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\nRemodeling of biological membran es often involves interactions with helical ribbon-like protein filame nts which polymerize on the membrane surface. Using a combination of m oving frame and level-set methods to describe membrane geometry\, we d erive the constrained Euler-PoincarĂ© equations governing a surface-bo und flexible filament. We provide direct numerical evidence that the f ilament can undergo growth-induced buckling which results in highly lo calized forces and moments being applied to the membrane. This lends s upport to the conjecture that buckling of surface-bound polymers plays a role in overcoming energy barriers which resist topological transit ions during cell division and vesicle formation. Our simulations also suggest that the chirality of curvature-sensing proteins plays a cruci al role in their ability to navigate the membrane surface.

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\n The twisting and writhing of a cell body and associated mechanical str esses is an underappreciated constraint on microbial self-propulsion. Multi-flagellated bacteria can even buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configu rations and steady-state dynamics then emerge which depend on the orga nism's mechanical properties and on the oriented distribution of flage lla along its surface. Modeling the cell body as a semi-flexible Kirch hoff rod and coupling the mechanics to a dynamically evolving flagella r orientation field\, we derive the Euler-PoincarĂ© equations governin g dynamics of the system and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium Prot eus mirabilis. We identify a sequence of bifurcations as the body is m ade more compliant\, due to both buckling and torsional instabilities. Our analysis reveals a minimal stiffness required of a cell\, below w hich its motility is severely hampered. URL:https://www.physics.wisc.edu/events/?id=8361 END:VEVENT END:VCALENDAR