The active force-length relationship is invisible during extensive eccentric contractions in skinned skeletal muscle fibres

Abstract

In contrast to experimentally observed progressive forces in eccentric contractions, cross-bridge and sliding-filament theories of muscle contraction predict that varying myofilament overlap will lead to increases and decreases in active force during eccentric contractions. Non-cross-bridge contributions potentially explain the progressive total forces. However, it is not clear whether underlying abrupt changes in the slope of the nonlinear force-length relationship are visible in long isokinetic stretches, and in which proportion cross-bridges and non-cross-bridges contribute to muscle force. Here, we show that maximally activated single skinned rat muscle fibres behave (almost across the entire working range) like linear springs. The force slope is about three times the maximum isometric force per optimal length. Cross-bridge and non-cross-bridge contributions to the muscle force were investigated using an actomyosin inhibitor. The experiments revealed a nonlinear progressive contribution of non-cross-bridge forces and suggest a nonlinear cross-bridge contribution similar to the active force-length relationship (though with increased optimal length and maximum isometric force). The linear muscle behaviour might significantly reduce the control effort. Moreover, the observed slight increase in slope with initial length is in accordance with current models attributing the non-cross-bridge force to titin.

Keywords: cross-bridge; lengthening contractions; linear muscle behaviour; muscle stretch; titin.

Figure 1.

Force–length relationship (FLR) and EDL muscle fibre. (a) The active isometric FLR can be directly explained with actin and myosin filament overlap [4]. Qualitative changes in overlap (see corresponding sarcomere configuration schematics (A)–(E) to the right) lead to slope changes of the FLR (indicated with open circles at lengths B, C, D). Forces in the range below D (including the force hump [12] left of E for very short sarcomere lengths, illustrated by the grey area) can be explained with myosin filament sliding through the Z-disc [8]. (b) Representative picture of a permeabilized single muscle fibre of a rat EDL muscle at optimal sarcomere length L_S0 = 2.5 µm in relaxed state. Only fibres with a homogeneous sarcomere pattern, without any lesions or damage were analysed. The photomicrograph was captured with a 20 × objective under bright-field illumination. The spot (×500 magnification) shows the striation pattern.

Figure 2.

The mean ± s.d. of force–length traces of eccentric isokinetic contractions. Solid black, blue, and green lines indicate the means. The shaded regions around the solid lines indicate the corresponding s.d. during active stretching. (a) Eccentric ramps show a small bump followed by a linear force increase. The small bump after initiation of the stretch could be due to short range stiffness [50] and passive properties of the fibre such as inertia or viscosity [35]. Eccentric ramps starting from 0.7, 0.85, and 1.0 L₀ comprise 17, 24, and 24 experiments, respectively. (b) Extensive ramps with stretch amplitude of 0.75 L₀ also show a linear force increase. Extensive ramps comprise 18 valid experiments. The stretch velocity is 11% v_max in all ramps. The force is normalized to maximum isometric force (F_im) and length to optimal fibre length (L₀). Isometric pre-stimulation is not shown. Crosses and triangles indicate measurements of passive and active isometric fibre forces, respectively. For comparison, the active isometric sarcomere FLR (dashed line) and passive sarcomere force–length data (solid grey line) of fast single skinned fibres from EDL muscles, reported by Stephenson & Williams [40] and Stephenson [51], are shown. Comparison of statistical linear mixed effect models accounting for repeated measurements (see table 2, Methods section) revealed a significant increase in slope with initial length.

Figure 3.

Force–length traces of eccentric isokinetic contractions at different BDM concentrations. Mean (solid black line) and s.d. (shaded regions around solid lines) of control contractions (without BDM, black solid line) and contractions with increasing concentrations of BDM (2, 5, 10 mM, coloured solid lines) with stretch velocity of 11% v_max and initial fibre lengths of 0.85 L₀ (a) and 1.0 L₀ (b), respectively. Eccentric experiments comprised 14 valid experiments for each concentration of BDM. Coloured dashed lines represent scaled isometric cross-bridge forces underlying the ramp contractions (method A, see §2f), which can be compared with the isometric FLR. Shaded rectangular areas indicate rightward-shifted plateau-region of FLR during eccentric contractions. Comparison of hierarchical statistical models (see table 2 and Methods section) revealed increasing progressive nonlinearity with increasing BDM concentration.

Figure 4.

Comparison of theoretical and experimental non-cross-bridge force traces during eccentric contractions. Blue solid lines indicate depressed force responses (around 94% cross-bridges abolished) due to 10 mM BDM application (mean (solid lines) ± s.d. (shaded regions around solid lines) of 14 valid experiments) for eccentric ramps with stretch velocity of 11% v_max and initial fibre lengths of 0.85 L₀ (a) and 1.0 L₀ (b), respectively. The blue dashed lines are expected to have non-cross-bridge forces (method B, see §2f) assuming a valid isometric FLR (black dashed lines) during eccentric contraction.