How to generate pentagonal symmetry using Turing systems

We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can be mimicked, such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids

Non-linear effects on Turing patterns: time oscillations and chaos.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, Turing patterns oscillate in time, a phenomenon which is expected to occur only in a three morphogen system. When varying a single parameter, a series of bifurcations lead to period doubling, quasi-periodic and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examined the Turing conditions for obtaining a diffusion driven instability and discovered that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. All this results demonstrates the limitations of the linear analysis for reaction-diffusion systems

Turing patterns resulting from a Sturm-Liouville problem

Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot \left( \mathcal{D} ( {\mathbf x} ) \nabla {\mathbf u} \right)$. We found that the conditions for Turing instability are the same as in the case of homogeneous diffusion but the nonlinear analysis must be generalized to consider general orthogonal eigenfunctions instead of the standard Fourier approach. The particular case $\mathcal{D} (x)= 1-x^2$, where solutions are linear combinations of Legendre polynomials, is studied in detail. From the developed general nonlinear analysis, conditions for producing stripes and spots are obtained, which are numerically verified using the Schaneknberg system. Unlike to the case with homogeneous diffusion, and due to the properties of the Legendre polynomials, stripped and spotted patterns with variable wavelength are produced, and a change from stripes to spots is predicted when the wavelength increases. The patterns obtained can model biological systems where stripes or spots accumulate close to the boundaries and the theory developed here can be applied to study Turing patterns associated to other eigenfunctions related with Sturm-Liouville problems.Comment: 15 pages, 4 figure

Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a wave-guide that exhibits a spatial-frequency selection analogous to that characteristic of a synthetic "cochlea". Both, experimental and theoretical results are reported here.Comment: 4 pages, 4 figure

A 3D geological model of Campo de Cartagena, SE Spain : Hydrogeological implications

Knowledge and understanding of geologic basins for hydrogeologic purposes requires an accurate 3D geological architecture representation. For model building, surface and subsurface data integration with the interpretation of geophysical survey and lithologic logs is needed. A methodology to reconstruct the geometric architecture of the sedimentary basin and relationships among stratigraphic formations, as well as to define hydrostratigraphic units, has been applied to the Campo de Cartagena Neogene formations. Data analysis included seismic reflection profiles and gravimetric data from oil exploration, electric resistivity surveys and 491 lithologic logs. The 3D model obtained from a close integration of stratigraphic and geophysical data was generated through a computerbased tool. It presents a common framework and a good starting point for hydrogeologic applications

Spatial patterning in modified Turing systems: Application to pigmentation patterns on marine fish

In this paper we extend the study of Turing models to investigate the rôle of boundary conditions, parameter modulation, domain growth, and coupling of models. Our numerical simulations show that such modifications lead to patterns that cannot be reproduced by the standard model. By comparing our results with pigmentation patterning on marine fish we conclude that such models may have wider application than originally imagined

The physiology of ex vitro pineapple ( Ananas comosus L. Merr. var MD-2) as CAM or C3 is regulated by environmental conditions: proteomic and transcriptomic profiles

Pineapple is one of the most important tropical crops worldwide. The use of Temporary Immersion Bioreactors (TIB) for the first stages of pineapple propagation enables precise control of plant growth, increases the rate of plant multiplication, decreases space, energy and labor requirements for pineapple plants in commercial micropropagation. Once the plantlets are ready to be taken from the reactors, they are carefully acclimatized to adapt to natural environmental conditions, and a facultative C3/CAM metabolism in the first two months of growth is characteristic of pineapple plants, depending on environmental conditions. We subjected two sets of micropropagated pineapple plants to C3 and CAM-inducing environmental conditions, determined by light intensity/relative humidity (respectively 40μmol.m-2s-1/85% and 260μmol.m-2.s-1/50%). Leaves of pineapple plants grown under CAM inducing conditions showed higher leaf thickness and more developed cuticles and hypodermic tissue. Proteomic profiles of several proteins, isoenzyme patterns and transcriptomic profiles were also measured. Five major spots were isolated and identified, two of them for the first time in Ananas comosus (OEE 1; OEE 2) and the other three corresponding to small fragments of the large subunit of Rubisco (LSU). PEPC and PEPCK were also detected by immunobloting of 2DE at the end of both ex vitro treatments (C3/CAM) during the dark period. Isoenzymes of SOD and CAT were identified by electrophoresis and the transcript levels of OEE 1 and CAT were associated with CAM metabolism in pineapple plants

Production, characterization and testing of antibacterial PVA membranes loaded with HA-Ag3PO4 nanoparticles, produced by SC-CO2 phase inversion

BACKGROUND: Silver-loaded hydroxyapatite nanoparticles were incorporated into poly(vinyl alcohol) (PVA) membranes obtained by supercritical CO2 (SC-CO2) assisted phase inversion. Ag3PO4 crystals of 2.2 ± 0.6 nm were dispersed in synthesized needle-like hydroxyapatite nanoparticles (20 × 65 nm) and were uniformly deposited on the internal surfaces of the PVA membranes. Operative conditions to produce membranes by SC-CO2, PVA concentration and the effect on membrane porosity and morphology were studied. RESULTS: Solutions at 20% w/w PVA produced membranes with cellular morphology and nanoporous walls, whereas 30% and 50% w/w solutions produced nanostructured membranes. Silver ions were released from PVA membranes mainly by diffusion according to the Peppas–Sahlin model. Membranes obtained at 20% w/w PVA showed a significant E. coli inhibition at an Ag concentration of 9 ppm, reaching the minimal inhibitory concentration (MIC) and improving the bactericidal activity of the nanoparticles. CONCLUSION: A concentration of Ag3PO4 crystals of about 22 ppm was calculated as being capable of completely destroying these bacteria, reaching the minimum bactericidal concentration (MBC)

Rotational Correlation Functions of Single Molecules

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict non-exponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.Comment: 5 pages, 4 figure