Modelling Microtubule-Molecular Motor Systems

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Microtubules are long slender filaments that are ubiquitous in nature. They form the axoneme of cilia; hair-like filaments that drive fluid flow at a macroscopic scale, often found on the surface of cells such as Volvox. Cilia also line the epithelia in the lungs and can coordinate their beating to transport mucus, preventing bacteria from entering the body. Their motion is driven by molecular motors such as dynein, which translocate along the microtubule length each carrying cargo and exerting a tangential force on the filament. This forcing leads to an instability-driven buckling, where the microtubules exhibit a rich and interesting set of behaviours. Our research involves the mathematical modelling of microtubules; specifically, we aim to create a biophysical model to describe microtubule deformation, accounting for the piconewton scale effects of the molecular motors. Over the project we aim to extend this to a model of an axoneme, to generate a model of a cilium, and extend further to consider the coupled behaviour of several cilia. Despite the level of detail in this model, we can still achieve fast simulations by using GPUs. Through these methods, we aim to elucidate the processes behind the collective behaviours of cilia observed in nature.