The (k,ℓ)(k,\ell)-rainbow index of random graphs

A tree in an edge colored graph is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers $k$, $\ell$ with $k\geq 3$, the \emph{$(k,\ell)$-rainbow index} $rx_{k,\ell}(G)$ of $G$ is the minimum number of colors needed in an edge-coloring of $G$ such that for any set $S$ of $k$ vertices of $G$, there exist $\ell$ internally disjoint rainbow trees connecting $S$. This concept was introduced by Chartrand et. al., and there have been very few related results about it. In this paper, We establish a sharp threshold function for $rx_{k,\ell}(G_{n,p})\leq k$ and $rx_{k,\ell}(G_{n,M})\leq k,$ respectively, where $G_{n,p}$ and $G_{n,M}$ are the usually defined random graphs.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1212.6845, arXiv:1310.278

Potato virus Y HC-Pro reduces the ATPase activity of NtMinD, which results in enlarged chloroplasts in HC-Pro transgenic tobacco

Potato virus Y (PVY) is an important plant virus and causes great losses every year. Viral infection often leads to abnormal chloroplasts. The first step of chloroplast division is the formation of FtsZ ring (Z-ring), and the placement of Z-ring is coordinated by the Min system in both bacteria and plants. In our lab, the helper-component proteinase (HC-Pro) of PVY was previously found to interact with the chloroplast division protein NtMinD through a yeast two-hybrid screening assay and a bimolecular fluorescence complementation (BiFC) assay in vivo. Here, we further investigated the biological significance of the NtMinD/HC-Pro interaction. We purified the NtMinD and HC-Pro proteins using a prokaryotic protein purification system and tested the effect of HC-Pro on the ATPase activity of NtMinD in vitro. We found that the ATPase activity of NtMinD was reduced in the presence of HC-Pro. In addition, another important chloroplast division related protein, NtMinE, was cloned from the cDNA of Nicotiana tabacum. And the NtMinD/NtMinE interaction site was mapped to the C-terminus of NtMinD, which overlaps the NtMinD/HC-Pro interaction site. Yeast three-hybrid assay demonstrated that HC-Pro competes with NtMinE for binding to NtMinD. HC-Pro was previously reported to accumulate in the chloroplasts of PVY-infected tobacco and we confirmed this result in our present work. The NtMinD/NtMinE interaction is very important in the regulation of chloroplast division. To demonstrate the influence of HC-Pro on chloroplast division, we generated HC-Pro transgenic tobacco with a transit peptide to retarget HC-Pro to the chloroplasts. The HC-Pro transgenic plants showed enlarged chloroplasts. Our present study demonstrated that the interaction between HC-Pro and NtMinD interfered with the function of NtMinD in chloroplast division, which results in enlarged chloroplasts in HC-Pro transgenic tobacco. The HC-Pro/NtMinD interaction may cause the formation of abnormal chloroplasts in PVY-infected plants

Medicago truncatula transporter database: a comprehensive database resource for M. truncatula transporters

<p>Abstract</p> <p>Background</p> <p><it>Medicago truncatula </it>has been chosen as a model species for genomic studies. It is closely related to an important legume, alfalfa. Transporters are a large group of membrane-spanning proteins. They deliver essential nutrients, eject waste products, and assist the cell in sensing environmental conditions by forming a complex system of pumps and channels. Although studies have effectively characterized individual <it>M. truncatula </it>transporters in several databases, until now there has been no available systematic database that includes all transporters in <it>M. truncatula</it>.</p> <p>Description</p> <p>The <it>M. truncatula </it>transporter database (MTDB) contains comprehensive information on the transporters in <it>M. truncatula</it>. Based on the TransportTP method, we have presented a novel prediction pipeline. A total of 3,665 putative transporters have been annotated based on International Medicago Genome Annotated Group (IMGAG) V3.5 V3 and the <it>M. truncatula </it>Gene Index (MTGI) V10.0 releases and assigned to 162 families according to the transporter classification system. These families were further classified into seven types according to their transport mode and energy coupling mechanism. Extensive annotations referring to each protein were generated, including basic protein function, expressed sequence tag (EST) mapping, genome locus, three-dimensional template prediction, transmembrane segment, and domain annotation. A chromosome distribution map and text-based Basic Local Alignment Search Tools were also created. In addition, we have provided a way to explore the expression of putative <it>M. truncatula </it>transporter genes under stress treatments.</p> <p>Conclusions</p> <p>In summary, the MTDB enables the exploration and comparative analysis of putative transporters in <it>M. truncatula</it>. A user-friendly web interface and regular updates make MTDB valuable to researchers in related fields. The MTDB is freely available now to all users at <url>http://bioinformatics.cau.edu.cn/MtTransporter/</url>.</p

De novo transcriptome analysis of Medicago falcata reveals novel insights about the mechanisms underlying abiotic stress-responsive pathway

BACKGROUND: The entire world is facing a deteriorating environment. Understanding the mechanisms underlying plant responses to external abiotic stresses is important for breeding stress-tolerant crops and herbages. Phytohormones play critical regulatory roles in plants in the response to external and internal cues to regulate growth and development. Medicago falcata is one of the stress-tolerant candidate leguminous species and is able to fix atmospheric nitrogen. This ability allows leguminous plants to grow in nitrogen deficient soils. METHODS: We performed Illumina sequencing of cDNA prepared from abiotic stress treated M. falcata. Sequencedreads were assembled to provide a transcriptome resource. Transcripts were annotated using BLASTsearches against the NCBI non-redundant database and gene ontology definitions were assigned. Acomparison among the three abiotic stress treated samples was carried out. The expression of transcriptswas confirmed with qRT-PCR. RESULTS: We present an abiotic stress-responsive M. falcata transcriptome using next-generation sequencing data from samples grown under standard, dehydration, high salinity, and cold conditions. We combined reads from all samples and de novo assembled 98,515 transcripts to build the M. falcata gene index. A comprehensive analysis of the transcriptome revealed abiotic stress-responsive mechanisms underlying the metabolism and core signalling components of major phytohormones. We identified nod factor signalling pathways during early symbiotic nodulation that are modified by abiotic stresses. Additionally, a global comparison of homology between the M. falcata and M. truncatula transcriptomes, along with five other leguminous species, revealed a high level of global sequence conservation within the family. CONCLUSIONS: M. falcata is shown to be a model candidate for studying abiotic stress-responsive mechanisms in legumes. This global gene expression analysis provides new insights into the biochemical and molecular mechanisms involved in the acclimation to abiotic stresses. Our data provides many gene candidates that might be used for herbage and crop breeding. Additionally, FalcataBase (http://bioinformatics.cau.edu.cn/falcata/) was built for storing these data. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12864-015-2019-x) contains supplementary material, which is available to authorized users