Stiffness and force in activated frog skeletal muscle fibers

Single fibers, isolated intact from frog skeletal muscles, were held firmly very near to each end by stiff metal clasps fastened to the tendons. The fibers were then placed horizontally between two steel hooks inserted in eyelets of the tendon clasps. One hook was attached to a capacitance gauge force transducer (resonance frequency up to approximately 50 kHz) and the other was attached to a moving-coil length changer. This allowed us to impose small, rapid releases (complete in less than 0.15 ms) and high frequency oscillations (up to 13 kHz) to one end of a resting or contracting fiber and measure the consequences at the other end with fast time resolution at 4 to 6 degrees C. The stiffness of short fibers (1.8-2.6 mm) was determined directly from the ratio of force to length variations produced by the length changer. The resonance frequency of short fibers was so high (approximately 40 kHz) that intrinsic oscillations were not detectably excited. The stiffness of long fibers, on the other hand, was calculated from measurement of the mechanical resonance frequency of a fiber. Using both short and long fibers, we measured the sinusoids of force at one end of a contracting fiber that were produced by relatively small sinusoidal length changes at the other end. The amplitudes of the sinusoidal length changes were small compared with the size of step changes that produce nonlinear force-extension relations. The sinusoids of force from long fibers changed amplitude and shifted phase with changes in oscillation frequency in a manner expected of a transmission line composed of mass, compliance, and viscosity, similar to that modelled by (Ford, L. E., A. F. Huxley, and R. M. Simmons, 1981, J. Physiol. (Lond.), 311:219-249). A rapid release during the plateau of tetanic tension in short fibers caused a fall in force and stiffness, a relative change in stiffness that putatively was much smaller than that of force. Our results are, for the most part, consistent with the cross-bridge model of force generation proposed by Huxley, A. F., and R. M. Simmons (1971, Nature (Lond.), 213:533-538). However, stiffness in short fibers developed markedly faster than force during the tetanus rise. Thus our findings show the presence of one or more noteworthy cross-bridge states at the onset and during the rise of active tension towards a plateau in that attachment apparently is followed by a relatively long delay before force generation occurs. A set of equations is given in the Appendix that describes the frequency dependence of the applied sinusoid and its response. This model predicts that frequency dependent changes can be used as a measure of a change in stiffness.