Quantification of flagellar gait changes with combined shape mode analysis and swimming simulations

Many different microswimmers propel themselves using flagella that beat
periodically. The shape of the flagellar beat and swimming speed have been
observed to change with fluid rheology. We quantify changes in the
flagellar waveforms of Chlamydomonas reinhardtii in response to changes in
fluid viscosity using (1) shape mode analysis and (2) a full swimmer
simulation to analyze how shape changes affect the swimming speed and to
explore the dimensionality of the shape space. By decomposing the gait
into the time-independent mean shape and the time-varying stroke, we find
that the flagellar mean shape substantially changes in response to
viscosity, while the changes in the time-varying stroke are more subtle.
Using the swimmer simulation, we quantify how the swimming speed is
affected by the dimensionality of the flagellar shape reconstruction, and
we show that the observed change in swimming speed with viscosity is
explained by the variations in mean flagellar shape and beat frequency,
while the changes in swimming speed from the different time-varying
strokes are on the scale of variation between cells.