Sarcomeres are subcellular organelles that act as the basic force producing units in muscles. A sarcomere is composed of the contractile filaments myosin (anisotropic band, A-band) and actin (isotropic band, I-band) as well as a series of structural proteins including titin, nebulin, and desmin. The arrays of serially-connected sarcomeres give skeletal muscle its characteristic striated appearance. The micro-scale striation patterns are good indicators of myofibril integrity and are useful in diagnosing muscle pathologies (Plotnikov et al., 2008; Ralston et al., 2008). More importantly, the striation periodicity, or the corresponding instantaneous sarcomere length (SL) and the rate of change in SL, have been identified as important indicators of the functional properties (e.g., force, power) of a muscle (Hill, 1938; Gordon et al., 1966; Lutz and Rome, 1994; Burkholder and Lieber, 1998).

SL and SL non-uniformities have been crucial for understanding and explaining basic muscle properties (Hill, 1953; Huxley and Peachey, 1961; Morgan, 1994) and muscle function within the constraints of animal bodies (Cutts, 1988; Mai and Lieber, 1990; Lutz and Rome, 1994). According to the classic cross-bridge theory, the maximal steady-state isometric force produced by a muscle depends on the overlap between thick and thin myofilaments, which depends on the SL (Gordon et al., 1966). The theoretical force-length (FL) curve can be derived from the lengths of the actin and myosin filaments (Gordon et al., 1966; Herzog et al., 1992) and has been validated in single muscle fiber (Gordon et al., 1966; ter Keurs et al., 1978; Edman, 1999) and single myofibril (Bartoo et al., 1993; Leonard and Herzog, 2010; Rassier and Pavlov, 2010) experiments. However, the relationship between force and the corresponding SLs has never been validated for whole muscles due to the technical difficulties in visualizing individual SLs in activated muscle. Nevertheless, the mean sarcomere length has been used frequently to infer the amount of force and power a muscle can generate (Rack and Westbury, 1969; Cutts, 1988; Mai and Lieber, 1990; Lutz and Rome, 1994; Vaz et al., 2012). Though convenient, the main caveat of such practice is that it neglects the great non-uniformity of SLs (also referred to as dispersion of SLs) in neighboring sarcomeres at a given location within a muscle, and the differing SLs and SL changes at different locations of a muscle (Llewellyn et al., 2008; Moo et al., 2016).

Typically, SLs for a given muscle are measured at a single spot, often in the mid-belly of the muscle, and at a given muscle length (Rack and Westbury, 1969; Cutts, 1988; Mai and Lieber, 1990; Lutz and Rome, 1994; Vaz et al., 2012). It is then assumed implicitly that the SLs measured at this location represent the SLs at other locations within the muscle, and the FL, force-velocity and power-velocity properties of muscles are implied based on these single SL measurements (Rack and Westbury, 1969; Cutts, 1988; Lutz and Rome, 1994; Burkholder and Lieber, 2001; Vaz et al., 2012). However, it has been shown throughout the muscle hierarchy, from single myofibrils (Leonard and Herzog, 2010; Johnston et al., 2016), to single fibers (Huxley and Peachey, 1961; Infantolino et al., 2010), to whole muscles (Llewellyn et al., 2008; Cromie et al., 2013; Chen et al., 2016; Moo et al., 2016) that SLs vary dramatically within a muscle with the range of SLs easily covering 1.0 μm, which is equivalent to a range of 40% of the optimal SLs for average mammalian skeletal muscles (Huxley and Peachey, 1961; Walker and Schrodt, 1974; Herzog et al., 1992). Furthermore, SL dispersion has been shown to increase drastically in single myofibrils during activation and force production (Telley et al., 2006; Leonard and Herzog, 2010; Rassier and Pavlov, 2010; Johnston et al., 2016). Nevertheless, single myofibrils lack many of the structural proteins that provide stability to entire muscles. Thus, the increased SL non-uniformities during activation observed in myofibrils might not occur in whole muscles.

We used state-of-the-art second harmonic generation (SHG) imaging techniques to visualize sarcomeres in whole muscle (Llewellyn et al., 2008; Moo et al., 2016) and a miniaturized buckle type tendon force transducer (Walmsley et al., 1978; Hodgson, 1983; Abraham et al., 1985; Herzog and Leonard, 1991; Kaya et al., 2003, 2008) to directly measure the force generated in the mouse tibialis anterior muscle. Using these approaches, the purposes of this study were (i) to measure the distribution of SLs in an activated intact muscle and to compare the SL non-uniformities to those found in passive muscle; and (ii) to assess the feasibility of using the mean SL measured at a specific location in the muscle to predict maximal isometric muscle force. We hypothesized that SL non-uniformities are the same in the relaxed and activated muscle and that the mean SLs measured in the mid-belly of the tibialis anterior is a good predictor of the maximal isometric muscle force.

The average mass of the mice was 29 ± 4 g (mean ± SD). The total number of individual sarcomeres analyzed for each of the “relaxed-short,” “activated-short,” “relaxed-long,” and “activated-long” groups were 2,856 sarcomeres, 4,454 sarcomeres, 2,564 sarcomeres, and 8,270 sarcomeres, respectively.

When relaxed, sarcomeres in the short muscle were shorter (~2.4 μm) than sarcomeres in the long muscle (~2.7 μm; Figure 3A). During activation, sarcomeres shortened by 7.1 and 6.7% at the short and long muscle lengths, respectively (Figure 3A). The shortening in sarcomere lengths during activation resulted in a decrease in the shortest SL (Figure 3B), but did not influence the longest SL (Figure 3C). As a consequence, the SL range increased during activation (Figure 3D). In a region of 159 × 2.8 μm², the local difference between the longest and shortest sarcomeres in activated muscle was as high as ~1 μm (Figure 3D).

The local dispersion of the resting SLs was about 4% CV for the short and long muscle lengths (Figure 4). Activation resulted in an increased SL dispersion at the short and long muscle lengths (Figure 4). The SL dispersion increased by ~93% in the activated-short muscle compared to that observed in the relaxed-short muscle. At the long muscle length, however, this increase in SL dispersion from the relaxed to the activated state was only ~34% (Figure 4B).

Mean SLs remained constant throughout the 600 ms contraction period for the short (~2.2 μm) and long muscle length (~2.5 μm; Figure 5A). The local CV and SL range for the activated TA was greater at the short compared to the long muscle length. At the short muscle length, the local CV and SL range remained constant throughout the 600 ms contraction time, while the local CV and SL range at the long muscle length decreased by ~12 and 9%, respectively, during the 600 ms contraction time (Figures 5B,C).

At the relaxed-short muscle length, 44% of the sarcomeres resided on the plateau of the force-length relationship. This number decreased to 14% during activation (Figure 6A). For the relaxed-long muscle length, 9% of the sarcomeres resided on the plateau of the force-length curve. This number increased to 27% during activation and exceeded the corresponding proportion seen at the short muscle length (Figure 6B).

SLs in the relaxed muscle had a normal distribution (Figures 7A,C). During activation, the SL distribution for the short muscle became bimodal, with mean lengths of 2.12 and 2.64 μm (Figure 7B). These two mean SLs gave rise to a weighted theoretical force of 0.90. The Gaussian-fitted mean SLs yielded a different theoretical force (0.90) compared to the force derived from the simple averaging of the pooled SLs (0.95) shown in Figure 3. In the activated-long muscle, the SL distribution became slightly positively skewed (Figure 7D) with mean SLs of 2.47 and 2.54 μm. These two mean SLs correspond to a weighted theoretical force of 0.97.

From the proportion of sarcomeres on the plateau region of the FL curve (Figure 6) and the SL-derived theoretical forces (Figure 7), the muscle is supposed to generate greater forces at the long (180° ankle flexion) than the short (90° ankle flexion) muscle length. Indeed, we measured a 9% greater force at the long compared to the short TA length (Figure 8) at 200 ms of the isometric contraction. Using Equation (2) and the mean SLs derived from the data pooled from nine animals (Figure 7), the force predicted by the mean SLs fell within ±5% of the measured value.

Out of the nine tested animals, muscle force was only successfully predicted once to be within ±5% of the measured value (Figure 9). The discrepancy between the predicted and the measured force values and SL was as big as ~35% of the isometric force for the short TA (Figure 9B) and ~0.5 μm in SL, respectively (Figure 9C). Muscle forces and SL PDF for individual animals (n = 9) are included in detail in the Supplementary Material S5.

Using an advanced multi-photon microscope and a novel tendon force transducer, in vivo individual sarcomere lengths and force in intact whole muscle were measured simultaneously during isometric tetanic contractions. Through a novel imaging protocol, inspired by previous studies on the sarcomere mechanics of the beating heart (Kobirumaki-Shimozawa et al., 2016), sarcomeres from the mid-belly region of the mouse TA were visualized in the relaxed and activated muscle. The primary goal of our study was to investigate the changes in sarcomere length distribution during activation. Sarcomere lengths were measured as the distance between adjacent A-band centroids. In agreement with previous in vivo studies (Llewellyn et al., 2008; Cromie et al., 2013; Moo et al., 2016), the dispersion of resting sarcomere lengths (SLs) was found to be ~4% at short and long TA lengths (Figure 4). SL dispersion increased during activation, thereby rejecting our first hypothesis (Figure 4). Increased SL dispersions during activation have been observed in experiments using isolated myofibrils (Telley et al., 2006; Leonard and Herzog, 2010; Rassier and Pavlov, 2010; Johnston et al., 2016), but were not expected in whole muscles where structural proteins and the passive collagen network surrounding fibers, fascicles, and the entire muscle were thought to prevent increases in sarcomere length non-uniformities upon muscle activation. This finding suggests that the presence of stabilizing connective tissues found in the extracellular matrix does not prevent an increase in SL non-uniformity in whole muscle during activation. In other words, the observations of great sarcomere length non-uniformities made in isolated fibers (Huxley and Peachey, 1961; Gordon et al., 1966) and myofibrils (Rassier and Pavlov, 2010; Johnston et al., 2016) also occur in entire, in vivo muscle preparations. Nevertheless, the connective tissues in the intact muscle likely attenuate the SL dispersion during activation as the high CV of 20–30% found in active rabbit psoas myofibrils (Rassier and Pavlov, 2010; Johnston et al., 2016) were reduced to 6–8% CV in the intact mouse TA (Figure 4).

We found that the increase in SL dispersion was more pronounced (~3 times higher) at the short compared to the long TA length. Passive tension in mouse TA starts developing at sarcomere lengths in excess of about 2.5 μm (Wood et al., 2014). Since the mean SL in the relaxed-long muscle was 2.6 μm (Figures 3A, 7), passive structural muscle elements were likely stretched at this length prior to activation and helped stabilize the A-bands during activation (Horowits and Podolsky, 1987). This is not the case for sarcomeres at the short muscle length (SL of ~2.3 μm; Figures 3A, 7) where the passive structural elements were likely slack prior to activation, possibly allowing for increased A-band shifts and increased SL non-uniformities upon muscle activation (Horowits and Podolsky, 1987). Another interesting finding was that the SLs at the long muscle length became more uniform during the 600 ms isometric contraction (Figures 5B,C). Future studies should investigate the mechanism and functional implication of this increased uniformity in SL at long muscle length.

The biggest CV measured in this study was merely ~8% (Figure 4B), which seems small but is obtained from a large number of individual sarcomeres. A better representation may be the range of SLs in a small muscle region (159 × 2.8 μm²) of no more than 30 serial sarcomeres, which was typically ~1 μm for the active TA (Figure 3D). This difference in SL corresponds to more than 40% of the optimal sarcomere length in mouse skeletal muscle. On the descending limb, a SL difference of 1 μm would theoretically correspond to a difference of 70% of the maximal isometric force, and on the ascending limb of the force-length curve, would be the difference between zero force and maximal force. Therefore, the secondary goal of this study was to evaluate the functional implications of this increased SL non-uniformity during activation. Specifically, we were interested if the mean SL, measured in both relaxed and activated states, is a good predictor of the force in the whole muscle. In the relaxed-short TA, 44% of all sarcomeres were located on the plateau of the force-length curve, while in the relaxed-long TA, 9% of all sarcomeres were on the plateau region (Figures 6A,B). The Gaussian-fitted mean SLs were 2.32 and 2.64 μm at the short and long MTU length, which corresponds to theoretical forces of 1.0 and 0.88, respectively (Figure 7). Based on these resting SLs, a muscle at the short length should produce ~14% more force than the same muscle at the long length. However, the experimentally measured forces showed the opposite result: the muscle at the long length generated ~9% greater force than that measured at the short length (Figure 8). If the mean SLs measured during activation were used instead, the resulting theoretical forces derived from the FL curve were within ±5% of the actual force measurements (see “Results”). Assessment of the proportions of SLs on the plateau regions of the FL curve in the activated muscle (Figures 6A,B) also suggested that the muscle should generate higher force at the long (27% sarcomeres on the plateau) rather than the short TA length (14% sarcomeres on the plateau). Therefore, we conclude that the active mean SL is a better predictor of muscle force than the resting mean SL. This finding may appear obvious, but in many studies, sarcomere lengths of relaxed muscles have been taken as indicators of the functional capacity of muscles in vivo (Rack and Westbury, 1969; Wickiewicz et al., 1983; Lieber and Boakes, 1988; Lutz and Rome, 1994), which seems inappropriate based on the current findings.

Encouraged by the fact that the muscle force was successfully predicted using the mean SL of the pooled data set, we went on to investigate if the Gaussian-fitted mean SL can predict force in the TAs of the individual animals. To our surprise, only in one out of nine cases did the predicted force fall within ±5% of the true values measured experimentally. The differences between the predicted and the measured forces ranged from about 11–35% of the maximal isometric force at the short TA length (Figure 9B). In terms of the SLs, the predicted values were ~0.2–0.5 μm off from the measured mean sarcomere length values (Figure 9C). In an intact whole muscle, the muscle architecture and the surrounding connective tissue likely alter the force transmission from the myofibril level to the whole muscle, making it unreliable to predict muscle force using the mean SL. Furthermore, we showed previously that sarcomere lengths vary dramatically for neighboring sarcomeres within the same region of the muscle, and that the mean sarcomere lengths vary substantially from one location of the muscle to the next (Moo et al., 2016). To complicate matters even further, sarcomere length changes associated with muscle length changes also differ between muscle locations (Moo et al., 2016). Therefore, the mean sarcomere lengths measured at one point and at one length of the muscle is likely not representative of the true mean sarcomere length, and thus might cause the erroneous force predictions observed here.

There are limitations in this study that need careful consideration when interpreting our results. First, a few layers of skin and fascia covering the TA were removed for optimal SHG imaging. However, as no visible changes were observed in the structure of the muscle (Figure 1), we assume that the sarcomere length measurements obtained in this manner are identical to those that would be obtained in the fully intact muscle. Second, the imaging protocol used in this study, though novel, does not allow for tracking of single myofibrils during activation. Instead, the muscle images acquired in the relaxed and activated states represent sarcomeres from the same region in the muscle (within an area of ~50 μm in diameter). Finally, due to the poor signal-to-noise ratio for the deep tissue images, sarcomere images were obtained from a tissue depth of up to ~100 μm only. Despite the aforementioned limitations, our study provides novel insight into sarcomere dynamics and the relationship between SL and force in intact muscles. Future studies should focus on studying the relationship between mean SL measured during activation and the resulting muscle force at multiple muscle lengths with smaller length increment to provide additional support for the current findings. As the sarcomeres across a whole muscle have variable lengths (Moo et al., 2016; O'Connor et al., 2016), future investigations should also study sarcomeres at different anatomical locations, for example at the distal TA, by following the current experimental protocols.

The results of this study warrant the following conclusions: (i) sarcomere length dispersion (non-uniformities) increases substantially from the relaxed (passive) to the activated state and reaches average differences of ~1.0 μm in a small segment of muscle comprised of ~30 consecutive sarcomeres; These differences in sarcomere length are associated with theoretical force differences of 70–100% of the maximal isometric force; and (ii) the mean sarcomere lengths measured at a single location in the relaxed muscle are poor indicators of the force potential of the muscle. Mean sarcomere lengths in the activated muscle are better predictors of force, but can still be erroneous by up to 35% under the present study conditions, which are optimal and probably cannot be replicated in a human study at this time.

Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work: EM, TL, and WH. Drafting the work or revising it critically for important intellectual content: EM and WH. Final approval of the version to be published: EM, TL, and WH. Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved: EM, TL, and WH.