Gait optimality for undulatory locomotion with applications to C. elegans phenotyping
File(s)
Author(s)
Hall, Madeleine Grace
Type
Thesis
Abstract
This thesis focuses on the optimality and efficiency of organism locomotion strategies, specifically of microscopic undulators, in two distinct parts. Undulators loco- mote by propagating waves of bending deformation along their bodies, and at the microscale (ie low Reynolds number) interactions between undulators and their surroundings are well-described by biomechanical models due to high viscosity and negligible inertia. Frameworks such as resistive force theory enable the determination of optimal gaits for micro-undulators, often defined as the waveform maximising the ratio of swimming speed to energetic cost.
Part I explores this avenue of research in a theoretical setting. Primary mathematical focus has been on finding optimal waveforms for straight-path forwards locomotion, but organisms do not move exclusively this way: turning and manoeuvring is key to survival. Here we establish a mathematical model, extend- ing previous approaches to modelling swimming micro-undulators, now introducing path curvature, to obtain optimal turning gaits. We obtain an analytical result demonstrating that high-curvature shapes minimise energetic cost when the penalty for bending is reduced. Imposing limitations on the curvature, and investigating multiple high-dimensional shape-spaces, we show that optimal turning results can be closely approximated as constant-curvature travelling waves.
Part II adopts an experimental approach. Quantitative phenotyping tools can be used in behavioural screens of the model organism C. elegans to detect differences between wildtype and mutant strains. Expanding the current set of tools to include more orthogonal features could enable increased detection of deficiencies. Here we develop efficiency as a phenotyping lens for C. elegans, quantifying the gait optimality of rare human genetic disease model strains. Genetic diseases in humans are modelled in C. elegans with disease-associated orthologs. We find worm gait efficiency is found to correlate highly with percentage time paused. High efficiencies are exhibited during reversals and backing motions, due to suppressed head-swinging and increase in speed.
Part I explores this avenue of research in a theoretical setting. Primary mathematical focus has been on finding optimal waveforms for straight-path forwards locomotion, but organisms do not move exclusively this way: turning and manoeuvring is key to survival. Here we establish a mathematical model, extend- ing previous approaches to modelling swimming micro-undulators, now introducing path curvature, to obtain optimal turning gaits. We obtain an analytical result demonstrating that high-curvature shapes minimise energetic cost when the penalty for bending is reduced. Imposing limitations on the curvature, and investigating multiple high-dimensional shape-spaces, we show that optimal turning results can be closely approximated as constant-curvature travelling waves.
Part II adopts an experimental approach. Quantitative phenotyping tools can be used in behavioural screens of the model organism C. elegans to detect differences between wildtype and mutant strains. Expanding the current set of tools to include more orthogonal features could enable increased detection of deficiencies. Here we develop efficiency as a phenotyping lens for C. elegans, quantifying the gait optimality of rare human genetic disease model strains. Genetic diseases in humans are modelled in C. elegans with disease-associated orthologs. We find worm gait efficiency is found to correlate highly with percentage time paused. High efficiencies are exhibited during reversals and backing motions, due to suppressed head-swinging and increase in speed.
Version
Open Access
Date Issued
2022-05
Date Awarded
2022-11
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Keaveny, Eric
Sponsor
Wellcome Trust (London, England)
Grant Number
215345/Z/19/Z
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)