Abstract
We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.
| Original language | English (US) |
|---|---|
| Article number | 20200111 |
| Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 379 |
| Issue number | 2201 |
| DOIs | |
| State | Published - 2021 |
Bibliographical note
Funding Information:Data accessibility. This article has no additional data. Authors’ contributions. This paper follows, in part, the PhD thesis dissertation by the first author, Lindsey Hiltner (November 2018). The thesis was supervised by M.C.C. The biological aspects of the work have been advised by the two mathematics biology coauthors, J.A. and M.V. Competing interests. We declare we have no competing interests. Funding. M.C.C. and L.H. knowledge the support from the National Science Foundation, grant nos DMS-DMREF 1729589 and DMS-1816740. M.C.C. also knowledge the hospitality of the Isaac Newton Institute at Cambridge University, UK and the support from the Simmons Foundation. J.A. and M.V. acknowledge the support of the National Science Foundation, grant no. DMS-1817156.
Publisher Copyright:
© 2021 The Author(s).
Keywords
- Absoltue minimizer
- Bacteriophage virus
- Chromonic liquid crystals
- Polyconvex functions
- Solid-liquid transition
- Toroidal clusters