The inertia of weighted unicyclic graphs

Let $G_w$ be a weighted graph. The \textit{inertia} of $G_w$ is the triple $In(G_w)=\big(i_+(G_w),i_-(G_w),$ $i_0(G_w)\big)$, where $i_+(G_w),i_-(G_w),i_0(G_w)$ are the number of the positive, negative and zero eigenvalues of the adjacency matrix $A(G_w)$ of $G_w$ including their multiplicities, respectively. $i_+(G_w)$, $i_-(G_w)$ is called the \textit{positive, negative index of inertia} of $G_w$, respectively. In this paper we present a lower bound for the positive, negative index of weighted unicyclic graphs of order $n$ with fixed girth and characterize all weighted unicyclic graphs attaining this lower bound. Moreover, we characterize the weighted unicyclic graphs of order $n$ with two positive, two negative and at least $n-6$ zero eigenvalues, respectively.Comment: 23 pages, 8figure

Single-Cell Transcriptomics of Proliferative Phase Endometrium: Systems Analysis of Cell–Cell Communication Network Using CellChat

The endometrium thickness increases by which endometrial angiogenesis occurs in parallel with the rapid growth of endometrium during the proliferative phase, which is orchestrated by complex cell–cell interactions and cytokine networks. However, the intercellular communication has not been fully delineated. In the present work, we studied the cell–cell interactome among cells of human proliferative phase endometrium using single-cell transcriptomics. The transcriptomes of 33,240 primary endometrial cells were profiled at single-cell resolution. CellChat was used to infer the cell–cell interactome by assessing the gene expression of receptor–ligand pairs across cell types. In total, nine cell types and 88 functionally related signaling pathways were found. Among them, growth factors and angiogenic factor signaling pathways, including EGF, FGF, IGF, PDGF, TGFb, VEGF, ANGPT, and ANGPTL that are highly associated with endometrial growth, were further analyzed and verified. The results showed that stromal cells and proliferating stromal cells represented cell–cell interaction hubs with a large number of EGF, PDGF incoming signals, and FGF outgoing signals. Endothelial cells exhibited cell–cell interaction hubs with a plenty of VEGF, TGFb incoming signals, and ANGPT outgoing signals. Unciliated epithelial cells, ciliated epithelial cells, and macrophages exhibited cell–cell interaction hubs with substantial EGF outgoing signals. Ciliated epithelial cells represented cell–cell interaction hubs with a large number of IGF and TGFb incoming signals. Smooth muscle cells represented lots of PDGF incoming signals and ANGPT and ANGPTL outgoing signals. This study deconvoluted complex intercellular communications at the single-cell level and predicted meaningful biological discoveries, which deepened the understanding of communications among endometrial cells

Computational Detection and Functional Analysis of Human Tissue-Specific A-to-I RNA Editing

A-to-I RNA editing is a widespread post-transcriptional modification event in vertebrates. It could increase transcriptome and proteome diversity through recoding the genomic information and cross-linking other regulatory events, such as those mediated by alternative splicing, RNAi and microRNA (miRNA). Previous studies indicated that RNA editing can occur in a tissue-specific manner in response to the requirements of the local environment. We set out to systematically detect tissue-specific A-to-I RNA editing sites in 43 human tissues using bioinformatics approaches based on the Fisher's exact test and the Benjamini & Hochberg false discovery rate (FDR) multiple testing correction. Twenty-three sites in total were identified to be tissue-specific. One of them resulted in an altered amino acid residue which may prevent the phosphorylation of PARP-10 and affect its activity. Eight and two tissue-specific A-to-I RNA editing sites were predicted to destroy putative exonic splicing enhancers (ESEs) and exonic splicing silencers (ESSs), respectively. Brain-specific and ovary-specific A-to-I RNA editing sites were further verified by comparing the cDNA sequences with their corresponding genomic templates in multiple cell lines from brain, colon, breast, bone marrow, lymph, liver, ovary and kidney tissue. Our findings help to elucidate the role of A-to-I RNA editing in the regulation of tissue-specific development and function, and the approach utilized here can be broadened to study other types of tissue-specific substitution editing

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Degree resistance distance of unicyclic graphs

Let G be a connected graph with vertex set V(G). The degree resistance distance of G is defined as the sum over all pairs of vertices of the terms [d(u)+d(v)] R(u,v), where d(u) is the degree of vertex u, and R(u,v) denotes the resistance distance between u and v. In this paper, we characterize n-vertex unicyclic graphs having minimum and second minimum degree resistance distance