Internal friction controls active ciliary oscillations near the instability threshold

Abstract

Ciliary oscillations driven by molecular motors cause fluid motion at micron scale. Stable oscillations require a substantial source of dissipation to balance the energy input of motors. Conventionally, it stems from external fluid. We show, in contrast, that external fluid friction is negligible compared to internal elastic stress through a simultaneous measurement of motion and flow field of an isolated and active Chlamydomonas cilium beating near the instability threshold. Consequently, internal friction emerges as the sole source of dissipation for ciliary oscillations. We combine these experimental insights with theoretical modeling of active filaments to show that an instability to oscillations takes place when active stresses are strain softening and shear thinning. Together, our results reveal a counterintuitive mechanism of ciliary beating and provide a general experimental and theoretical methodology to analyze other active filaments, both biological and synthetic ones.

Flagellar energetics from high-resolution imaging of beating patterns in tethered mouse sperm

“…Our findings suggest instead that internal friction within the passive structures of the flagellum, and within the motors themselves, may be as large as the external hydrodynamic friction. These are in line with recent observations also made in algal cilia ( Mondal et al, 2020 ). These sources of internal dissipation could therefore play a significant role in determining beating patterns in sperm ( Camalet and Jülicher, 2000 ).…”

“…As previously mentioned, we have used here Pa μm 4 based on experimental measurements elsewhere ( Lindemann and Lesich, 2016 ). While the existence of internal friction in the fluid-filled region around the axoneme is expected ( Riedel-Kruse et al, 2007 ; Mondal et al, 2020 ), direct measurements of the value of are not available.…”

“…To quantitatively analyze beat patterns in a statistically meaningful way, we need to image swimming sperm over several beat cycles. While rapid progress is being made on full three-dimensional tracking ( Muschol et al, 2018 ; Dardikman-Yoffe et al, 2020 ; Gadêlha et al, 2019 ), it is unlikely that sufficient beat cycles can be reliably recorded with freely swimming sperm that can quickly move out of focal plane or the FOV ( Mondal et al, 2020 ). Instead, we image flagella beating freely in the focal plane in cells tethered chemically at their heads to a glass slide.…”

“…These coefficients have previously been used in a number of studies, notably by Jülicher and co-workers ( Riedel-Kruse et al, 2007 ) for analyzing experimental data on wall-tethered sperm and, more recently, by Mondal et al, 2020 , for tethered axonemes isolated from cilia. The cross-sectional radius of the cylindrical filament, , is further not constant along the sperm body.…”

Light-powered reactivation of flagella and contraction of microtubules network: towards building an artificial cell

“…Instead, sliding is converted into rhythmic bending deformations that propagate along the contour length of axonemes at a frequency that depends on ATP concentration (Figure 3C-E and SI Videos 1-2). We did not observe beating activity for ATP concentrations below the critical value of [ATP] critical =60 μM 53,54 , suggesting that a minimum number of active molecular motors are required to generate rhythmic motion in axonemes. The critical beat frequency was f critical ~14.6 Hz.…”