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Bistability in the synchronization of actuated microfilaments

  • Hanliang Guo (a1), Lisa Fauci (a2), Michael Shelley (a3) (a4) and Eva Kanso (a1) (a3)

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.

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Type Description Title

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)

 Video (6.1 MB)
6.1 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)

 Video (16.3 MB)
16.3 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)

 Video (8.2 MB)
8.2 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)

 Video (9.7 MB)
9.7 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)

 Video (9.8 MB)
9.8 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)

 Video (11.3 MB)
11.3 MB


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