Viscoelastic properties of C. reinhardtii flagella

eng Eukaryotic flagella are slender organelles that protrude for the cell body of many organisms, ranging from microalga to animals. Flagella share a highly conserved structure arranged as a circular array of interlinked doublet microtubules and a central pair of microtubules. Molecular motors are regularly attached along the flagellum and produce doublet translation that turns into bending due to local constraints. Despite their significance in cell biology and physiology, the mechanism of coordination of these molecular motors into a regular waveform is still under debate. In particular, the feedback mechanism of the waveform onto the motors is unknown. Viscoelastic properties of flagella relate forces and torques to the shape of the flagellum, and are therefore crucial to understand this feedback mechanism, and ultimately the emergence of regular beating patterns. However our understanding of these mechanical properties remain parcellar. Flagella have been considered as homogeneous, isotropic Euler-Bernoulli beams. However, they display interdoublet shear resistance, basal compliance and might dissipate energy through internal friction. In fact, previous work focused primarily on static responses to external forcings. A dynamic analysis therefore seems necessary. Beyond the flagellar level, coordination of multiple flagella, whether pertaining to the same cell or to different cells or organisms, is essential for biological functions such as motility, foraging, escaping or feeding current generation. Indeed, ciliary arrays often exhibit synchronized beating. Multiciliated tissues form metachronal waves that enhance fluid transport efficiency and biflagellate cilia like Chlamydomonas reinhardtii typically beat in phase to propel the phase forward. The physical origin of these coordinations is not fully understood. Metachronal waves seem to be of hydrodynamic origin, likewise for flagella belonging to different somatic cells in Volvox carteri. However, basal bodies -- flagellar anchorings to the cell body -- seem to determine the beating plane in Tetrahymena, while cytoplasmic actin and microtubule networks interacting with basal bodies are necessary for metachrony in Xenopus embryo ciliated cells. At the single-cell level, Chlamydomonas can be phase-locked by an external flow much stronger than a typical flagellum-generated flow. In contrast, cell mutants lacking striated fibers connecting the basal bodies do not display synchronization, indicating that intracellular coupling is necessary and hydrodynamic coupling is not sufficient for synchronization for same-cell flagella. Here we use the model organism Chlamydomonas reinhardtii to tackle these questions. In the first part, we develop a novel experiment that effectively makes interflagellar hydrodynamic coupling vanish with minute hydrodynamic effects. This setup allows us to probe the effect of intracellular mechanical coupling alone on synchronization. The results show that internal coupling is sufficient for In-Phase synchrony, whereas hydrodynamic coupling is necessary for Anti-Phase synchrony, naturally displayed by the flagellar dominance mutant ptx1. These findings shed light onto the mathematical structure of the synchronization process in those cells, in particular onto the origin of the noise in inter-flagellar dynamics, and its potential role in gait switching mechanism. In the second part, we develop a model that takes into account our current knowledge on viscoelastic properties of flagella, in particular basal degrees of freedom and internal dissipation. In order to infer static and dynamic mechanical properties, a background time-dependent flow is included. We then present an inference method based on a model reduction approach. We show that this approach allows to infer internal timescales of the system, and test it experimentally on passivated pipette-held Chlamydomonas cells under a time-dependent external flow driven by a piezoelectric stage. Together, these results deepen our understanding of mechanical properties and synchronization of flagella, and show the crucial role of basal bodies mechanical properties, perhaps biologically driven, to the coordination of the flagellar beat and between flagella.