Properties of an excitable dynein model for bend propagation in cilia and flagella.

Murase & Shimizu (1986, J. theor. Biol. 119, 409) introduced an excitable dynein-microtubule system based on a three-state mechanochemical cycle of dynein to demonstrate bend propagation in the absence of a curvature control mechanism. To examine the essential behavior of this class of models in a viscous fluid, we have represented the force generated by the complex dynein mechanochemistry by a formal model consisting of "force" and "activation" functions vs. sliding distance. Since the model has excitable properties with threshold phenomena and hysteresis switching between two opposed subsystems, it closely resembles the more realistic dynein kinetic scheme in its overall properties but is specified by fewer parameters. This model displays both bend initiation and bend propagation when the filaments at the basal end are either fixed or free to slide. A passive region is necessary at one end of the axoneme in order to obtain stable wave propagation; bends propagate towards the end with the passive region. Stable bend propagation is highly sensitive to small perturbations in external force distribution.