BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:UW-Madison-Physics-Events BEGIN:VEVENT SEQUENCE:0 UID:UW-Physics-Event-8361 DTSTART:20230817T190000Z DURATION:PT1H0M0S DTSTAMP:20260414T031152Z LAST-MODIFIED:20230727T153227Z LOCATION:5310 Chamberlin SUMMARY:Biophysical applications of Lie groups and moving frames\, Gra duate Program Event\, Wilson B Lough\, Department of Physics Graduate Student DESCRIPTION:Living matter is often composed of microstructures which p ossess rotational degrees of freedom\, in addition to the translationa l degrees of freedom which describe the point-like material particles of classical continuum mechanics. Dynamics of these materials must acc ount for interactions between microstructures which are mediated by co uple stresses. Lie theory and Cartan's method of moving frames provide s a natural framework in which both translational and rotational aspec ts of microstructured materials can be treated in a unified manner. In this framework\, the state of the material is described by a collecti on of fields which take values in the special Euclidean group and its Lie algebra. These fields are governed by Euler-Poincaré equations wh ich enforce the local balance of linear and angular momentum. In this dissertation\, we develop theoretical and computational tools for mode ling these generalized continua. We then apply these methods to a numb er of biophysical systems.
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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-Poincaré 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-Poincaré 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