Elastohydrodynamics and motility of microswimmers

: From methods of simulation to emergence of their beat

Abstract

Fluid-structure interactions at low Reynolds number are fundamental to a wide array of biological problems. This thesis is concerned with fluid-structure problems where the structure is long, slender and elastic: elastic filaments. We present advancements to coarse-grained methods for simulation of three-dimensional elastic filaments, coupled to rigid bodies taking into account hydrodynamic interactions. The method is validated against previous work in the literature. The method is demonstrated in three applications: sperm-egg scattering, helical Chlamydomonas swimming, and pumping of fluid by cilia arrays.
Now capable of solving for the dynamics of model microswimmers, we turn to the problem of the emergence of flagella beating. In eukaryotic cilia and flagella, the axoneme is comprised of a set doublet-microtubules arranged in a circle, and bending of the flagellum is a result of sliding between neighbouring doublet-microtubules forced by dynein molecular motors. Exactly how dynein organises to produce periodic flagella beating is debated, and several mechanisms have been proposed. We extend planar models of sliding-controlled flagella to three dimensions, and show the emergence of helical travelling waves of motor populations corresponding to helical flagella beating. We show the relationship between frequency of beating in the head-frame (equal to the frequency of motor oscillations), frequency of sperm rolling and frequency of lab-frame beating. On inclusion of a stiff bridge connecting two neighbouring DMTs, circular waves of dynein around the axoneme collapses into standing waves of dynein on either side of the bridge, resembling two teams of dynein that oppose each other, recreating experimentally observed dynein organisation in sea-urchin flagella. The structure of the axoneme has been shown to vary between species, and we hope the model presented here will provide a base for further research in order to link features of nanoscale axoneme structure to experimentally observed waveforms.

Motivated by the model microorganism Chlamydomonas, we finally examine synchronisation phenomena of multiple flagella, each driven by sliding-controlled dynein. Previous experimental and modelling work have highlighted the inability of hydrodynamics to facilitate synchronisation, and instead it is believed that a distal striated fibre connecting the flagella basal bodies is responsible. We propose a mechanism of synchronisation in which the distal fibre directly couples doublet-microtubule sliding at the base of the flagella. As a result, this coupling mechanism relies on sliding forces internal to the axoneme, and can facilitate synchronisation in complete absence of hydrodynamic interactions.

Date of Award	18 Mar 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Hermes Gadelha (Supervisor) & Alan R Champneys (Supervisor)