How geometric frustration shapes twisted fibres, inside and out: competing morphologies of chiral filament assembly

Abstract

Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure-finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. 'frustration escape'). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

“…The standard computational approach for studying self-assembly, using coarse-grained molecular modeling (17)(18)(19), provides access to these pathways and equilibria with more physically detailed models, in which interactions emerge because of distance-dependent energy functions rather than the rate-controlled events of RD models. A coarse molecular model thus naturally can accommodate a range of structures or defects (17,19,20) and capture emergent cooperativity, strain, and localization of components (21,22). However, they are still relatively limited in the length and timescales of dynamics they can access, which does not extend to the cell scale.…”

Chiral and achiral mechanisms of self-limiting assembly of twisted bundles

“…The former, dislocations and disclinations in the cross sectional lattice [41,42,50] or tilt-grain boundaries in the "smectic-like" order of crystalline bundles [60], have been predicted to arise as means to mitigate the costs of geometric frustration associated with introducing twist to the respective 2D columnar and 3D solid order of bundles. The latter effect of anisotropic crosssection shape may result in widely observed twisted, tape morphologies of bundles, and it has also been predicted to occur as elastically-driven response of surface shape to twist frustration [38,39]. While these effects left out the present study, it is reasonable to expect that the would influence the quantitative, but not quantitative, conclusions presented above.…”

“…The following subsections introduce the continuum energetics associated with each of these types of order. As many of these elastic costs have been described elsewhere [14,39,43], hereonly a brief review of key results if given, citing previous work where possible, and relegating details of new analytical results in the appendices.…”

Constant spacing in filament bundles

“…equi-triangular packing). Physical models of twisted cohesive bundles have shown that this metric frustration promotes accumulation of inter-filament stresses [62] or else stabilize topological defects [20] in the cross sectional order of twisted cohesive bundles. Notably, the Gaussian curvature of helical domains is concentrated in the core, as the metric flattens in the limit r W  ¥.…”