In order to further develop fundamental science and technologies of the future, it is pivotal to learn how to design, produce, and control the structure, properties, and dynamic behavior of soft materials within a broad range of spatial length scales, from the nanometer scale to macroscale. The ability of soft matter to form a plethora of complex and functional structures with tunable local and non-local responses to external excitation can easily be exploited once well understood.
This colloquium focuses on mathematical studies of chromonic liquid crystals, also called liquid crystals of life, since their properties are found in many biological systems such as condensed DNA in free solution, encapsidated DNA in bacteriophage viruses, known to attack bacteria, and so being at the core of infection processes. The chromonic liquid crystal family embraces a very broad range of materials, examples of which include nucleotides, DNA and RNA, dyes and food additives (e.g. the dye Sunset Yellow), proteins, and pharmaceutical products. We explore the quantitative relations between two systems, Hexagonal Chromonic Phases of Sunset Yellow and Encapsidated Bacteriophage Viruses, differing in length scales of the order of one milion. We study modeling and analysis of molecular (1 nm) self-assembly into supramolecular aggregates (nm-μm) with properties defined by a balance of anisotropic surface tension and bulk m) with properties defined by a balance of anisotropic surface tension and bulk elasticity. While the in-vitro liquid crystal experiments provide information on living systems, viruses teach us how to construct drug delivery devices. The semiflexible polymer nature of DNA molecules turns the viral genome into a ”drill” able to penetrate several rows of cancer cells.
The analysis of constrained free boundary problems for chromonic clusters is central to the present work. These include mathematical studies of packing of viral DNA, showing that the spooling configuration present in nature is the one with minimum energy. We also present a newly designed numerical method to compute such configurations.