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.

The Aedes aegypti larval transcriptome: a comparative perspective with emphasis on trypsins and the domain structure of peritrophins

The genome sequence of Aedes aegypti was recently reported. A significant amount of Expressed Sequence Tags (ESTs) were sequenced to aid in the gene prediction process. In the present work we describe an integrated analysis of the genomic and EST data, focusing on genes with preferential expression in larvae (LG), adults (AG) and in both stages (SG). A total of 913 genes (5.4% of the transcript complement) are LG, including ion transporters and cuticle proteins that are important for ion homeostasis and defense. From a starting set of 245 genes encoding the trypsin domain, we identified 66 putative LG, AG, and SG trypsins by manual curation. Phylogenetic analyses showed that AG trypsins are divergent from their larval counterparts (LG), grouping with blood-induced trypsins from Anopheles gambiae and Simulium vittatum. These results support the hypothesis that blood-feeding arose only once, in the ancestral Culicomorpha. Peritrophins are proteins that interlock chitin fibrils to form the peritrophic membrane (PM) that compartmentalizes the food in the midgut. These proteins are recognized by having chitin-binding domains with 6 conserved Cys and may also present mucin-like domains (regions expected to be highly O-glycosylated). PM may be formed by a ring of cells (type 2, seen in Ae. aegypti larvae and Drosophila melanogaster) or by most midgut cells (type 1, found in Ae. aegypti adult and Tribolium castaneum). LG and D. melanogaster peritrophins have more complex domain structures than AG and T. castaneum peritrophins. Furthermore, mucin-like domains of peritrophins from T. castaneum (feeding on rough food) are lengthier than those of adult Ae. aegypti (blood-feeding). This suggests, for the first time, that type 1 and type 2 PM may have variable molecular architectures determined by different peritrophins and/or ancillary proteins, which may be partly modulated by diet.

In vivo infection by Trypanosoma cruzi: The conserved FLY domain of the gp85/trans-sialidase family potentiates host infection

Trypanosoma cruzi is a protozoan parasite that infects vertebrates, causing in humans a pathological condition known as Chagas` disease. The infection of host cells by T. cruzi involves a vast collection of molecules, including a family of 85 kDa GPI-anchored glycoproteins belonging to the gp85/trans-sialidase superfamily, which contains a conserved cell-binding sequence (VTVXNVFLYNR) known as FLY, for short. Herein, it is shown that BALB/c mice administered with a single dose (1 mu g/animal, intraperitoneally) of FLY-synthetic peptide are more susceptible to infection by T. cruzi, with increased systemic parasitaemia (2-fold) and mortality. Higher tissue parasitism was observed in bladder (7.6-fold), heart (3-fold) and small intestine (3.6-fold). Moreover, an intense inflammatory response and increment of CD4(+) T cells (1.7-fold) were detected in the heart of FLY-primed and infected animals, with a 5-fold relative increase of CD4(+)CD25(+)FoxP3(+) T (Treg) cells. Mice treated with anti-CD25 antibodies prior to infection, showed a decrease in parasitaemia in the FLY model employed. In conclusion, the results suggest that FLY facilitates in vivo infection by T. cruzi and concurs with other factors to improve parasite survival to such an extent that might influence the progression of pathology in Chagas` disease.

Cell-cell signal-dependent dynamic interactions between HD-GYP and GGDEF domain proteins mediate virulence in Xanthomonas campestris

RpfG is a paradigm for a class of widespread bacterial two-component regulators with a CheY-like receiver domain attached to a histidine-aspartic acid-glycine-tyrosine-proline (HD-GYP) cyclic di-GMP phosphodiesterase domain. In the plant pathogen Xanthomonas campestris pv. campestris (Xcc), a two-component system comprising RpfG and the complex sensor kinase RpfC is implicated in sensing and responding to the diffusible signaling factor (DSF), which is essential for cell-cell signaling. RpfF is involved in synthesizing DSF, and mutations of rpfF, rpfG, or rpfC lead to a coordinate reduction in the synthesis of virulence factors such as extracellular enzymes, biofilm structure, and motility. Using yeast two-hybrid analysis and fluorescence resonance energy transfer experiments in Xcc, we show that the physical interaction of RpfG with two proteins with diguanylate cyclase (GGDEF) domains controls a subset of RpfG-regulated virulence functions. RpfG interactions were abolished by alanine substitutions of the three residues of the conserved GYP motif in the HD-GYP domain. Changing the GYP motif or deletion of the two GGDEF-domain proteins reduced Xcc motility but not the synthesis of extracellular enzymes or biofilm formation. RpfG-GGDEF interactions are dynamic and depend on DSF signaling, being reduced in the rpfF mutant but restored by DSF addition. The results are consistent with a model in which DSF signal transduction controlling motility depends on a highly regulated, dynamic interaction of proteins that influence the localized expression of cyclic di-GMP.

PILZ Protein Structure and Interactions with PILB and the FIMX EAL Domain: Implications for Control of Type IV Pilus Biogenesis

The PilZ protein was originally identified as necessary for type IV pilus (T4P) biogenesis. Since then, a large and diverse family of bacterial PilZ homology domains have been identified, some of which have been implicated in signaling pathways that control important processes, including motility, virulence and biofilm formation. Furthermore, many PilZ homology domains, though not PilZ itself, have been shown to bind the important bacterial second messenger bis(3`-> 5`)cyclic diGMP (c-diGMP). The crystal structures of the PilZ orthologs from Xanthomonas axonopodis pv Citri (PilZ(XAC1133), this work) and from Xanthomonas campestris pv campestris (XC1028) present significant structural differences to other PilZ homologs that explain its failure to bind c-diGMP. NMR analysis of PilZ(XAC1133) shows that these structural differences are maintained in solution. In spite of their emerging importance in bacterial signaling, the means by which NZ proteins regulate specific processes is not clear. In this study, we show that PilZ(XAC1133) binds to PilB, an ATPase required for TV polymerization, and to the EAL domain of FiMX(XAC2398), which regulates TV biogenesis and localization in other bacterial species. These interactions were confirmed in NMR, two-hybrid and far-Western blot assays and are the first interactions observed between any PilZ domain and a target protein. While we were unable to detect phosphodiesterase activity for FimXX(AC2398) in vitro, we show that it binds c-diGMP both in the presence and in the absence of PilZ(XAC1133). Site-directed mutagenesis studies for conserved and exposed residues suggest that PilZ(XAC1133) interactions with FimX(XAC2398) and PilB(XAC3239) are mediated through a hydrophobic surface and an unstructured C-terminal extension conserved only in PilZ orthologs. The FimX-PilZ-PilB interactions involve a full set of ""degenerate"" GGDEF, EAL and PilZ domains and provide the first evidence of the means by which PilZ orthologs and FimX interact directly with the TP4 machinery. (C) 2009 Elsevier Ltd. All rights reserved.