Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Symmetry, Equivalence and Molecular Self-Organization



K Van Workum, Jack F. Douglas


Abstract: Self-organization is central to the formation of numerous biological structures and the emulation of this process through the creation of synthetic counterparts offers great promise for nanofabrication. Our approach to understanding the principles governing this process is inspired by existing models and measurements on the self-organization of actin, tubulin and the ubiquitous icosahedral structures of viral capsids. We introduce a family of simple potentials that give rise to the self-organization of chain-like, random surface ( membrane ), tubular ( nanotube ) and hollow icosahedral structures that are similar in many respects to their biological counterparts. The potentials involve equivalent particles and an interplay between directional (dipolar, multipolar) and short range (van der Waals) interactions. Specifically, we find that the dipolar potential, having a continuous rotational symmetry about the dipolar axis, gives rise to chain formation, while particles with multi-polar potentials having discrete rotational symmetries (square quadrupole or triangular ring of dipoles or hexapole ) lead to the self-organization of sheet, nanotube, and hollow icosahedral geometries. These changes in the geometry of self-organization are accompanied by significant changes in the character of the thermodynamic self-organization transitions and the kinetics of the growth process.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)


dipole moments, nanotube, polymerization transition, random surface, self-organization, Viral Capsid Organization


Van, K. and Douglas, J. (2006), Symmetry, Equivalence and Molecular Self-Organization, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), [online], (Accessed May 22, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created March 1, 2006, Updated February 17, 2017