Passive tension is borne by a muscle when it is lengthened beyond slack length. This increased tension resists further stretch, even in the absence of muscle activation. Passive mechanical properties vary among muscles (Brown et al., 1996; Shah et al., 2004; Prado et al., 2005; Ward et al., 2009), differentiate between healthy and pathologic muscle (Abrams et al., 2000; Fridén and Lieber, 2003; Lieber et al., 2003; Meyer and Lieber, 2012), and adapt in response to altered use (Brown et al., 1996; Takahashi et al., 2007). However, understanding the underlying basis for these passive properties requires measuring passive mechanical muscle properties and identifying sources of passive tension at each size scale.

Passive tension is generally attributed to both the extracellular matrix (ECM) and intracellular titin (also known as connectin), both of which have viscoelastic properties. Muscle ECM, which is dominated by collagen in terms of mass, is organized into three interconnected levels – epimysium surrounds whole muscles, perimysium surrounds fascicles, and endomysium surrounds individual fibers (Borg and Caulfield, 1980; Trotter et al., 1995). These distinctions represent anatomical definitions with very little structural or functional basis. These various connective tissue layers provide structural support and play an important role in force transmission between fibers and tendon (Trotter and Purslow, 1992). Another passive load bearing structure is titin (Wang, 1985; Maruyama, 1986), which is a large (∼4 MDa) protein that spans from the sarcomere M-line to the Z-disk (Maruyama et al., 1985) and bears tension with increased sarcomere strain (Trombitas et al., 1995).

The relative contribution of ECM and titin may be muscle (Prado et al., 2005), size-scale (Meyer and Lieber, 2011; Smith et al., 2011), and strain dependent (Trombitas et al., 1995). Titin clearly bears passive load in myofibrils (Linke et al., 1994; Bartoo et al., 1997) and functions at low muscle strains (Wang et al., 1991; Linke et al., 1994; Trombitas et al., 1995; Brynnel et al., 2018). ECM is thought to dominate at the fiber bundle (Meyer and Lieber, 2011; Smith et al., 2011) and whole muscle (Olsson et al., 2006) level and act at high strains (Williams and Goldspink, 1984; Linke et al., 1994; Brown et al., 2011a; Meyer and Lieber, 2011). Unfortunately, most passive mechanical studies are performed at only one size scale and then extrapolated to other scales to predict structure-function relationships (Fridén and Lieber, 2003; Lieber et al., 2003; Ward et al., 2009; Brown et al., 2011a; Meyer and Lieber, 2011). With increasing size, additional layers of ECM are included in the sample, which may result in a non-linear scaling relationship in skeletal muscle. However, experimental data are not available to support or refute this concept.

In contrast to passive tension, active muscle tension clearly results from intracellular interaction among actin and myosin contractile proteins within individual sarcomeres and whole muscle active tension is accurately modeled by linearly scaling the number of sarcomeres acting in series and in parallel. At the whole muscle level, muscle architecture (i.e., the arrangement of muscle fibers within a muscle) predicts both active isometric force (Powell et al., 1984) and excursion (Winters et al., 2011) to a first approximation. Exceptions to this statement are based on higher order effects in muscles that may occur due to myofascial force transmission among muscles (Maas et al., 2001, 2003) or history-dependent changes in active force (Edman et al., 1982; Joumaa and Herzog, 2014). However, since neither myofascial force transmission nor history-dependent changes are generalizable to date, they are not typically included in biomechanical models of active muscle force. Since passive tension is mediated by both intra- and extra-cellular contributions (which are poorly understood at the various scales) scaling laws for passive muscle mechanical properties are not currently known. Indeed, our previous study of active muscle properties showed that active tension scaled linearly with sarcomere number but passive tension predictions were off by 25% to 150% depending on muscle and strain (c.f. Figure 3 of reference Winters et al., 2011).

Thus, the purpose of this study was to measure the passive mechanical properties of single muscle fibers, fiber bundles, fascicles, and whole muscles from the same samples of three architecturally diverse muscles from New Zealand White rabbits. Fiber number, titin isoform, and collagen content were also measured to provide insights into, which, if any of these parameters affect passive modulus at each scale.

Whole muscle architectural parameters and single fiber, fiber bundle, and fascicle dimensions were measured at each scale for the TA, EDL, and ED2 (Table 1). Specimen diameter and slack sarcomere length were not significantly different among TA, EDL, and ED2 for any size scale (Table 1). However, in vivo sarcomere length operating range was significantly different among muscles (Table 1; p < 0.05).

Measured stress increased for a given strain for all three muscles as scale increased (Figure 2). For the TA and EDL, fascicles, bundles and fibers clustered together compared to the very high stress observed for the whole muscles (Figures 2A,B). Interestingly, the ED2 fascicles were intermediate in their stress-strain relationship between the fiber, bundle and whole muscle scales (Figure 2C). These relationships became more obvious upon examining the passive modulus, which increased with increasing size scale (p < 0.0001; Figure 3) and was significantly different among muscles (p < 0.0001). Importantly, modulus at each scale was muscle dependent as evidenced by the highly significant muscle × scale interaction term (p < 0.0001). There were relatively small differences in modulus between fibers and bundles. The most dramatic modulus differences occurred between the fascicle and whole muscle levels where muscles were from 5- to 10-fold higher in modulus compared to fascicles and from 10- to 100-fold higher in modulus compared to fibers. These results explicitly demonstrate that passive modulus varies across the three muscles and size scale.

Given that typical muscle sarcomere strains average about 20% (Burkholder and Lieber, 2001), we quantified modulus at strains of 10%, 20%, and 30% (Figure 4). The main result was the same for any strain – modulus was significantly different among scales (p < 0.0001) and muscles (p < 0.0001) with a highly significant muscle × scale interaction term (p < 0.0001). This result explicitly demonstrates the dependence of muscle passive mechanical properties on both the scale of the specimen and the specific muscle studied. Importantly, none of the conclusions of this report depend on a single strain measurement either during a functional movement or anatomical limitation. The data presented across very large strain ranges (Figure 3) and several select strain ranges (Figure 5) provide ample quantitative values to be used in future modeling studies.

To further quantify scaling rules, modulus was compared against the estimated number of fibers in each specimen on a log-log plot. Data were accurately fit using a simple power law equation (y = ax^b; TA: r² = 0.84; EDL: r² = 0.93; ED2: r² = 0.92), which further illustrates the non-linear scaling relationship that occurs across size scales. Furthermore, the TA exhibited a different scaling pattern than EDL or ED2 based on the different exponent value extracted from the power law (b in y = ax^b; TA = 0.23 ± 0.02; EDL = 0.37 ± 0.02; ED2 = 0.41 ± 0.02; p < 0.001).

To provide structural insight into the differential passive tension results described above, titin molecular mass and collagen content of each specimen were measured (Figure 5). Collagen content increased significantly with scale (p < 0.0001), was significantly different across muscles (p < 0.0001) and showed a significant muscle × scale interaction (p < 0.0001; Figure 5A), suggesting differences in collagen organization among these three muscles. Titin molecular mass did not differ significantly across scale for any muscle tested (p = 0.24; Figure 5B), but did vary by muscle (p < 0.0001) with TA titin size significantly smaller than either EDL or ED2 at all scales (p < 0.001). No significant scale x muscle interaction was observed (p = 0.49).

The results of these experiments demonstrate two important concepts. First, passive modulus is not a constant for muscle that can be easily applied across scales. Second, modulus increases across scales in a non-linear, muscle-specific manner, emphasizing that extracellular sources of passive tension dominate at the whole muscle level.

Magid and Law (1985) first demonstrated that frog muscle fibers and whole muscles have the same passive modulus, demonstrating that passive tension was mediated intracellularly across scale in frog muscle. This finding led to spectacular experiments that have elucidated the nature of the intracellular titin protein. However, more current findings suggest that their finding may be species specific (Meyer and Lieber, 2018). Human muscle fibers demonstrate different passive mechanical properties compared to bundles, which contain a connective tissue matrix layer (i.e., perimysium) that individual fibers do not (Fridén and Lieber, 2003; Lieber et al., 2003; Ward et al., 2009). Differences between fibers and bundles manifest themselves functionally as well in mouse (Meyer and Lieber, 2011, 2018), rat (Brown et al., 2011a), and rabbit (Brown et al., 2011b) skeletal muscle: bundles exhibit a larger stress at a given strain that is non-linear, whereas individual fibers often demonstrate a highly linear response (Figure 2). In our sample, linear fits to fiber stress-strain data explained over 90% of the experimental variability. By comparing a group of dissected individual fibers to a fiber bundle, the non-linearity and modulus increase was shown to be due to the properties of the ECM (Purslow and Trotter, 1994; Meyer and Lieber, 2011). Here, we found that the non-linearity and magnitude of stress-strain curves increase considerably across the fiber, bundle, fascicle, and whole muscle size scales (Figure 2) and that passive modulus correspondingly increases with size scale. Fiber passive modulus measured only 3.2%, 1.6% or 0.85% of the whole muscle values for TA, EDL, and ED2, respectively, at 20% strain (Figure 4B) demonstrating that whole muscle passive tension is dominated by extracellular structures.

It was also interesting to note that the ED2, with the very high fascicle and muscle stiffness (Figure 4), had an extremely small anatomical sarcomere length range (6.1% strain, 0.17 μm; Table 1) suggesting that it probably functions over a very narrow sarcomere length range. This may suggest that it acts as a passive strut (stabilizer) rather than a muscle that moves limbs over a wide range of motion. The TA, with the lowest stiffness is monoarticular and likely functions over the largest range during normal ankle rotation (24% strain, 0.58 μm; Table 1). The EDL with intermediate stiffness may function over a relatively small range since ankle and digital rotation during normal movement are often complementary, even though it’s potential anatomical range is quite large (49% strain, 1.18 μm; Table 1). None of these interpretations are confounded by sarcomere length differences across size scales which were all very close to 2.5 μm. Future studies measuring fiber and sarcomere length during movement are necessary to explicitly test these hypotheses. Muscle fiber activation would certainly shorten sarcomeres and the anatomical studies performed herein do not necessarily emulate sarcomere length changes during movement.

It is interesting that the passive moduli of whole muscles were an order of magnitude larger than fascicles, suggesting either the fascicles tested contained an incomplete perimysium or that the epimysium is dramatically stiffer than the other ECM layers. Thus, there may be a level of connective tissue organization above fascicles that is not appreciated based on current concepts of muscle structure. Unfortunately, this presents a challenge to further clarification as there are currently not tools available that can measure muscle structure with micron resolution across distances of many millimeters. We recently reported the existence of perimysial cables of this dimension (Gillies et al., 2017) but these data are currently only obtainable on fixed/embedded specimens through the very tedious serial blockface electron microscopic method (Gillies et al., 2014).

Titin is thought to be the primary determinant of passive stiffness (Prado et al., 2005) and slack sarcomere length (Wang et al., 1991) at small size scales such as myofibrils and fibers. Titin isoforms in TA were smaller than in EDL or ED2 (Figure 5B), and, while not significant, TA did have a shorter slack sarcomere length compared to EDL and ED2 (Table 1) which may be related. Our results in rabbit muscle are in contrast to the recent report by Brynnel et al. (2018) who showed that whole mouse diaphragm, soleus and EDL muscle stiffness were all increased by the same amount when the PEVK region of titin was reduced in size by homologous recombination. Deletion of 47 exons in this region was predicted to shorten the titin filament by 63 nm which agreed well with the measured shift in the length-tension curve and increase in passive stiffness. Currently, it is not clear whether differences between these studies are species-specific or another as yet unidentified structural property of skeletal muscle.

Inspection of the biomechanical modeling literature reveals that passive mechanical properties of muscle are nearly universally considered to scale to muscle architecture properties. The definitions used for passive mechanical properties vary markedly across the numerous studies (see Table 1 of reference Meyer and Lieber, 2018). However, the data reported here clearly demonstrate that passive modulus scales in a highly non-linear fashion from fiber to whole muscle, and that the passive scaling is muscle-specific so that generic generalization across muscles is not justified. This also suggests that extrapolating whole muscle function from reduced specimen preparations may not be justified. We previously pointed this out based on the finding that active muscle force was easily predicted based on known sarcomere and architectural properties whereas passive force was not (44). In addition, the structures responsible for mediating passive tension may be fundamentally different across size scales and strains. While titin is the most significant predictor of passive tension at small size scales (e.g., myofibrils and fibers), collagen content is the strongest predictor of whole muscle passive function at any strain. These findings suggest that a fundamental difference exists among fibers, bundles, fascicles, and whole muscles, and investigators should not simply rely on reduced preparations such as muscle biopsies to infer whole muscle passive mechanical properties.

The authors confirm that the publication of this paper involves no conflicts of interest of any kind.

The datasets generated for this study are available on request to the corresponding author.

The animal study was reviewed and approved by the University of California, Institutional Animal Care and Use Committee (IACUC).

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.