Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the “grooves” of two neighboring filaments. We develop a coarse-grained model to investigate the interplay between the geometry of binding and mechanics of both linker and filament distortion, and we show that crosslinking in parallel bundles of helical filaments generates intrinsic torques of the type that tend to wind bundle superhelically about its central axis. Crosslinking mediates a non-linear competition between the preference for bundle twist and the size-dependent mechanical cost of filament bending, ultimately giving rise a rich phase diagram including dispersed filaments, macroscopic condensates and bundles of finite diameter.
Superhelically twisted, rope-like assemblies are common structural elements in a range of biological materials deriving from the assembly of protein filaments, including cellulose, fibrin and certain fiber-forming collagens. To study the intermolecular forces arising within the common geometry as well as the collective mechanical properties of these fibrous assemblies, we develop the unique, nonlinear elastic properties of twisted filament bundles deriving from generic properties of two-dimensional line-ordered materials. Within the framework of continuum elasticity, we show that interfilament twist generically gives rise to stresses in the cross-section of bundles that generically frustrate their lateral growth. Surprisingly, we find that these twist-induced stresses can be relieved, in part, by topological defects—certain arrangements disclinations, dislocations and grain-boundary “scars”— in the cross-sectional packing of the bundle. Therefore, we predict a novel spectrum of low energy structures occurring generically for filament bundles of sufficient twist, punctuated by a complex array energetically-stabilized lattice defects, making this important class of biological materials a new example of a condensed matter system in which defects are necessary components of the thermodynamic groundstate.
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