Mean-field limit and Semiclassical Expansion of a Quantum Particle System

We consider a quantum system constituted by $N$ identical particles interacting by means of a mean-field Hamiltonian. It is well known that, in the limit $N\to\infty$, the one-particle state obeys to the Hartree equation. Moreover, propagation of chaos holds. In this paper, we take care of the $\hbar$ dependence by considering the semiclassical expansion of the $N$-particle system. We prove that each term of the expansion agrees, in the limit $N\to\infty$, with the corresponding one associated with the Hartree equation. We work in the classical phase space by using the Wigner formalism, which seems to be the most appropriate for the present problem.Comment: 44 pages, no figure

Derivation of the Fick's Law for the Lorentz Model in a low density regime

We consider the Lorentz model in a slab with two mass reservoirs at the boundaries. We show that, in a low density regime, there exists a unique stationary solution for the microscopic dynamics which converges to the stationary solution of the heat equation, namely to the linear profile of the density. In the same regime the macroscopic current in the stationary state is given by the Fick's law, with the diffusion coefficient determined by the Green-Kubo formula.Comment: 33 pages, 7 figure

miRVine: a microRNA expression atlas of grapevine based on small RNA sequencing

We analyzed 70 small RNA libraries, prepared from berries, inflorescences, tendrils, buds, carpels, stamens and other samples at different developmental stages. One-hundred and ten known and 175 novel miRNAs have been identified and a wide grapevine expression atlas has been described. The distribution of miRNA abundance reveals that 22 novel miRNAs are specific to stamen, and two of them are, interestingly, involved in ethylene biosynthesis, while only few miRNAs are highly specific to other organs. Thirty-eight miRNAs are present in all our samples, suggesting a role in key regulatory circuit. On the basis of miRNAs abundance and distribution across samples and on the estimated correlation, we suggest that miRNA expression define organ identity. We performed target prediction analysis and focused on miRNA expression analysis in berries and inflorescence during their development, providing an initial functional description of the identified miRNAs

Russell-like bodies in plant seeds share common features with prolamin bodies and occur upon recombinant protein production

Although many recombinant proteins have been produced in seeds at high yields without adverse effects on the plant, endoplasmic reticulum (ER) stress and aberrant localization of endogenous or recombinant proteins have also been reported. The production of murine interleukin-10 (mIL-10) in Arabidopsis thaliana seeds resulted in the de novo formation of ER-derived structures containing a large fraction of the recombinant protein in an insoluble form. These bodies containing mIL-10 were morphologically similar to Russell bodies found in mammalian cells. We confirmed that the compartment containing mIL-10 was enclosed by ER membranes, and 3D electron microscopy revealed that these structures have a spheroidal shape. Another feature shared with Russell bodies is the continued viability of the cells that generate these organelles. To investigate similarities in the formation of Russell-like bodies and the plant-specific protein bodies formed by prolamins in cereal seeds, we crossed plants containing ectopic ER-derived prolamin protein bodies with a line accumulating mIL-10 in Russell-like bodies. This resulted in seeds containing only one population of protein bodies in which mIL-10 inclusions formed a central core surrounded by the prolamin-containing matrix, suggesting that both types of protein aggregates are together removed from the secretory pathway by a common mechanism. We propose that, like mammalian cells, plant cells are able to form Russell-like bodies as a self-protection mechanism, when they are overloaded with a partially transport-incompetent protein, and we discuss the resulting challenges for recombinant protein production

Semiclassical Propagation of Coherent States for the Hartree equation

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in $L^2$ by C \sqrt {\var}, \var being the Planck constant. Finally we present a full formal asymptotic expansion

Effects of abiotic stress on plants: a systems biology perspective

The natural environment for plants is composed of a complex set of abiotic stresses and biotic stresses. Plant responses to these stresses are equally complex. Systems biology approaches facilitate a multi-targeted approach by allowing one to identify regulatory hubs in complex networks. Systems biology takes the molecular parts (transcripts, proteins and metabolites) of an organism and attempts to fit them into functional networks or models designed to describe and predict the dynamic activities of that organism in different environments. In this review, research progress in plant responses to abiotic stresses is summarized from the physiological level to the molecular level. New insights obtained from the integration of omics datasets are highlighted. Gaps in our knowledge are identified, providing additional focus areas for crop improvement research in the future

cDNA-AFLP analysis of plant and pathogen genes expressed in grapevine infected with Plasmopara viticola

<p>Abstract</p> <p>Background</p> <p>The oomycete <it>Plasmopara viticola </it>(Berk. and Curt.) Berl. and de Toni causes downy mildew in grapevine (<it>Vitis vinifera </it>L.). This pathogen is strictly biotrophic, thus completely dependent on living host cells for its survival. The molecular basis of compatibility and disease development in this system is poorly understood. We have carried out a large-scale cDNA-AFLP analysis to identify grapevine and <it>P. viticola </it>genes associated with the infection process.</p> <p>Results</p> <p>We carried out cDNA-AFLP analysis on artificially infected leaves of the susceptible cultivar Riesling at the oil spot stage, on water-treated leaves and on a sample of pure sporangia as controls. Selective amplifications with 128 primer combinations allowed the visualization of about 7000 transcript-derived fragments (TDFs) in infected leaves, 1196 of which (17%) were differentially expressed. We sequenced 984 fragments, 804 of which were identified as grapevine transcripts after homology searching, while 96 were homologous to sequences in <it>Phytophthora </it>spp. databases and were attributed to <it>P. viticola</it>. There were 82 orphan TDFs. Many grapevine genes spanning almost all functional categories were downregulated during infection, especially genes involved in photosynthesis. Grapevine genes homologous to known resistance genes also tended to be repressed, as were several resistance gene analogs and carbonic anhydrase (recently implicated in pathogen resistance). In contrast, genes encoding cytoskeletal components, enzymes of the phenylpropanoid and beta-oxidation pathways, and pathogenesis related proteins were primarily upregulated during infection. The majority of <it>P. viticola </it>transcripts expressed <it>in planta </it>showed homology to genes of unknown function or to genomic <it>Phytophthora </it>sequences, but genes related to metabolism, energy production, transport and signal transduction were also identified.</p> <p>Conclusion</p> <p>This study provides the first global catalogue of grapevine and <it>P. viticola </it>genes expressed during infection, together with their functional annotations. This will help to elucidate the molecular basis of the infection process and identify genes and chemicals that could help to inhibit the pathogen.</p