Simulation of ciliary beating by an excitable dynein model: oscillations, quiescence and mechano-sensitivity

Murase et al. (1989, J. theor. Biol. 139, 413) showed that an excitable dynein model can generate flagellar-like bending waves of low amplitude along an axoneme suspended in a viscous fluid. Either regular base-to-tip and irregular tip-to-base propagating waves can be produced. The present study shows that if the force-vs.-distance functions (or the potential energy functions as their integral form) that represent the functional properties of dyneins differ in the basal region, as compared with the rest of the active length of a short axoneme, and also differ between the opposing doublets, ciliary-like repetitive beats can be simulated. Depending on the parameter values, a cilium beats once and then becomes resting or quiescent, at the end of either its recovery or effective stroke. Interestingly, a quiescent cilium exhibits repetitive beats when a steady flow of water is applied to a part of the cilium in a suitable direction and at an appropriate speed. This kind of responsiveness to external stimuli, called directional mechano-sensitivity, may account for metachronal waves over a layer of cilia. As in the previous model for flagellar movement, the present model requires a passive region at the tip, but does not need a curvature feedback control, to generate ciliary-like beating patterns.