Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with an isotropic phase.

Nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere; the well-known examples are crystals and nematic liquid crystal droplets. In this work, we explore experimentally and theoretically the toroidal in shape nuclei of columnar lyotropic chromonic liquid crystals coexisting with the isotropic phase. The geometry of these toroids depends strongly on concentrations of the disodium cromoglycate (DSCG) and the crowding agent, polyethylene glycol (PEG). High concentrations of DSCG and PEG result in thick toroids with small central holes, while low concentrations yield thin toroids with wide holes. The multitude of the observed shapes is explained by the balance of bending elasticity and anisotropic interfacial tension.

A theoretical modeling framework for motile and colonial harmful algae.

Climate change is leading to an increase in severity, frequency, and distribution of harmful algal blooms across the globe. For many harmful algae species in eutrophic lakes, the formation of such blooms is controlled by three factors: the lake hydrodynamics, the vertical motility of the algae organisms, and the ability of the organisms to form colonies. Here, using the common cyanobacterium Microcystis aeruginosa as an example, we develop a model that accounts for both vertical transport and colony dynamics. At the core of this treatment is a model for aggregation. For this, we used Smoluchowski dynamics containing parameters related to Brownian motion, turbulent shear, differential setting, and cell-to-cell adhesion. To arrive at a complete description of bloom formation, we place the Smoluchowski treatment as a reaction term in a set of one-dimensional advection-diffusion equations, which account for the vertical motion of the algal cells through molecular and turbulent diffusion and self-regulating buoyant motion. Results indicate that Smoluchowski aggregation qualitatively describes the colony dynamics of M. aeruginosa. Further, the model demonstrates wind-induced mixing is the dominant aggregation process, and the rate of aggregation is inversely proportional to algal concentration. Because blooms of Microcystis typically consist of large colonies, both of these findings have direct consequences to harmful algal bloom formation. While the theoretical framework outlined in this manuscript was derived for M. aeruginosa, both motility and colony formation are common among bloom-forming algae. As such, this coupling of vertical transport and colony dynamics is a useful step for improving forecasts of surface harmful algal blooms.

Shear flow of active matter in thin channels.

We study the shear flow of active filaments confined in a thin channel for extensile and contractile fibers. We apply the Ericksen-Leslie equations of liquid crystal flow with an activity source term. The dimensionless form of this system includes the Ericksen, activity, and Reynolds numbers, together with the aspect ratio of the channel, as the main driving parameters. We perform a normal mode stability analysis of the base shear flow. For both types of fibers, we arrive at a comprehensive description of the stability properties and their dependence on the parameters of the system. The transition to unstable frequencies in extensile fibers occurs at a positive threshold value of the activity parameter, whereas for contractile ones a complex behavior is found at low absolute value of the activity number. The latter might be an indication of the biologically relevant plasticity and phase transition issues. In contrast with extensile fibers, flows of contractile ones are also found to be highly sensitive to the Reynolds number. The work on extensile fibers is guided by experiments on active filaments in confined channels and aims at quantifying their findings in the prechaotic regime.

Ion-dependent DNA configuration in bacteriophage capsids.

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Fine structure of viral dsDNA encapsidation.

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.

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

Electro-osmosis in nematic liquid crystals.

We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. We verify the model by comparing its predictions to the results of the experiments on the substrate-controlled liquid-crystal-enabled electrokinetics. In the experiments, a nematic liquid crystal confined to a thin planar cell with surface-patterned anchoring conditions exhibits electro-osmotic flows along the "guiding rails" imposed by the spatially varying director. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix and the full set of nematic viscosities.