Multicomponent microscopic shells buckle into various polyhedra, as observed in many organelles.

From:
Graziano Vernizzi (1) Rastko Sknepnek (1) and Monica Olvera de la Cruz (1,2,3)
(1) Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208;
(2) Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208; and
(3) Department of Chemistry, Northwestern University, Evanston, IL 60208

“Platonic and Archimedean geometries in multicomponent elastic membranes”, Proc Natl Acad Sci U S A. 2011 March 15; 108(11): 4292–4296, doi: 10.1073/pnas.1012872108

ABSTRACT Large crystalline molecular shells, such as some viruses and fullerenes, buckle spontaneously into icosahedra. Meanwhile multicomponent microscopic shells buckle into various polyhedra, as observed in many organelles. Although elastic theory explains one-component icosahedral faceting, the possibility of buckling into other polyhedra has not been explored. We show here that irregular and regular polyhedra, including some Archimedean and Platonic polyhedra, arise spontaneously in elastic shells formed by more than one component. By formulating a generalized elastic model for inhomogeneous shells, we demonstrate that coassembled shells with two elastic components buckle into polyhedra such as dodecahedra, octahedra, tetrahedra, and hosohedra shells via a mechanism that explains many observations, predicts a new family of polyhedral shells, and provides the principles for designing microcontainers with specific shapes and symmetries for numerous applications in materials and life sciences.

Page 66 / 360