128 research outputs found

    The extremal solution of a boundary reaction problem

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    We consider Delta u = 0 in Omega, partial derivative u/partial derivative v = lambda f(u) on Gamma(1), u= 0 on Gamma(2) where lambda > 0, f(u) = e(u) or f(u) = (1 + u)(p), Gamma(1), Gamma(2) is a partition of partial derivative Omega and Omega subset of R-N. We determine sharp conditions on the dimension N and p > 1 such that the extremal solution is bounded, where the extremal solution refers to the one associated to the largest lambda for which a solution exists.7479581

    A new critical curve for the Lane-Emden system

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    We study stable positive radially symmetric solutions for the Lane-Emden system Δu=vp-\Delta u=v^p in RN\R^N, Δv=uq-\Delta v=u^q in RN\R^N, where p,q1p,q\geq 1. We obtain a new critical curve that optimally describes the existence of such solutions.Comment: 13 pages, 1 figur

    Stable solutions for the bilaplacian with exponential nonlinearity

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    Let lambda* > 0 denote the largest possible value of lambda such that {Delta(2)u = lambda e(u) in B, u =partial derivative u/partial derivative n = 0 on partial derivative B} has a solution, where B is the unit ball in R-N and n is the exterior unit normal vector. We show that for lambda = lambda* this problem possesses a unique weak solution u*. We prove that u* is smooth if N = 13, in which case u*( r) = - 4 log r + log( 8( N - 2)( N - 4)/lambda*) + o( 1) as r -> 0. We also consider the problem with general constant Dirichlet boundary conditions.39256559

    Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

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    In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray-Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis

    Rad51 Polymerization Reveals a New Chromatin Remodeling Mechanism

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    Rad51 protein is a well known protagonist of homologous recombination in eukaryotic cells. Rad51 polymerization on single-stranded DNA and its role in presynaptic filament formation have been extensively documented. Rad51 polymerizes also on double-stranded DNA but the significance of this filament formation remains unclear. We explored the behavior of Saccharomyces cerevisiae Rad51 on dsDNA and the influence of nucleosomes on Rad51 polymerization mechanism to investigate its putative role in chromatin accessibility to recombination machinery. We combined biochemical approaches, transmission electron microscopy (TEM) and atomic force microscopy (AFM) for analysis of the effects of the Rad51 filament on chromatinized templates. Quantitative analyses clearly demonstrated the occurrence of chromatin remodeling during nucleoprotein filament formation. During Rad51 polymerization, recombinase proteins moved all the nucleosomal arrays in front of the progressing filament. This polymerization process had a powerful remodeling effect, as Rad51 destabilized the nucleosomes along considerable stretches of DNA. Similar behavior was observed with RecA. Thus, recombinase polymerization is a powerful mechanism of chromatin remodeling. These remarkable features open up new possibilities for understanding DNA recombination and reveal new types of ATP-dependent chromatin dynamics

    Cdk1 Targets Srs2 to Complete Synthesis-Dependent Strand Annealing and to Promote Recombinational Repair

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    Cdk1 kinase phosphorylates budding yeast Srs2, a member of UvrD protein family, displays both DNA translocation and DNA unwinding activities in vitro. Srs2 prevents homologous recombination by dismantling Rad51 filaments and is also required for double-strand break (DSB) repair. Here we examine the biological significance of Cdk1-dependent phosphorylation of Srs2, using mutants that constitutively express the phosphorylated or unphosphorylated protein isoforms. We found that Cdk1 targets Srs2 to repair DSB and, in particular, to complete synthesis-dependent strand annealing, likely controlling the disassembly of a D-loop intermediate. Cdk1-dependent phosphorylation controls turnover of Srs2 at the invading strand; and, in absence of this modification, the turnover of Rad51 is not affected. Further analysis of the recombination phenotypes of the srs2 phospho-mutants showed that Srs2 phosphorylation is not required for the removal of toxic Rad51 nucleofilaments, although it is essential for cell survival, when DNA breaks are channeled into homologous recombinational repair. Cdk1-targeted Srs2 displays a PCNA–independent role and appears to have an attenuated ability to inhibit recombination. Finally, the recombination defects of unphosphorylatable Srs2 are primarily due to unscheduled accumulation of the Srs2 protein in a sumoylated form. Thus, the Srs2 anti-recombination function in removing toxic Rad51 filaments is genetically separable from its role in promoting recombinational repair, which depends exclusively on Cdk1-dependent phosphorylation. We suggest that Cdk1 kinase counteracts unscheduled sumoylation of Srs2 and targets Srs2 to dismantle specific DNA structures, such as the D-loops, in a helicase-dependent manner during homologous recombinational repair

    The SUMO Isopeptidase Ulp2p Is Required to Prevent Recombination-Induced Chromosome Segregation Lethality following DNA Replication Stress

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    SUMO conjugation is a key regulator of the cellular response to DNA replication stress, acting in part to control recombination at stalled DNA replication forks. Here we examine recombination-related phenotypes in yeast mutants defective for the SUMO de-conjugating/chain-editing enzyme Ulp2p. We find that spontaneous recombination is elevated in ulp2 strains and that recombination DNA repair is essential for ulp2 survival. In contrast to other SUMO pathway mutants, however, the frequency of spontaneous chromosome rearrangements is markedly reduced in ulp2 strains, and some types of rearrangements arising through recombination can apparently not be tolerated. In investigating the basis for this, we find DNA repair foci do not disassemble in ulp2 cells during recovery from the replication fork-blocking drug methyl methanesulfonate (MMS), corresponding with an accumulation of X-shaped recombination intermediates. ulp2 cells satisfy the DNA damage checkpoint during MMS recovery and commit to chromosome segregation with similar kinetics to wild-type cells. However, sister chromatids fail to disjoin, resulting in abortive chromosome segregation and cell lethality. This chromosome segregation defect can be rescued by overproducing the anti-recombinase Srs2p, indicating that recombination plays an underlying causal role in blocking chromatid separation. Overall, our results are consistent with a role for Ulp2p in preventing the formation of DNA lesions that must be repaired through recombination. At the same time, Ulp2p is also required to either suppress or resolve recombination-induced attachments between sister chromatids. These opposing defects may synergize to greatly increase the toxicity of DNA replication stress
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