  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.
