A two-degree-of-freedom filament oscillator model yields bistable metachronal waves on a spherical ciliate, with higher stiffness selecting more efficient diaplectic waves.

Summary. The manuscript develops a filament oscillator model for filamentous cilia covering a sphere, in which each cilium is reduced to two dynamic degrees of freedom: a phase that maps onto a prescribed beat-shape sequence and an orientation angle for that sequence. Using numerical techniques that simultaneously resolve emergent coordination and propulsion, the authors report that varying a stiffness-related parameter yields bistability between symplectic-like and diaplectic metachronal waves at sufficiently low stiffness, while only diaplectic waves emerge above a critical stiffness. They further claim that diaplectic waves produce more efficient propulsion owing to shorter wavelengths, and that introducing beat-plane tilt induces ciliate rotation while leaving the emergent wave states and swimming speeds largely unchanged.

Significance. If the reported bistability, critical stiffness, and efficiency ranking are robust, the work would supply a concrete mechanistic link between an effective cilium stiffness, metachronal wave type, and propulsive performance for a spherical ciliate geometry—an important and still incompletely understood setting in biofluid dynamics. The simultaneous computation of coordination and free swimming, together with the explicit comparison of flow fields and efficiency between the two wave states, would be a useful contribution. The filament oscillator reduction, if adequately validated, could also offer a computationally tractable platform for larger-scale ciliate studies. These strengths remain conditional on the model’s fidelity and on quantitative support that cannot be assessed from the abstract alone.