Elastohydrodynamics
elastohydrodynamics
Coordinated motion of active filaments on spherical surfaces
Filaments (slender, microscopic elastic bodies) are prevalent in biological and industrial settings. In the biological case, the filaments are often active, in that they are driven internally by motor proteins, with the prime examples being cilia and flagella. For cilia in particular, which can appear in dense arrays, their resulting motions are coupled through the surrounding fluid, as well as through surfaces to which they are attached. In this talk, I present numerical simulations exploring the coordinated motion of active filaments and how it depends on the driving force, density of filaments, as well as the attached surface. In particular, we find that when the surface is spherical, its topology introduces local defects in coordinated motion which can then feedback and alter the global state. This is particularly true when the surface is not held fixed and is free to move in the surrounding fluid. These simulations take advantage of a computational framework we developed for fully 3D filament motion that combines unit quaternions, implicit geometric time integration, quasi-Newton methods, and fast, matrix-free methods for hydrodynamic interactions and it will also be presented.
Sperm have got the bends
The journey of development begins with sperm swimming through the female reproductive tract en-route to the egg. In order to successfully complete this journey sperm must beat a single flagellum, propelling themselves through a wide range of fluids, from liquified semen to viscous cervical mucus. It is well-known that the beating tail is driven by an array of 9 microtubule doublets surrounding a central pair, with interconnecting dynein motors generating shear forces and driving elastic wave propagation. Despite this knowledge, the exact mechanism by which coordination of these motors drives oscillating waves along the flagellum remains unknown; hypothesised mechanisms include curvature control, sliding control, and geometric clutch. In this talk we will discuss the mechanisms of flagellar bending, and present a simple model of active curvature that is able to produce many of the various sperm waveforms that are seen experimentally, including those in low and high viscosity fluids and after a cell has ‘hyperactivated’ (a chemical process thought to be key for fertilization). We will show comparisons between these simulated waveforms and sperm that have been experimentally tracked, and discuss methods for fitting simulated mechanistic parameters to these real cells.