A Continuous-Binding Cross-Linker Model for Passive Airway Smooth Muscle

Although the active properties of airway smooth muscle (ASM) have garnered much modeling attention, the passive mechanical properties are not as well studied. In particular, there are important dynamic effects observed in passive ASM, particularly strain-induced fluidization, which have been observed both experimentally and in models; however, to date these models have left an incomplete picture of the biophysical, mechanistic basis for these behaviors. The well-known Huxley cross-bridge model has for many years successfully described many of the active behaviors of smooth muscle using sliding filament theory; here, we propose to extend this theory to passive biological soft tissue, particularly ASM, using as a basis the attachment and detachment of cross-linker proteins at a continuum of cross-linker binding sites. The resulting mathematical model exhibits strain-induced fluidization, as well as several types of force recovery, at the same time suggesting a new mechanistic basis for the behavior. The model is validated by comparison to new data from experimental preparations of rat tracheal airway smooth muscle. Furthermore, experiments in noncontractile tissue show qualitatively similar behavior, suggesting support for the protein-filament theory as a biomechanical basis for the behavior.