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

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

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

Genome-wide microarray analysis of tomato roots showed defined responses to iron deficiency

<p>Abstract</p> <p>Background</p> <p>Plants react to iron deficiency stress adopting different kind of adaptive responses. Tomato, a <it>Strategy I </it>plant, improves iron uptake through acidification of rhizosphere, reduction of Fe³⁺to Fe²⁺and transport of Fe²⁺into the cells. Large-scale transcriptional analyses of roots under iron deficiency are only available for a very limited number of plant species with particular emphasis for <it>Arabidopsis thaliana</it>. Regarding tomato, an interesting model species for <it>Strategy I </it>plants and an economically important crop, physiological responses to Fe-deficiency have been thoroughly described and molecular analyses have provided evidence for genes involved in iron uptake mechanisms and their regulation. However, no detailed transcriptome analysis has been described so far.</p> <p>Results</p> <p>A genome-wide transcriptional analysis, performed with a chip that allows to monitor the expression of more than 25,000 tomato transcripts, identified 97 differentially expressed transcripts by comparing roots of Fe-deficient and Fe-sufficient tomato plants. These transcripts are related to the physiological responses of tomato roots to the nutrient stress resulting in an improved iron uptake, including regulatory aspects, translocation, root morphological modification and adaptation in primary metabolic pathways, such as glycolysis and TCA cycle. Other genes play a role in flavonoid biosynthesis and hormonal metabolism.</p> <p>Conclusions</p> <p>The transcriptional characterization confirmed the presence of the previously described mechanisms to adapt to iron starvation in tomato, but also allowed to identify other genes potentially playing a role in this process, thus opening new research perspectives to improve the knowledge on the tomato root response to the nutrient deficiency.</p

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

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

Cloning and expression analysis of a Petunia hybrida flower specific mitotic-like cyclin

AbstractA cyclin cDNA clone (Pethy;CycB1;1) was isolated from a Petunia hybrida ovary specific cDNA library. Sequence comparison revealed that Pethy;CYCB1;1 protein is highly homologous to mitotic B1 cyclins. Northern analysis and in situ hybridisation experiments showed that its expression is developmentally regulated and restricted to flower organs. We have attempted to define some of the cell division patterns which contribute to shaping each floral organ by analysing Pethy;CycB1;1 expression on Petunia flower sections. While in sepals, epidermis and parenchyma cell division patterns were comparable, there were two distinct cell division patterns in petals. In the epidermis, Pethy;CYCB1;1 expression was found both at the petal tip and along epidermis, whereas in the parenchyma only at the petal tips. In reproductive organs cell divisions were detected only in sporophytic tissues. No signals were detected inside meiotic cells

The ascorbic acid content of tomato fruits is associated with the expression of genes involved in pectin degradation

<p>Abstract</p> <p>Background</p> <p>High levels of ascorbic acid (AsA) in tomato fruits provide health benefits for humans and also play an important role in several aspects of plant life. Although AsA metabolism has been characterized in detail, the genetic mechanisms controlling AsA accumulation in tomatoes are poorly understood. The transcriptional control of AsA levels in fruits can be investigated by combining the advanced genetic and genomic resources currently available for tomato. A comparative transcriptomic analysis of fruit tissues was carried out on an introgression line containing a QTL promoting AsA accumulation in the fruit, using a parental cultivar with lower AsA levels as a reference.</p> <p>Results</p> <p>Introgression line IL 12-4 (<it>S. pennellii </it>in a <it>S. lycopersicum </it>background) was selected for transcriptomic analysis because it maintained differences in AsA levels compared to the parental genotypes M82 and <it>S. pennellii </it>over three consecutive trials. Comparative microarray analysis of IL 12-4 and M82 fruits over a 2-year period allowed 253 differentially-expressed genes to be identified, suggesting that AsA accumulation in IL 12-4 may be caused by a combination of increased metabolic flux and reduced utilization of AsA. In particular, the upregulation of a pectinesterase and two polygalacturonases suggests that AsA accumulation in IL12-4 fruit is mainly achieved by increasing flux through the L-galactonic acid pathway, which is driven by pectin degradation and may be triggered by ethylene.</p> <p>Conclusions</p> <p>Based on functional annotation, gene ontology classification and hierarchical clustering, a subset of the 253 differentially-expressed transcripts was used to develop a model to explain the higher AsA content in IL 12-4 fruits in terms of metabolic flux, precursor availability, demand for antioxidants, abundance of reactive oxygen species and ethylene signaling.</p

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

miRNAs are the most abundant class of small non-coding RNAs, and they are involved in post-transcriptional regulations, playing a crucial role in the refinement of genetic programming during plant development. Here we present a comprehensive picture of miRNA regulation in Vitis vinifera L. plant during its complete life cycle. Furthering our knowledge about the post-transcriptional regulation of plant development is fundamental to understand the biology of such an important crop