Evidence suggests that the giant muscle protein titin functions as a tunable spring in active muscle. However, the mechanisms for increasing titin stiffness with activation are not well understood. Previous studies have suggested that during muscle activation, titin binds to actin, which engages the PEVK region of titin, thereby increasing titin stiffness. In this study, we investigated the role of PEVK titin in active muscle stiffness during rapid unloading. We measured elastic recoil of active and passive soleus muscles from TtnΔ112-158 mice characterized by a 75% deletion of PEVK titin and increased passive stiffness. We hypothesized that activated TtnΔ112-158 muscles are stiffer than wild-type muscles as a result of the increased stiffness of PEVK titin. Using a servomotor force lever, we compared the stress–strain relationships of elastic elements in active and passive muscles during rapid unloading and quantified the change in stiffness upon activation. The results show that the elastic modulus of TtnΔ112-158 muscles increased with activation. However, elastic elements developed force at 7% longer lengths and exhibited 50% lower active stiffness in TtnΔ112-158 soleus muscles than in wild-type muscles. Thus, despite having a shorter, stiffer PEVK segment, during rapid unloading, TtnΔ112-158 soleus muscles exhibited reduced active stiffness compared with wild-type soleus muscles. These results are consistent with the idea that PEVK titin contributes to active muscle stiffness; however, the reduction in active stiffness of TtnΔ112-158 muscles suggests that other mechanisms compensate for the increased PEVK stiffness.

Muscles are highly versatile and adaptable organs capable of a wide array of functions that enable animals to navigate unexpected perturbations within their environment (Azizi and Roberts, 2010; Biewener and Daley, 2007; Dickinson et al., 2000). The sliding-filament and swinging cross-bridge theories of muscle contraction have long been used to predict muscle force under different conditions. However, over the last 20 years it has become increasingly clear that conventional models based on these theories perform well when muscles are isometric and fully activated but are less accurate at predicting muscle force during natural dynamic movements (Dick et al., 2017; Lee et al., 2013; Nishikawa et al., 2018). Specifically, traditional cross-bridge theories fail to predict muscle force during stretch or shortening of active muscle (Herzog, 2014; McGowan et al., 2013). Gaps in our understanding of the molecular mechanisms underlying these properties limit our ability to predict muscle function during in vivo movements.

Accumulating evidence suggests that the giant muscle protein titin may be a key element to understanding the molecular basis of many elusive muscle properties (Leonard and Herzog, 2010; Nishikawa et al., 2018; Rode et al., 2009; Schappacher-Tilp et al., 2015). As the largest known protein, titin spans a half sarcomere from the Z-disk to the M-band and maintains sarcomere structure (Horowits and Podolsky, 1987). The viscoelastic I-band region of titin is composed of three elements in series: a relatively compliant proximal tandem Ig-domain, a stiff PEVK region, named for its predominant residues, and a stiff distal Ig-domain located near the A-band (Linke et al., 1996, 1998; Prado et al., 2005). In skeletal muscle, a unique N2A sequence spans the proximal Ig and PEVK segments (Bang et al., 2001; Linke et al., 1998). It is well accepted that I-band titin contributes to passive muscle force (Granzier and Irving, 1995; Trombitás et al., 1995). The proximal tandem Ig domain straightens at low passive forces, followed by stretch of the stiffer PEVK region at higher forces (Granzier and Labeit, 2004; Linke et al., 1998). Both the proximal Ig and PEVK domains undergo intense alternative splicing, which gives rise to isoforms that differ in stiffness (Linke et al., 1998; Prado et al., 2005). Muscles with longer titin isoforms are more compliant than those with shorter isoforms (Prado et al., 2005). To contribute to active muscle force and stiffness, titin stiffness must increase with muscle activation.

Mounting evidence suggests that titin functions as a Ca2+-dependent viscoelastic element in muscle (Freundt and Linke, 2019; Leonard and Herzog, 2010; Nishikawa, 2020; Schappacher-Tilp et al., 2015). Titin has been implicated in the increase in active muscle stiffness prior to cross-bridge formation (Bagni et al., 2002, 2004; Cornachione et al., 2016) and the increased force of active myofibrils stretched beyond overlap (Leonard and Herzog, 2010; Powers et al., 2016). However, a complete understanding of the molecular mechanisms that increase titin stiffness is still lacking. Recent work demonstrated that the N2A region of titin binds to actin in the presence of calcium (Dutta et al., 2018; Nishikawa et al., 2020). Binding at this location in I-band titin would eliminate the straightening of the proximal tandem Ig domains, shorten titin's equilibrium length, and allow for stretch of only the PEVK region in active muscle (Nishikawa, 2020).

The focus of this study was to further investigate whether PEVK titin contributes to active muscle stiffness in intact soleus muscles. To quantify the change in muscle stiffness with activation, we measured the elastic recoil of active and passive soleus muscles during rapid unloading. Active muscles shorten biphasically in response to a rapid decrease in load (Jewell and Wilkie, 1958; Lappin et al., 2006; Monroy et al., 2017; Wilkie, 1956). There is an initial fast phase of shortening, attributed to elastic elements, followed by a slow phase of shortening due to cross-bridge cycling (Jewell and Wilkie, 1958; Wilkie, 1956). We measured the initial fast phase of shortening during rapid unloading to estimate the stress–strain relationship of elastic elements in active and passive muscles. Recent work demonstrated that the stress–strain relationship of intact soleus muscles during rapid unloading shifts towards shorter lengths during activation, indicating that elastic structures stiffen with activation (Monroy et al., 2017). In addition, mdm muscles, characterized by a mutation to the N2A region of titin (Garvey et al., 2002), failed to show a shift in the stress–strain relationship with activation. These data support the hypothesis that during activation, titin's equilibrium length decreases, and titin and muscle stiffness increase (Nishikawa, 2020).

Intact muscles are composite materials made up of not only muscle tissue but also connective tissue, nerves and blood vessels. Various elastic structures such as tendons, aponeuroses, the extracellular matrix (ECM), titin and cross-bridges can contribute to the elastic properties of whole muscles. Thus, each element's contribution can be difficult to differentiate at the whole-muscle level (Gindre et al., 2013; Roberts, 2016). We designed unloading experiments of intact muscles to better understand the relative contributions of elastic elements to active muscle stiffness. By matching the initial stress and change in stress in active and passive unloading tests, the recoil distance of linear elastic elements outside muscles, such as tendons, will remain constant. The contribution of in-series elastic elements can be ruled out because the stiffness of linear elements is independent of their initial length. Any change in stiffness with activation may be due to parallel elastic elements such as collagen in the ECM or titin.

In this study, we used the TtnΔ112-158 mouse model characterized by a 47 exon (1586 amino acid) deletion to the PEVK region, which corresponds to a 75% reduction in PEVK segment length (Brynnel et al., 2018). Recent work on skinned muscle fibers demonstrated that titin-based passive stiffness was more than 5-fold higher in TtnΔ112-158 than in wild-type muscles (Brynnel et al., 2018). However, maximum isometric force was not different between genotypes. TtnΔ112-158 mice exhibit similar growth rates to wild-type mice and average running speed was not different from that of wild-type mice after 5 weeks of training (Brynnel et al., 2018). Given that passive stiffness increased in TtnΔ112-158 muscles, we hypothesized that active muscle stiffness is also greater in TtnΔ112-158 muscles as a result of increased titin stiffness. We compared results from TtnΔ112-158 muscles with previously reported data for wild-type muscles (Monroy et al., 2017) to determine the effect of the PEVK deletion on active muscle stiffness. We predicted that the stress–strain relationship of intact TtnΔ112-158 soleus muscles during rapid unloading would shift towards shorter lengths during activation, and that the elastic modulus should be greater in TtnΔ112-158 muscles than in wild-type muscles as a consequence of the significantly shorter PEVK segment.

Animals

TtnΔ112-158 mice were obtained from the Granzier laboratory at the University of Arizona, and a breeding colony was established at the Claremont Colleges. The TtnΔ112-158 deletion corresponds to a deletion of 47 exons which encode 1586 amino acids in the PEVK region of titin, and represents ∼75% of the wild-type PEVK sequence (Brynnel et al., 2018). Soleus muscles were extracted from TtnΔ112-158 mice euthanized with an overdose of isoflurane followed by cervical dislocation. The Institutional Animal Care and Use Committee at the Claremont Colleges approved the experimental protocol (IACUC Protocol #019-004) and use of these animals.

Whole-muscle experiments

Whole-muscle ex vivo experiments were conducted on 17 soleus muscles from age-matched TtnΔ112-158 mice of both sexes (age 98.8±9.5 days, 10 females, 7 males). The experimental setup was described in previous publications (Hessel et al., 2021; Monroy et al., 2017). In brief, the soleus muscles were dissected and tied off securely at the muscle–tendon junction to minimize the contribution of extramuscular connective tissues to the experiments. The distal end of each muscle was attached to an inflexible hook and the proximal end was attached to a dual servomotor muscle lever (Series 300B, Aurora Scientific, Inc., Aurora, ON, Canada). All experiments were conducted at a constant temperature (21–23°C) in a Krebs–Henseleit bath (in mmol l−1: 137 NaCl, 5 KCl, 1 NaH2PO4, 24 NaHCO3, 2 CaCl2, 1 MgSO4 and 11 dextrose, pH 7.4) buffered with 95% O2 and 5% CO2. Muscles were stimulated using an electrical field generated between two platinum electrodes connected to an Aurora Scientific 701C bi-phase stimulator. At this temperature, maximum isometric tetanic force remains stable for several hours and within 10% of the maximum isometric stress at a normal body temperature of 37°C (James et al., 2015). A custom LabVIEW (National Instruments Corp., Austin, TX, USA) program was used to control the muscle lever and record force, length and time at a sampling rate of 4 kHz.

At the start of each experiment, a muscle was stretched to its optimal length (L0), defined as the length at which maximum isometric twitch force is produced. Muscles were stimulated at 70–80 Hz for 800–1000 ms to measure maximum isometric tetanic force (Monroy et al., 2017). Maximum isometric stress (P0, N cm−2) was determined by dividing maximum isometric tetanic force by the physiological cross-sectional area (PCSA), calculated using standard methods (Hakim et al., 2013; Lieber and Ward, 2011; Monroy et al., 2017). Briefly, to determine PCSA, muscle mass was multiplied by the cosine of the pennation angle (8.5 deg; Burkholder et al., 1994), and divided by the product of muscle fiber length (Lf) and the density of mammalian skeletal muscle (1.06 g cm−3; Sacks and Roy, 1982). Brynnel et al. (2018) reported that fiber and muscle lengths (Lf) were ∼13.5% longer in TtnΔ112-158 muscles. However, the fiber length to muscle length ratio was not different from that of wild-type muscles. The maximum isometric tetanic force was measured periodically throughout an experiment, and a muscle was removed from the analysis if force dropped by more than 10%. Of the 17 muscles used in these experiments, two muscles were removed from the analysis because of a decrease in maximum force.

Elastic properties

A series of rapid unloading tests was used to measure elastic recoil of active and passive soleus muscles from TtnΔ112-158 mice (Fig. 1). The initial stress and change in stress were matched for active and passive trials (Fig. 1A,B). Muscles were stimulated isometrically at optimal length to an initial stress followed by a series of 5–8 step decreases in load that varied from 5% to 90% of initial stress. Muscles were allowed to recover for ∼4–5 min between each trial. The order of the tests was somewhat random although the greatest step decrease in load was often conducted at the end because muscles needed longer to recover from these trials. Among muscle preparations, the initial stress ranged from 6.7 to 15.1 N cm−2, which corresponded to 40–70% maximum isometric tetanic stress (P0). Maximum isometric tetanic stress ranged from 15 to 28 N cm−2. The duration of stimulation was varied to achieve the desired initial stress in activated muscles.

Fig. 1.

Representative passive and active unloading tests from a single TtnΔ112-158 soleus muscle. (A,B) Muscles were activated (A) or stretched passively (B) to the same initial force, after which the load was reduced. In this example, the muscle was activated or stretched to 50% of its maximum isometric tetanic force. The muscle was subjected to five step decreases in load that ranged from 5% to 85% of the initial force. (C,D) In both the active (C) and passive (D) trials, muscles recoiled elastically during rapid unloading. The initial rapid change in muscle length was measured in response to the rapid decrease in force. Note that the active muscles continue to shorten following elastic recoil as a result of interaction of the contractile proteins.

Fig. 1.

Representative passive and active unloading tests from a single TtnΔ112-158 soleus muscle. (A,B) Muscles were activated (A) or stretched passively (B) to the same initial force, after which the load was reduced. In this example, the muscle was activated or stretched to 50% of its maximum isometric tetanic force. The muscle was subjected to five step decreases in load that ranged from 5% to 85% of the initial force. (C,D) In both the active (C) and passive (D) trials, muscles recoiled elastically during rapid unloading. The initial rapid change in muscle length was measured in response to the rapid decrease in force. Note that the active muscles continue to shorten following elastic recoil as a result of interaction of the contractile proteins.

Muscles were stretched passively (1.02–1.07 L0) to a length at which the initial steady-state passive stress equaled the initial active stress. Because of some variability in the initial stress, the actual unloading steps varied slightly between active and passive trials. In wild-type muscles, the initial stresses were more variable (2.9–12.1 Ncm−2), but most (11 out of 14) fell within the same range of stresses as in the current study (Monroy et al., 2017). Wild-type muscles were stretched to 1.09–1.17 L0 until the passive force reached 10–40% P0 (Monroy et al., 2017).

For each test, the initial rapid recoil distance (mm, L/L0) was measured (Fig. 1C,D). When the load is reduced rapidly, active muscles shorten biphasically, with an initial rapid change in length due to recoil of elastic elements and a later slow phase due to cross-bridge cycling (Jewell and Wilkie, 1958; Lappin et al., 2006; Monroy et al., 2007, 2017; Wilkie, 1956). We measured the distance shortened from the onset of unloading to the intersection of the lines that best fit the initial and slow phases of shortening (Fig. 1C; Lappin et al., 2006; Monroy et al., 2017). In passive muscles, we measured the distance shortened to the steady-state length following initial oscillations (Fig. 1D). Data collected from each muscle and state were used to model the stress–strain relationships.

Muscles were modeled as exponential springs (Lappin et al., 2006; Monroy et al., 2017). When the change in load is small, muscles recoil a short distance, and when the change in load is large, muscles recoil a disproportionately greater distance. Therefore, the stress–strain relationship of the elastic elements in muscle was modeled using the following equation:
formula
(1)
MATLAB (MathWorks) was used find the constants F0 and d that best predicted the observed elastic recoil data. The constant F0 describes the initial length of an exponential spring, the constant d describes the shape of the unloading curve, and x describes strain. Because the elastic modulus is defined as the initial slope of the stress–strain curve, d describes how the elastic modulus changes with muscle stress, with greater d values corresponding to greater compliance (lower elastic modulus) during elastic recoil. The elastic modulus (Eqn 2) is the derivative of Eqn 1:
formula
(2)
The exponential model (Eqn 1) fitted the observed muscle data when the change in load was between 5% and 90% of the initial stress. For the range of initial stresses and loads used in our experiments, the model explained most of the variance in observed length changes in active (R2=0.988±0.001) and passive muscles (R2=0.971±0.003).

Statistics

Analyses were conducted using lme4 (Bates et al., 2015), Tidyverse (Wickham et al., 2019) and MASS (Venables and Ripley, 2002) packages in R Studio statistical software (https://www.rstudio.com/products/rstudio/). Alpha values were set at 0.05. Data were best Box–Cox transformed to meet assumptions of normality and homoscedasticity when necessary. We compared recoil during rapid unloading in TtnΔ112-158 with that in wild-type soleus muscles reported in Monroy et al. (2017). We used a linear mixed model with the following main effects: genotype (TtnΔ112-158, wild type), activation state (active, passive), muscle stress, their interactions, and individual as a random effect nested within genotype, to compare log-transformed stress–strain relationships among activation states and genotypes. The dependent variables were strain, x-intercept and elastic modulus. When there was a significant interaction between genotype and activation state, a Tukey's HSD test was used to determine the significance of differences among groups.

Similar to a previous report (Brynnel et al., 2018), TtnΔ112-158 soleus muscles exhibited greater passive tension with increasing muscle length than wild-type soleus muscles (Fig. 2A; F=4.95, P=0.035). There was a significant interaction between genotype and length on the log-transformed passive stress–strain relationship, indicating a 2-fold difference in slope and greater passive stiffness in TtnΔ112-158 muscles (Fig. 2A; F=8.16, P=0.005). Maximum isometric tetanic stress did not differ between genotypes (Table 1; t=1.1, P=0.28), but optimal muscle length was significantly longer in TtnΔ112-158 muscles (Table 1; t=6.66, P<0.0001). Fig. 2B shows the active and passive force–length relationships from TtnΔ112-158 and wild-type soleus muscles. The passive stiffness of TtnΔ112-158 muscles along the ascending limb of the length–tension relationship and at optimal length was equivalent to that of wild-type muscles within their physiological range of lengths (gray shaded area, Fig. 2B).

Fig. 2.

Active and passive force–length relationships of TtnΔ112-158 muscles. (A) Passive force–length relationships for TtnΔ112-158 and wild-type soleus muscles. Data were normalized to the muscle's physiological cross-sectional area and optimal length (L0). The slope of the log-transformed stress–strain relationship was significantly greater in TtnΔ112-158 than in wild-type muscles, indicating greater passive stiffness (wild type n=14, TtnΔ112-158n=15, F=8.16, P=0.005). (B) Active (solid symbols) and passive (open symbols) force–length relationships from TtnΔ112-158 (n=4) and wild-type soleus muscles (n=4). Passive and maximum tetanic force were binned in 5 mm intervals. Data represent means±s.e.m. The x-axis shows the length change in millimeters from optimal length (L0=0). The gray bar shows the range of lengths over which the passive stiffness of TtnΔ112-158 soleus muscles is equivalent to the passive stiffness of wild-type muscles within physiological changes in length.

Fig. 2.

Active and passive force–length relationships of TtnΔ112-158 muscles. (A) Passive force–length relationships for TtnΔ112-158 and wild-type soleus muscles. Data were normalized to the muscle's physiological cross-sectional area and optimal length (L0). The slope of the log-transformed stress–strain relationship was significantly greater in TtnΔ112-158 than in wild-type muscles, indicating greater passive stiffness (wild type n=14, TtnΔ112-158n=15, F=8.16, P=0.005). (B) Active (solid symbols) and passive (open symbols) force–length relationships from TtnΔ112-158 (n=4) and wild-type soleus muscles (n=4). Passive and maximum tetanic force were binned in 5 mm intervals. Data represent means±s.e.m. The x-axis shows the length change in millimeters from optimal length (L0=0). The gray bar shows the range of lengths over which the passive stiffness of TtnΔ112-158 soleus muscles is equivalent to the passive stiffness of wild-type muscles within physiological changes in length.

Table 1.

Physiological characteristics of wild-type and TtnΔ112-158 soleus muscles

Physiological characteristics of wild-type and TtnΔ112-158 soleus muscles
Physiological characteristics of wild-type and TtnΔ112-158 soleus muscles

In general, passive muscles recoiled farther than when the same muscles were activated to the same initial stress followed by the same decrease in load (Fig. 3A,B). In both genotypes, activation resulted in a leftward shift of the stress–strain relationship during rapid unloading (Fig. 3C). Surprisingly, the shift of the stress–strain relationship with activation was smaller in TtnΔ112-158 compared with wild-type muscles. The x-intercepts of the log-transformed stress–strain relationship during unloading (Fig. 4), represent the muscle lengths at which tension develops (i.e. equilibrium length) in elastic elements. There was a significant interaction between genotype and activation state on the x-intercept (Fig. 4; F=11.28, P=0.002), indicating that activation affected the equilibrium length differently in the two genotypes. Tension developed at a ∼7.0% longer length in activated TtnΔ112-158 than in wild-type muscles (Fig. 4A; t=5.05, P=0.001). However, there was no significant difference between the x-intercepts of passive log-transformed stress–strain relationships (Fig. 4B; t=1.04, P=0.73).

Fig. 3.

Changes in stress and length during active versus passive unloading. (A) Active TtnΔ112-158 soleus muscles recoiled less than when the muscle was passively stretched to the same initial stress. (B) Wild-type muscles exhibited a greater difference between active and passive trials. (C) The stress–strain relationships were estimated from the recoil data in A and B. In both genotypes, there was a leftward shift of the stress–strain relationship with activation, but the shift was smaller in TtnΔ112-158 than in wild-type muscles.

Fig. 3.

Changes in stress and length during active versus passive unloading. (A) Active TtnΔ112-158 soleus muscles recoiled less than when the muscle was passively stretched to the same initial stress. (B) Wild-type muscles exhibited a greater difference between active and passive trials. (C) The stress–strain relationships were estimated from the recoil data in A and B. In both genotypes, there was a leftward shift of the stress–strain relationship with activation, but the shift was smaller in TtnΔ112-158 than in wild-type muscles.

Fig. 4.

Log-transformed stress–strain relationships during rapid unloading. (A) Active and (B) passive stress (N cm−2)–strain relationships for wild-type and TtnΔ112-158 soleus muscles. Symbols indicate individual muscles (wild type n=14, TtnΔ112-158n=15). In A, the slopes of the log-transformed stress–strain relationship were significantly greater for active wild-type than for TtnΔ112-158 muscles (Tukey's HSD, t=7.61, P<0.0001). In B, the slopes of the passive log-transformed stress–strain relationships did not differ between genotypes (Tukey's HSD, t=2.59, P=0.07).

Fig. 4.

Log-transformed stress–strain relationships during rapid unloading. (A) Active and (B) passive stress (N cm−2)–strain relationships for wild-type and TtnΔ112-158 soleus muscles. Symbols indicate individual muscles (wild type n=14, TtnΔ112-158n=15). In A, the slopes of the log-transformed stress–strain relationship were significantly greater for active wild-type than for TtnΔ112-158 muscles (Tukey's HSD, t=7.61, P<0.0001). In B, the slopes of the passive log-transformed stress–strain relationships did not differ between genotypes (Tukey's HSD, t=2.59, P=0.07).

The slopes of the log-transformed stress–strain relationships also differed significantly (Fig. 4; F=46.52, P<0.0001). The slope of the active wild-type log-transformed stress–strain relationship was ∼1.5 times greater than that for active TtnΔ112-158 muscles (t=7.61, P<0.0001). However, the slopes of the passive log-transformed stress–strain relationships did not differ significantly between genotypes (t=2.59, P=0.07). Contrary to our hypothesis, these data suggest that active TtnΔ112-158 muscles were significantly less stiff than active wild-type muscles but passive TtnΔ112-158 muscles did not differ from passive wild-type muscles.

During unloading, the elastic modulus increased linearly with initial muscle stress (Fig. 5A,B; F=29.66, P≤0.0001) and was greater when muscles were activated. Interestingly, there was no significant interaction between genotype and activation state (F=0.32, P=0.58) largely because of the similarity between passive muscles from the two genotypes. However, there was a significant interaction between genotype, state and stress (F=8.03, P=0.009), suggesting that the elastic modulus differed among genotypes and activation state as stress increased. When compared separately, the slope of the elastic modulus–stress relationship was more than 1.5 times greater in active wild-type than in TtnΔ112-158 muscles (Fig. 5A; t=−7.67, P≤0.0001) but was not different between passive TtnΔ112-158 and wild-type muscles (Fig. 5B; t=0.31, P=0.99).

Fig. 5.

Relationship between elastic modulus during unloading and initial stress. (A) Active wild-type (y=105.1x, R2=0.71, n=14) and active TtnΔ112-158 muscles (y=70.2x, R2=0.6, n=15). The slope of the elastic modulus–stress relationship was ∼1.5 times greater in active wild-type than in TtnΔ112-158 muscles (F=7.17, P=0.01). (B) Passive wild-type (y=40.6x, R2=0.9, n=14) and passive TtnΔ112-158 muscles (y=50.0x, R2=0.82, n=15) did not differ significantly (F=1.45, P=0.25). Dashed lines indicate 95% confidence intervals.

Fig. 5.

Relationship between elastic modulus during unloading and initial stress. (A) Active wild-type (y=105.1x, R2=0.71, n=14) and active TtnΔ112-158 muscles (y=70.2x, R2=0.6, n=15). The slope of the elastic modulus–stress relationship was ∼1.5 times greater in active wild-type than in TtnΔ112-158 muscles (F=7.17, P=0.01). (B) Passive wild-type (y=40.6x, R2=0.9, n=14) and passive TtnΔ112-158 muscles (y=50.0x, R2=0.82, n=15) did not differ significantly (F=1.45, P=0.25). Dashed lines indicate 95% confidence intervals.

The focus of this study was to test the hypothesis that the PEVK region of titin contributes to active muscle stiffness and that a large deletion to PEVK titin should result in greater stiffness during activation. Using TtnΔ112-158 mice with ∼75% of PEVK titin deleted, we quantified the effect of a shorter PEVK segment on elastic recoil of muscles during rapid unloading. We used these data to estimate the stress–strain relationship and elastic modulus of activated muscles. Our results show that the elastic modulus of elastic elements in TtnΔ112-158 muscles increased with activation. However, compared with that of wild-type muscles, the change the stress–strain relationship of TtnΔ112-158 soleus muscles was reduced. The elastic modulus was 50% lower, and the equilibrium length was 7% longer in active TtnΔ112-158 than in wild-type muscles. Thus, despite having a shorter, stiffer PEVK segment, during rapid unloading, TtnΔ112-158 soleus muscles exhibited reduced active stiffness compared with wild-type soleus muscles. These results are consistent with the idea that PEVK titin contributes to active muscle stiffness; however, the reduction in active stiffness of TtnΔ112-158 muscles suggests that other mechanisms compensate for the increased PEVK stiffness.

Contributions of elastic element to passive muscle stiffness

TtnΔ112-158 muscles exhibited a ∼2-fold increase in passive tension with stretch compared with wild-type muscles. These observations are consistent with another study on TtnΔ112-158 muscles which demonstrated increased passive tension in soleus, diaphragm and EDL muscles (Brynnel et al., 2018). It is well accepted that the PEVK region of titin contributes as much as 70% to passive muscle stiffness (Brynnel et al., 2018; Prado et al., 2005) and is responsible for nearly all the longitudinal force in single myofibrils (Granzier and Irving, 1995; Trombitás et al., 1995). The PEVK region is subject to intense differential splicing (Freiburg et al., 2000; Guo et al., 2010) and muscles that express shorter titin isoforms, due in part to splicing of the PEVK, have increased passive stiffness (Freiburg et al., 2000; Neagoe et al., 2003; Prado et al., 2005; Spierts et al., 1997). Using a KCl/KI treatment to selectively degrade titin, Brynnel et al. (2018) showed that titin-based passive tension was ∼5-fold higher in TtnΔ112-158 5th toe EDL muscles. ECM-based passive tension also increased but did not contribute more than 20% to total passive stiffness within physiological sarcomere lengths (2.2–3.2 µm) (Brynnel et al., 2018). At longer sarcomere lengths (>3.2 µm), ECM stiffness increased greatly. It is possible that ECM-based stiffness also increased in TtnΔ112-158 soleus muscles. Soleus muscles express one of the longest titin isoforms at 3.6 MDa and have relatively low passive stiffness of which ∼25% is due to titin and the remaining 75% is attributed to ECM-based stiffness (Prado et al., 2005). The increase in passive stiffness appears to be largely accounted for by increased titin stiffness; however, we cannot rule out a possible change in ECM architecture that may also contribute to the elevated passive stiffness in TtnΔ112-158 soleus muscles.

Despite differences in passive tension with stretch, the stress–strain relationships of passive muscles during rapid unloading were not different between genotypes. However, the initial and final muscle lengths were quite different. Wild-type muscles were stretched ∼10% farther than TtnΔ112-158 muscles to reach the same range of initial stresses. It is possible that TtnΔ112-158 muscles were never stretched beyond the toe region of the stress–strain relationship whereas wild-type muscles were stretched to longer lengths with greater stiffness. Thus, the differences in passive stiffness during unloading appear reduced compared with the differences in passive force with stretch.

The similarities in passive unloading trials between genotypes may also be due to the viscoelastic properties of muscle in which much of the energy stored during stretch was dissipated during unloading. Slack tests of passively stretched single myofibrils from rabbit psoas demonstrated that unloading is initially due to titin recoil but is dampened by viscous drag within milliseconds (Minajeva et al., 2002). Models of non-linear viscoelastic properties of cardiac tissues also suggest that titin contributes to unloading behavior (Granzier and Irving, 1995; Wu et al., 2000). Viscous properties of muscle have been attributed to titin–actin interactions (Kellermayer and Granzier, 1996; Kulke et al., 2001), weakly attached cross-bridges, and collagen fibrils (Meyer et al., 2011; Moss and Halpern, 1977). The stress–strain relationships of unloading behavior in passive TtnΔ112-158 and wild-type muscles represent the entire range of shortening in response to varying changes in load. Had we evaluated the initial velocity in response to small changes in load, we might have reduced the effect of viscous forces and observed differences in elastic recoil between genotypes.

Contributions of elastic elements to active muscle stiffness

Activated TtnΔ112-158 muscles showed a leftward shift towards shorter lengths and an increase in the slope of the log-transformed stress–strain relationship. These data suggest that upon activation, the equilibrium length decreased and the stiffness of non-cross-bridge elements increased. The observed strains in this study fall within the range of previously reported values for various other muscles. For example, active frog muscles recoil by as much as 20% from their optimal length (Lappin et al., 2006) and the telson muscle of horseshoe crabs shortens as much as 210 nm per half-sarcomere during rapid unloading (Akimoto and Sugi, 1999; Sugi et al., 2000). Such large strains of elastic elements in active muscles cannot be solely attributed to cross-bridges or sarcomere filament lattice (Lappin et al., 2006; Linari et al., 2003; Roberts, 2016). In addition, mdm mouse muscles, characterized by a small deletion to N2A titin, exhibited no change in the stress–strain relationship with activation (Monroy et al., 2017) or an increase in stiffness during stretch of activated single myofibrils (Powers et al., 2016). These results support the hypothesis that N2A titin mediates a change in titin stiffness (Monroy et al., 2017; Powers et al., 2016), which could potentially explain the shift in the observed stress–strain relationship and increase in the elastic modulus with muscle activation.

Intact muscles are composed of several elastic elements that could potentially contribute to active muscle stiffness (Gindre et al., 2013; Roberts, 2016). During rapid unloading, cross-bridges are unlikely to contribute to active muscle stiffness because the shortening velocity greatly exceeds maximum contraction velocity (Vmax) and only a small number of cross-bridges are likely to be attached (Stehle and Brenner, 2000). In addition, the few cross-bridges that remain attached during unloading would be expected to recoil by only ∼1% of muscle length (Huxley, 1974). Using blebbistatin to greatly reduce cross-bridge interactions, Tomalka et al. (2020) demonstrated that during stretch of active fibers, non-cross-bridge elements store elastic energy that recoils during shortening and increases the work of stretch–shortening cycles. In addition, the elastic energy released was higher than that of passive muscles, suggesting the engagement of a non-cross-bridge elastic element during activation (Tomalka et al., 2020).

By matching the initial stress and change in stress in active and passive load-clamp tests, the recoil of series elastic elements, such as tendons, is held constant because the stiffness of linear elements is independent of their initial length. Thus, any differences in stiffness between active and passive trials should be due to the engagement of a non-cross-bridge element with activation. However, recent work on aponeurosis stiffness associated with the lateral gastrocnemius of wild turkeys demonstrated that biaxial loading influences aponeurosis stiffness and elastic energy storage (Arellano et al., 2019). Thus, an increase in muscle width with activation could potentially load an aponeurosis in the transverse direction, which leads to an increase in its longitudinal stiffness. In addition, it is possible the structure of tendons and other series elastic elements differs between TtnΔ112-158 and wild-type muscles. To our knowledge, little is known about tendon or aponeurosis architecture in TtnΔ112-158 mice. Future work is needed to investigate the contribution of aponeurosis to recoil of TtnΔ112-158 muscles.

The recoil of non-linear parallel elastic elements in the ECM may differ between passive and active trials because their stiffness is dependent on the initial length. As a parallel elastic spring, the ECM could potentially contribute more to the elastic recoil of passively stretched muscles than muscles activated at optimal length. In addition, the ECM could also contribute to active muscle recoil if it were strained during activation at optimal length. To reduce the contribution of the ECM to active muscle recoil, Monroy et al. (2017) performed the same active unloading tests on intact wild-type soleus muscles at L0 and 85% L0, where the ECM is unloaded. Their findings showed that elastic recoil of wild-type muscles starting at optimal length did not differ from that of muscles starting at 85% L0. Thus, in wild-type muscles, the ECM does not contribute significantly to recoil at L0. However, the ECM may contribute more to passive and active recoil of TtnΔ112-158 muscles. There was a small but significant increase in ECM-based passive stiffness of 5th toe EDL muscles from TtnΔ112-158 mice (Brynnel et al., 2018). Assuming this is the case for all TtnΔ112-158 muscles, it is likely that ECM-based stiffness is also increased in TtnΔ112-158 soleus muscles. In addition, if the ECM is strained in passively stretched muscles, then the change in stiffness with activation would appear reduced. It is also possible that the ECM contributes to active muscle stiffness as there is significant passive stiffness at optimal length in TtnΔ112-158 soleus muscles. Thus, the smaller change in stiffness with activation in TtnΔ112-158 soleus muscles suggests a greater contribution of the ECM to active and passive muscle recoil. Additional experiments at shorter muscle lengths could potentially eliminate contributions from the ECM and isolate the effects of titin on active muscle stiffness.

The change in muscle stiffness with activation falls in line with the hypothesis that titin functions as a tunable spring in muscle (Leonard and Herzog, 2010; Nishikawa, 2020; Rode et al., 2009; Schappacher-Tilp et al., 2015). Several lines of evidence suggest that N2A titin binds to actin in the presence of calcium, thereby decreasing titin's equilibrium length and increasing its stiffness (Dutta et al., 2018; Nishikawa et al., 2020). Single molecule force spectroscopy experiments demonstrated that in the presence of calcium (pCa<4.0), rupture forces increased and off-rates decreased between N2A and actin (Dutta et al., 2018). In addition, mdm muscles and single mdm myofibrils which carry a deletion to N2A titin showed reduced active stiffness (Monroy et al., 2017; Powers et al., 2016), decreased force enhancement with active stretch (Mishra and Nishikawa, 2022; Tahir et al., 2020) and reduced eccentric work during stretch–shortening cycles (Hessel et al., 2017, 2021). The binding of titin to actin at the N2A region would eliminate the straightening of the proximal Ig domains and engage the PEVK region at shorter sarcomere lengths (Nishikawa, 2020). Based on this mechanism, PEVK titin is the main contributor to active muscle stiffness.

Compensatory mechanisms in TtnΔ112-158 muscles

While the slope of the elastic modulus–stress relationship increased by ∼30% with activation in TtnΔ112-158 muscles, it was still more than 50% less than the increase in the elastic modulus of active wild-type muscles. In addition, the equilibrium length was ∼7% longer in active TtnΔ112-158 muscles than in active wild-type muscles. We expected a greater increase in active muscle stiffness in TtnΔ112-158 muscles because of their shorter, stiffer PEVK segment. However, the results suggest that muscle stiffness increased with activation in TtnΔ112-158 muscles but to a lesser extent than in wild-type muscles. Other studies have demonstrated that muscles with shorter, stiffer titin isoforms exhibit greater residual force enhancement with stretch (Shalabi et al., 2017) and greater stiffness at the onset of activation prior to cross-bridge formation than muscles with longer, more compliant isoforms (Cornachione et al., 2016; Nocella et al., 2012). It is possible that additional mechanisms are necessary to compensate for the significant increase in PEVK stiffness in TtnΔ112-158 muscles.

TtnΔ112-158 muscles likely compensate for increased titin and muscle stiffness to maintain lower passive stiffness. Results from this study showed that optimal muscle length was significantly longer in TtnΔ112-158 muscles. These data are in agreement with Brynnel et al. (2018), who found that TtnΔ112-158 muscles developed longitudinal hypertrophy; muscle and fiber lengths were longer, but sarcomere lengths were shorter. Thus, there was an increased number of sarcomeres in series, to potentially reduce the operating range of sarcomere lengths and passive muscle stiffness. By fixing the hindlimbs of TtnΔ112-158 mice in plantar flexed and dorsiflexed positions, Brynnel et al. (2018) estimated the range of sarcomere lengths that hindlimb muscles experience during movement. The soleus and other hindlimb muscles operate at roughly 40% shorter sarcomere lengths (1.8–2.27 μm) and within a shorter range than wild-type muscles (Brynnel et al., 2018). The length–tension relationship from TtnΔ112-158 muscles shown in Fig. 2B supports their predictions that TtnΔ112-158 muscles would have to operate at optimal length and along the ascending limb of the length–tension relationship to maintain passive stiffness equivalent to that of wild-type muscles. Future work is needed to understand the impacts of a shorter physiological working range of lengths.

It is also possible that there was a shift in the fiber-type composition of TtnΔ112-158 soleus muscles as a result of the PEVK mutation. Typically, wild-type soleus muscles are primarily composed of type I and type IIA fibers (Schiaffino and Reggiani, 2011). Following training, rat soleus muscles have been shown to switch to a higher proportion of type II fibers and exhibit lower active stiffness (Goubel and Marini, 1987). Thus, an increase in the proportion of type II fibers could reduce the effect of having a stiffer titin, and potentially explain in part the lower active stiffness observed in TtnΔ112-158 muscles. TtnΔ112-158 muscles exhibited similar maximum isometric twitch and tetanic forces to wild-type muscles. However, TtnΔ112-158 muscles showed a 40% increase in the rate of force development, indicating faster contractile properties (Brynnel et al., 2018). A comparison of myosin heavy chain expression between genotypes showed a small (5%) increase in IIA/IIX myosin heavy chain isoforms in soleus muscles of TtnΔ112-158 mice (Brynnel et al., 2018). However, this slight increase in IIA/IIX fibers is unlikely to explain the 50% reduction in active stiffness observed TtnΔ112-158 muscles.

Several non-exclusive mechanisms have been shown to increase PEVK stiffness. Small (10–20%) increases in PEVK stiffness are known to occur via phosphorylation of serine residues (Hidalgo et al., 2014), calcium binding to glutamate-rich segments (Labeit et al., 2003), hydrostatic interactions between PEVK and actin, and an increase in pH (Sudarshi Premawardhana et al., 2020). Most of the glutamate-rich regions of PEVK are located in the N-terminus, which is deleted in the TtnΔ112-158 mouse (Brynnel et al., 2018). It is possible that the reduced active stiffness observed in TtnΔ112-158 muscles is due in part to the loss of calcium binding to E-rich regions. The PEVK deletion in TtnΔ112-158 mice does not include the N2A region (Brynnel et al., 2018) and therefore should not directly affect the proposed calcium-sensitive increase in titin stiffness by N2A–actin binding. However, it is possible that the segment of PEVK missing in TtnΔ112-158 muscles interferes indirectly with N2A–actin binding. For example, hydrostatic binding between PEVK and actin could facilitate N2A–actin binding by bringing titin closer to actin. A reduction in PEVK length may therefore decrease both PEVK and N2A–actin interactions in the presence of calcium, and result in lower titin stiffness in active muscles. Future studies are needed to identify which processes compensate for the PEVK deletion and increased PEVK stiffness in TtnΔ112-158 muscles.

Conclusions

The results from whole-muscle experiments suggest the existence of a tunable viscoelastic element that increases muscle stiffness with activation. Even with confounding effects of the ECM and other elastic structures, our study suggests a role for PEVK titin in active muscle stiffness. The data presented here support the hypothesis that titin binds to actin in a Ca2+-dependent manner, which engages the PEVK region in active muscle. Interestingly, active TtnΔ112-158 muscles exhibited reduced active stiffness compared with wild-type muscles despite the expression of a shorter PEVK segment and increased passive stiffness. TtnΔ112-158 muscles likely compensate for the increased PEVK stiffness by operating at shorter muscle lengths where passive stiffness is low. Additional mechanisms likely also compensate for the increased PEVK stiffness in TtnΔ112-158 muscles.

The authors wish to thank Kiisa Nishikawa for her insightful comments on previous versions of the manuscript. We are also grateful for the use of the TtnΔ112-158 mice provided by the Granzier lab at the University of Arizona.

Author contributions

Conceptualization: K.L.H., J.A.M.; Methodology: K.L.H., J.R.B., J.A.M.; Writing - original draft: K.L.H., J.R.B., J.A.M.; Writing - review & editing: K.L.H., J.A.M.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Data availability

Data are available from the Dryad digital repository (Hurley et al., 2022): https://doi.org/10.5061/dryad.xd2547dhh.

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Competing interests

The authors declare no competing or financial interests.