Mechanics of stretch in activated crustacean slow muscle. II. Dynamic changes in force in response to stretch

1. The mechanical dynamics of the ventral superficial muscles (VSM) of the abdomen of the hermit crab, Pagurus pollicarus, have been analyzed to develop a quantitative model of gradedly excitable arthropod muscle. Such a model is important for understanding the role of proprioceptive reflexes in posture and movement. 2. The decay in force produced after ramp stretch of both passive and active muscle was approximated by the use of regression equations involving a direct term and one to three exponential terms. A second-order equation produced an acceptable description of this decay over short (0.5 s) sampling durations. 3. The rate constants of the regression equation did not vary with stretch length, velocity, or activation level of the muscle. For the two-exponential-term model, the rate constants were approximately 90 and 9 s-1 for a sample duration of 0.3 s. An additional rate constant of approximately 1 s-1 was needed to adapt the model to longer sample times. 4. The direct term and the middle-order (9 s-1) residual were both functions of stretch length and activation level. The high-order (90 s-1) residual was primarily a function of stretch length and velocity. Transfer functions omitting the velocity dependence adequately described the mechanical dynamics of the muscle for physiological ranges of stretch velocity. 5. White-noise length perturbations were used to calculate spectral density functions of muscle force and length. These measurements confirmed the principal observations of the ramp stretch analysis: the frequency response of the muscle was independent of the level of activation; the magnitude of the stiffness increased over the stretch frequency range of 4-40 Hz and was then almost constant; and the phase response of the muscle became slightly positive over the same range of stretch frequency. 6. The speed of activation of the muscle to different stimulus frequencies was estimated by fitting a single exponential equation to the rise in isometric tension at the onset of stimulation of the motor nerve. The rate constant increased with stimulus frequency, but its maximum value was only 1.8 s-1, about one-fourth of the middle mechanical rate constant. 7. Because muscle activation is slower than the mechanical dynamics, it is unlikely that the nervous system can regulate muscle dynamics. However, it is possible that mechanical impedance could be regulated to maintain a desired time-averaged value.