Quenched and topological disorder in filament networks and kinked bundles

The filament networks are common in the living world, from the intracellular cytoskeleton in our cells to the extracellular matrix outside them. These filament networks typically include highly cross-linked bundles of nearly parallel filaments. In this talk, I explore the structure and mechanics of cross-linked filament bundles focusing on the role of quenched defects in bundles.
Experiments and simulations have shown that cross-linked bundles often contain highly localized bends, referred as kinks. This is surprising since the elastic ground state of the constituent filaments is straight. Simulations confirm that kinks occur in the absence of external forces or torques. In this talk, I show that kinks can be attributed to one of three classes of defects in the bundle: loops, braids, and dislocations. I determine the angle of the kinks associated with these defects and show that braids admit a discontinuous transition between kinks and straight defects as a function of a single control parameter related to the cross-linker binding energy, size, and filament bending modulus. Using this analysis and a similar one associated with loops and dislocations, I discuss the role of the defects of each type for kink production i n various biopolymer bundle systems including collagen fibers, F-actin bundles, and condensed DNA.
I examine the slow dynamics of defects in the annealing of bundles with transient cross linkers, showing how they combine, annihilate, or diffuse off the ends of the bundle as it ages. The addition of an external compressive load on the bundle leads to braid/anti-braid pair production in a way resembling the Schwinger effect for particle-antiparticle pair production in a strong electric field.
Finally, I observe that these defects introduce soft hinges into the stiff bundles even if they do not lead to a kink. This suggests that defects may play an important role in the collective elastic response of the network of biopolymer bundles.