Mathematical Modelling and Computational Simulation Studies of Flagellate Motility

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Cellular swimming is almost exclusively actuated via one of two types of slender appendages, cilia and flagella, though our focus is the latter. While flagella ultrastructure differs between prokaryotes and eukaryotes, unifying and fundamental micromechanical principles apply and thus the diverse areas of flagellate cellular biology are governed by the same underlying mechanics. The importance of such mechanics is exemplified by surface swimming - vital in understanding bacterial behaviour in surface colonisation and thus biofilm initation as well as sperm cell interactions with the surfaces of microdevices and the female reproductive tract. Further examples include the control and regulation of the flagellum and why it adopts any given beat pattern, for which there are numerous schools of thought but minimal mechanical analyses, despite the usefulness of the latter in refining our understanding. The strategic aim of this theoretical project will be to further develop our mechanical understanding of flagellate motility by mathematical modelling and computational simulation. Specifically, this project aims to develop new software to perform high-accuracy numerical simulation of flagellates, which will then be used to examine complex swimming behaviours and mechanics. This will be complemented by a theoretical study of the regulation and control of flagella in different microorganisms, examining recent hypotheses in the field and aiming to extend current understanding via consideration of additional structural features. One example will be the study of the mechanical fundamentals for the motility of the genus of protist parasites, Leishmania, which infects up to 1 million humans each year. The objective of a first study will be to characterise and understand how aspects of Leishmania motility, such as the fact the cells are dragged along by their flagella rather than pushed and the fact the cell bodies are very large compared to other flagellates, impacts on their behaviour during the swimming stages of their life cycle. This includes surface swimming behaviour, with epithelial attachment and detachment, while the parasite is resident in its host, the sandfly. It also includes the behaviour of these cells in background flows, as is relevant for bloodstream forms of the parasite in the initial stages of human infection, and neither aspect of Leishmania's behaviour has been subject to detailed mechanical analysis and computational simulation. The prospect of additional studies in collaboration with Drs Eva Gluenz and Richard Wheeler, Dunn School of Pathology, University of Oxford to further improve our understanding of Leishmania motility will also be explored. Further objectives for the project can include the mechanical analysis of hypothesised mechanisms for flagellar regulation within the biological literature and from biological colleagues. One example is whether spatially heterogeneous molecular motor rigor within the eukaryotic flagellum explains the asymmetry of the flagellum during a process known as hyperactivation, which has been observed to be necessary for natural fertilisation in mammals. These latter studies will also require the further development of filament elastohydrodynamic simulations and thus, in addition to biological and modelling novelty, such studies will also be novel from a computational physics viewpoint. Consequently, this project falls within the EPSRC research areas of (i) mathematical biology (ii) fluid dynamics and (iii) continuum mechanics.