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.

A phenomenological model for interfacial water near hydrophilic polymers.

We propose a minimalist phenomenological model for the 'interfacial water' phenomenon that occurs near hydrophilic polymeric surfaces. We achieve this by combining a Ginzburg-Landau approach with Maxwell's equations which leads us to a well-posed model providing a macroscopic interpretation of experimental observations. From the derived governing equations, we estimate the unknown parameters using experimental measurements from the literature. The resulting profiles of the polarization and electric potential show exponential decay near the surface, in qualitative agreement with experiments. Furthermore, the model's quantitative prediction of the electric potential at the hydrophilic surface is in excellent agreement with experiments. The proposed model is a first step towards a more complete parsimonious macroscopic model that will, for example, help to elucidate the effects of interfacial water on cells (e.g. neuronal excitability), the effects of infrared neural stimulation or the effects of drugs mediated by interfacial water.

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.

Chromonic liquid crystals and packing configurations of bacteriophage viruses.

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'.

Stability analysis of flow of active extensile fibers in confined domains.

In this article, we study shear flow of active extensile filaments confined in a narrow channel. They behave as nematic liquid crystals that we assumed are governed by the Ericksen-Leslie equations of balance of linear and angular momentum. The addition of an activity source term in the Leslie stress captures the role of the biofuel prompting the dynamics. The dimensionless form of the governing system includes the Ericksen, activity, and Reynolds numbers together with the aspect ratio of the channel as the main driving parameters affecting the stability of the system. The active system that guides our analysis is composed of microtubules concentrated in bundles, hundreds of microns long, placed in a narrow channel domain, of aspect ratios in the range between 10-2 and 10-3 dimensionless units, which are able to align due to the combination of adenosine triphosphate-supplied energy and confinement effects. Specifically, this work aims at studying the role of confinement on the behavior of active matter. It is experimentally observed that, at an appropriately low activity and channel width, the active flow is laminar, with the linear velocity profile and the angle of alignment analogous to those in passive shear, developing defects and becoming chaotic, at a large activity and a channel aspect ratio. The present work addresses the laminar regime, where defect formation does not play a role. We perform a normal mode stability analysis of the base shear flow. A comprehensive description of the stability properties is obtained in terms of the driving parameters of the system. Our main finding, in addition to the geometry and magnitude of the flow profiles, and also consistent with the experimental observations, is that the transition to instability of the uniformly aligned shear flow occurs at a threshold value of the activity parameter, with the transition also being affected by the channel aspect ratio. The role of the parameters on the vorticity and angular profiles of the perturbing flow is also analyzed and found to agree with the experimentally observed transition to turbulent regimes. A spectral method based on Chebyshev polynomials is used to solve the generalized eigenvalue problems arising in the stability analysis.

Debonding waves in gel thin films.

We develop a mathematical model for the sliding of a gel sheet adhered to a moving substrate. The sliding takes place by the motion of detached region between the gel sheet and the substrates, i.e. the propagation of a Schallamach wave. Efficient numerical methods are developed to solve the problem. Numerical examples illustrate that the model can describe the Schallamach wave and are consistent with the existing experiments qualitatively.

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.

Subsurface nitrate reduction under wetlands takes place in narrow superficial zones.

This study aims to investigate the depth distribution of the Nitrate Reduction Potential (NRP) on a natural and a re-established wetland. The obtained NRP provides a valuable data of the driving factors affecting denitrification, the Dissimilatory Nitrate Reduction to Ammonium (DNRA) process and the performance of a re-established wetland. Intact soil cores were collected and divided in slices for the determination of Organic Matter (OM) through Loss of Ignition (LOI) as well as Dissolved Organic Carbon (DOC) and NRP spiking nitrate in batch tests. The Nitrate Reduction (NR) was fitted as a pseudo-first order rate constant (k) from where NRPs were obtained. NR took place in a narrow superficial zone showing a dropping natural logarithmic trend along depth. The main driving factor of denitrification, besides depth, was OM. Although, DOC and LOI could not express by themselves and absolute correlation with NRP, high amounts of DOC ensured enough quantity and quality of labile OM for NR. Besides, high concentration of LOI but a scarce abundance of DOC failed to drive NR. DNRA was only important in superficial samples with high contents of OM. Lastly, the high NRP of the re-established wetland confirms that wetlands can be restored satisfactorily.

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.

Effects of enhanced denitrification on hydrodynamics and microbial community structure in a soil column system.

Enhanced heterotrophic denitrification by adding glucose was investigated by means of a soil column experiment which simulated the groundwater flow. The carbon-to-nitrogen ratio was the main factor determining denitrification potential under experimental conditions. The influence of stimulated denitrification on the autochthonous microbial community was investigated by quantitative PCR (qPCR), and denaturing gradient gel electrophoresis (DGGE). The qPCR detection of the nosZ genes encoding nitrous oxide reductase, and the comparison of the abundances of 16S rRNA genes revealed that the addition of glucose enhanced denitrification leading to an increase in both the total eubacteria and, in particular, in the ratio of denitrifying bacteria, which represented the 21% of the total native eubacteria on the basis of nosZ/16S rRNA gene ratio. Microbial community profiling by DGGE indicated that ribotypes closely related to the genera Acidovorax and Hydrogenophaga (Comamonadaceae family) became enriched in the soil column. The effects of biomass occurrence in the column system on soil hydrodynamics, assessed by tracer studies, revealed a reduction of porosity and a significant increase of dispersivity that could be caused by the appearance of new functional microbial biomass in the aquifer material under enhanced denitrifying conditions. The importance of investigating the microbial growth in relation to the hydrodynamic effects, during enhanced denitrification, has been revealed in the column system experiments associated with the bioremediation. Combining microbial characterisation and hydrodynamic data in a soil column system permits us to gain an insight to the limiting factors of different stimulation strategies that can be applied in the field.

Denitrification in presence of acetate and glucose for bioremediation of nitrate-contaminated groundwater.

With the current increasing interest in aquifer denitrification, recent attention has been given to cost-effective in-situ treatments such as Enhanced In-Situ Biological Denitrification (EISBD), which intends to stimulate the indigenous bacterial activity by injecting an external organic substrate and/or nutrients to the aquifer matrix. Within this context, laboratory batch assays have been conducted to develop a strategy for in-situ denitrification of a nitrate-contaminated aquifer in Argentona, Catalonia (Spain). The assays were run under aerobic and anaerobic conditions at a temperature of 17 degrees C to better simulate the conditions of the aquifer. Acetate and glucose were added to assess their potential to promote heterotrophic denitrifying bacteria activity. Overall, the results revealed that indigenous micro-organisms had the potential of reducing nitrate under appropriate conditions. Nitrate removal was complete and faster under anaerobic conditions, though high nitrate removals were also attained under initial aerobic conditions when a readily organic compound was amended at a sufficient dosage. The results also revealed that a significant amount of the available organic carbon was consumed by processes other than denitrification, namely aerobic oxidation and other microbial oxidation processes. To sum up, the results of this study demonstrated that addition of organic compounds into the groundwater is a promising method for in-situ bioremediation of nitrate in the Argentona aquifer. This approach could potentially be applied to a number of situations in which nitrate concentration is elevated and where indigenous micro-organisms with potential to reduce nitrate are present within the aquifer material.