Conditions for metachronal coordination in arrays of model cilia

Fanlong Meng, Rachel R Bennett, Nariya Uchida, Ramin Golestanian

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On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units and, as such, exemplifies a bottom-up study of a rich active matter system.
Original languageEnglish
Article numbere2102828118
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number32
Early online date6 Aug 2021
Publication statusPublished - 10 Aug 2021

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS. We thank Andrej Vilfan and Masao Doi for fruitful discussions. This work has received support from the Max Planck School Matter to Life and the MaxSynBio Consortium, which are jointly funded by the Federal Ministry of Education and Research of Germany, and the Max Planck Society. F.M. received partial support from the Alexander von Humboldt Foundation, Strategic Priority Research Program of Chinese Academy of Sciences Grant XDA17010504, and National Natural Science Foundation of China Grant 12047503. R.R.B. acknowledges a doctoral scholarship from the Engineering and Physical Sciences Research Council (EPSRC) and a University of Bristol Vice-Chancellor’s Fellowship.

Publisher Copyright:
© 2021 National Academy of Sciences. All rights reserved.


  • metachronal wave
  • cilia
  • hydrodynamic interactions


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