The chiral beat of algal flagella: force and torque via imaging

Abstract

Flagella allow eukaryotic cells to move and pump fluid. We present the first three-dimensional, time-resolved imaging of the flagellar waveform of Chlamydomonas reinhardtii, a model alga found in fresh water. During the power stroke, we find that the flagella show rotational symmetry about the cell's centreline, but during the recovery stroke they display mirror symmetry about the same axis. We use our three-dimensional imaging data to test the applicability of resistive force theory when a force-free configuration is approximated using a cell on a micropipette. The inferred values of cells' swimming speeds and rotation rates show good agreement with experimental results on freely swimming cells.

The three-dimensional coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics

“…Again, breaking the symmetry between the two flagella produces more complex swimming. In the case of opposite sign and asymmetric out-of-plane curvatures, the trajectory of Chlamydomonas becomes helical (distinct from the previous helical case; figure 4 g ), in further agreement with 3D observations [ 54 , 60 ].…”

“…Most importantly, the 3D elastohydrodynamic model is able to predict a bewildering array of complex 3D swimming trajectories that may arise via simple symmetry-breaking features of the flagella beat in 3D, from circular to helical trajectories ( figure 4 ), in agreement with [ 54 , 60 ]. This offers numerous modelling opportunities motivated by recent 3D observations of this important model microorganism [ 54 , 60 ]. We also report novel sperm-scattering results in which sperm swimming can either be enhanced or reduced by the presence of a free body ( figure 5 ).…”

“…Our simulations revealed that the non-local hydrodynamic coupling increases the elastohydrodynamic propulsion of the Chlamydomonas swimming. Most importantly, the 3D elastohydrodynamic model is able to predict a bewildering array of complex 3D swimming trajectories that may arise via simple symmetry-breaking features of the flagella beat in 3D, from circular to helical trajectories (figure 4), in agreement with [54,60]. This offers numerous modelling opportunities motivated by recent 3D observations of this important model microorganism [54,60].…”

“…Motivated by recent empirical studies observing three-dimensional beating of Chlamydomonas flagella [ 54 , 60 ], we show here that it is straightforward to implement 3D beating of Chlamydomonas using the CG framework. For the simplicity of this demonstration, we introduce a constant out-of-plane curvature in the d 1 direction of the two flagella, so that the time-dependent preferred curvature is .…”

“…Instead, the Chlamydomonas is trapped into perfect circular paths with radius r , linearly proportional to the mean out-of-plane curvature , shown in figure 4 d . Interestingly, any incongruity in the mean intrinsic curvature between the two flagella is sufficient to allow Chlamydomonas to swim progressively via an array of helical paths in 3D, depending on differences in the orientation of their beating-planes, as observed experimentally [ 54 , 60 ].…”