Muscle contraction results from force-generating cross-bridge interactions between myosin and actin. Cross-bridge cycling kinetics underlie fundamental contractile properties, such as active force production and energy utilization. Factors that influence cross-bridge kinetics at the molecular level propagate through the sarcomeres, cells, and tissue to modulate whole-muscle function. Conversely, movement and changes in muscle length can influence cross-bridge kinetics on the molecular level. Reduced, single-molecule and single-fiber experiments have shown that increasing the strain on cross-bridges may slow their cycling rate and prolong their attachment duration. However, whether these strain-dependent cycling mechanisms persist in intact muscle tissue, which encompasses more complex organization and passive elements, remains unclear. To investigate this multi-scale relationship, we adapted traditional step-stretch protocols for use with mouse soleus muscle during isometric tetanic contractions, enabling novel estimates of length-dependent cross-bridge kinetics in intact skeletal muscle. Compared to rates at optimal muscle length (Lo), we found that cross-bridge detachment rates increased by ~20% at 90% of Lo (shorter) and decreased by ~20% at 110% of Lo (longer). These data indicate that cross-bridge kinetics vary with whole-muscle length during intact, isometric contraction, which could intrinsically modulate force-generation and energetics, and suggests a multi-scale feedback pathway between whole-muscle function and cross-bridge activity.

Small step analysis

Striated muscle responds to a sudden length increase with a force response that has classically been described by four phases (1–4). In phase 1, force rises instantaneously as attached cross-bridges and elastic elements are strained (Fig. 2, σ₀ to σ₁). In phase 2, force decays as cross-bridges detach in a synchronized manner (Fig. 2, σ₁ to σ₂). Next, force rises in phase 3 due to cross-bridge recruitment, and finally the force response plateaus at an elevated level (phase 4) due to passive properties (i.e., of stretching tendon, connective tissue, titin and collagen) and changes in active (i.e. altered cross-bridge activity) biomechanical properties of the muscle at the new, longer muscle length. These phases are a time-domain representation of the same processes observed via smaller-amplitude length perturbation analysis (0.05-1.25% muscle length), in which frequency-dependent shifts in the elastic and viscous moduli (i.e. viscoelastic stress-strain stiffness response) describe enzymatic and mechanical properties of the muscle (5–7). Thus, the time-dependent modulus response, Y(t) (=σ(t)/ε(t), where σ(t) and ε(t) represent the muscle stress response and muscle strain as a function of time, respectively) a step-function change in muscle length can be characterized as described by Palmer et al. (7):

The molecular, cellular, and tissue characteristics described by Eq. 1 are outlined below, with this model appropriately describing Y(t) for the measured stress-strain response between σ₁ and σ_final, with the initial time-point occurring at the onset of the strain stimulus (i.e. time=0 at t₀ for σ₀)—as further described below and illustrated in Fig. 2. The A-process reflects the viscoelastic mechanical response of passive, structural elements in the muscle and holds no enzymatic dependence. Parameter A represents the combined mechanical stress of the muscle and tendon, while parameter k describes the viscoelasticity of these passive elements; a k value of 0 (minimum possible value for the fractional derivative) represents a purely elastic response and a k value of 1 represents a purely viscous response (8,9). The B- and C- processes characterize work-producing (cross-bridge recruitment) and work-absorbing (cross-bridge detachment) characteristics of the contracting muscle, respectively (7,10–12). Thus, these B- and C- processes are analogous to the work-producing and work-absorbing process described above during phase 3 for cross-bridge recruitment and phase 2 for cross-bridge detachment. The parameters B and C represent the mechanical stress from the cross-bridges, and the rate parameters b and c reflect cross-bridge kinetics (13). More specifically, molecular processes contributing to cross-bridge recruitment or force generation underlie the cross-bridge recruitment rate, 2πb, and processes contributing to cross-bridge detachment or force decay underlie the cross-bridge detachment rate, 2πc.

To best emulate physiological length changes, both the proximal and distal tendons of the muscle preparations were left intact. However, the tendons add an additional in-series elastic element that should be considered when applying small step analysis to ensure that the muscle (and not tendon) is primarily experiencing the perturbation. Using methods described by Cui et al. 2008 (14), we calculated tendon area and length to provide an estimate of tendon stiffness with:

where E is the elastic modulus (reported to be approximately 62 N/mm² for mouse soleus tendon (15)), A_T is calculated tendon area (0.59 mm²), and l_T is the calculated tendon length (5.67±0.14 mm) at L_o. Therefore, we can roughly estimate an in-series elastic element with a stiffness of 6.45 N/mm. Our average L_o was 15.22±0.37 mm, so a 1% length­-step stretched the MTU on average 0.15 mm. During this step, we measured an average rise in force (represented as phase 1) around 0.16 N, for MTU stiffness (K_MTU) of 1.05 N/mm. Therefore, we can solve for the stiffness of the muscle (K_M) using:       

which estimates K_m to be on average 1.25 N/mm. These values suggest that the stiffness of the tendon is approximately five times that of the stiffness of the muscle, and thus we assume that for a given length increase, the muscle fibers experience the majority of the length change from the step-length perturbations imposed herein.

Animal models

All procedures were approved by the Institutional Animal Care and Use Committee at Washington State University and complied with the Guide for the Use and Care of Laboratory Animals published by the National Institutes of Health. Male C57BL/6 mice (7 weeks old) were sourced from Simonsen Laboratories. Ten mice were anesthetized by isoflurane inhalation (3% volume in 95% O₂-5% CO₂ flowing at 2 L/min), then a soleus muscle was removed, preserving as much of the proximal and distal tendons as possible. After removal, the whole MTU was immediately placed in the experimental chamber containing oxygenated Ringer’s solution.

Tetanic step procedure

Soleus muscles were suspended in a temperature controlled, oxygenated chamber with the distal tendon sutured onto a force transducer (Aurora Scientific 407A, Aurora, ON), and the proximal tendon sutured onto a length controller (Aurora Scientific 305C, Aurora, ON). Muscles equilibrated with the Ringer’s solution (154 mM NaCl, 5.6 mM KCl, 1 mM MgCl₂, 2.2 mM CaCl₂, 10 mM glucose, 20 mM HEPES, pH 7.4, (16)) for at least 5 minutes. Muscles were field stimulated (Aurora scientific 701C, Aurora, ON) via parallel electrode plates along the length of the chamber at 20 V and 100 Hz to measure maximum isometric tetanic force (Figure 1A). Optimal MTU length (L_o) was determined by tetanically stimulating the muscle at multiple lengths (minimum of 5 lengths, each followed by at least 3 minutes rest) to produce a force-length curve. L_o was then defined as the length that generated maximum active force along the MTU force-length curve. Once L_o was established, the MTU was set to one of three lengths: L_o, 90% of L_o, or 110% of L_o. Tetanic contraction was then induced in the muscle for 2 seconds, with a length step (1% increase in MTU length) applied at 1 second and held for the remainder of the activation period (Figure 2). This procedure was then repeated for the remaining two lengths and then again for all three lengths at the other test temperature. The order of MTU length and temperature of the chamber (17°C or 27°C) was randomized for each experiment.

After mechanical experiments were completed, muscle and tendons were separated, measured, and weighed to estimate the physiological cross-sectional area (CSA, (17)):

where m is muscle mass, θ is pennation angle (=8.5° for soleus muscle (18)), L_f is fiber length calculated from fiber-to-muscle length ratio (=0.71 for soleus muscle (19)), and ρ is muscle density (=1.06 mg/mm³ (20)). Average soleus muscle CSA was 0.78±0.05 mm². Force was then divided by the CSA to calculate stress.

Statistical analysis

All data are listed as mean ± SEM. Sequential quadratic programming methods in Matlab (v. 9.4.0, The Mathworks, Natick MA) was used for constrained nonlinear least-squares fitting of Eq. 1 to moduli data for each muscle. Statistical analysis of experimental data were performed in SPSS (IBM Statistics, Chicago, IL), implementing linear mixed models with muscle length and temperature as repeated measures where appropriate. This approach matches data from the same muscle to provide more statistical power than a one-way ANOVA. First-order autoregression was assumed for the covariance structure and post-hoc analyses were performed using least-significant difference corrections where appropriate. Statistical significance is reported at p<0.05.

References

MaxForce_ProcRSocB.csv

This file contains the force data obtained from each mouse (1 soleus muscle), from each condition. 

Step_Kinetics_ProcRSocB.csv

Paramaters from the data fits to Eq 1 (see methods) for each muscle at each condition.