Active beating modes of two clamped filaments driven by molecular motors

A Synthetic Minimal Beating Axoneme

Cilia and flagella are beating rod-like organelles that enable the directional movement of microorganisms in fluids and fluid transport along the surface of biological organisms or inside organs. The molecular motor axonemal dynein drives their beating by interacting with microtubules. Constructing synthetic beating systems with axonemal dynein capable of mimicking ciliary beating still represents a major challenge. Here, the bottom-up engineering of a sustained beating synthoneme consisting of a pair of microtubules connected by a series of periodic arrays of approximately eight axonemal dyneins is reported. A model leads to the understanding of the motion through the cooperative, cyclic association-dissociation of the molecular motor from the microtubules. The synthoneme represents a bottom-up self-organized bio-molecular machine at the nanoscale with cilia-like properties.

Self-sustaining oscillation of two axonemal microtubules based on a stochastic bonding model between microtubules and dynein

The motility of cilia and flagella plays important physiological roles, and there has been a great deal of research on the mechanisms underlying the motility of molecular motors. Although recent molecular structural analyses have revealed the components of the ciliary axoneme, the mechanisms involved in the regulation of dynein activity are still unknown, and how multiple dyneins coordinate their movements remains unclear. In particular, the mode of binding for axonemal dynein has not been elucidated. In this study, we constructed a thermodynamic stochastic model of microtubule-dynein coupling and reproduced the experiments of Aoyama and Kamiya on the minimal component of axonemal microtubule-dynein. We then identified the binding mode of axonemal dynein and clarified the relationship between dynein activity distribution and axonemal movement. Based on our numerical results, the slip-bond mechanism agrees quantitatively with the experimental results in terms of amplitude, frequency, and propagation velocity, implying that axial microtubule-dynein coupling may follow a slip-bond mechanism. Moreover, the frequency and propagation velocity decayed in proportion to the fourth power of microtubule length, and the critical load of the trigger for the oscillation agreed well with Euler's critical load.

Active beating modes of two clamped filaments driven by molecular motors

Biological cilia pump the surrounding fluid by asymmetric beating that is driven by dynein motors between sliding microtubule doublets. The complexity of biological cilia raises the question about minimal systems that can re-create similar patterns of motion. One such system consists of a pair of microtubules that are clamped at the proximal end. They interact through dynein motors that cover one of the filaments and pull against the other one. Here, we study theoretically the static shapes and the active dynamics of such a system. Using the theory of elastica, we analyse the shapes of two filaments of different lengths with clamped ends. Starting from equal lengths, we observe a transition similar to Euler buckling leading to a planar shape. When further increasing the length ratio, the system assumes a non-planar shape with spontaneously broken chiral symmetry after a secondary bifurcation and then transitions to planar again. The predicted curves agree with experimentally observed shapes of microtubule pairs. The dynamical system can have a stable fixed point, with either bent or straight filaments, or limit cycle oscillations. The latter match many properties of ciliary motility, demonstrating that a two-filament system can serve as a minimal actively beating model.