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Bistability in the synchronization of actuated microfilaments

Published online by Cambridge University Press:  11 December 2017

Hanliang Guo
Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
Lisa Fauci
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
Michael Shelley
Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY 10010, USA Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Eva Kanso*
Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY 10010, USA
Email address for correspondence:


Cilia and flagella are essential building blocks for biological fluid transport and locomotion at the micrometre scale. They often beat in synchrony and may transition between different synchronization modes in the same cell type. Here, we investigate the behaviour of elastic microfilaments, protruding from a surface and driven at their base by a configuration-dependent torque. We consider full hydrodynamic interactions among and within filaments and no slip at the surface. Isolated filaments exhibit periodic deformations, with increasing waviness and frequency as the magnitude of the driving torque increases. Two nearby but independently driven filaments synchronize their beating in-phase or anti-phase. This synchrony arises autonomously via the interplay between hydrodynamic coupling and filament elasticity. Importantly, in-phase and anti-phase synchronization modes are bistable and coexist for a range of driving torques and separation distances. These findings are consistent with experimental observations of in-phase and anti-phase synchronization in pairs of cilia and flagella and could have important implications on understanding the biophysical mechanisms underlying transitions between multiple synchronization modes.

JFM Papers
© 2017 Cambridge University Press 

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Guo et al. supplementary movie 1

Long term dynamics of single filament with M_b=1, vertical initial condition. (Figure 2a in the main text)

Download Guo et al. supplementary movie 1(Video)
Video 6 MB

Guo et al. supplementary movie 2

Long term dynamics of single filament with M_b=1, tilted initial condition. (Figure 4 in the main text)

Download Guo et al. supplementary movie 2(Video)
Video 16 MB

Guo et al. supplementary movie 3

Long term dynamics of single filament with M_b=3, vertical initial condition. (Figure 2b in the main text)

Download Guo et al. supplementary movie 3(Video)
Video 10 MB

Guo et al. supplementary movie 4

Long term dynamics of single filament with M_b=3, tilted initial condition. (Figure 4 in the main text)

Download Guo et al. supplementary movie 4(Video)
Video 10 MB

Guo et al. supplementary movie 5

Long term dynamics of a pair of filaments with M_b=1, d=0.7, initial phase difference dphi_0=0.49. (Figure 5a in the main text)

Download Guo et al. supplementary movie 5(Video)
Video 8 MB

Guo et al. supplementary movie 6

Long term dynamics of a pair of filaments with M_b=3, d=0.7, initial phase difference dphi_0=0.49. (Figure 5b in the main text)

Download Guo et al. supplementary movie 6(Video)
Video 11 MB