Hydrodynamic Synchronization of Spontaneously Beating Filaments

Abstract

Using a geometric feedback model of the flagellar axoneme accounting for dynein motor kinetics, we study elastohydrodynamic phase synchronization in a pair of spontaneously beating filaments with waveforms ranging from sperm to cilia and Chlamydomonas. Our computations reveal that both in-phase and anti-phase synchrony can emerge for asymmetric beats while symmetric waveforms go in-phase, and elucidate the mechanism for phase slips due to biochemical noise. Model predictions agree with recent experiments and illuminate the crucial roles of hydrodynamics and mechanochemical feedback in synchronization.

Spontaneous oscillations, beating patterns, and hydrodynamics of active microfilaments

“…However, simulations at lower activity levels (not shown) reveal that the direction of propulsion is reversed when waves propagate in the retrograde direction. This hints at the importance of dynein level regulation for efficient sperm motility, and also has consequences for the hydrodynamic synchronization of nearby interacting flagella [59].…”

Measurements of the unsteady flow field around beating cilia

“…2018). Studies of internal dynamics and kinematics of flagella/cilia (Tam & Hosoi 2007, 2011; Chakrabarti & Saintillan 2019 a , b ) have made use of non local slender-body theory to model the hydrodynamics (Keller & Rubinow 1976). Finally, studies of suspensions of microswimmers have focused on the onset of collective motion and the effect on the rheology of the active suspension (Saintillan 2018).…”

Geometric phase methods with Stokes theorem for a general viscous swimmer

“…2009; Hu et al. 2015; Chakrabarti & Saintillan 2019 a ) and with walls (Barta & Liron 1988; Das & Lauga 2018; Walker et al. 2019).…”

“…2019; Chakrabarti et al. 2020), while including models for internal activation allows us to understand how spermatozoa and cilia generate their waveforms (Ishimoto & Gaffney 2018; Chakrabarti & Saintillan 2019 a , b ; Man, Ling & Kanso 2020). These approaches have also been extended to consider the dynamics of microswimmers in complex media (Koens & Lauga 2016 a ; Wróbel et al.…”

“…The success of the Gray & Hancock (1955) resistive-force model for spermatozoa swimming inspired a great effort into the modelling of microscopic biological swimmers † Email address for correspondence: lmk42@cam.ac.uk in viscous fluids. Hydrodynamic models of these systems now include long-range hydrodynamic interactions in flagella and cilia (Keller & Rubinow 1976;Lighthill 1976;Johnson 1979;Gueron & Liron 1992;Man, Koens & Lauga 2016;, interactions between the swimmers body and its flagella (Higdon 1979;Smith et al 2009;Hu et al 2015;Chakrabarti & Saintillan 2019a) and with walls (Barta & Liron 1988;Das & Lauga 2018;Walker et al 2019). These hydrodynamic models have also been coupled with elasticity to investigate the fluid-structure interactions at the heart of biological flagella (Kim & Powers 2005;Ishimoto & Gaffney 2018;du Roure et al 2019;Chakrabarti et al 2020), while including models for internal activation allows us to understand how spermatozoa and cilia generate their waveforms (Ishimoto & Gaffney 2018;Chakrabarti & Saintillan 2019a,b;Man, Ling & Kanso 2020).…”