A dynamic calcium-force relationship model for sag behavior in fast skeletal muscle

In vitro studies using isolated or skinned muscle fibers suggest that the sigmoidal relationship between the intracellular calcium concentration and force production may depend upon muscle type and activity. The goal of this study was to investigate whether and how the calcium-force relationship changes during force production under physiological conditions of muscle excitation and length in fast skeletal muscles. A computational framework was developed to identify the dynamic variation in the calcium-force relationship during force generation over a full physiological range of stimulation frequencies and muscle lengths in cat gastrocnemius muscles. In contrast to the situation in slow muscles such as the soleus, the calcium concentration for the half-maximal force needed to drift rightward to reproduce the progressive force decline, or sag behavior, observed during unfused isometric contractions at the intermediate length under low-frequency stimulation (i.e., 20 Hz). The slope at the calcium concentration for the half-maximal force was required to drift upward for force enhancement during unfused isometric contractions at the intermediate length under high-frequency stimulation (i.e., 40 Hz). The slope variation in the calcium–force relationship played a crucial role in shaping sag behavior across different muscle lengths. The muscle model with dynamic variations in the calcium-force relationship also accounted for the length-force and velocity-force properties measured under full excitation. These results imply that the calcium sensitivity and cooperativity of force-inducing crossbridge formation between actin and myosin filaments may be operationally altered in accordance with the mode of neural excitation and muscle movement in intact fast muscles.