Curvature-induced cross-hatched order in two-dimensional semiflexible polymer networks

TL;DR

This paper explores how curvature in cylindrical geometries induces a cross-hatched fiber order in 2D semiflexible polymer networks, revealing a universal physical principle with implications for biological tissues and synthetic materials.

Contribution

It demonstrates that curvature-induced order arises from the energy trade-off in semiflexible fibers confined to cylinders, providing a new understanding of fiber organization in curved biological and synthetic systems.

Findings

Curvature causes fibers to adopt a cross-hatched pattern.

The order depends on the radius of the cylinder.

A simple model explains the physical mechanism behind this order.

Abstract

A recurring motif in the organization of biological tissues are networks of long, fibrillar protein strands effectively confined to cylindrical surfaces. Often, the fibers in such curved, quasi-2D geometries adopt a characteristic order: the fibers wrap around the central axis at an angle which varies with radius and, in several cases, is strongly bimodally distributed. In this Letter, we investigate the general problem of a 2D crosslinked network of semiflexible fibers confined to a cylindrical substrate, and demonstrate that in such systems the trade-off between bending and stretching energies, very generically, gives rise to cross-hatched order. We discuss its general dependency on the radius of the confining cylinder, and present an intuitive model that illustrates the basic physical principle of curvature-induced order. Our findings shed new light on the potential origin of some curiously universal fiber orientational distributions in tissue biology, and suggests novel ways in which synthetic polymeric soft materials may be instructed or programmed to exhibit preselected macromolecular ordering.