Topological defects produce kinks in biopolymer filament bundles

Abstract

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate, analytically, numerically, and experimentally, that such bundles can be kinked, that is, have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross-links, a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross-links, the last two effects lead to the topologically protected kinked states. Finally, we explore, numerically and analytically, the transition of the metastable kinked state to the stable straight bundle.

Braiding Dynamics in Semiflexible Filament Bundles under Oscillatory Forcing

“…Because of this effect, the large- limit also exhibits kinks. We note that this large- limit occurs around , which we believe is obtainable in some biopolymer systems, including condensed DNA [ 9 , 10 ], cross-linked intermediate filaments [ 11 , 12 ] and perhaps for collagen [ 5 , 13 , 14 , 15 ]. We should note that we introduced the torque with the opposite sign from that used here in Ref.…”

“…For a more complete description of the group of braid operations, please see Ref. [ 5 ] and the references therein. The case of a single braid, or a braid/anti-braid pair is particularly simple to analyze because, in these configurations, two filaments within the three-filament bundle remain cross-linked everywhere, while the third filament passes back and forth in between them as shown in Figure 1 A,B.…”

“…Previously, we have shown that bundles support a set of topological defects -loop, braids, and dislocations 4 . The lifetime of these defects is quite long, growing with the length of the bundle, since they cannot be removed by local rearrangements of the cross linking on the bundle.…”

“…We explore here a particular type of stress relaxation through the production and movement of defects in cross-linked bundles. Previously, we showed that bundles support a set of topological defects—loop, braids, and dislocations [ 5 ]. The lifetime of these defects is quite long, growing with the length of the bundle, since they cannot be removed by local rearrangements of the cross linking on the bundle.…”

Braiding Dynamics in Semiflexible Filament Bundles Under Oscillatory Forcing

“…We explore here particular type of stress relaxation through the production and movement of defects in cross-linked bundles. Previously, we have shown that bundles support a set of topological defects -loop, braids, and dislocations 4 . The lifetime of these defects is quite long, growing with the length of the bundle, since they cannot be removed by local rearrangements of the cross linking on the bundle.…”