Geometric Clutch model version 3: the role of the inner and outer arm dyneins in the ciliary beat

Abstract

The Geometric Clutch model of ciliary and flagellar beating uses the transverse force (t-force) that develops between the outer doublets of the axoneme as the regulator for activating and deactivating the dynein motors and organizing the flagellar beat. The version of the model described here adds detail to the formulations used in the two previous versions as follows: (1) In place of two opposing sets of dyneins, the new model has four sets of dyneins, corresponding to two sets on each side of the axoneme acting in series. (2) The four sets of dyneins are each subdivided into two ranks representing inner and outer arm dyneins. (3) The force produced by each dynein is governed by a force-velocity relationship that is independently specified for the inner and outer arms. Consistent with the original model, the new version of the Geometric Clutch model can simulate both the effective and recovery stroke phases of the ciliary beat using a single uniform algorithm. In addition, the new version can operate with the outer arms disabled. Under this condition, the simulation exhibits a beat pattern similar to the original but the beat frequency is reduced to approximately one third. These results are contingent on using force-velocity relationships for the inner and outer arms similar to those described by Brokaw [1999: Cell Motil. Cytoskeleton 42:134-148], where the inner arms contribute most of the driving force at low shear velocities. This constitutes the first examination of the effects of the force-velocity characteristics of dynein on a cilia-like beat in a theoretical framework.