LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

Semilinear elliptic problems near resonance with a nonprincipal eigenvalue

We consider the Dirichlet problem for the equation -Delta u = lambda u +/- (x, u) + h(x) in a bounded domain, where f has a sublinear growth and h is an element of L-2. We find suitable conditions on f and It in order to have at least two solutions for X near to an eigenvalue of -Delta. A typical example to which our results apply is when f (x, u) behaves at infinity like a(x)vertical bar u vertical bar(q-2)u, with M > a(x) > delta > 0, and I < q < 2. (C) 2007 Elsevier Inc. All rights reserved.

Heat Conduction Equation Solution in the Presence of a Change of State in a Bounded Axisymmetric Cylindrical Domain

The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions, it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in nondimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples. [DOI: 10.1115/1.4003542]

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

Modified silicas covalently bounded to 5,10,15,20-tetrakis(2-hydroxy-5-nitrophenyl)porphyrinato iron(III): synthesis, spectroscopic and EPR characterization. Catalytic studies

In this work we have studied cyclooctene epoxidation with PhIO, using a new iron porphyrin, 5,10,15,20-tetrakis(2-hydroxy-5-nitrophenyl)porphyrinato iron(III), supported on silica matrices via eletrostatic interaction and / or covalent bonds as catalyst. These catalysts were obtained and immobilized on the solid supports propyltrimethylammonium silica (SiN+); propyltrimethylammonium and propylimidazole silica [SiN+(IPG)] and chloropropylsilica (CPS) via elestrostatic interactions and covalent binding. Characterization of the supported catalysts by UV-Vis spectroscopy and EPR (Electron paramagnetic resonance) indicated the presence of a mixture of FeII and FeIII species in all of the three obtained catalysts. In the case of (Z)-cyclooctene epoxidation by PhIO the yields observed for cis-epoxycyclooctane were satisfactory for the reactions catalyzed by the three materials (ranging from 68% to 85%). Such results indicate that immobilization of metalloporphyrins onto solid supports via groups localized on the ortho positions of their mesophenyl rings can lead to efficient catalysts for epoxidation reactions. The catalyst 1-CPS is less active than 1-SiN and 1-SiN(IPG), this argues in favour of the immobilization of this metalloporphyrin onto solids via electrostatic interactions, which is easier to achieve and results in more active oxidation catalysts. Interestingly, the activity of the supported catalysts remained the same even after three successive recyclings; therefore, they are stable under the oxidizing conditions.

Adaptive Immunity against Leishmania Nucleoside Hydrolase Maps Its C-Terminal Domain as the Target of the CD4+ T Cell-Driven Protective Response

Nucleoside hydrolases (NHs) show homology among parasite protozoa, fungi and bacteria. They are vital protagonists in the establishment of early infection and, therefore, are excellent candidates for the pathogen recognition by adaptive immune responses. Immune protection against NHs would prevent disease at the early infection of several pathogens. We have identified the domain of the NH of L. donovani (NH36) responsible for its immunogenicity and protective efficacy against murine visceral leishmaniasis (VL). Using recombinant generated peptides covering the whole NH36 sequence and saponin we demonstrate that protection against L. chagasi is related to its C-terminal domain (amino-acids 199-314) and is mediated mainly by a CD4+ T cell driven response with a lower contribution of CD8+ T cells. Immunization with this peptide exceeds in 36.73 +/- 12.33% the protective response induced by the cognate NH36 protein. Increases in IgM, IgG2a, IgG1 and IgG2b antibodies, CD4+ T cell proportions, IFN-gamma secretion, ratios of IFN-gamma/IL-10 producing CD4+ and CD8+ T cells and percents of antibody binding inhibition by synthetic predicted epitopes were detected in F3 vaccinated mice. The increases in DTH and in ratios of TNF alpha/IL-10 CD4+ producing cells were however the strong correlates of protection which was confirmed by in vivo depletion with monoclonal antibodies, algorithm predicted CD4 and CD8 epitopes and a pronounced decrease in parasite load (90.5-88.23%; p = 0.011) that was long-lasting. No decrease in parasite load was detected after vaccination with the N-domain of NH36, in spite of the induction of IFN-gamma/IL-10 expression by CD4+ T cells after challenge. Both peptides reduced the size of footpad lesions, but only the C-domain reduced the parasite load of mice challenged with L. amazonensis. The identification of the target of the immune response to NH36 represents a basis for the rationale development of a bivalent vaccine against leishmaniasis and for multivalent vaccines against NHs-dependent pathogens.

ASSOCIATION OF A MYOSIN MOTOR WITH MEMBRANE-BOUNDED PIGMENT GRANULES IN FRESHWATER SHRIMP CHROMATOPHORES: EVIDENCE FROM THE NITELLA ACTIN-CABLE ASSAY

We have adapted an actin-mosin motility assay to examine the interactions in vitro between actin cables isolated from the giant internodal cells of the freshwater alga, Nitella, and pigment granules extracted from red ovarian chromatophores of the freshwater palaemonid shrimp, Macrobrachium olfersi. The chromatophore pigment mass consists of large (0.5-1.0-mu m diameter) membrane-bounded granules, and small (140-nm diameter), a membranous granules, both structurally continuous with the abundant smooth endoplasmic reticulum. Our previous immunocytochemical studies show a myosin motor to be stably associated with the pigment mass; however, to which granule type or membrane the myosin motor is attached is unclear. Here, we show that sodium vanadate, a myosin ATPase inhibitor, markedly increases the affinity of isolated, large, membrane-bounded granules for Nitella actin cables to which they become permanently attached. This interaction does not occur in granule preparations containing ATP with uninhibited, active myosin without vanadate. We propose that a stable state of elevated affinity is established between the granule-located myosin motor and the Nitella actin cables, resulting from a vanadate-inhibited acto-myosin-ADP complex. This finding provides further evidence for a myosin motor positioned on the surface of the membrane-bounded pigment granules in shrimp ovarian chromatophores.

Genetic variability and natural selection at the ligand domain of the Duffy binding protein in brazilian Plasmodium vivax populations

Background: Plasmodium vivax malaria is a major public health challenge in Latin America, Asia and Oceania, with 130-435 million clinical cases per year worldwide. Invasion of host blood cells by P. vivax mainly depends on a type I membrane protein called Duffy binding protein (PvDBP). The erythrocyte-binding motif of PvDBP is a 170 amino-acid stretch located in its cysteine-rich region II (PvDBP(II)), which is the most variable segment of the protein. Methods: To test whether diversifying natural selection has shaped the nucleotide diversity of PvDBP(II) in Brazilian populations, this region was sequenced in 122 isolates from six different geographic areas. A Bayesian method was applied to test for the action of natural selection under a population genetic model that incorporates recombination. The analysis was integrated with a structural model of PvDBP(II), and T-and B-cell epitopes were localized on the 3-D structure. Results: The results suggest that: (i) recombination plays an important role in determining the haplotype structure of PvDBP(II), and (ii) PvDBP(II) appears to contain neutrally evolving codons as well as codons evolving under natural selection. Diversifying selection preferentially acts on sites identified as epitopes, particularly on amino acid residues 417, 419, and 424, which show strong linkage disequilibrium. Conclusions: This study shows that some polymorphisms of PvDBP(II) are present near the erythrocyte-binding domain and might serve to elude antibodies that inhibit cell invasion. Therefore, these polymorphisms should be taken into account when designing vaccines aimed at eliciting antibodies to inhibit erythrocyte invasion.

Purification, crystallization and preliminary crystallographic analysis of the catalytic domain of the extracellular cellulase CBHI from Trichoderma harzianum

The filamentous fungus Trichoderma harzianum has a considerable cellulolytic activity that is mediated by a complex of enzymes which are essential for the hydrolysis of microcrystalline cellulose. These enzymes were produced by the induction of T. harzianum with microcrystalline cellulose (Avicel) under submerged fermentation in a bioreactor. The catalytic core domain (CCD) of cellobiohydrolase I (CBHI) was purified from the extracellular extracts and submitted to robotic crystallization. Diffraction-quality CBHI CCD crystals were grown and an X-ray diffraction data set was collected under cryogenic conditions using a synchrotron-radiation source.

Lossless filter for multiple repeats with bounded edit distance

Background: Identifying local similarity between two or more sequences, or identifying repeats occurring at least twice in a sequence, is an essential part in the analysis of biological sequences and of their phylogenetic relationship. Finding such fragments while allowing for a certain number of insertions, deletions, and substitutions, is however known to be a computationally expensive task, and consequently exact methods can usually not be applied in practice. Results: The filter TUIUIU that we introduce in this paper provides a possible solution to this problem. It can be used as a preprocessing step to any multiple alignment or repeats inference method, eliminating a possibly large fraction of the input that is guaranteed not to contain any approximate repeat. It consists in the verification of several strong necessary conditions that can be checked in a fast way. We implemented three versions of the filter. The first is simply a straightforward extension to the case of multiple sequences of an application of conditions already existing in the literature. The second uses a stronger condition which, as our results show, enable to filter sensibly more with negligible (if any) additional time. The third version uses an additional condition and pushes the sensibility of the filter even further with a non negligible additional time in many circumstances; our experiments show that it is particularly useful with large error rates. The latter version was applied as a preprocessing of a multiple alignment tool, obtaining an overall time (filter plus alignment) on average 63 and at best 530 times smaller than before (direct alignment), with in most cases a better quality alignment. Conclusion: To the best of our knowledge, TUIUIU is the first filter designed for multiple repeats and for dealing with error rates greater than 10% of the repeats length.

KeaA, a Dictyostelium kelch-domain protein that regulates the response to stress and development

Background: The protein kinase YakA is responsible for the growth arrest and induction of developmental processes that occur upon starvation of Dictyostelium cells. yakA-cells are aggregation deficient, have a faster cell cycle and are hypersensitive to oxidative and nitrosoative stress. With the aim of isolating members of the YakA pathway, suppressors of the death induced by nitrosoative stress in the yakA-cells were identified. One of the suppressor mutations occurred in keaA, a gene identical to DG1106 and similar to Keap1 from mice and the Kelch protein from Drosophila, among others that contain Kelch domains. Results: A mutation in keaA suppresses the hypersensitivity to oxidative and nitrosoative stresses but not the faster growth phenotype of yakA-cells. The growth profile of keaA deficient cells indicates that this gene is necessary for growth. keaA deficient cells are more resistant to nitrosoative and oxidative stress and keaA is necessary for the production and detection of cAMP. A morphological analysis of keaA deficient cells during multicellular development indicated that, although the mutant is not absolutely deficient in aggregation, cells do not efficiently participate in the process. Gene expression analysis using cDNA microarrays of wild-type and keaA deficient cells indicated a role for KeaA in the regulation of the cell cycle and pre-starvation responses. Conclusions: KeaA is required for cAMP signaling following stress. Our studies indicate a role for kelch proteins in the signaling that regulates the cell cycle and development in response to changes in the environmental conditions.

A Component of the Xanthomonadaceae Type IV Secretion System Combines a VirB7 Motif with a N0 Domain Found in Outer Membrane Transport Proteins

Type IV secretion systems (T4SS) are used by Gram-negative bacteria to translocate protein and DNA substrates across the cell envelope and into target cells. Translocation across the outer membrane is achieved via a ringed tetradecameric outer membrane complex made up of a small VirB7 lipoprotein (normally 30 to 45 residues in the mature form) and the C-terminal domains of the VirB9 and VirB10 subunits. Several species from the genera of Xanthomonas phytopathogens possess an uncharacterized type IV secretion system with some distinguishing features, one of which is an unusually large VirB7 subunit (118 residues in the mature form). Here, we report the NMR and 1.0 angstrom X-ray structures of the VirB7 subunit from Xanthomonas citri subsp. citri (VirB7(XAC2622)) and its interaction with VirB9. NMR solution studies show that residues 27-41 of the disordered flexible N-terminal region of VirB7(XAC2622) interact specifically with the VirB9 C-terminal domain, resulting in a significant reduction in the conformational freedom of both regions. VirB7(XAC2622) has a unique C-terminal domain whose topology is strikingly similar to that of N0 domains found in proteins from different systems involved in transport across the bacterial outer membrane. We show that VirB7(XAC2622) oligomerizes through interactions involving conserved residues in the N0 domain and residues 42-49 within the flexible N-terminal region and that these homotropic interactions can persist in the presence of heterotropic interactions with VirB9. Finally, we propose that VirB(7XAC2622) oligomerization is compatible with the core complex structure in a manner such that the N0 domains form an extra layer on the perimeter of the tetradecameric ring.