A model of flagellar and ciliary functioning which uses the forces transverse to the axoneme as the regulator of dynein activation

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Abstract
Ciliary and flagellar motion is driven by the dynein‐tubulin interaction between adjacent doublets of the axoneme, and the resulting sliding displacements are converted into axonemal bends that are propagated. When the axoneme is bent in the normal beating plane, force develops across the axoneme in the plane of the bend. This transverse force (t‐force) has maximal effect on the interdoublet spacing of outer doublets 2–4 on one side of the axoneme and doublets 7–9 on the opposite side. Episodes of sliding originates as the t‐force brings these doublets into closer proximity (allowing dynein bridges to form) and are terminated when these doublets are separated from each other by the t‐force. A second factor, the adhesive force of the dynein‐tubulin attachments (bridges), also acts to pull neighboring doublets closer together. This force resists termination of a sliding episode once initiated, and acts locally to give the population of dynein bridges a type of excitability. In other words, as bridges form, the probability of nearby bridges attaching is increased by a positive feedback exerted through the interdoublet spacing. A conceptual working hypothesis explaining the behavior of cilia and flagella is proposed based on the above concepts. Additionally, the feasibility of this proposed mechanism is demonstrated using a computer simulation. The simulation uses a Monte Carlo‐type algorithm for dynein attachment and adhesive force, together with a geometric evaluation of the t‐force on the key microtubule pairs. This model successfully develops spontaneous oscillations from any starting configuration (including a straight position). It is compatible with the physical dimensions, mechanical properties and bridge forces measured in real cilia and flagella. In operation, it exhibits many of the observed actions of cilia and flagella, most notably wave propagation and the ability to produce both cilia‐like and flagella‐like waveforms.