125 research outputs found
(Total) Vector Domination for Graphs with Bounded Branchwidth
Given a graph of order and an -dimensional non-negative
vector , called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
such that every vertex in (resp., in ) has
at least neighbors in . The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the -tuple dominating set problem (this is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto , where is the size of solution.Comment: 16 page
Minimal vertex covers on finite-connectivity random graphs - a hard-sphere lattice-gas picture
The minimal vertex-cover (or maximal independent-set) problem is studied on
random graphs of finite connectivity. Analytical results are obtained by a
mapping to a lattice gas of hard spheres of (chemical) radius one, and they are
found to be in excellent agreement with numerical simulations. We give a
detailed description of the replica-symmetric phase, including the size and the
entropy of the minimal vertex covers, and the structure of the unfrozen
component which is found to percolate at connectivity . The
replica-symmetric solution breaks down at . We give a simple
one-step replica symmetry broken solution, and discuss the problems in
interpretation and generalization of this solution.Comment: 32 pages, 9 eps figures, to app. in PRE (01 May 2001
The helper NLR immune protein NRC3 mediates the hypersensitive cell death caused by the cell-surface receptor Cf-4
Cell surface pattern recognition receptors (PRRs) activate immune responses that can include the hypersensitive cell death. However, the pathways that link PRRs to the cell death response are poorly understood. Here, we show that the cell surface receptor-like protein Cf-4 requires the intracellular nucleotide-binding domain leucine-rich repeat containing receptor (NLR) NRC3 to trigger a confluent cell death response upon detection of the fungal effector Avr4 in leaves of Nicotiana benthamiana. This NRC3 activity requires an intact N-terminal MADA motif, a conserved signature of coiled-coil (CC)-type plant NLRs that is required for resistosome-mediated immune responses. A chimeric protein with the N-terminal α1 helix of Arabidopsis ZAR1 swapped into NRC3 retains the capacity to mediate Cf-4 hypersensitive cell death. Pathogen effectors acting as suppressors of NRC3 can suppress Cf-4-triggered hypersensitive cell-death. Our findings link the NLR resistosome model to the hypersensitive cell death caused by a cell surface PRR
Two NLR immune receptors acquired high-affinity binding to a fungal effector through convergent evolution of their integrated domain
A subset of plant NLR immune receptors carry unconventional integrated domains in addition to their canonical domain architecture. One example is rice Pik-1 that comprises an integrated heavy metal-associated (HMA) domain. Here, we reconstructed the evolutionary history of Pik-1 and its NLR partner, Pik-2, and tested hypotheses about adaptive evolution of the HMA domain. Phylogenetic analyses revealed that the HMA domain integrated into Pik-1 before Oryzinae speciation over 15 million years ago and has been under diversifying selection. Ancestral sequence reconstruction coupled with functional studies showed that two Pik-1 allelic variants independently evolved from a weakly binding ancestral state to high-affinity binding of the blast fungus effector AVR-PikD. We conclude that for most of its evolutionary history the Pik-1 HMA domain did not sense AVR-PikD, and that different Pik-1 receptors have recently evolved through distinct biochemical paths to produce similar phenotypic outcomes. These findings highlight the dynamic nature of the evolutionary mechanisms underpinning NLR adaptation to plant pathogens
Nonrepetitive Colouring via Entropy Compression
A vertex colouring of a graph is \emph{nonrepetitive} if there is no path
whose first half receives the same sequence of colours as the second half. A
graph is nonrepetitively -choosable if given lists of at least colours
at each vertex, there is a nonrepetitive colouring such that each vertex is
coloured from its own list. It is known that every graph with maximum degree
is -choosable, for some constant . We prove this result
with (ignoring lower order terms). We then prove that every subdivision
of a graph with sufficiently many division vertices per edge is nonrepetitively
5-choosable. The proofs of both these results are based on the Moser-Tardos
entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek
for the nonrepetitive choosability of paths. Finally, we prove that every graph
with pathwidth is nonrepetitively -colourable.Comment: v4: Minor changes made following helpful comments by the referee
The signal sequence influences post-translational ER translocation at distinct stages
The metazoan Sec61 translocon transports polypeptides into and across the membrane of the endoplasmic reticulum via two major routes, a well-established co-translational pathway and a post-translational alternative. We have used two model substrates to explore the elements of a secretory protein precursor that preferentially direct it towards a co- or post-translational pathway for ER translocation. Having first determined the capacity of precursors to enter ER derived microsomes post-translationally, we then exploited semi-permeabilized mammalian cells specifically depleted of key membrane components using siRNA to address their contribution to the membrane translocation process. These studies suggest precursor chain length is a key factor in the post-translational translocation at the mammalian ER, and identify Sec62 and Sec63 as important components acting on this route. This role for Sec62 and Sec63 is independent of the signal sequence that delivers the precursor to the ER. However, the signal sequence can influence the subsequent membrane translocation process, conferring sensitivity to a small molecule inhibitor and dictating reliance on the molecular chaperone BiP. Our data support a model where secretory protein precursors that fail to engage the signal recognition particle, for example because they are short, are delivered to the ER membrane via a distinct route that is dependent upon both Sec62 and Sec63. Although this requirement for Sec62 and Sec63 is unaffected by the specific signal sequence that delivers a precursor to the ER, this region can influence subsequent events, including both Sec61 mediated transport and the importance of BiP for membrane translocation. Taken together, our data suggest that an ER signal sequence can regulate specific aspects of Sec61 mediated membrane translocation at a stage following Sec62/Sec63 dependent ER delivery.Nicholas Johnson, Sarah Haßdenteufel, Melanie Theis, Adrienne W. Paton, James C. Paton, Richard Zimmermann, Stephen Hig
1α,25(OH)2-3-Epi-Vitamin D3, a Natural Physiological Metabolite of Vitamin D3: Its Synthesis, Biological Activity and Crystal Structure with Its Receptor
Background: The 1 alpha,25-dihydroxy-3-epi-vitamin-D(3) (1 alpha,25(OH)(2)-3-epi-D(3)), a natural metabolite of the seco-steroid vitamin D(3), exerts its biological activity through binding to its cognate vitamin D nuclear receptor (VDR), a ligand dependent transcription regulator. In vivo action of 1 alpha,25(OH)(2)-3-epi-D(3) is tissue-specific and exhibits lowest calcemic effect compared to that induced by 1 alpha,25(OH)(2)D(3). To further unveil the structural mechanism and structure-activity relationships of 1 alpha,25(OH)(2)-3-epi-D3 and its receptor complex, we characterized some of its in vitro biological properties and solved its crystal structure complexed with human VDR ligand-binding domain (LBD).
Methodology/Principal Findings: In the present study, we report the more effective synthesis with fewer steps that provides higher yield of the 3-epimer of the 1 alpha,25(OH)(2)D(3). We solved the crystal structure of its complex with the human VDR-LBD and found that this natural metabolite displays specific adaptation of the ligand-binding pocket, as the 3-epimer maintains the number of hydrogen bonds by an alternative water-mediated interaction to compensate the abolished interaction with Ser278. In addition, the biological activity of the 1 alpha,25(OH)(2)-3-epi-D(3) in primary human keratinocytes and biochemical properties are comparable to 1 alpha,25(OH)(2)D(3).
Conclusions/Significance: The physiological role of this pathway as the specific biological action of the 3-epimer remains unclear. However, its high metabolic stability together with its significant biologic activity makes this natural metabolite an interesting ligand for clinical applications. Our new findings contribute to a better understanding at molecular level how natural metabolites of 1 alpha,25(OH)(2)D(3) lead to significant activity in biological systems and we conclude that the C3-epimerization pathway produces an active metabolite with similar biochemical and biological properties to those of the 1 alpha,25(OH)(2)D(3)
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