Graph editing to a fixed target

For a fixed graph H, the H-Minor Edit problem takes as input a graph G and an integer k and asks whether G can be modified into H by a total of at most k edge contractions, edge deletions and vertex deletions. Replacing edge contractions by vertex dissolutions yields the H-Topological Minor Edit problem. For each problem we show polynomial-time solvable and NP-complete cases depending on the choice of H. Moreover, when G is AT-free, chordal or planar, we show that H-Minor Edit is polynomial-time solvable for all graphs H

Minimal disconnected cuts in planar graphs

The problem of finding a disconnected cut in a graph is NP-hard in general but polynomial-time solvable on planar graphs. The problem of finding a minimal disconnected cut is also NP-hard but its computational complexity is not known for planar graphs. We show that it is polynomial-time solvable on 3-connected planar graphs but NP-hard for 2-connected planar graphs. Our technique for the first result is based on a structural characterization of minimal disconnected cuts in 3-connected K 3,3 -free-minor graphs and on solving a topological minor problem in the dual. We show that the latter problem can be solved in polynomial-time even on general graphs. In addition we show that the problem of finding a minimal connected cut of size at least 3 is NP-hard for 2-connected apex graphs

List coloring in the absence of a linear forest.

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H

The yeast P5 type ATPase, Spf1, regulates manganese transport into the endoplasmic reticulum

The endoplasmic reticulum (ER) is a large, multifunctional and essential organelle. Despite intense research, the function of more than a third of ER proteins remains unknown even in the well-studied model organism Saccharomyces cerevisiae. One such protein is Spf1, which is a highly conserved, ER localized, putative P-type ATPase. Deletion of SPF1 causes a wide variety of phenotypes including severe ER stress suggesting that this protein is essential for the normal function of the ER. The closest homologue of Spf1 is the vacuolar P-type ATPase Ypk9 that influences Mn2+ homeostasis. However in vitro reconstitution assays with Spf1 have not yielded insight into its transport specificity. Here we took an in vivo approach to detect the direct and indirect effects of deleting SPF1. We found a specific reduction in the luminal concentration of Mn2+ in ∆spf1 cells and an increase following it’s overexpression. In agreement with the observed loss of luminal Mn2+ we could observe concurrent reduction in many Mn2+-related process in the ER lumen. Conversely, cytosolic Mn2+-dependent processes were increased. Together, these data support a role for Spf1p in Mn2+ transport in the cell. We also demonstrate that the human sequence homologue, ATP13A1, is a functionally conserved orthologue. Since ATP13A1 is highly expressed in developing neuronal tissues and in the brain, this should help in the study of Mn2+-dependent neurological disorders

Mitochondrial Oxidative Stress Alters a Pathway in Caenorhabditis elegans Strongly Resembling That of Bile Acid Biosynthesis and Secretion in Vertebrates

Mammalian bile acids (BAs) are oxidized metabolites of cholesterol whose amphiphilic properties serve in lipid and cholesterol uptake. BAs also act as hormone-like substances that regulate metabolism. The Caenorhabditis elegans clk-1 mutants sustain elevated mitochondrial oxidative stress and display a slow defecation phenotype that is sensitive to the level of dietary cholesterol. We found that: 1) The defecation phenotype of clk-1 mutants is suppressed by mutations in tat-2 identified in a previous unbiased screen for suppressors of clk-1. TAT-2 is homologous to ATP8B1, a flippase required for normal BA secretion in mammals. 2) The phenotype is suppressed by cholestyramine, a resin that binds BAs. 3) The phenotype is suppressed by the knock-down of C. elegans homologues of BA–biosynthetic enzymes. 4) The phenotype is enhanced by treatment with BAs. 5) Lipid extracts from C. elegans contain an activity that mimics the effect of BAs on clk-1, and the activity is more abundant in clk-1 extracts. 6) clk-1 and clk-1;tat-2 double mutants show altered cholesterol content. 7) The clk-1 phenotype is enhanced by high dietary cholesterol and this requires TAT-2. 8) Suppression of clk-1 by tat-2 is rescued by BAs, and this requires dietary cholesterol. 9) The clk-1 phenotype, including the level of activity in lipid extracts, is suppressed by antioxidants and enhanced by depletion of mitochondrial superoxide dismutases. These observations suggest that C. elegans synthesizes and secretes molecules with properties and functions resembling those of BAs. These molecules act in cholesterol uptake, and their level of synthesis is up-regulated by mitochondrial oxidative stress. Future investigations should reveal whether these molecules are in fact BAs, which would suggest the unexplored possibility that the elevated oxidative stress that characterizes the metabolic syndrome might participate in disease processes by affecting the regulation of metabolism by BAs

ATP-binding cassette (ABC) transporters in normal and pathological lung

ATP-binding cassette (ABC) transporters are a family of transmembrane proteins that can transport a wide variety of substrates across biological membranes in an energy-dependent manner. Many ABC transporters such as P-glycoprotein (P-gp), multidrug resistance-associated protein 1 (MRP1) and breast cancer resistance protein (BCRP) are highly expressed in bronchial epithelium. This review aims to give new insights in the possible functions of ABC molecules in the lung in view of their expression in different cell types. Furthermore, their role in protection against noxious compounds, e.g. air pollutants and cigarette smoke components, will be discussed as well as the (mal)function in normal and pathological lung. Several pulmonary drugs are substrates for ABC transporters and therefore, the delivery of these drugs to the site of action may be highly dependent on the presence and activity of many ABC transporters in several cell types. Three ABC transporters are known to play an important role in lung functioning. Mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene can cause cystic fibrosis, and mutations in ABCA1 and ABCA3 are responsible for respectively Tangier disease and fatal surfactant deficiency. The role of altered function of ABC transporters in highly prevalent pulmonary diseases such as asthma or chronic obstructive pulmonary disease (COPD) have hardly been investigated so far. We especially focused on polymorphisms, knock-out mice models and in vitro results of pulmonary research. Insight in the function of ABC transporters in the lung may open new ways to facilitate treatment of lung diseases

Reconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs

A k-colouring of a graph G=(V,E) is a mapping c:V→{1,2,…,k} such that c(u)≠c(v) whenever uv is an edge. The reconfiguration graph of the k-colourings of G contains as its vertex set the k-colourings of G, and two colourings are joined by an edge if they differ in colour on just one vertex of G. We introduce a class of k-colourable graphs, which we call k-colour-dense graphs. We show that for each k-colour-dense graph G, the reconfiguration graph of the ℓ-colourings of G is connected and has diameter O(|V|2), for all ℓ≥k+1. We show that this graph class contains the k-colourable chordal graphs and that it contains all chordal bipartite graphs when k=2. Moreover, we prove that for each k≥2 there is a k-colourable chordal graph G whose reconfiguration graph of the (k+1)-colourings has diameter Θ(|V|2)

Computing subset transversals in H-free graphs

We study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph H as an induced subgraph. By combining known and new results, we determine the computational complexity of both problems on H-free graphs for every graph H except when H=sP1+P4 for some s≥1 . As part of our approach, we introduce the Subset Vertex Cover problem and prove that it is polynomial-time solvable for (sP1+P4) -free graphs for every s≥1