolated F_max values are not used to indicate the degree of activation; instead, the measured maximal isometric force values were used.

Fig. 5.

Force-velocity (F-V) curves for fully and partially activated muscles and the extrapolated maximal shortening velocity (V_max) values. Two separate groups of experiments were performed (red and blue curves). The red group compared the differences between fully and 72% activated muscles, n = 6. The blue group compared the differences between fully and 58% activated muscles, n = 6. A: all 12 fully activated curves obtained from fitting individual data sets. B: the same data sets as in A combined together in red and blue groups and fitted with a single Hill’s hyperbola for each group. C: 72% (red, n = 6) and 58% (blue, n = 6) activated curves from each individual F-V measurement. D: F-V data points grouped together for the red and blue groups and fitted with a single Hill’s hyperbola for each group. E: the curves from B and D are replotted without the data points. F: extrapolated V_max from individual F-V curves (n = 6 for the partial activation groups and n = 12 for the fully activated. *P < 0.05). F_max, maximal active force; L_ref, reference length.

Table 1.

Coefficients of Hill’s equation from the fitting of F-V data without correction for internal load

	a, %Fmax	b, Lref/s	c, %Fmax·Lref·s−1
Full activation	13.95 ± 0.60	0.043 ± 0.003	5.59 ± 0.32
72% Activation	11.04 ± 0.70 (79.4%, P < 0.01)	0.041 ± 0.004 (96.2%, NS)	3.97 ± 0.32 (71.4%, P < 0.01)
Full activation	11.89 ± 0.43	0.037 ± 0.002	4.89 ± 0.26
58% Activation	8.69 ± 1.01 (73.8%, P < 0.05)	0.039 ± 0.006 (109.4%, NS)	2.84 ± 0.32 (59.8%, P < 0.05)

Values are means ± SE; n = 6 for each group. The two paired observations (Full vs. 72% activation and Full vs. 58% activation) were obtained in two sets of independent experiments. Statistical comparisons were made within the paired parameters. Maximal shortening velocity (V_max) = c/a – b. F_max, maximal active force; F-V, force-velocity; L_ref, reference length; NS, statistically not significant.

Table 2.

Maximal shortening velocity at zero external load

	Vmax, Lref/s
	Individual Curves	Combined Fit
Full activation	0.359 ± 0.018	0.358
72% Activation	0.321 ± 0.023 (89.1%, NS)	0.313 (87.4%)
Full activation	0.379 ± 0.018	0.371
58% Activation	0.291 ± 0.021 (77.8%, P < 0.05)	0.297 (75.2%)

Values are means ± SE; n = 6 for each group. The maximal shortening velocity (V_max) values were obtained in two ways, from fitting of individual curves (Fig. 5, A and C) and from a combined fit of grouped data (Fig. 5, B and D). L_ref, reference length; NS, statistically not significant.

The F-P curves derived from the F-V curves (shown in Fig. 5) are plotted in Fig. 6. The curves for the fully activated muscles are plotted in Fig. 6A and, for the partially activated, in Fig. 6B. Figure 6C shows the averaged F-P curves, and Fig. 6D shows the mean value of maximal power (P_max) at different degrees of activation. Also see Table 3 for mean P_max ± SE.

Fig. 6.

Force-power (F-P) curves for fully and partially activated muscles. A: F-P curves for the fully activated muscles. These curves were derived from the force-velocity (F-V) curves shown in Fig. 5A. B: F-P curves for 72% (red) and 58% (blue) activated muscles. These curves were derived from the F-V curves shown in Fig. 5C. C: averaged F-P curves. These curves were averaged from the same color curves in A and B. D: maximal power (P_max) values averaged from individual curves. **P < 0.01 in comparison with fully activated. The n numbers are the same as in Fig. 5. F_max, maximal active force; L_ref, reference length.

Table 3.

Maximal powers without (P_max) and with (P_max) correction for internal load

	Pmax, %Fmax·Lref·s−1	Pmax, %Fmax·Lref·s−1
Full activation	2.54 ± 0.12	2.48 ± 0.12
72% Activation	1.74 ± 0.10 (68.9%, P < 0.01)	1.81 ± 0.11 (73.2%, P < 0.01)
Full activation	2.41 ± 0.16	2.33 ± 0.15
58% Activation	1.20 ± 0.08 (50.6%, P < 0.01)	1.33 ± 0.08 (57.7%, P < 0.01)

Values are means ± SE; n = 6 for each group. F_max, maximal active force; L_ref, reference length.

Determining internal load and the absolute maximal shortening velocity.

The V_max values shown in Fig. 5 were obtained by extrapolating the F-V curves to zero external load. In striated muscle the internal load can be estimated by extrapolating F-V curves obtained from the same muscle at different degrees of activation (7) and finding the point where the curves cross. Justification for this practice is that at absolute zero load, the shortening velocity is independent of the number of activated crossbridges, and therefore full and partial activation should produce the same maximal velocity. To differentiate from the V_max that represents maximal shortening velocity obtained under zero external load (but with a finite internal load), we use the symbol V_max to represent the absolute maximal shortening velocity obtained under both zero external and zero internal load.

In Fig. 7, the mean F-V curves from Fig. 5E are replotted but with the curves extended into the “negative” force range. The force range is negative because we define zero external load as zero force in the graph. The assumption that there is an internal load is supported by the fact that the full and partial activation curves do cross each other, and the assumption that the internal load is constant and independent of the degree of activation is supported by the fact that the full and 72% activation curves cross each other at virtually the same negative force point (absolute zero load) where the full and 58% activation curves cross each other (−4.6% and −4.7% F_max, respectively; also see the inset in Fig. 7).

Fig. 7.

Determination of internal load by extrapolation of the force-velocity (F-V) curves into the negative force range. Note that the zero force on the horizontal axis indicates zero externally applied isotonic load. The point where the full and partial activation curves cross each other indicates the true zero load (both external and internal) on muscle and from that point the amount of internal load (F_i) and the absolute maximal shortening velocity (V_max) can be determined (7, 31). The inset shows the same curves in an expanded force-scale. Note that the blue and red curves were derived from two independent sets of experiments. The two sets of curves cross each other at −4.6% and −4.7%, indicating internal loads of 4.6% and 4.7% maximal active force (F_max), which correspond to V_max values of 0.617 and 0.562 L_ref/s, respectively. L_ref, reference length.

When the absolute zero load is used (instead of the zero external load) in plotting the F-V data, new sets of F-V curves are obtained. See Table 4 for the Hill’s constants for the refitted curves where the internal load was taken into account. Also see Table 3 for a comparison of maximal power outputs calculated with and without the internal load, P_max and P_max, respectively.

Table 4.

Coefficients of Hill’s equation from F-V data with correction for internal load

	a, %Fmax	b, Lref/s	c, %Fmax·Lref·s−1
Full activation	7.61 ± 0.49	0.043 ± 0.003	4.60 ± 0.26
72% Activation	5.21 ± 0.58 (68.8%, P < 0.01)	0.041 ± 0.004 (96.2%, NS)	3.27 ± 0.27 (71.4%, P < 0.01)
Full activation	5.91 ± 0.35	0.037 ± 0.002	3.96 ± 0.21
58% Activation	3.32 ± 0.82 (57.2%, P < 0.05)	0.039 ± 0.006 (74.3%, NS)	2.30 ± 0.26 (58.8%, P < 0.01)

Values are means ± SE; n = 6 for each group. The two paired observations (Full vs. 72% activation and Full vs. 58% activation) were obtained in two sets of independent experiments. Statistical comparisons were made within the paired parameters. Absolute maximal shortening velocity (V_max) = c/a – b. F_max, maximal active force; F-V, force-velocity; L_ref, reference length; NS, statistically not significant.

MLC20 phosphorylation in fully and partially activated ASM strips.

MLC20 phosphorylation at different degrees of activation is shown in Fig. 8. Because the muscle strips were frozen at different levels of activation, unlike that in the F-V measurements, each strip only contributed to one data point; a separate set of muscle strips was used for this group of experiments, and therefore the degrees of partial activation did not match exactly those seen in the F-V experiments. The two levels of partial activation were 52.8 ± 3.1% and 70.5 ± 1.5% F_max.

Fig. 8.

20-kDa Myosin light chain (MLC20) phosphorylation in fully and partially activated muscles. A: an example of Western blot bands showing phosphorylated (p-MLC20) and nonphosphorylated (Non p-MLC20) MLC20 in fully, 53% activated, and resting muscles. B: an example of Western blot bands showing phosphorylated (p-MLC20) and nonphosphorylated (Non p-MLC20) in fully, 71% activated, and resting muscles. C: percentage of MLC20 phosphorylation produced by electrical field stimulation after subtracting phosphorylation at rest. (n = 6 for the partial activation groups and n = 12 for the fully activated; **P < 0.01 in comparison with the fully activated.) Note that the muscle preparations used in this group of experiments were separate from those used for force-velocity (F-V) measurements; the % of partial activations was slightly different from the F-V group.

DISCUSSION

In the present study, we have investigated ASM mechanical properties at a fixed time after contraction in response to different degrees of activation. In our experimental setting, which was chosen to avoid the influence of time-dependent factors, we found that MLC20 phosphorylation is directly and linearly correlated with the active stress, stiffness, and power of the muscle. Our data show the presence of an internal load that explains the lack of dependence of V_max on MLC20 phosphorylation.

A model of smooth muscle contractile unit with Huxley type crossbridge kinetics.

Findings from the present study can be explained by the Huxley sliding-filament crossbridge model (18). However, because the structure of the contractile unit in smooth muscle is different from the sarcomeric structure of striated muscle due to the side-polar nature of smooth muscle myosin filament (34), we start the discussion by defining how, in the absence of influence by time-dependent variables, activation (the number of activated crossbridges) affects force, stiffness, power, and maximal shortening velocity in the smooth muscle model.

Figure 9 illustrates two contractile units of smooth muscle, one fully activated and the other partially activated. Although the contractile unit structure of smooth muscle is still a concept, there is supporting evidence for the side-polar myosin filament as the main feature of the unit (15, 17). In such a unit the crossbridges interacting with the same actin filament are arranged in parallel, and therefore the total force pulling on the actin filament is the sum of forces produced by individual bridges that are active.

Fig. 9.

Schematic illustration of smooth muscle contractile units. A: a fully activated contractile unit. The side-polar myosin filament is sandwiched by two actin filaments. The antiparallel arrows indicate the opposite directions of movement of actin filaments because of active crossbridge action. The activated (phosphorylated) myosin crossbridges are shown in red. B: a partially activated contractile unit. Inactive (unphosphorylated) crossbridges are shown in white.

There are four major assumptions associated with this model based on Huxley crossbridge kinetics (18), and they have been verified by the experiments carried out in this study. The assumptions and their respective corollaries are as follows: 1) The crossbridges are a major source of compliance in striated (9) and smooth (33) muscle, and therefore the degree of activation should be proportional to the stiffness of the activated muscle, assuming that the compliance from the myofilaments is relatively small and invariable at different degrees of activation. 2) MLC20 is a built-in switch on a myosin crossbridge, and its phosphorylation activates the bridge. Therefore, the extent of phosphorylation of the whole muscle should be proportional to the degree of activation of the muscle. 3) Each activated crossbridge is an independent force-generator. There are two corollaries associated with this assumption. First, the maximal shortening velocity of the muscle achieved in the absence of any load, both internal and external, is independent of the degree of muscle activation [as observed in striated muscle (7)] and only dependent on the intrinsic myosin ATPase activity (i.e., how fast the myosin hydrolyzes ATP). Second, the curvature of the F-V curves obtained under full and partial activation should be the same, and the curves should superimpose exactly when force values are normalized by their respective maximal isometric force. These corollaries are elaborated later when the mathematical model is discussed. 4) There is an internal load associated with each muscle preparation. This implies that the true maximal shortening velocity (achieved only in the absence of both internal and external loads) cannot be directly measured from a single F-V curve. However, because the third assumption stipulates that the true maximal velocity is activation independent, by finding a convergence point from multiple F-V curves obtained at different levels of activation one can determine the true maximal velocity and at the same time the internal load. A corollary is therefore that F-V curves obtained from a muscle preparation at different degrees of activation should converge at a common point where both internal and external loads are zero and where the velocity represents the true maximal velocity (V_max) of the muscle. Another corollary is that the velocity, obtained in the absence of external load but the presence of internal load (i.e., V_max), will be dependent on the degree of activation.

The assumptions and corollaries are further explained below. The convergence of F-V curves obtained at different degrees of activation (Fig. 7) supports the assumption that there is an internal load. In two sets of experiments (full versus 58% activation and full versus 72% activation) the predicted values of internal load (4.6% and 4.7% of F_max) are virtually the same. In a porcine trachealis preparation, we used the same method to estimate the internal load and found it to be 5.1% of F_max (31), similar to the values found in the present study. In the following analysis of F-V data the internal load is taken into account by adding the amount of internal load to the externally applied load.

For the contractile units shown in Fig. 9, the following hyperbolic (Hill) equations can be used to describe their shortening velocities as functions of the total load (F) on the muscle that includes both the load (or resistance to shortening) stemming from within the muscle preparation (internal load, F_i) and the externally applied load (F_e):

$$V_{\text{f}}=\frac{b\left[F_{\max }-(F_{\text{i}}+F_{\text{e}})\right]}{(F_{\text{i}}+F_{\text{e}})+a}$$ (1)

$$V_{\text{p}}=\frac{b_{\text{p}}\left[n{F}_{\max }-(F_{\text{i}}+F_{\text{e}})\right]}{(F_{\text{i}}+F_{\text{e}})+a_{\text{p}}}$$ (2)

where V is velocity, a and b are Hill’s constants, and the subscripts f and p denote full and partial activation, respectively. In a fully activated muscle, the isometric force is denoted by F_max. In a partially activated muscle, the degree of activation is expressed as a fraction of the fully activated, that is, nF_max, where n is the fraction of active crossbridges (i.e., n = 1 denotes full activation and 0 < n < 1 denotes partial activation). Figure 10, A and B shows V_f and V_p as functions of the total load (F) on the muscle, which is obtained by adding the internal load (see results) to the externally applied load, that is, F = F_i + F_e. The two curves shown in Fig. 10A and Fig. 10B are simply visual representations of Eq. 1 and Eq. 2 using experimentally determined Hill’s constants, a, b, a_p, and b_p from Table 4. When normalized by their respective isometric forces, the two curves are superimposed (Fig. 10, C and D) as predicted based on assumption 3. This fact implies that partial activation merely reduces the number of active crossbridges without altering the intrinsic properties of the remaining active bridges in their cyclic interaction with the actin filaments. Mathematically, superimposition of the two curves (Fig. 10, C and D) means that the Hill’s constants b and b_p are not altered by the degree of activation, and therefore b_p = b, which is supported by experimental results showing no statistical difference between the two constants (Table 4). Furthermore, superimposition of the curves means that the relative curvature of a F-V curve (defined as a/F_max) (25) is not altered by partial activation, which is also shown to be true experimentally (Fig. 10, C and D) as predicted based on assumption 3.

Fig. 10.

Normalized force-velocity (F-V) curves of fully and partially activated smooth muscles with internal loads. The curves are the same as those shown in Fig. 7 except that the origin of the force axis indicates zero internal and zero external load. The Hill’s constants for these curves were recalculated taking into account the internal load and are listed in Table 4. A: fully (red) and 72% activated (black) F-V curves without force normalization. B: fully (blue) and 58% activated (black) F-V curves without force normalization. C: fully (red) and 72% activated (black) F-V curves with force normalization. D: fully (blue) and 58% activated (black) F-V curves with force normalization. F_max, maximal active force; V_max, absolute maximal shortening velocity.

From the above discussion, it is clear that the true maximal shortening velocity (V_max), which occurs in the absence of both internal and external loads (i.e., F_i = F_e = 0), should be independent of the degree of activation. This is because the crossbridges in a contractile unit are acting in parallel in pulling the actin filament (Fig. 9), and when there is no load, the maximal rate of filament sliding is determined by the maximal cycling rate of individual crossbridges regardless of how many of them are active (except for n = 0, which corresponds to the relaxed state where there is no shortening velocity to speak of). This is analogous to the speed of a wagon pulled by horses in parallel. When there is load on the wagon it will travel faster if there are more horses (pulling in parallel) because the total load is shared by the horses (i.e., more horses = less load on each horse). Here, the load on the wagon is analogous to the external load (F_e). When the wagon is empty, the load shared by the horses is just the weight of the wagon, which is analogous to the internal load (F_i). The empty wagon will travel at a high speed (V_max) but not at the true maximal speed (V_max) when the horses are cut loose from the wagon. Here, V_max is determined by the maximal speed of individual horses and not by the number of them.

Therefore, because V_max is independent of the degree of activation (nF_max) when F_i = F_e = 0, and because b_p = b, Eqs. 1 and 2 under zero load conditions can be rewritten respectively as:

$${\mathbf{V}}_{\max }=\frac{b{F}_{\max }}{a}$$ (3)

$${\mathbf{V}}_{\max }=\frac{bn{F}_{\max }}{a_{\text{p}}}$$ (4)

Equate Eqs. 3 and 4 and we obtain

$$a_{\text{p}}=na$$ (5)

The curvature of the F-V curve for partial activation is a_p/nF_max. Because a_p = na, the curvature becomes na/nF_max; that is, the fraction of activated bridge (n) has no influence on the curvature when partial activation does not alter the kinetics of the actomyosin crossbridge interaction, as evidenced in Fig. 10, C and D [see also an analysis by Seow (25) regarding the relationship between a/F_max and the crossbridge kinetics, i.e., the rates of transition between states in the crossbridge cycle].

Substituting a_p with na in Eq. 2, we obtain a general equation for all degrees of activation, including full activation where n = 1.

$$V=\frac{b\left[n{F}_{\max }-(F_{\text{i}}+F_{\text{e}})\right]}{(F_{\text{i}}+F_{\text{e}})+na}$$ (6)

Figure 11 is a visual representation of Eq. 6 with different n values. The Hill’s constants used in this simulation are listed in Table 4 for the full versus 58% activation group; analysis on this group of data indicates an internal load of 4.6% F_max (Fig. 7). In Fig. 11B the curves in Fig. 11A are plotted in an expanded time scale. If we assume there is an internal load of 4.6% F_max, the velocities obtained at zero external load (V_max) would be dependent on the degree of activation, as shown in Fig. 11B where the vertical dotted line crosses the curves. These velocities are plotted in Fig. 12 for various internal loads and zero external load. As one can see, except for V_max where F_i = 0, V_max is dependent on the degree of activation. Included in Fig. 12 is a function of V_max at 58% activation and with an internal load of 4.6% F_max (closed circles); the values of V_max found experimentally at full and 58% activation are plotted as stars on the figure, showing good agreement with the model prediction, as expected. Data from the full versus 72% activation group were not plotted in Fig. 12, because the model output displayed in Fig. 12 was based on the Hill’s constants obtained from the full versus 58% activation group. Data from the full versus 72% activation group produced similar curves as those shown in Fig. 12 (data not shown).

Fig. 11.

A: model output of force-velocity (F-V) curves at different degrees (n) of activation based on Eq. 6 and with Hill’s constants taken from curve-fitting the data for the fully activated muscles (Table 4, Full vs. 58% group). B: the same curve from A but with expanded time scale. The vertical dotted line indicates 4.6% of maximal active force (F_max), the amount of internal load determined from the paired group (Full vs. 58% activation). Note that maximal shortening velocity (V_max) is activation dependent, whereas V_max, the absolute maximal shortening velocity, is not. L_ref, reference length.

Fig. 12.

Model prediction of maximal shortening velocity (V_max) values at different degrees of activation (%F_max) and different amounts of internal load (F_i) based on Eq. 6 and with Hill’s constants taken from curve-fitting the data for the fully activated muscles (Table 4, Full vs. 58% group). Closed circles are model outputs for an internal load of 4.6% F_max, matching the internal load estimated from the Full vs. 58% activation group of data. The two star points are measured V_max values from the Full vs. 58% activated group. F_max, maximal active force; V_max, absolute maximal shortening velocity.

From Fig. 10 it is clear that the F-V curves obtained in partial activation can be made to superimpose on their respective full activation curves. The superimposition was achieved by simply rescaling the force by a factor of 1/n without changing the velocity values. Because power equals force times velocity, and partial activation only affects force, the power output of partially activated muscles is directly proportional to %F_max, the degree of activation. That is, P_max is proportional to %F_max. This forms the basis for the model output shown in Fig. 13 (open circles). The red closed circles are experimentally measured P_max (Fig. 13A), active muscle stiffness (Fig. 13B), and MLC20 phosphorylation (Fig. 13C). Note that the measured values are all normalized by their respective maximal values obtained at full activation. The agreement between the model output and the data validates the four assumptions made in the above model description and shows a tight correlation among isometric force, active stiffness, maximal power output, and the level of MLC20 phosphorylation. The simplest explanation for this observation is that the four parameters are a direct reflection of the number of activated crossbridges.

Fig. 13.

Comparison of model output (open circles) with measured values (red closed circles). As described in text, the theoretical maximal power output (P_max) is directly proportional to the number of activated crossbridges, which in turn is proportional to the degree of activation expressed in %F_max. A: measured maximal power after correction for internal load is directly proportional to the degree of activation (%F_max) and matches the prediction of power output as a function the degree of activation. B: active muscle stiffness is directly proportional to the degree of activation, as is the predicted power output. C: level of 20-kDa myosin light chain (MLC20) phosphorylation is directly proportional to the degree of activation, as is the predicted power output.

Relation to striated muscle model.

Results from the present study can be explained by the striated muscle model in terms of crossbridges as independent force generators (18) as well as a major source of compliance (8). The characteristic hyperbolic F-V relationship in striated muscle stems from the effect of load on individual crossbridges and their collective cyclic interaction with actin filaments (3, 18). Partial activation in striated muscle appears to alter the shape of the F-V curve, but after accounting for the number of activated crossbridges and internal load, it can be shown that the kinetics of the crossbridge cycle is not affected by partial activation (7) as evidenced by the superimposition of normalized F-V curves obtained at different degrees of activation. Results from the present study indicate that smooth muscle is not different from striated muscle in terms of the crossbridge mechanism that underlies the F-V properties. However, it should be stressed that this is true only when the smooth muscle F-V properties are assessed at a fixed time point, as they were in the present study.

Unlike striated muscle, in which crossbridges are activated by calcium binding to troponin C, activation of smooth muscle crossbridges occurs through MLC20 phosphorylation. However, after they are activated, the behavior of smooth muscle crossbridges when assessed at a single time point is similar to that of striated muscle. The one-to-one correlation between the level of MLC20 phosphorylation and other indices of muscle activation (F_max, stiffness, and P_max) (Fig. 13) suggests that the phosphorylation is best understood as an on/off switch for the crossbridges.

Limitations of the model.

We have shown that the F-V properties measured at a single time point can be explained by the Huxley model (18), but it is obvious that results obtained at a single time point represent only a snapshot of a real contraction. Changes in F-V properties over time require a model that incorporates the influence of time-dependent variables. The latch-bridge model (14) was developed to explain variable F-V properties during the time course of contraction. The cornerstones of the latch-bridge model are the direct correlation between MLC20 phosphorylation and maximal shortening velocity as well as the nonlinear correlation between MLC20 phosphorylation and isometric force (14). The biggest challenge faced by the model is that these “cornerstones” are not found in many smooth muscle studies (11, 13, 21, 23, 25), as mentioned in the introduction. Moreover, many structural proteins and enzymes undergo time-dependent changes during contraction that affect force and velocity. These changes need to be taken into account to fully understand the F-V properties during the time course of ASM contraction.

Relation to results from skinned ASM preparations.

Similarity between results from skinned ASM preparations and the present results obtained at a fixed time point suggest that the skinning process may have removed some influences stemming from the time-dependent regulatory pathways. Dogan et al. (6) showed linear correlation between calcium activation and MLC20 phosphorylation; Jones et al. (20) showed linear correlation between the steady-state ATP hydrolysis rate and isometric force that were dependent on free Ca²⁺ concentration. These findings suggest that MLC20 phosphorylation activates the crossbridges and do not support the occurrence of latch-bridges. During the time course of a contraction induced by a constant level of Ca²⁺, the same study showed that the rate of ATP hydrolysis declines whereas MLC20 phosphorylation and force stay constant (20), a result that cannot be explained by either the Huxley model (18) or the latch-bridge model (14). One could argue that this is an artifact from measuring the responses at different manually fixed levels of Ca²⁺; however, evidence of changes in crossbridge cycling rate not correlated with changes in Ca²⁺ levels or MLC20 phosphorylation has also been shown in intact smooth muscle (11, 23). It is evident that mechanisms other than reduced MLC20 phosphorylation are responsible for the decline in ATP hydrolysis/velocity of shortening during a sustained contraction.

Development of a comprehensive theory for smooth muscle contraction.

We know that in smooth muscle contraction, temporally and spatially well-coordinated excitation-contraction coupling drives many subcellular signaling events (28) resulting in chemical modification of many proteins and enzymes following different time courses (12). Note that many of the protein modifications do not alter actomyosin interaction directly but involve restructuring of the cytoskeletal scaffolds that support the crossbridge interaction. Changes in cytoskeletal structure alter cell stiffness (4, 30) and intracellular force transmission mechanisms (35, 36), as well as rearrangement of contractile units (26). Therefore, a comprehensive model for smooth muscle should consist of an actomyosin core mechanism connected with peripheral (cytoskeletal) mechanisms that modify the mechanical properties of the cell and give rise to the time-dependent variation in force, stiffness, and shortening velocity at the cell level. To formulate such a comprehensive theory, we need to decide whether the actomyosin core mechanism should be built on the Huxley model or the latch-bridge model. Before the discrepancies between experimental findings (11, 13, 21, 23–25) and the latch-bridge model are resolved, the simpler Huxley model is the choice by Occam’s rule, especially considering that the present study shows that the Huxley’s crossbridge mechanism is at the heart of smooth muscle contraction when time-dependent variables are held constant.

GRANTS

This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada and a project grant from the Canadian Institutes of Health Research.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

L.L., L.W., P.D.P., C.Y.S., and P.C. conceived and designed research; L.L., L.W., and P.C. performed experiments; L.L., L.W., P.D.P., C.Y.S., and P.C. analyzed data; L.L., L.W., P.D.P., C.Y.S., and P.C. interpreted results of experiments; L.L., C.Y.S., and P.C. prepared figures; C.Y.S. and P.C. drafted manuscript; L.L., L.W., P.D.P., C.Y.S., and P.C. edited and revised manuscript; L.L., L.W., P.D.P., C.Y.S., and P.C. approved final version of manuscript.