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Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plank-shaped molecular compounds, we develop a first-principles effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses available data for a collection of viruses, aimed at applications to viral design. The outcome of the work is a mathematical model and its numerical algorithm, based on the method of finite elements, and computer simulations to identify and label the ordered and disordered regions of the capsid and calculate the inner pressure. It also presents the tools for the local reconstruction of the DNA "scaffolding" and the center curve of the filament within the capsid.

Sunset Yellow (SSY) is an aromatic heterocycle nano-sheet functionalized by hydrophilic sulphanate groups. SSY forms chromonic stacks and liquid crystal (LC) phases in aqueous solution. The DNA oligomer 5\ensuremath{'}-GCGCTTAAGCGC-3\ensuremath{'} is a self-complementary strand which forms duplexed B-form helices in aqueous solution, which, similarly, aggregate into chromonic stacks and form LC phases. Binary aqueous solutions of these two molecules were investigated using polarized optical microscopy, x-ray diffraction, and spectroscopy. At lower solute concentrations and/or higher temperatures these solutions form uniformly mixed single phases, including isotropic, chiral nematic, and hexagonal columnar LCs. At higher solute concentrations and/or lower temperatures, the uniform columnar solution separates into two columnar phases, one containing SSY with trace DNA and the other containing both SSY and DNA aggregates. The study of these solutions indicates that the mixed and unmixed phases are composed of single component SSY or DNA chromonic stacks, with the DNA stacks containing a small fraction of intercalated SSY, evidenced by structurally induced circular dichroism in the SSY absorption band. In the columnar monophase, the hexagonal lattice sites are occupied randomly by either DNA or SSY columns, with the column spacing varying continuously with the SSY-DNA mass ratio. The results demonstrate significant selectivity in the chromonic stacking of both molecules. The binding mode of these chromonic LCs may have applications to adaptive optics and nucleic acid chemistry.

An experimental and theoretical study of lyotropic chromonic liquid crystals (LCLCs) confined in cylinders with degenerate planar boundary conditions elucidates LCLC director configurations. When the Frank saddle-splay modulus is more than twice the twist modulus, the ground state adopts an inhomogeneous escaped-twisted configuration. Analysis of the configuration yields a large saddle-splay modulus, which violates Ericksen inequalities but not thermodynamic stability. Lastly, we observe point defects between opposite-handed domains, and we explain a preference for point defects over domain walls.

The dye sunset yellow (SY) forms columnar aggregates via pi-pi stacking in aqueous solutions. These aggregates develop orientational and translational order at elevated concentrations to exhibit the nematic (N) and columnar (C) mesophases. Positional-order correlation lengths of the aggregates in the directions parallel and perpendicular to the stacking direction were measured as functions of temperature, concentration, and ionic content of solutions with synchrotron x-ray scattering in magnetically aligned samples. Average length of aggregates (i.e., the number of SY molecules in an aggregate) grows monotonically with concentration while their effective transverse separation decreases. The scission energy, E , determined from the Arrhenius thermal evolution of the longitudinal correlation length, is found to be 4.3+/-0.3 kBT and 3.5+/-0.2 kBT , in the N and C phases, respectively. Temperature and concentration dependence of E suggests that chromonic aggregation is not an isodesmic process. The aggregate length decreases with decreasing pH when HCl is added to the solution.

X-ray scattering and various optical techniques are utilized to study the aggregation process and chromonic liquid crystal phase of the anionic monoazo dye Sunset Yellow FCF. The x-ray results demonstrate that aggregation involves pi-pi stacking of the molecules into columns, with the columns undergoing a phase transition to an orientationally ordered chromonic liquid crystal phase at high dye concentration. Optical absorption measurements on dilute solutions reveal that the aggregation takes place at all concentrations, with the average aggregation number increasing with concentration. A simple theory based on the law of mass action and an isodesmic aggregation process is in excellent agreement with the experimental data and yields a value for the "bond" energy between molecules in an aggregate. Measurements of the birefringence and order parameter are also performed as a function of temperature in the chromonic liquid crystal phase. The agreement between these results and a more complicated theory of aggregation is quite reasonable. Overall, these results both confirm that the aggregation process for some dyes is isodesmic and provide a second example of a well-characterized chromonic system.

We report on the optical properties of the nematic (N) phase formed by lyotropic chromonic liquid crystals (LCLCs) in well aligned planar samples. LCLCs belong to a broad class of materials formed by one-dimensional molecular self-assembly and are similar to other systems such as "living polymers" and "wormlike micelles." We study three water soluble LCLC forming materials: disodium chromoglycate, a derivative of indanthrone called Blue 27, and a derivative of perylene called Violet 20. The individual molecules have a planklike shape and assemble into rodlike aggregates that form the phase once the concentration exceeds about 0.1 M. The uniform surface alignment of the N phase is achieved by buffed polyimide layers. According to the light absorption anisotropy data, the molecular planes are on average perpendicular to the aggregate axes and thus to the nematic director. We determined the birefringence of these materials in the N and biphasic N-isotropic (I) regions and found it to be negative and significantly lower in the absolute value as compared to the birefringence of typical thermotropic low-molecular-weight nematic materials. In the absorbing materials Blue 27 and Violet 20, the wavelength dependence of birefringence is nonmonotonic because of the effect of anomalous dispersion near the absorption bands. We describe positive and negative tactoids formed as the nuclei of the new phase in the biphasic N-I region (which is wide in all three materials studied). Finally, we determined the scalar order parameter of the phase of Blue 27 and found it to be relatively high, in the range 0.72-0.79, which puts the finding into the domain of general validity of the Onsager model. However, the observed temperature dependence of the scalar order parameter points to the importance of factors not accounted for in the athermal Onsager model, such as interaggregate interactions and the temperature dependence of the aggregate length.

We describe director distortions in the nematic liquid crystal (LC) caused by a spherical particle with tangential surface orientation of the director and show that light transmittance through the distorted region is a steep function of the particle's size. The effect allows us to propose a real-time microbial sensor based on a nontoxic lyotropic chromonic LC (LCLC) that detects and amplifies the presence of immune complexes. A cassette is filled with LCLC, antibody, and antigen-bearing particles. Small and isolated particles cause no macroscopic distortions of the LCLC. Upon antibody-antigen binding, the growing immune complexes distort the director and cause detectable optical transmittance between crossed polarizers.