Graduate Program Events
Remodeling of biological membranes often involves interactions with helical ribbon-like protein filaments which polymerize on the membrane surface. Using a combination of moving frame and level-set methods to describe membrane geometry, we derive the constrained Euler-Poincaré equations governing a surface-bound flexible filament. We provide direct numerical evidence that the filament can undergo growth-induced buckling which results in highly localized forces and moments being applied to the membrane. This lends support to the conjecture that buckling of surface-bound polymers plays a role in overcoming energy barriers which resist topological transitions during cell division and vesicle formation. Our simulations also suggest that the chirality of curvature-sensing proteins plays a crucial role in their ability to navigate the membrane surface.
The twisting and writhing of a cell body and associated mechanical stresses 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 configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a dynamically evolving flagellar orientation field, we derive the Euler-Poincaré equations governing dynamics of the system and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium Proteus mirabilis. We identify a sequence of bifurcations as the body is made more compliant, due to both buckling and torsional instabilities. Our analysis reveals a minimal stiffness required of a cell, below which its motility is severely hampered.