Mathematical Modelling and Computational Simulation Studies of Flagellate Motility

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute


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.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509711/1 01/10/2016 30/09/2021
1941986 Studentship EP/N509711/1 01/10/2017 30/06/2021 Benjamin Walker
Description 1. The behaviours of a human-pertinent microswimmer, the cause of leishmaniasis which affects millions worldwide, were investigated via simulation and image processing, facilitating understanding of this parasite and suggesting mechanisms that may be of utility in disease control, prevention and cure.
2. Methods of controlling swimmers on the microscale were suggested and proven in simulation, and a link between classical results of fluid mechanics was linked to behaviours of human-pertinent microorganisms.
3. A novel image analysis technique was developed and tested, with the potential to realise a new generation of sperm analysis for use in fertility studies, in addition to it being applicable to a range of organisms, all automated and linking biology with imaging science.
4. New methods of simulation of slender filaments were devised, implemented and published, potentially enabling the study of ciliopathies and flagellum regulation on previously-unrealisable scales with modest computational needs.
5. Novel methods of automated statistical comparisons of the shapes of beating flagella, applicable to a breadth of organisms and representing a new generation of analysis.
Exploitation Route Outcomes of this funding lay the foundation for new analytical techniques to revolutionise diagnostics of flagellated swimmers, notably including bovine and human spermatozoa. Theoretical studies stemming from this award may be built upon to improve our understanding of microorganisms and their motility, of relevance to those studying human pathogens such as Leishmania, and to physicists and cell biologists more generally.
Sectors Agriculture, Food and Drink,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology

Description Microswimming with Kenta Ishimoto 
Organisation University of Kyoto
Country Japan 
Sector Academic/University 
PI Contribution Research ideas and specialist skills
Collaborator Contribution Research ideas and specialist skills
Impact 5 publications in pee-reviewed journals, in the fields of mathematics, biology and physics.
Start Year 2017
Description Mathematics talk to Y9-Y10 students on a school visit 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact ~20 pupils attended for a school visit to the University, giving them an overview of mathematical biology and sparking discussion and engagement with practical problems.
Year(s) Of Engagement Activity 2018,2019
Description Royal Institute Mathematics Masterclass 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact 30 pupils attended a Masterclass that was written and delivered by myself, broadening their idea of mathematics and sparking in-depth questions relating to both mathematics and its applications in society.
Year(s) Of Engagement Activity 2019