Bifurcation Analysis of Active Filament Models

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• Bethany Clarke, Imperial College London
• Thursday 15 June 2023, 13:00-14:00
• MR14, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Marco Vona.

Slender filaments such as microtubules are ubiquitous in nature, driving fluid flow at the microscopic scale. Molecular motors like dynein and kinesin translocate along microtubules, causing a range of both steady and time-dependent behaviours. The coordinated motion of microtubules can lead to phenomena like cytoplasmic streaming and ciliary beating, generating fluid flows on larger scales. In this talk we provide a comprehensive overview of the emerging dynamics of the most fundamental model that captures the effect of molecular motors on a single filament; the follower force model, whereby a compressive force is imposed at the filament tip. We vary both the strength of this force and the slenderness of the filament to explore the resulting state space, using a filament model built on Kirchoff’s rod theory and which employs unit quaternions and implicit time integration to handle the development of the filament’s local frame over time [1]. Employing a Jacobian-Free Newton-Krylov method, we establish both steady and time-periodic solutions to the model, as well as new, quasi-periodic solutions. We classify and fully characterize the bifurcations yielding different states and analyse their stability. In doing so, we provide a clear picture of the full bifurcation diagram for the fundamental model of microtubule-motor protein complexes.

References:

[1] S. F. Schoeller, A. K. Townsend, T. A. Westwood and E. E. Keaveny, Methods for suspensions of passive and active filaments, Journal of Computational Physics, 424 (2021)

This talk is part of the DAMTP BioLunch series.

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