| Many interesting problems in cellular biophysics involve the dynamics of filamentary elastic objects with bend and twist degrees of freedom, moving in a viscous environment. Motivated by the mysterious macrofiber formation in B. subtilis and the rotational dynamics of bacterial flagella, we have sought to establish a general theoretical structure to deal with elastic filament dynamics, analyze these equations for model systems, and to determine the important physical parameters that set the dynamical scales for these systems.;We first studied the novel problem of a rotationally forced elastic filament in a viscous fluid [1] to examine the competition between twist injection, twist diffusion, and writhing motions. Two dynamical regimes separated by a Hopf bifurcation were discovered: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling.;Next, we extended elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality [2]. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom was developed using the natural frame of space curves, spanning from the inviscid limit to the viscously-overdamped regime applicable to cellular biology.;To be able to measure the elastic properties of cell-sized objects, such as bacterial fibers [3], we utilized an optical trapping system to study the relaxation of a single fiber of B. subtilis which was bent and then released. By analyzing the relaxation time, the bending modulus of the bacterial cell wall was measured to be 1.6 ± 0.6 × 10 −12 erg·cm. This number is important in understanding the scales of forces and torques that are present in macrofiber formation and motion, lending insight into the mechanism behind these phenomena. |
