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Swimming mediated by ciliary beating: comparison with a squirmer model

  • Hiroaki Ito (a1), Toshihiro Omori (a1) and Takuji Ishikawa (a1)

Abstract

The squirmer model of Lighthill and Blake has been widely used to analyse swimming ciliates. However, real ciliates are covered by hair-like organelles, called cilia; the differences between the squirmer model and real ciliates remain unclear. Here, we developed a ciliate model incorporating the distinct ciliary apparatus, and analysed motion using a boundary element–slender-body coupling method. This methodology allows us to accurately calculate hydrodynamic interactions between cilia and the cell body under free-swimming conditions. Results showed that an antiplectic metachronal wave was optimal in the swimming speed with various cell-body aspect ratios, which is consistent with former theoretical studies. Exploiting oblique wave propagation, we reproduced a helical trajectory, like Paramecium, although the cell body was spherical. We confirmed that the swimming velocity of model ciliates was well represented by the squirmer model. However, squirmer modelling outside the envelope failed to estimate the energy costs of swimming; over 90 % of energy was dissipated inside the ciliary envelope. The optimal swimming efficiency was given by the antiplectic wave; the value was 6.7 times larger than in-phase beating. Our findings provide a fundamental basis for modelling swimming micro-organisms.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: omori@bfsl.mech.tohoku.ac.jp

References

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JFM classification

Type Description Title
VIDEO
Movies

Ito et al. supplementary movie 1
Swimming of the model ciliate with in-phase beating

 Video (8.1 MB)
8.1 MB
VIDEO
Movies

Ito et al. supplementary movie 2
Swimming of the model ciliate with antiplectic metachronal wave

 Video (8.8 MB)
8.8 MB
VIDEO
Movies

Ito et al. supplementary movie 3
Swimming of the model ciliate with symplectic metachronal wave

 Video (8.5 MB)
8.5 MB
VIDEO
Movies

Ito et al. supplementary movie 4
Swimming of the model ciliate with oblique metachronal wave

 Video (8.1 MB)
8.1 MB

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