Double-sigmoid model for fitting fatigue profiles in mouse fast- and slow-twitch muscle

We present a curve-fitting approach that permits quantitative comparisons of fatigue profiles obtained with different stimulation protocols in isolated slow-twitch soleus and fast-twitch extensor digitorum longus (EDL) muscles of mice. Profiles from our usual stimulation protocol (125 Hz for 500 ms, evoked once every second for 100-300 s) could be fitted by single-term functions (sigmoids or exponentials) but not by a double exponential. A clearly superior fit, as confirmed by the Akaiki Information Criterion, was achieved using a double-sigmoid function. Fitting accuracy was exceptional; mean square errors were typically <1% and r(2) > 0.9995. The first sigmoid (early fatigue) involved approximately 10% decline of isometric force to an intermediate plateau in both muscle types; the second sigmoid (late fatigue) involved a reduction of force to a final plateau, the decline being 83% of initial force in EDL and 63% of initial force in soleus. The maximal slope of each sigmoid was seven- to eightfold greater in EDL than in soleus. The general applicability of the model was tested by fitting profiles with a severe force loss arising from repeated tetanic stimulation evoked at different frequencies or rest periods, or with excitation via nerve terminals in soleus. Late fatigue, which was absent at 30 Hz, occurred earlier and to a greater extent at 125 than 50 Hz. The model captured small changes in rate of late fatigue for nerve terminal versus sarcolemmal stimulation. We conclude that a double-sigmoid expression is a useful and accurate model to characterize fatigue in isolated muscle preparations.