Interaction between series compliance and sarcomere kinetics determines internal sarcomere shortening during "xed-end contraction

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1 BM=1313=Binni=Venkatachala=BG Journal of Biomechanics 33 (2000) 1249}1255 Interaction between series compliance and sarcomere kinetics determines internal sarcomere shortening during "xed-end contraction Yasuo Kawakami, Richard L. Lieber * Department of Life Sciences, University of Tokyo, Komaba 3-8-1, Meguro, Tokyo , Japan Departments of Orthopaedics and Bioengineering, Veterans Awairs Medical Center, University of California, San Diego, San Diego, CA 92161, USA Accepted 6 April 2000 Abstract The interaction between contractile force and in-series compliance was investigated for the intact skeletal muscle}tendon unit (MTU) of Rana pipiens semitendinosus muscles during "xed-end contraction. It was hypothesized that internal sarcomere shortening is a function of the length}force characteristics of contractile and series elastic components. The MTUs (n"18) were dissected, and, while submerged in Ringer's solution, muscles were activated at nine muscle lengths (!2 to#6 mm relative to optimal length in 1 mm intervals), while measuring muscle force and sarcomere length (SL) by laser di!raction. The MTU was clamped either at the bone (n"6), or at the proximal and distal ends of the aponeuroses (n"6). Muscle "bers were also trimmed along with aponeuroses down to 5}20 "bers and identical measurements were performed (n"6). The magnitude of shortening decreased as MTU length increased. The magnitude of shortening ranged from!0.08 to 0.3 μm, and there was no signi"cant di!erence between SL as a function of clamp location. When aponeuroses were trimmed, sarcomere shortening was not observed at and longer. These results suggest that the aponeurosis is the major contributor to in-series compliance. Results also support our hypothesis but there also appear to be other factors a!ecting internal sarcomere shortening. The functional consequence of internal sarcomere shortening as a function of sarcomere length was to skew the muscle length}tension relationship to longer sarcomere lengths Elsevier Science Ltd. All rights reserved. Keywords: Frog; Semitendinosus muscle; Contractile and elastic components 1. Introduction Theoretically, muscle is divided into contractile and elastic components, the latter of which can be further divided into elements arranged in series with or parallel to muscle "bers. Muscle "bers and tendinous tissues have been proposed to represent anatomical bases of contractile and elastic components, respectively (Ettema and Huijing, 1989; Lieber et al., 1992; Zajac, 1989). Compliance of the series elastic component (SEC) a!ects forcetransmission kinetics from muscle "bers to bone. Its mechanical importance has long been recognized (since Hill, 1951) and understanding in-series compliance is a key factor in modelling muscle mechanics (Herzog * Corresponding author. Tel.: # ; fax: # address: rlieber@ucsd.edu (R.L. Lieber). et al., 1992; Lieber et al., 1992; van Soest et al., 1995). In spite of a number of studies on the mechanical properties of muscle "bers and tendinous tissues per se, little is known how these structures interact with each other. Such information is quite important since these components function as a unit in intact skeletal muscle. Besides, the structural constituents of in-series compliance have not been clearly determined. Based on the two component model, Lieber et al. (1992) simulated "xed-end muscle contraction. They theorized that "ber shortening occurs internally resulting from elongation of SEC by muscle force development. This theory clearly demonstrated the interaction between contractile and elastic components, but it was not experimentally tested. In this study we carried out experiments on "xed-end contraction of frog muscle}tendon unit to actually test the proposed theory. We hypothesized that internal sarcomere shortening results from the interaction between muscle force (i.e., more shortening for larger /00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S ( 0 0 )

2 1250 Y. Kawakami, R.L. Lieber / Journal of Biomechanics 33 (2000) 1249}1255 force) and compliance of SEC (i.e., more shortening for more compliant SEC), each of which is a distinct function of muscle}tendon length (Lieber et al., 1992). We also aimed to locate in-series compliance by manipulating the tissues involved. Finally, functional implications of the in-series compliance within a muscle}tendon system were investigated. 2. Materials and methods The muscle}tendon unit (dorsal head) of the frog semitendinosus (ST) muscle (Rana pipiens) was used because of its well-established sarcomere length}tension relationship (Gordon et al., 1966) and longitudinal "ber architecture with pennation angle not measurably di!erent from 03 (Lieber and Boakes, 1988). Frogs were sacri"ced by double pithing. Eighteen frogs (six frogs for each experiment) were used in the following three experiments, which were carried out independently (Fig. 1). This study carried approval of the institutional review board of the Veterans A!airs Medical Center, University of California, San Diego Experiment 1. Testing of the whole muscle}tendon unit The ST muscle}tendon unit (MTU) was carefully isolated along its attachments to the pelvis and tibia. This was done by removing small portions of bone where the muscle attached from the pelvis and tibia. The MTU along with the bones were submerged in chilled Ringer's solution, and the tibia was secured "rmly by a clamp which was connected to a micromanipulator. The pelvis was "xed onto the moving arm of a dual-mode servomotor which measured the force exerted by the muscle. After muscle stimulation threshold was determined, stimulation intensity was increased until no further increase in twitch force was observed. Activations were performed at this intensity (&10 V). Stimulation con"guration implemented platinum electrodes closely approximating the muscle length to ensure that current passed through the muscle "bers and not merely around them via the Ringer's solution. Muscle length was then adjusted to the length at which twitch force was maximum ( ). Next, maximum tetanic force (P ) was measured by directly activating the muscle for 0.4 s at 100 Hz, 0.3 ms pulse duration at the supramaximal intensity. The sarcomere length at rest and during contraction was measured by laser di!raction method as described by Lieber et al. (1984) and Lieber and Boakes (1988). The He}Ne laser beam was transilluminated through the muscle at a position midway between the midbelly of the muscle and distal end of "bers where the di!raction pattern was most clear. The length of the MTU was systematically changed by the micromanipulator by 1 mm increments, from!2 to #6 mm with respect to (i.e., nine lengths). These lengths are referred hereafter to as!2,!1,, #1,2, #6. Further shortening than!2 resulted in bending of the whole MTU due to slack, and was not tested. Force and sarcomere length were simultaneously measured at each MTU length. The maximal force and average sarcomere length over the last 100 ms of contraction were used as representative of muscle force and sarcomere length Experiment 2. Testing of MTU without tendon To investigate the e!ect of the tendon on internal sarcomere shortening, the MTU was clamped immediately at the ends of proximal and distal aponeuroses using the same apparatus as in experiment 1. The lengths tested, stimulation condition, and measured parameters were identical to experiment 1. Care was taken not to concentrate stress on a particular portion of the aponeurosis by securing the whole tendons with the clamp and moving arm of the motor Experiment 3. Testing of MTU without tendon and aponeurosis Fig. 1. Schematic representation of the experiments. The muscle}tendon unit was clamped either at the bone (experiment 1, n"6), at the proximal and distal ends of the aponeuroses (experiment 2, n"6). In additional experiment (experiment 3, n"6), "bers were trimmed along with aponeuroses down to approximately 5}20 "bers and identical measurements were performed. Arrows indicate where laser di!raction patterns were observed. Even in experiment 2 where the proximal and distal tendons were excluded, there still were proximal and distal aponeuroses attached to "bers. In experiment 3, the "bers as well as aponeuroses were trimmed under a dissecting microscope down to 5}20 "bers. Care was taken not to damage remaining "bers. The lengths tested and parameters measured were identical to experiments

3 1 and 2. Stimulation condition was also identical except that the threshold and supramaximal stimulation required lower intensities for this experiment Statistical analyses The measured values are indicated by means and standard errors of mean unless otherwise indicated. The e!ect of muscle lengths on the magnitude of sarcomere shortening was tested by a one-way analysis of variance (ANOVA) with repeated measures followed by a Tukey post hoc test. The results of three experiments in terms of sarcomere length, sarcomere shortening, and relative muscle force were compared by one-way factorial ANOVA followed by a Fisher's PLSD post hoc test. The level of signi"cance was set to P(0.05. Y. Kawakami, R.L. Lieber / Journal of Biomechanics 33 (2000) 1249} Results Muscle force was related to MTU length in all experiments (Fig. 2). There was no signi"cant di!erence in "ber length at between three experiments (11.1}12.8 mm). The "ber length, estimated from "ber and sarcomere lengths at and sarcomere lengths at di!erent lengths, ranged from 91 to 147% for!2 to #6. To compensate for di!erences between experimental animals in terms of their size, force was normalized to the maximum isometric force generating capacity of that muscle. The passive force was subtracted from the total force to give muscle force. In experiment 1, maximal force at #1 was slightly (not signi"cantly) greater than at, Fig. 2. Relationships between muscle length and muscle force. Muscle force is expressed relative to the maximum isometric force of each muscle (, experiment 1;, experiment 2;, experiment 3). * signi"- cant di!erence between experiment 3 and experiments 1 and 2(P(0.05). The "ber length ranged from 11 to 16 mm, corresponding to 91}147%. The force}length curves covered ascending, plateau, and descending portions. Fig. 3. Typical changes in muscle force and sarcomere length during contractions. The data are for di!erent muscle lengths in experiment 1. Sarcomere shortening was observed, which was more pronounced at shorter lengths. which was determined by twitch contractions. The relative force at longer lengths tended to be smaller in experiment 3 compared with the other two experiments, and there was a signi"cant di!erence at #2. Sarcomere shortening was observed during contraction, and the magnitude of shortening (the di!erence in sarcomere length between resting and active conditions) was smaller at longer lengths (Fig. 3). At, sarcomere length decreased from 2.31 to 2.07 μm in experiment 1, and from 2.37 to 2.12 μm in experiment 2. There was no signi"cant di!erence in sarcomere lengths between experiments 1 and 2 at all muscle lengths. Neither was the di!erence signi"cant between the two experiments in the magnitude of sarcomere shortening. At lengths longer than, muscle force did not plateau and there was a continuous rise in force during stimulation. On the other hand, sarcomere length decreased after the onset of contraction, followed by a constant phase. In experiment 3, sarcomere shortening was much smaller and not signi"cant at and longer, which was signi"cantly di!erent from those in experiments 1 and 2 at all lengths. At longer lengths, sarcomeres contracted almost isometrically, i.e., force increased at the same

4 1252 Y. Kawakami, R.L. Lieber / Journal of Biomechanics 33 (2000) 1249}1255 Fig. 4. Typical changes in muscle force and sarcomere length during contraction. Data from experiment 1 (solid lines, left ordinate) and 3 (dashed lines, right ordinate). Sarcomere shortening was observed at shorter lengths in experiment 1 but not in experiment 3. Fig. 5. The relationships between initial sarcomere length and the magnitude of sarcomere shortening. Results from experiments 1 ( ), 2( ), and 3 ( ) are plotted. Prediction from a model (Lieber et al., 1992) are also indicated (dashed curve). Experimental results coincided with the model only around. sarcomere length in all experiments. However, at shorter lengths, force was exerted by shortening sarcomeres in experiment 1, and the "nal sarcomere length was much smaller than the initial length. In experiment 3, sarcomeres contracted almost isometrically at all lengths except at the shortest length (!2). Thus, initial and "nal sarcomere length did not di!er substantially (Fig. 4). 4. Discussion In this study we hypothesized that internal sarcomere shortening occurs as a function of interactions between contractile and elastic components, based on a previously formulated theoretical model. We assumed that the present results from dissected muscles represent the behavior of the muscle}tendon in the living system. In the living system, however, muscle force is controlled at various activation levels and muscles operate at various velocities. The present results thus might represent only the maximal possible interactions within the muscle tested. However, internal "ber shortening has actually been observed in vivo (Gri$ths, 1991), so the authors believe that the present "ndings re#ect muscle}tendon interaction in vivo. Sarcomere shortening in experiments 1 and 2 and that of the model (Lieber et al., 1992) coincided only around, and at other lengths the measurements diverged from the prediction (Fig. 5). At, sarcomere shortening was 0.2 μm in experiment 1, which was approximately 10% of the initial length. This result is also comparable with the previous study (Lieber and Leonard, 1989). However, at!2 the amount of shortening was larger than what was predicted from the model. In contrast, at lengths longer than, sarcomere shortening was smaller than in the model. These results might indicate that sarcomere shortening during "xed-end contraction is not exclusively explained by the amount of SEC and length}force characteristics of sarcomeres, which does not support our initial hypothesis. At lengths shorter than, however, the compliance of SEC might be much greater than previously modelled, as discussed later in detail. However, in experiment 3 where tendinous structures were almost entirely removed, sarcomere shortening, although much smaller in amount, still existed at these lengths. This "nding suggests the existence of SEC within "bers (Higuchi et al., 1995; Purslow, 1989). At longer lengths, inter-sarcomere dynamics (see below) could also have in#uenced the results. That there was no signi"cant di!erence in sarcomere shortening between experiments 1 and 2 suggest that the tendon (including bone}tendon junction) do not act as the major in-series compliance during "xed-end contraction. The tendon has been shown to be much sti!er than the aponeurosis (Ettema and Huijing, 1989; Lieber et al., 1991). The tendon might have been too sti! to be lengthened by the contractile force. On the other hand, in experiment 3, the sarcomere shortening was greatly decreased, with no signi"cant di!erence between passive and active conditions at lengths and longer. This result would indicate that sarcomere shortening is predominantly a!ected by the aponeurosis. Roeleveld et al. (1993) observed dynamic response of muscle with and without tendon and found no di!erence. They concluded that tendon acts like a sti! force transmitter. However, they did not consider the role of aponeurosis, which appears to be a major source of in-series compliance.

5 Y. Kawakami, R.L. Lieber / Journal of Biomechanics 33 (2000) 1249} Fig. 6. Compliance of the aponeurosis as a function of initial aponeurosis length (top) and strain of the aponeurosis induced by muscle force (bottom). Due to greater compliance at lengths shorter than, strain increase at these lengths in spite of decreases in muscle force. related to varying aponeurosis force}length characteristics as a function of muscle length. Although the mechanism for this result awaits further studies, possible candidates might include shifting of aponeurosis force}length curve with respect to length (Ettema and Huijing, 1989) and/or aponeurosis slackness at short length (Huijing et al., 1989). There was no apparent damage in aponeurosis at high strain. The consequence of this aponeurosis behavior would be that the aponeurosis becomes mechanically unstable at lengths shorter than, since muscle force decreases and cannot fully stretch the aponeurosis. However, these lengths are out of the physiological range (see below) and do not appear to be used by the muscle in vivo. As shown in Fig. 3, muscle force increased during contraction at long lengths (&creep phenomenon'). Gordon et al. (1966) and Lieber and Baskin (1983) have shown that the creep phenomenon results from the interaction between sarcomeres in series. In the present study, sarcomere shortening was smaller than the model prediction (Lieber et al., 1992) at long lengths, where force creep was observed. This suggests that the e!ect of inter-sarcomere dynamics was in#uential, and this could be another factor in the interaction between sarcomere kinetics and in-series compliance. Sarcomere shortening at the expense of SEC elongation might have been masked by the elongation of sarcomeres at the measurement site. The measurement site, however, was controlled for all experiments; thus inter-sarcomere dynamics, if any, would have equally a!ected the results of three experiments. Compliance of aponeurosis was estimated based on the data from experiment 2. From the amount of sarcomere shortening by contraction, "ber length change was estimated, which was subtracted from MTU length to give aponeurosis length change. This aponeurosis length change was divided by muscle force to determine compliance of aponeurosis. Compliance of aponeurosis was greatest at shortest length, and decreased as the initial aponeurosis length increased (Fig. 6, top). The estimated strain of aponeurosis by contraction, was positively related to muscle force at and longer, but when MTU length was shorter than, aponeurosis strain increased in spite of a decrease in muscle force (Fig. 6, bottom). The strain at (11%) was slightly greater than previously reported value (8%, Lieber et al., 1991) and compliance increased up to 1.6 mm/n at the shortest length. This large compliance might be part of the reasons for the di!erences between the present results and model calculations (Lieber et al., 1992). At high aponeurosis strain, muscle force decreased with increasing aponeurosis strain. This result might be Fig. 7. The relationship between muscle length and relative force for the experiment 1. The measurements (, solid line) and estimated results from completely sti! SEC based on the measurements (, dashed line) are plotted. The existence of in-series compliance resulted in a skew of the curve to longer length.

6 1254 Y. Kawakami, R.L. Lieber / Journal of Biomechanics 33 (2000) 1249}1255 If there is no interaction between muscle "bers and SEC, initial sarcomere length will remain unchanged during contraction. The consequences of this assumption of completely &sti!' muscle were tested by using initial sarcomere lengths and estimating muscle force from the "nal length}force relationship obtained from the present &actual' muscle. The length}force curves in these two conditions were plotted in Fig. 7, which clearly shows that the length}force curve is shifted to longer length by the presence of SEC, as suggested previously (Lieber et al., 1992). The two curves cross at 2.1 μm for the &actual' muscle, i.e., in the optimal region of the length}force curve. At lengths longer than, the force of &actual' muscle is greater at a given length than the &sti!' muscle. This would favor muscle force development at these lengths. Interestingly, the length range where the force of &actual' muscle is smaller, is not in the physiological range (Mai and Lieber, 1990). Lutz and Rome (1994) showed that frog muscular system operates at optimal length at maximal activation during power generation for jumping. They argue that during evolution muscle architecture has been adjusted to give the appropriate gear ratio (change of body movement/change in sarcomere length). It appears that the muscle}tendon unit has also been evolved to optimize muscle}tendon interactions to maximize performance. The amount of SEC as well as the size and architecture of "bers have been shown to vary greatly among di!erent muscles (Trestik and Lieber, 1993; Zajac, 1989). This fact suggests that the di!erences in the design of muscle}tendon unit re#ect distinct functional demands imposed on the muscles. The tendon of gastrocnemius muscle, for example, is 7 times the length of the semitendinosus tendon (Zajac, 1989), while the gastrocnemius has a much greater physiological cross-sectional area (Trestik and Lieber, 1993). These properties suggest that the tendon compliance plays a much more important role for this muscle. Supporting evidence for this notion has been provided in many previous studies (Ho!er et al., 1989; Huijing et al., 1989; Roberts et al., 1997; Trestik and Lieber, 1993; van Soest et al., 1995). Acknowledgements The authors thank Dr. Gordon Lutz, Michel Sam, and Shannon Bremner (University of California, San Diego) for their excellent technical assistance and helpful discussions. We also would like to thank Yvonne Hall and Fumiko Kawakami for secretarial assistance. This work was partly supported by NIH grant AR40050, the Veterans A!airs Medical Research and Rehabilitation R & D Services, and Mizuno International Sports Exchange Foundation. 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