Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Gel-Electrophoresis and Diffusion of Ring-Shaped DNA

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of hernias. It is included in the model as long range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in polymer gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling-ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial 2D obstacle arrays (W.D. Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In the zero-field case an exact solution of the model steady-state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres

Orthogonal photoswitching in a multifunctional molecular system

The wavelength-selective, reversible photocontrol over various molecular processes in parallel remains an unsolved challenge. Overlapping ultraviolet-visible spectra of frequently employed photoswitches have prevented the development of orthogonally responsive systems, analogous to those that rely on wavelength-selective cleavage of photo-removable protecting groups. Here we report the orthogonal and reversible control of two distinct types of photoswitches in one solution, that is, a donor-acceptor Stenhouse adduct (DASA) and an azobenzene. The control is achieved by using three different wavelengths of irradiation and a thermal relaxation process. The reported combination tolerates a broad variety of differently substituted photoswitches. The presented system is also extended to an intramolecular combination of photoresponsive units. A model application for an intramolecular combination of switches is presented, in which the DASA component acts as a phase-transfer tag, while the azobenzene moiety independently controls the binding to alpha-cyclodextrin

Worldwide Relationships in the Fern Genus Pteridium (Bracken) Based on Nuclear Genome Markers

PREMISE: Spore-bearing plants are capable of dispersing very long distances. However, it is not known if gene flow can prevent genetic divergence in widely distributed taxa. Here we address this issue, and examine systematic relationships at a global geographic scale for the fern genus Pteridium. METHODS: We sampled plants from 100 localities worldwide, and generated nucleotide data from four nuclear genes and two plastid regions. We also examined 2801 single nucleotide polymorphisms detected by a restriction site-associated DNA approach. RESULTS: We found evidence for two distinct diploid species and two allotetraploids between them. The “northern” species (Pteridium aquilinum) has distinct groups at the continental scale (Europe, Asia, Africa, and North America). The northern European subspecies pinetorum appears to involve admixture among all of these. A sample from the Hawaiian Islands contained elements of both North American and Asian P. aquilinum. The “southern” species, P. esculentum, shows little genetic differentiation between South American and Australian samples. Components of African genotypes are detected on all continents. CONCLUSIONS: We find evidence of distinct continental-scale genetic differentiation in Pteridium. However, on top of this is a clear signal of recent hybridization. Thus, spore-bearing plants are clearly capable of extensive long-distance gene flow; yet appear to have differentiated genetically at the continental scale. Either gene flow in the past was at a reduced level, or vicariance is possible even in the face of long-distance gene flow

Photoactivation of MDM2 Inhibitors:Controlling Protein-Protein Interaction with Light

Selectivity remains a major challenge in anticancer therapy, which potentially can be overcome by local activation of a cytotoxic drug. Such triggered activation can be obtained through modification of a drug with a photoremovable protecting group (PPG), and subsequent irradiation in the chosen place and time. Herein, the design, synthesis and biological evaluation is described of a photoactivatable MDM2 inhibitor, PPG-idasanutlin, which exerts no functional effect on cellular outgrowth, but allows for the selective, noninvasive activation of antitumor properties upon irradiation visible light, demonstrating activation with micrometer, single cell precision. The generality of this method has been demonstrated by growth inhibition of multiple cancer cell lines showing p53 stabilization and subsequent growth inhibition effects upon irradiation. Light activation to regulate protein-protein interactions between MDM2 and p53 offers exciting opportunities to control a multitude of biological processes and has the potential to circumvent common selectivity issues in antitumor drug development

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Diversity of ferns and lycophytes in Brazil

This compilation of ferns and lycophytes in Brazil is an update of the one published in 2010 in Catálogo de Plantas e Fungos do Brasil. The methodology consisted in collecting data from regional checklists, taxonomic revisions, and selected databases. Invited specialists improved the list accessing a website housed at the Jardim Botânico do Rio de Janeiro. The results show 1,253 species: 1,111 of ferns and 142 of lycophytes. This number is 6.5% higher than the previous one (1,176 spp.). The percentage of endemic species decreased from 38.2% to 36.7%. We recognized 36 families and 133 genera (vs. 33 families, 121 genera in 2010). The 10 most diverse families are Pteridaceae (196 spp.), Dryopteridaceae (179), Polypodiaceae (164), Hymenophyllaceae (90), Thelypteridaceae (86), Aspleniaceae (78), Lycopodiaceae (64), Selaginellaceae (55), Anemiaceae (51), and Cyatheaceae (45). The three most diverse genera are still Elaphoglossum (87 spp.), Thelypteris (85), and Asplenium (74). The richest phytogeographic domain continues to be in the Atlantic Rainforest with 883 species which also has the largest number of endemic and threatened species, followed by the Amazon Rainforest (503), Cerrado (269), Pantanal (30), Caatinga (26), and Pampa (eight). Minas Gerais remains as the richest state (657 spp. vs. 580 in 2010).Esta compilação de samambaias e licófitas do Brasil é uma atualização daquela de 2010, no Catálogo de Plantas e Fungos do Brasil. A metodologia consistiu na reunião de dados de listas regionais, revisões de grupos e bancos de dados selecionados. Especialistas convidados melhoraram a lista através do acesso a um sítio da web do Jardim Botânico do Rio Janeiro. Os resultados apontam uma diversidade de 1.253 espécies, sendo 1.111 samambaias e 142 licófitas. Este número é 6,5% maior que o anterior (1.176 espécies). As espécies endêmicas decresceram de 38,2% para 36,7%. Foram reconhecidas 36 famílias e 133 gêneros (vs. 33 famílias, 121 gêneros em 2010). As dez famílias mais diversas são: Pteridaceae (196 espécies), Dryopteridaceae (179), Polypodiaceae (164), Hymenophyllaceae (90), Thelypteridaceae (86), Aspleniaceae (78), Lycopodiaceae (64), Selaginellaceae (55), Anemiaceae (51) e Cyatheaceae (45). Os três gêneros mais diversos continuam sendo Elaphoglossum (87 espécies), Thelypteris (85) e Asplenium (74). O Domínio Fitogeográfico mais rico continua sendo a Mata Atlântica (883 espécies) e também com mais espécies endêmicas e ameaçadas, seguido pela Amazônia (503 espécies), Cerrado (269), Pantanal (30), Caatinga (26) e Pampa (oito). Minas Gerais permanece como o estado com maior riqueza (657 espécies vs. 580 em 2010)