Flagellar swimmers oscillate between pusher- and puller-type swimming

Abstract

Self-propulsion of cellular microswimmers generates flow signatures, commonly classified as pusher and puller type, which characterize hydrodynamic interactions with other cells or boundaries. Using experimentally measured beat patterns, we compute that the flagellated green alga Chlamydomonas oscillates between pusher and puller, rendering it an approximately neutral swimmer, when averaging over its full beat cycle. Beyond a typical distance of 100μm from the cell, inertia attenuates oscillatory microflows. We show that hydrodynamic interactions between cells oscillate in time and are of similar magnitude as stochastic swimming fluctuations. From our analysis, we also find that the rate of hydrodynamic dissipation varies in time, which implies that flagellar beat patterns are not optimized with respect to this measure.

Coarse-Graining the Fluid Flow around a Human Sperm

“…With this breakdown of the beat cycle from the systematic reduction of the flow field one has that the sperm continually switches between pusher and puller modalities, as previously observed for C. reinhardtii [8]. In addition, the cross-like structure of the PCA phase portrait orbit in Fig.…”

“…[11]) and are popular since singularity flows have a clear theoretical interpretation, as the first terms of a multipole expansion. However temporal averaging may be illadvised [8], since the time dependence of microswimmer flows persists on lengthscales associated with cell-cell hydrodynamic interaction, increasing the complexity of information that needs to be retained.…”

“…4b. While Klindt & Friedrich [8] suggest using unsteady Stokes singularities in multipole expansions, we approximate the steady PCA modes with Stokeslets, though these are regularized [18] in order to avoid actual singularities. Hence for the velocity field of PCA mode s, we considerũ…”

“…For instance, flows have been reconstructed from the flagellar waveform for the algae C. reinhardtii, using numerical simulation [7,8], though validation of simulations to actual swimmer dynamics has been limited to the approximation of resistive force theory [9] and required resistance coefficients that varied extensively between different sperm. Furthermore, flows around microswimmers have been measured using micro-PIV for Gardia protozoan flagellates [10], though reported with limited resolution.…”

Hydrodynamic synchronization of flagellar oscillators

“…In short, synchronization arises from a "resonance" between a phase-dependence of the active driving and the phasedependence of the hydrodynamic friction coefficients. In a coarse-grained theoretical description of flagellar beating, phase-dependent driving forces of the flagellar beat can be computed from the phase-dependent rate of hydrodynamic dissipation [30,70]. Figure 5 shows the phase-dependence of the hydrodynamic dissipation rate computed for a free-swimming Chlamydomonas cell.…”