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Register a new userDisordered biopolymer filament bundles: Topological defects and kinks
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Valentin M. Slepukhin
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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, i.e., 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.
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We use continuum theory to show that chirality is a key thermodynamic control parameter for the aggregation of biopolymers: chirality produces a stable disperse phase of hexagonal bundles under moderately poor solvent conditions, as has been observed in {it in-vitro} studies of F-actin [O. Pelletier {it et al.}, Phys. Rev. Lett. {bf 91}, 148102 (2003)]. The large characteristic radius of these chiral bundles is not determined by a mysterious long-range molecular interaction but by in-plane shear elastic stresses generated by the interplay between a chiral torque and an unusual, but universal, non-linear gauge term in the strain tensor of ordered chains that is imposed by rotational invariance.
We discuss the response of biopolymer filament bundles bound by transient cross linkers to compressive loading. These systems admit a mechanical instability at stresses typically below that of traditional Euler buckling. In this instability, there is thermally-activated pair production of topological defects that generate localized regions of bending -- kinks. These kinks shorten the bundles effective length thereby reducing the elastic energy of the mechanically loaded structure. This effect is the thermal analog of the Schwinger effect, in which a sufficiently large electric field causes electron-positron pair production. We discuss this analogy and describe the implications of this analysis for the mechanics of biopolymer filament bundles of various types under compression.
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