Morphogenesis and self-organization of persistent filaments confined within flexible biopolymeric shells

Abstract

We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics simulations. Compliant, DNA-like filaments are found to undergo a continuous crossover from two distinct surface-ordered quadrupolar states, both characterized by tetrahedral patterns of topological defects, to either longitudinal or latitudinal bipolar structures with increasing polymer concentrations. These transitions, along with the intermediary arrangements that they involve, may be attributed to the combination of an orientational wetting phenomenon with subtle density- and contour-length-dependent variations in the elastic anisotropies of the corresponding liquid crystal phases. Conversely, the organization of rigid, microtubule-like polymers evidences a progressive breakdown of continuum elasticity theory as chain dimensions become comparable to the equilibrium radius of the encapsulating membrane. In this case, we observe a gradual shift from prolate, tactoid-like morphologies to oblate, erythrocyte-like structures with increasing contour lengths, which is shown to arise from the interplay between nematic ordering, polymer and membrane buckling. We further provide numerical evidence of a number of yet-unidentified, self-organized states in such confined systems of stiff achiral filaments, including spontaneous spiral smectic assemblies, faceted polyhedral and twisted bundle-like arrangements. Our results are quantified through the introduction of several order parameters and an unsupervised learning scheme for the localization of surface topological defects, and are in excellent agreement with field-theoretical predictions as well as classical elastic theories of thin rods and spherical shells.