The depression of isometric force after active shortening is a well-accepted characteristic of skeletal muscle, yet its mechanisms remain unknown. Although traditionally analyzed at steady state, transient phenomena caused, at least in part, by cross-bridge kinetics may provide novel insight into the mechanisms associated with force depression (FD). To identify the transient aspects of FD and its relation to shortening speed, shortening amplitude, and muscle mechanical work, in situ experiments were conducted in soleus muscle-tendon units of anesthetized cats. The period immediately after shortening, in which force recovers toward steady state, was fit by using an exponential recovery function (R2 > 0.99). Statistical analyses revealed that steady-state FD (FDss) increased with shortening amplitude and mechanical work. This FDss increase was always accompanied by a significant decrease in force recovery rate. Furthermore, a significant reduction in stiffness was observed after all activated shortenings, presumably because of a reduced proportion of attached cross bridges. These results were interpreted with respect to the two most prominent proposed mechanisms of force depression: sarcomere length nonuniformity theory (7, 32) and a stress-induced inhibition of cross-bridge binding in the newly formed actin-myosin overlap zone (14, 28). We hypothesized that the latter could describe both steady-state and transient aspects of FD using a single scalar variable, the mechanical work done during shortening. As either excursion (overlap) or force (stress) is increased, mechanical work increases, and cross-bridge attachment would become more inhibited, as supported by this study in which an increase in mechanical work resulted in a slower recovery to a more depressed steady-state force.
- shortening-induced depression
- mechanical work
- stress-induced cross-bridge inhibition
- sarcomere length nonuniformity
- rate of force redevelopment
steady-state force depression (FDss), the reduction of isometric force after active shortening compared with a purely isometric force at the corresponding final length, is a well-accepted characteristic of skeletal muscle that has been demonstrated in both whole muscle (e.g., Refs. 1, 15, 28, 30, 32) and single-fiber (e.g., Refs. 7, 13, 25, 34) preparations. It has been shown that FDss increases with increasing amplitudes of shortening (1, 6, 15, 28, 30, 32, 34), with decreasing speeds of shortening (1, 6, 15, 28, 30, 32, 34), with increasing force during shortening (6, 15), and with increasing mechanical work done by the muscle during shortening (18). Furthermore, Sugi and Tsuchiya (34) showed, in single muscle fibers of the frog, that force depression (FD) was accompanied by a proportional reduction in fiber stiffness. Despite this thorough characterization of the steady-state behavior, the underlying mechanisms of FDss remain unknown.
Our current understanding of FDss is based almost exclusively on steady-state observations, whereas transient phenomena have not been considered. The behavior of muscle during the force recovery phase (after activated shortening) may contain valuable information to help elucidate the mechanisms of FDss. Previous studies measured force recovery rates to evaluate cross-bridge cycling kinetics in single fibers subjected to unloaded rapid shortening-restretch (3, 19, 33). The force recovery rates, according to Huxley's cross-bridge model (22), are primarily determined by the cross-bridge attachment rate (3).
However, FDss only occurs after loaded shortening, for which few data are available on transient force recovery. Ekelund and Edman (9) showed that an increase in FDss was accompanied by a decreased rate of force redevelopment at a given tension level. Likewise, De Ruiter et al. (6) observed that the redevelopment of force in human adductor pollicis was slowed after active shortening, particularly after shortening with large amplitudes and slow speeds. Lee and Herzog (26) analyzed force recovery in human adductor pollicis at a number of discrete time points and reported that FD decreased over time, but approached a steady state.
According to the Huxley-Simmons cross-bridge model (23), force generation after rapid shortening is composed of two distinct phases: 1) a rapid phase of force recovery caused by cross-bridge rotation, and 2) a slow phase of force recovery caused by cross-bridge attachments. Force generation in the rapid phase occurs within milliseconds and results from the stretching of elastic elements as the cross bridges rotate to positions of low potential energies. The rates of force recovery previously observed with respect to FDss (6, 9, 26), as well as those analyzed in this study, are in excess of seconds and represent the slow phase associated with cross-bridge attachment. Because the proportion of attached cross bridges decreases during shortening compared with isometric, the rate of force recovery primarily indicates the rate of cross-bridge attachment relative to detachment.
The aims of this study were to analyze and quantify the effects of shortening amplitude, shortening speed, and muscle mechanical work on FDss and transient force recovery after active shortening. Specifically, we conducted in situ experiments on cat soleus in which the amplitude and speed of shortening were systematically varied. The isometric period after active shortening, in which the force recovers to a steady-state value, was analyzed via an exponential force recovery function. Parameters describing the transient force recovery were statistically analyzed to identify shortening amplitude-, speed-, and work-dependence. Stiffness was measured at steady state after shortening and was compared with values obtained from the corresponding isometric reference contractions. On the basis of our findings, we hypothesize that FDss is caused by a stress-induced inhibition of cross-bridge attachments in the newly formed actin-myosin overlap zone (14, 28). We believe that this inhibition of cross-bridge attachments is caused by the stretch of actin (24), which might cause angular distortions of the cross-bridge binding sites (4) and a reduced probability of cross-bridge attachment.
On the basis of these ideas, we hypothesized that an increase in the mechanical work, caused either by an increase in the force during shortening (greater stress on the muscle, and thus greater inhibition) or by an increase in the amount of shortening (larger newly formed overlap zone, and thus a greater number of affected cross bridges) would result in a proportional decrease in the probability of cross-bridge attachment. As a result, an increase in work would decrease the cross-bridge attachment rate and therefore cause a decrease in the rate of force redevelopment and a decrease in steady-state isometric force after active shortening. Because this mechanism is based on cross-bridge kinetics, we expect it to explain both the transient and steady-state aspects of force depression.
MATERIALS AND METHODS
Force depression after active shortening was determined in cat soleus muscle by using experimental methods previously described (15) and approved by the Life Sciences Animal Ethics Committee of the University of Calgary. Briefly, the soleus, soleus tendon, and calcaneus were exposed via a single incision on the posterior, lateral shank of each hindlimb of four adult outbred cats (8 muscles). A reference length was determined, corresponding to an included ankle angle of 80°, and the soleus tendon was isolated from the remaining Achilles tendon and cut from the calcaneus with a remnant piece of bone. The tibial nerve was exposed via an incision on the posterior, lateral thigh and instrumented with a bipolar nerve cuff electrode for soleus stimulation. A hammock secured the cat in a prone position, and bilateral bone pins fixed the pelvis, thigh, and shank of the experimental hindlimb to a stereotaxic frame. The bone block at the distal end of the soleus tendon was attached with sutures to a servohydraulic muscle puller (MTS, Eden Prairie, MN; natural frequency >10 kHz), and forces (100 N = 10 V) and excursions (50 mm = 10 V) were measured continuously at 1,000 Hz. Soleus length changes were measured by the muscle puller using a linear variable differential transformer with a resolution ≈ 0.01 mm.
Soleus was activated with a 30-Hz stimulation of the tibial nerve, at a voltage that exceeded the α-motoneuron threshold by at least a factor of three (15). Stimulation pulses were monopolar with a 0.1-ms duration. This stimulation produces fused tetanic contractions in soleus, without causing appreciable fatigue (16). An adjustable infrared heat lamp and a regular drip of warm saline (0.9%) were used to maintain muscle temperature at 35 ± 1°C.
The force-length relationship was determined for each muscle, as previously described (16). First, the length of active insufficiency at which tetanic 30-Hz stimulation failed to produce force was found. The muscle-tendon length was then increased in 2-mm increments until the (active) descending limb was identified. All contractions were maintained for 3 s, with a 1-min rest between contractions. The length corresponding to maximum active force (=total force-passive force) was considered the reference length and termed 0 mm. Lengths beyond 0 mm were considered positive and comprised the descending limb, and lengths below 0 mm were considered negative and comprised the ascending limb of the force-length relationship (16, 32).
FD after active shortening was determined on the descending limb of the force-length relationship. The amplitude of shortening (3, 6, and 9 mm; i.e., ∼3–9% of total muscle-tendon length and 7–21% of optimal fiber length) and the speed of shortening (3, 9, and 27 mm/s; i.e., ∼7, 21, and 63% of optimal fiber length/s) were systematically varied (Fig. 1). For each muscle, the test battery started with an initial isometric reference contraction at 0 mm, followed by test contractions of 3-, 6-, and 9-mm shortening amplitude at 3 mm/s, followed by a repeat isometric reference contraction at 0 mm. This series of contractions was then repeated for shortening speeds of 9 and 27 mm/s. The 0-mm reference length served as the final length for all experiments; thus shortening occurred on the descending limb and ended at optimal length. Thus all FD experiments were evaluated at the plateau of the force-length relation. A 2-min rest interval, sufficient for complete recovery of the cat soleus (17), was allowed between each contraction. To ensure that force measures were repeatable, consecutive isometric reference contractions at 0 mm were required to produce the same force (±0.1 N) throughout the test battery. Therefore, if the force declined because of fatigue, damage, or a shift in optimal length, the muscle was rejected from the study.
In all tests, the muscle was maximally activated before length change, such that all shortenings began with the soleus on its tetanic plateau (Figs. 1 and 2). Stimulation was continued throughout the shortening event, and the stimulated muscle was held isometrically for 5 s at the final length, to allow the force to reach steady state. After these 5 s, the muscle was subjected to a short (1 mm), fast (32 mm/s) stretch to measure the stiffness at steady state. Stretch parameters were chosen to produce an elongation within the mechanical breaking point of bound cross bridges (yield point), at a rate near the lower end of the physiologically relevant range (12, 17). Activation continued for 1 s after the stiffness measurement, after which stimulation was stopped (Fig. 2).
We defined FDss as the difference between the depressed force at steady state (Finf) and the corresponding isometric reference force (Fiso) (Fig. 2). Similarly, a steady-state stiffness depression (SDss) was defined as the difference between the stiffness obtained in the isometric reference contractions and the active shortening test contractions. The mechanical work performed by the muscle was calculated as the area under the force-displacement graph.
To quantify the transient force recovery, F(t), the force-time data after activated shortening were analyzed by using an exponential recovery function, (1) where A is the amount of recoverable force (difference between steady-state force and the initial force immediately after shortening), and k is the exponential force recovery rate. Values of Finf, A, and k were obtained for each experiment by fitting the entire 0–5 s of force-time data after shortening with Eq. 1 (R2 > 0.98) using a Levenberg-Marquardt error minimization algorithm in a commercial curve-fitting program (DeltaGraph 4.0, SPSS). Fits obtained in this period were biased toward the steady-state force. This resulted in accurate estimates of Finf, with low estimates of k, as evidenced by excellent model agreement at steady state, and moderate agreement in the early transient response (Fig. 3A). To obtain more accurate early transient parameter estimates, the model was fit to the first 1.0 s of force-time data, yielding larger k estimates, lower Finf estimates, more accurate (lower) estimates of the initial force, similar estimates of A, and excellent transient agreement (R2 > 0.99, Fig. 3B).
Stiffness was calculated from the linear portion of the force-time trace during quick stretching (26). In every case, a least squares regression showed the central 50% of the force-time trace to be highly linear (R2 > 0.99). This linear slope, when divided by the constant rate of stretch (32 mm/s), gives the stiffness of the tissue (N/mm) at steady state.
Statistical analyses were conducted to observe the relation between the controlled variables and both steady-state and transient aspects of the force after activated shortening. A complete block-design ANOVA (SPSS statistical software, 12.0, SPSS) was used to test the effects of shortening speed and shortening amplitude on transient and steady-state variables (FDss, SDss, k, A). Values of k and A were obtained from the early transient fits (0–1 s) and Finf values from the entire 5-s recovery. Because of the nature of the experimental design (3 amplitudes, 3 speeds, left and right leg), a complete block design was required, which accounted for the within-animal correlation of the left and right legs of each animal. Regression analyses were used to observe the correlation between measured quantities (FDss, SDss, A, k) and mechanical work. Regressions were conducted within each muscle and for all muscles pooled together, to determine whether the trends observed in each tissue were similar and representative of the tissue's general behavior.
Student's t-tests were employed to observe changes in steady-state stiffness between isometric reference and shortening test contractions, for all experimental conditions.
An increase in the amplitude of shortening, for a given speed of shortening, was associated with an increase in A (Fig. 4A), a decrease in k (Fig. 5A), a decrease in Finf, and an increase in FDss (Figs. 6A and 7, A, C, and E). An increase in shortening speed, for a given amplitude of shortening, resulted in increases in k and A (Figs. 4B and 5B). FDss was lowest at the highest speed, with no significant difference between the two slower speeds (Fig. 6B). The effects of changes in shortening amplitude and speed on transient force recovery are shown in Fig. 7.
Mechanical work, across all muscles and conditions, correlated positively with FDss (Fig. 9A) and negatively with k (Fig. 9B); it did not significantly correlate with either A or SDss (P > 0.05). These correlations were confirmed for each individual muscle, and they were stronger than the correlations across all muscles because of the great differences in soleus strength (17–44 N) associated with the size of the animals (2.5–4.7 kg).
Stiffness was significantly decreased in the force depressed compared with the isometric reference state (Figs. 10 and 11). However, stiffness was not different for different speeds or amplitudes of shortening. Similar stiffness decreases were observed from isometric contractions at the longest starting length (+9 mm) (Figs. 10 and 11).
The exponential recovery function (Eq. 1) provided a means of evaluating the entire region of transient force recovery and excellent agreement with experimental data in all cases (R2 > 0.99). Furthermore, the function parameters identify important quantities of the force recovery: the amount of recoverable force (A), the depressed force at steady state (Finf), and the exponential rate of recovery (k), allowing for improved insight to the muscle's force recovery.
Our steady-state results support the findings of previous studies, showing that FDss (= Fiso − Finf) increased with shortening amplitude (1, 6, 15, 28, 30, 32, 34), decreased with larger shortening speeds (1, 6, 15, 28, 30, 32, 34), and increased with mechanical work done during shortening (6, 18). An increase in shortening amplitude increases the distance over which the contractile force operates and thus, for a fixed speed of shortening, increases the mechanical work. An increase in the shortening speed, in accordance with the force-velocity relationship (21), reduces the maximal contractile force, and thus reduces the work for a given shortening amplitude.
A exhibited large increases with shortening speed (negative correlation with work) and slight increases with shortening amplitude (positive correlation with work) and thus did not correlate with work. The large reduction of force during the shortening phase at high speeds is most likely associated with the force-velocity characteristic of the muscle. At high speeds of shortening, the muscle's ability to produce force is low (21). This result, in conjunction with the relatively small decrease in FDss with speed, explains why the amount of recovered force increased dramatically with speed.
Lee and Herzog (26) found that differences in FD at the end of the shortening phase were highly correlated with those at steady state, suggesting that FD is produced during shortening, rather than in the transient recovery phase. Furthermore, they found that the FD differences at the end of shortening were larger than those at steady state. Therefore, the increases in FDss that they observed with increased shortening amplitude were associated with increased FD at the end of shortening and thus a larger amount of recovered force. This was supported by our results in which both FDss and A increased with shortening amplitude.
Values of k decreased with shortening amplitude and increased greatly with shortening speed, such that the recovery rate was lowest after large amplitudes of muscle shortening performed at low speeds (Figs. 5 and 7, C and D). These findings provide statistically significant, numerical support for the qualitative observations of De Ruiter et al. (6) that “The slow rise of force during redevelopment of tension was particularly noticeable after contractions with relatively long shortening steps at slow velocities.” The shortening speed and amplitude trends of the recovery rate oppose those of mechanical work, further evidenced by the observed negative k-work correlation (Fig. 9B). These trends, when viewed with those of FDss, indicate that an increase in the mechanical work done during shortening results in a slower recovery to a more depressed steady-state force.
Stress-induced inhibition of cross-bridge binding.
In this proposed mechanism, as stress on the muscle during shortening increases, the cross bridges in the newly formed actin-myosin overlap zone have a decreased probability of binding because of strain in the myofilaments, resulting in larger FDss (14, 28). This mechanism has received support in recent studies that showed thick and thin myofilament compliance when subjected to physiological loads (24). Such compliance may result in angular distortions of the cross-bridge binding sites on actin and, in turn, may affect cross-bridge attachment kinetics (4). Thus an increase in stress may increase the angular distortions and decrease the probability of cross-bridge attachment.
According to this mechanism, FDss increases with increases in mechanical stress, increases in the newly formed overlap zone, or both. Thus an increase in the mechanical work, caused either by an increase in the force during shortening (greater stress) or by an increase in the amount of shortening (larger overlap zone), would result in a proportional decrease in the probability of cross-bridge attachment. As a result, this mechanism would predict FDss to 1) increase with shortening amplitude, 2) decrease with speed, and 3) positively correlate with mechanical work; these predictions are supported by our experimental results (Figs. 6, A and B, and 9A).
Furthermore, this mechanism suggests that an increase in mechanical work would decrease the cross-bridge attachment rate. According to the Huxley-Simmons cross-bridge model (23), a decrease in cross-bridge attachment rate, for similar detachment rates, would decrease the rate of force redevelopment. Therefore, this mechanism would predict the rate of force recovery to decrease with increased mechanical work. Our results support this with a negative k-work correlation (Fig. 9B), as well as the slower rate of force recovery with increasing shortening amplitude and decreasing speed of shortening (Figs. 5 and 7, C and D).
Because this mechanism provides that FDss results from an inhibition of cross-bridge attachment, which reduces the proportion of attached cross bridges, there should be an accompanying decrease in stiffness with FDss (10). Prior studies support this theory, demonstrating that the stiffness reduction was proportional to the magnitude of FD in frog single muscle fibers (34) and proportional to shortening amplitude in human adductor pollicis in vivo (26). Our results indicated a significant reduction of stiffness after every activated shortening, yet this reduction did not exhibit the expected FD proportionality and was sensitive to neither the speed nor the amplitude of shortening (Figs. 10 and 11). We are uncertain as to the cause of the discrepancy between our results and those previously observed (26, 34). However, because the stiffness reduction (12 ± 3%) was always larger than the steady-state force reduction (6 ± 2%), a possible explanation could be that, whereas the number of attached cross bridges decreased proportionally, the average force per cross bridge increased, possibly because of a smaller percentage of cross bridges in the weakly bound state. This would account for the stiffness discrepancy while maintaining the steady-state and transient aspects of the stress-induced mechanism. This interpretation is one of many and, without further experiments designed to test that specific hypothesis, must be viewed as purely speculative.
Sarcomere length nonuniformity theory.
Sarcomere length nonuniformity theory attributes FD to a dispersion of sarcomere lengths developed during active shortening (7, 32). After forces between longer and shorter sarcomeres equilibrate, the muscle produces a force smaller than that of an isometric contraction (in which sarcomere lengths are relatively similar) at the same final length. According to this theory, a larger force during shortening would cause a greater dispersion of sarcomere lengths, as would an increase in the excursion (32). Therefore, because Edman et al. (7) showed that FD was positively correlated with the distribution of sarcomere lengths, one would expect an increase in nonuniformities, caused either by increased amounts of shortening, increased forces during shortening, or increased mechanical work, to increase FDss. Our steady-state results support this idea, exhibiting an increase in FDss with increasing mechanical work, increasing shortening amplitude, and decreasing shortening speed (Figs. 6 and 9B).
To date, we are unaware of any studies that have specifically examined force recovery rates and the development of sarcomere length nonuniformities; however, the rate of force recovery after activated shortening has been associated with the readjustment of sarcomere lengths within the muscle after shortening (5). Within the sarcomere length nonuniformity theory, it is seen as the stabilization of the dispersion of sarcomere lengths, such that during the isometric recovery period after activated shortening, the strong segments continue to shorten at a very low rate, while the weak segments are stretched until the forces are matched and the lengths are stabilized (7). Therefore, one would expect that an increase in sarcomere length dispersion would require greater readjustment, owing to a larger number of sarcomere-length stabilizations, and thus would yield a slower rate of force recovery. As a result, this theory would predict the rate of force recovery to decrease with increasing FDss. Our data support this prediction (Fig. 9B), making the sarcomere length nonuniformity hypothesis an attractive mechanism for FD. However, one must use caution when interpreting the transient data as indicative of sarcomere length readjustment, because the existence of such readjustment is disputable. Edman et al. (7) observed a continued redistribution of length during the isometric phase after active shortening; however, similar readjustments were not observed by Sugi and Tsuchiya (34). Both studies were conducted in isolated muscle fibers of frog tibialis anterior muscle and showed that unloaded shortening produced fairly uniform length changes and that loaded shortening produced large length nonuniformities, yet Sugi and Tsuchiya observed that the shortening-induced nonuniformities did not change during the postshortening isometric phase.
If sarcomeres shortened uniformly, then all would be at maximal overlap at the final length (optimal length = 0 mm). However, if length nonuniformities are developed during shortening, then some sarcomeres shorten very little (similar overlap to that of the starting length), and others would shorten a great deal (beyond the plateau, and on to the ascending limb) to balance out the force (32). According to Morgan et al. (32), the few sarcomeres that shorten would increase their overlap and thus become stiffer than those at the starting length. However, most of the sarcomeres shorten very little and thus would have only a slight increase in stiffness with respect to starting length. As a result, there should be little change in stiffness from the original starting length (slight increase), but a decrease compared with that of the 0-mm final length (see example in Ref. 32). Although our results supported this theory with a statistically significant decrease in stiffness after all activated shortenings with respect to the optimal length (0 mm), we also observed a similarly significant decrease relative to the longest starting length (+9 mm) (Figs. 10 and 11), a result that cannot be explained by the sarcomere length nonuniformity theory.
Passive structures, such as titin, may also have an effect on the development of FD. When loaded, passive structures are expected to contribute to the shortening velocity by means of elastic recoil (8, 31). Recently, Minajeva et al. (31) quantified the passive-component contributions to unloaded shortening velocity in single myofibrils, showing that passive shortening velocity increased progressively with sarcomere length and decreased with titin degradation. Our experimental data (Fig. 2) show that the passive force (0.8 N) at optimal length contributes less than 2% to the 44-N total force. We therefore feel that the FD observed at the optimal length would be primarily affected by active force components and that passive contributions, although a distinct possibility, would have minimal effect owing to the small loads present in the elastic structures. However, because passive components can affect the sarcomere shortening velocity (8, 31), their contributions should be considered in future FD studies in which shortenings are preceded by stretch or take place from long lengths and a considerable passive component of force is present.
It was recently proposed that myofilament compliance may significantly influence the rate of force recovery (29). Martyn et al. (29) measured the rate of rapid phase force recovery, and its activation dependence, in single fibers after active length changes. Their model was able to explain the observed force transients, provided that myofilament compliance comprised 60–70% of the total fiber compliance (29). However, the true amount of myofilament compliance remains unclear. Some studies indicate that only ∼10–20% of the compliance in single fibers comes from non-cross-bridge structures (2, 11, 27, 35), whereas Higuchi et al. (20) suggested it could be as high as 50%. These findings have significant implications regarding the rapid-phase force generation associated with cross-bridge rotation, but because of their very short time scale (milliseconds) have limited effect on the slow-phase force transients typically associated with cross-bridge attachments, as addressed in our study.
In this study, we sought to characterize the transient force recovery of the cat soleus muscle after activated shortening. To the best of our knowledge, this is the first study to investigate the transient aspects of FD by modeling, quantifying, and analyzing the muscle's continuous force recovery after activated shortening. Our results indicate that FD increases with mechanical work and is accompanied by a decrease in the rate of force redevelopment. These findings lend support to our hypothesis that both steady-state and transient aspects of FD could be described by a stress-induced inhibition of cross-bridge binding in the newly formed actin-myosin overlap zone (14, 28) using a single scalar variable, the mechanical work done during shortening. Future work should incorporate this mechanism in a theoretical cross-bridge model and compare modeling output to the experimental results described herein.
Alberta Ingenuity Fund and the Natural Sciences and Engineering Research Council of Canada supported this research.
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