Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes

The (1,2)-Step Competition Graph of a Tournament

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C1,2(D), as the graph on V(D) where {x,y}∈E(C1,2(D)) if and only if there exists a vertex z≠x,y, such that either dD−y(x,z)=1 and dD−x(y,z)≤2 or dD−x(y,z)=1 and dD−y(x,z)≤2. In this paper, we characterize the (1,2)-step competition graphs of tournaments and extend our results to the (i,k)-step competition graph of a tournament

Digraphs with Isomorphic Underlying and Domination Graphs: Pairs of Paths

A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv ϵ E (dom (D)) whenever (u, z) ϵ A (D) or (v, z) ϵ A (D) for any other vertex z ϵ A (D). Here, we consider directed graphs whose underlying graphs are isomorphic to their domination graphs. Specifically, digraphs are completely characterized where UGc (D) is the union of two disjoint paths

A Characterization of Connected (1,2)-Domination Graphs of Tournaments

Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is an edge of G whenever x and y form a (1,2)-dominating pair in D. In this paper, we characterize all connected graphs that can be (I, 2)-dominating graphs of tournaments

Kings and Heirs: A Characterization of the (2,2)-domination Graphs of Tournaments

In 1980, Maurer coined the phrase king when describing any vertex of a tournament that could reach every other vertex in two or fewer steps. A (2,2)-domination graph of a digraph D, dom2,2(D), has vertex set V(D), the vertices of D, and edge uv whenever u and v each reach all other vertices of D in two or fewer steps. In this special case of the (i,j)-domination graph, we see that Maurer’s theorem plays an important role in establishing which vertices form the kings that create some of the edges in dom2,2(D). But of even more interest is that we are able to use the theorem to determine which other vertices, when paired with a king, form an edge in dom2,2(D). These vertices are referred to as heirs. Using kings and heirs, we are able to completely characterize the (2,2)-domination graphs of tournaments

Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0,1}-Matrix Ranks

A digraph D is a local out-tournament if the outset of every vertex is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corresponding results for biclique covers and partitions of the digraph are provided

Characterization of digraphs with equal domination graphs and underlying graphs

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)] whenever (u,z)∈A(D) or (v,z)∈A(D) for every other vertex z∈V(D). The underlying graph of a digraph D, UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given

Genetic Abolishment of Hepatocyte Proliferation Activates Hepatic Stem Cells

Quiescent hepatic stem cells (HSCs) can be activated when hepatocyte proliferation is compromised. Chemical injury rodent models have been widely used to study the localization, biomarkers, and signaling pathways in HSCs, but these models usually exhibit severe promiscuous toxicity and fail to distinguish damaged and non-damaged cells. Our goal is to establish new animal models to overcome these limitations, thereby providing new insights into HSC biology and application. We generated mutant mice with constitutive or inducible deletion of Damaged DNA Binding protein 1 (DDB1), an E3 ubiquitin ligase, in hepatocytes. We characterized the molecular mechanism underlying the compensatory activation and the properties of oval cells (OCs) by methods of mouse genetics, immuno-staining, cell transplantation and gene expression profiling. We show that deletion of DDB1 abolishes self-renewal capacity of mouse hepatocytes in vivo, leading to compensatory activation and proliferation of DDB1-expressing OCs. Partially restoring proliferation of DDB1-deficient hepatocytes by ablation of p21, a substrate of DDB1 E3 ligase, alleviates OC proliferation. Purified OCs express both hepatocyte and cholangiocyte markers, form colonies in vitro, and differentiate to hepatocytes after transplantation. Importantly, the DDB1 mutant mice exhibit very minor liver damage, compared to a chemical injury model. Microarray analysis reveals several previously unrecognized markers, including Reelin, enriched in oval cells. Here we report a genetic model in which irreversible inhibition of hepatocyte duplication results in HSC-driven liver regeneration. The DDB1 mutant mice can be broadly applied to studies of HSC differentiation, HSC niche and HSCs as origin of liver cancer

High and low levels of an NTRK2-driven genetic profile affect motor- and cognition-associated frontal gray matter in prodromal Huntington’s disease

This study assessed how BDNF (brain-derived neurotrophic factor) and other genes involved in its signaling influence brain structure and clinical functioning in pre-diagnosis Huntington’s disease (HD). Parallel independent component analysis (pICA), a multivariate method for identifying correlated patterns in multimodal datasets, was applied to gray matter concentration (GMC) and genomic data from a sizeable PREDICT-HD prodromal cohort (N = 715). pICA identified a genetic component highlighting NTRK2, which encodes BDNF’s TrkB receptor, that correlated with a GMC component including supplementary motor, precentral/premotor cortex, and other frontal areas (p < 0.001); this association appeared to be driven by participants with high or low levels of the genetic profile. The frontal GMC profile correlated with cognitive and motor variables (Trail Making Test A (p = 0.03); Stroop Color (p = 0.017); Stroop Interference (p = 0.04); Symbol Digit Modalities Test (p = 0.031); Total Motor Score (p = 0.01)). A top-weighted NTRK2 variant (rs2277193) was protectively associated with Trail Making Test B (p = 0.007); greater minor allele numbers were linked to a better performance. These results support the idea of a protective role of NTRK2 in prodromal HD, particularly in individuals with certain genotypes, and suggest that this gene may influence the preservation of frontal gray matter that is important for clinical functioning.This project was supported by 1U01NS082074 (V.C. and J.T., co-principal investigators) from the National Institutes of Health, National Institute of Neurological Disorders and Stroke. The PREDICT-HD study was supported by NIH/NINDS grant 5R01NS040068 awarded to J.P.; CHDI Foundation, Inc., A3917 and 6266 awarded to J.P.; Cognitive and Functional Brain Changes in Preclinical Huntington’s Disease (HD) 5R01NS054893 awarded to J.P.; 4D Shape Analysis for Modeling Spatiotemporal Change Trajectories in Huntington’s 1U01NS082086; Functional Connectivity in Premanifest Huntington’s Disease 1U01NS082083; and Basal Ganglia Shape Analysis and Circuitry in Huntington’s Disease 1U01NS082085 awarded to Christopher A. Ross

The RAB39B p.G192R mutation causes X-linked dominant Parkinson’s disease

Objective: To identify the causal gene in a multi-incident U.S. kindred with Parkinson’s disease (PD). Methods: We characterized a family with a classical PD phenotype in which 7 individuals (5 males and 2 females) were affected with a mean age at onset of 46.1 years (range, 29-57 years). We performed whole exome sequencing on 4 affected and 1 unaffected family members. Sanger-sequencing was then used to verify and genotype all candidate variants in the remainder of the pedigree. Cultured cells transfected with wild-type or mutant constructs were used to characterize proteins of interest. Results: We identified a missense mutation (c.574G > A; p.G192R) in the RAB39B gene that closely segregated with disease and exhibited X-linked dominant inheritance with reduced penetrance in females. The mutation occurred in a highly conserved amino acid residue and was not observed among 87,725 X chromosomes in the Exome Aggregation Consortium dataset. Sequencing of the RAB39B coding region in 587 familial PD cases yielded two additional mutations (c.428C > G [p.A143G] and c.624_626delGAG [p.R209del]) that were predicted to be deleterious in silico but occurred in families that were not sufficiently informative to assess segregation with disease. Experiments in PC12 and SK-N-BE(2)C cells demonstrated that p.G192R resulted in mislocalization of the mutant protein, possibly by altering the structure of the hypervariable C-terminal domain which mediates intracellular targeting. Conclusions: Our findings implicate RAB39B, an essential regulator of vesicular-trafficking, in clinically typical PD. Further characterization of normal and aberrant RAB39B function might elucidate important mechanisms underlying neurodegeneration in PD and related disorders. Electronic supplementary material The online version of this article (doi:10.1186/s13024-015-0045-4) contains supplementary material, which is available to authorized users