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, wh..., , , [https://doi.org/10.5061/dryad.sbcc2frj6](https://doi.org/10.5061/dryad.sbcc2frj6)

## Code/Software

MATLAB programs related to the paper. There are two main scripts: one to generate lower dimensional shape model using the data attached and determining how many shape modes and frequencies in the time-dependent coefficients and one to perform the numerical swimming simulation. Supporting routines for both the shape model script and the simulation script are in appropriately named source directories, 'ShapeModel_Source' and 'Simulation_Source'.

The folder titled 'Shape Models' is where the .mat files containing the data structure for reconstructing the flagellar shapes are saved to, and already contains sample shape model reconstructions for the different cells in the data set, using 4 shape modes and 2 Fourier coefficients, as is used in the majority of the paper. The folder titled 'Simulation_Data' is currently empty, but if you run the simulation script, information from the simulat...,