941 resultados para Virulence Factor Expression
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Transactivator protein C is required for the expression of bacteriophage Mu late genes from lys, I, P and mom promoters during lytic life cycle of the phage. The mechanism of transcription activation of mom gene by C protein is well understood. C activates transcription at Pmom by initial unwinding of the promoter DNA, thereby facilitating RNA polymerase (RNAP) recruitment. Subsequently, C interacts with the (sic) subunit of RNAP to enhance promoter clearance. The mechanism by which C activates other late genes of the phage is not known. We carried out promoter-polymerase interaction studies with all the late gene promoters to determine the individual step of C mediated activation. Unlike at P-mom, at the other three promoters, RNAP recruitment and closed complex formation are not C dependent. Instead, the action of C at P-lys, P-I, and P-P is during the isomerization from closed complex to open complex with no apparent effect at other steps of initiation pathway. The mechanism of transcription activation of mom and other late promoters by their common activator is different. This distinction in the mode of activation (promoter recruitment and escape versus isomerization) by the same activator at different promoters appears to be important for optimized expression of each of the late genes.
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Glioblastoma (grade IV glioma/GBM) is the most common primary adult malignant brain tumor with poor prognosis. To characterize molecular determinants of tumor-stroma interaction in GBM, we profiled 48 serum cytokines and identified macrophage colony-stimulating factor (MCSF) as one of the elevated cytokines in sera from GBM patients. Both MCSF transcript and protein were up-regulated in GBM tissue samples through a spleen tyrosine kinase (SYK)-dependent activation of the PI3K-NF kappa B pathway. Ectopic overexpression and silencing experiments revealed that glioma-secreted MCSF has no role in autocrine functions and M2 polarization of macrophages. In contrast, silencing expression of MCSF in glioma cells prevented tube formation of human umbilical vein endothelial cells elicited by the supernatant from monocytes/microglial cells treated with conditioned medium from glioma cells. Quantitative proteomics based on stable isotope labeling by amino acids in cell culture showed that glioma-derived MCSF induces changes in microglial secretome and identified insulin-like growth factor-binding protein 1 (IGFBP1) as one of the MCSF-regulated proteins secreted by microglia. Silencing IGFBP1 expression in microglial cells or its neutralization by an antibody reduced the ability of supernatants derived from microglial cells treated with glioma cell-conditioned medium to induce angiogenesis. In conclusion, this study shows up-regulation of MCSF in GBM via a SYK-PI3K-NF kappa B-dependent mechanism and identifies IGFBP1 released by microglial cells as a novel mediator of MCSF-induced angiogenesis, of potential interest for developing targeted therapy to prevent GBM progression.
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Specific and coordinated regulation of innate immune receptor-driven signaling networks often determines the net outcome of the immune responses. Here, we investigated the cross-regulation of toll-like receptor (TLR)2 and nucleotide-binding oligomerization domain (NOD)2 pathways mediated by Ac2PIM, a tetra-acylated form of mycobacterial cell wall component and muramyl dipeptide (MDP), a peptidoglycan derivative respectively. While Ac2PIM treatment of macrophages compromised their ability to induce NOD2-dependent immunomodulators like cyclooxygenase (COX)-2, suppressor of cytokine signaling (SOCS)-3, and matrix metalloproteinase (MMP)-9, no change in the NOD2-responsive NO, TNF-alpha, VEGF-A, and IL-12 levels was observed. Further, genome-wide microRNA expression profiling identified Ac2PIM-responsive miR-150 and miR-143 to target NOD2 signaling adaptors, RIP2 and TAK1, respectively. Interestingly, Ac2PIM was found to activate the SRC-FAK-PYK2-CREB cascade via TLR2 to recruit CBP/P300 at the promoters of miR-150 and miR-143 and epigenetically induce their expression. Loss-of-function studies utilizing specific miRNA inhibitors establish that Ac2PIM, via the miRNAs, abrogate NOD2-induced PI3K-PKC delta-MAPK pathway to suppress beta-catenin-mediated expression of COX-2, SOCS-3, and MMP-9. Our investigation has thus underscored the negative regulatory role of Ac2PIM-TLR2 signaling on NOD2 pathway which could broaden our understanding on vaccine potential or adjuvant utilities of Ac2PIM and/or MDP.
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The expression of a biologically active human IFN4 depends on the presence of a frameshift deletion polymorphism within the first exon of the interferon lambda 4 (IFNL4) gene. In this report, we use the lung carcinoma-derived cell line, A549, which is genetically viable to express a functional IFN4, to address transcriptional requirements of the IFNL4 gene. We show that the GC-rich DNA-binding transcription factor (TF) specificity protein 1 (Sp1) is recruited to the IFNL4 promoter and has a role in induction of gene expression upon stimulation with viral RNA mimic poly(I:C). By using RNAi and overexpression strategies, we also show key roles in IFNL4 gene expression for the virus-inducible TFs, nuclear factor kappa-light-chain-enhancer of activated B cells (NF-B), IFN regulatory factor 3 (IRF3), and IRF7. Interestingly, we also observe that overexpression of IFN4 influences IFNL4 promoter activity, which may further be dependent on the retinoic acid-inducible gene-I (RIG-I)-like receptor pathway. Together, our work for the first time reports on the functional characterization of the human IFNL4 promoter.
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Lateral appendages often show allometric growth with a specific growth polarity along the proximo-distal axis. Studies on leaf growth in model plants have identified a basipetal growth direction with the highest growth rate at the proximal end and progressively lower rates toward the distal end. Although the molecular mechanisms governing such a growth pattern have been studied recently, variation in leaf growth polarity and, therefore, its evolutionary origin remain unknown. By surveying 75 eudicot species, here we report that leaf growth polarity is divergent. Leaf growth in the proximo-distal axis is polar, with more growth arising from either the proximal or the distal end; dispersed with no apparent polarity; or bidirectional, with more growth contributed by the central region and less growth at either end. We further demonstrate that the expression gradient of the miR396-GROWTH-REGULATING FACTOR module strongly correlates with the polarity of leaf growth. Altering the endogenous pattern of miR396 expression in transgenic Arabidopsis thaliana leaves only partially modified the spatial pattern of cell expansion, suggesting that the diverse growth polarities might have evolved via concerted changes in multiple gene regulatory networks.
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The ability of Mycobacterium tuberculosis to resist intraphagosomal stresses, such as oxygen radicals and low pH, is critical for its persistence. Here, we show that a cytoplasmic redox sensor, WhiB3, and the major M. tuberculosis thiol, mycothiol (MSH), are required to resist acidic stress during infection. WhiB3 regulates the expression of genes involved in lipid anabolism, secretion, and redox metabolism, in response to acidic pH. Furthermore, inactivation of the MSH pathway subverted the expression of whiB3 along with other pH-specific genes in M. tuberculosis. Using a genetic biosensor of mycothiol redox potential (E-MSH), we demonstrated that a modest decrease in phagosomal pH is sufficient to generate redox heterogeneity in E-MSH of the M. tuberculosis population in a WhiB3-dependent manner. Data indicate that M. tuberculosis needs low pH as a signal to alter cytoplasmic E-MSH, which activates WhiB3-mediated gene expression and acid resistance. Importantly, WhiB3 regulates intraphagosomal pH by down-regulating the expression of innate immune genes and blocking phagosomal maturation. We show that this block in phagosomal maturation is in part due to WhiB3-dependent production of polyketide lipids. Consistent with these observations, Mtb Delta whiB3 displayed intramacrophage survival defect, which can be rescued by pharmacological inhibition of phagosomal acidification. Last, Mtb Delta whiB3 displayed marked attenuation in the lungs of guinea pigs. Altogether, our study revealed an intimate link between vacuolar acidification, redox physiology, and virulence in M. tuberculosis and discovered WhiB3 as crucial mediator of phagosomal maturation arrest and acid resistance in M. tuberculosis.
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The alarmone (p)ppGpp regulates transcription, translation, replication, virulence, lipid synthesis, antibiotic sensitivity, biofilm formation, and other functions in bacteria. Signaling nucleotide cyclic di-GMP (c-di-GMP) regulates biofilm formation, motility, virulence, the cell cycle, and other functions. In Mycobacterium smegmatis, both (p) ppGpp and c-di-GMP are synthesized and degraded by bifunctional proteins Rel(Msm) and DcpA, encoded by rel(Msm) and dcpA genes, respectively. We have previously shown that the Delta rel(Msm) and Delta dcpA knockout strains are antibiotic resistant and defective in biofilm formation, show altered cell surface properties, and have reduced levels of glycopeptidolipids and polar lipids in their cell wall (K. R. Gupta, S. Kasetty, and D. Chatterji, Appl Environ Microbiol 81:2571-2578, 2015, http://dx.doi.org/10.1128/AEM.03999-14). In this work, we have explored the phenotypes that are affected by both (p) ppGpp and c-di-GMP in mycobacteria. We have shown that both (p) ppGpp and c-di-GMP are needed to maintain the proper growth rate under stress conditions such as carbon deprivation and cold shock. Scanning electron microscopy showed that low levels of these second messengers result in elongated cells, while high levels reduce the cell length and embed the cells in a biofilm-like matrix. Fluorescence microscopy revealed that the elongated Delta rel(Msm) and Delta dcpA cells are multinucleate, while transmission electron microscopy showed that the elongated cells are multiseptate. Gene expression analysis also showed that genes belonging to functional categories such as virulence, detoxification, lipid metabolism, and cell-wall-related processes were differentially expressed. Our results suggests that both (p) ppGpp and c-di-GMP affect some common phenotypes in M. smegmatis, thus raising a possibility of cross talk between these two second messengers in mycobacteria. IMPORTANCE Our work has expanded the horizon of (p) ppGpp and c-di-GMP signaling in Gram-positive bacteria. We have come across a novel observation that M. smegmatis needs (p) ppGpp and c-di-GMP for cold tolerance. We had previously shown that the Delta rel(Msm) and Delta dcpA strains are defective in biofilm formation. In this work, the overproduction of (p) ppGpp and c-di-GMP encased M. smegmatis in a biofilm-like matrix, which shows that both (p) ppGpp and c-di-GMP are needed for biofilm formation. The regulation of cell length and cell division by (p) ppGpp was known in mycobacteria, but our work shows that c-di-GMP also affects the cell size and cell division in mycobacteria. This is perhaps the first report of c-di-GMP regulating cell division in mycobacteria.
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The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.
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Microbe-Associated Molecular Patterns and virulence effectors are recognized by plants as a first step to mount a defence response against potential pathogens. This recognition involves a large family of extracellular membrane receptors and other immune proteins located in different sub-cellular compartments. We have used phage-display technology to express and select for Arabidopsis proteins able to bind bacterial pathogens. To rapidly identify microbe-bound phage, we developed a monitoring method based on microarrays. This combined strategy allowed for a genome-wide screening of plant proteins involved in pathogen perception. Two phage libraries for high-throughput selection were constructed from cDNA of plants infected with Pseudomonas aeruginosa PA14, or from combined samples of the virulent isolate DC3000 of Pseudomonas syringae pv. tomato and its avirulent variant avrRpt2. These three pathosystems represent different degrees in the specificity of plant-microbe interactions. Libraries cover up to 26107 different plant transcripts that can be displayed as functional proteins on the surface of T7 bacteriophage. A number of these were selected in a bio-panning assay for binding to Pseudomonas cells. Among the selected clones we isolated the ethylene response factor ATERF-1, which was able to bind the three bacterial strains in competition assays. ATERF-1 was rapidly exported from the nucleus upon infiltration of either alive or heat-killed Pseudomonas. Moreover, aterf-1 mutants exhibited enhanced susceptibility to infection. These findings suggest that ATERF-1 contains a microbe-recognition domain with a role in plant defence. To identify other putative pathogen-binding proteins on a genome-wide scale, the copy number of selected-vs.-total clones was compared by hybridizing phage cDNAs with Arabidopsis microarrays. Microarray analysis revealed a set of 472 candidates with significant fold change. Within this set defence-related genes, including well-known targets of bacterial effectors, are over-represented. Other genes non-previously related to defence can be associated through this study with general or strain-specific recognition of Pseudomonas.
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Background: Human melanoma frequently colonizes bone marrow (BM) since its earliest stage of systemic dissemination, prior to clinical metastasis occurrence. However, how melanoma cell adhesion and proliferation mechanisms are regulated within bone marrow stromal cell (BMSC) microenvironment remain unclear. Consistent with the prometastatic role of inflammatory and angiogenic factors, several studies have reported elevated levels of cyclooxygenase-2 (COX-2) in melanoma although its pathogenic role in bone marrow melanoma metastasis is unknown. Methods: Herein we analyzed the effect of cyclooxygenase-2 (COX-2) inhibitor celecoxib in a model of generalized BM dissemination of left cardiac ventricle-injected B16 melanoma (B16M) cells into healthy and bacterial endotoxin lipopolysaccharide (LPS)-pretreated mice to induce inflammation. In addition, B16M and human A375 melanoma (A375M) cells were exposed to conditioned media from basal and LPS-treated primary cultured murine and human BMSCs, and the contribution of COX-2 to the adhesion and proliferation of melanoma cells was also studied. Results: Mice given one single intravenous injection of LPS 6 hour prior to cancer cells significantly increased B16M metastasis in BM compared to untreated mice; however, administration of oral celecoxib reduced BM metastasis incidence and volume in healthy mice, and almost completely abrogated LPS-dependent melanoma metastases. In vitro, untreated and LPS-treated murine and human BMSC-conditioned medium (CM) increased VCAM-1-dependent BMSC adherence and proliferation of B16M and A375M cells, respectively, as compared to basal medium-treated melanoma cells. Addition of celecoxib to both B16M and A375M cells abolished adhesion and proliferation increments induced by BMSC-CM. TNF alpha and VEGF secretion increased in the supernatant of LPS-treated BMSCs; however, anti-VEGF neutralizing antibodies added to B16M and A375M cells prior to LPS-treated BMSC-CM resulted in a complete abrogation of both adhesion-and proliferation-stimulating effect of BMSC on melanoma cells. Conversely, recombinant VEGF increased adherence to BMSC and proliferation of both B16M and A375M cells, compared to basal medium-treated cells, while addition of celecoxib neutralized VEGF effects on melanoma. Recombinant TNFa induced B16M production of VEGF via COX-2-dependent mechanism. Moreover, exogenous PGE2 also increased B16M cell adhesion to immobilized recombinant VCAM-1. Conclusions: We demonstrate the contribution of VEGF-induced tumor COX-2 to the regulation of adhesion-and proliferation-stimulating effects of TNFa, from endotoxin-activated bone marrow stromal cells, on VLA-4-expressing
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Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.
To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.
Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.
With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.
Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.
Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.
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With recent advances in high-throughput sequencing, mapping of genome-wide transcription factor occupancy has become feasible. To advance the understanding of skeletal muscle differentiation specifically and transcriptional regulation in general, I determined the genome-wide occupancy map for myogenin in differentiating C2C12 myocyte cells. I then analyzed the myogenin map for underlying sequence content and the association between occupied elements and expression trajectories of adjacent genes. Having determined that myogenin primarily associates with expressed genes, I performed a similar analysis on occupancy maps of other transcription factors active during skeletal muscle differentiation, including an extensive analysis of co-occupancy. This analysis provided strong motif evidence for protein-protein interactions as the primary driving force in the formation of Myogenin / Mef2 and MyoD / AP-1 complexes at jointly-occupied sites. Finally, factor occupancy analysis was extended to include bHLH transcription factors in tissues other than skeletal muscle. The cross-tissue analysis led to the emergence of a motif structure used by bHLH TFs to encode either tissue-specific or "general" (public) access in a variety of lineages.
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Increasing evidence links metabolic signals to cell proliferation, but the molecular wiring that connects the two core machineries remains largely unknown. E2Fs are master regulators of cellular proliferation. We have recently shown that E2F2 activity facilitates the completion of liver regeneration after partial hepatectomy (PH) by regulating the expression of genes required for S-phase entry. Our study also revealed that E2F2 determines the duration of hepatectomy-induced hepatic steatosis. A transcriptomic analysis of normal adult liver identified "lipid metabolism regulation" as a major E2F2 functional target, suggesting that E2F2 has a role in lipid homeostasis. Here we use wild-type (E2F2(+/+)) and E2F2 deficient (E2F2(-/-)) mice to investigate the in vivo role of E2F2 in the composition of liver lipids and fatty acids in two metabolically different contexts: quiescence and 48-h post-PH, when cellular proliferation and anabolic demands are maximal. We show that liver regeneration is accompanied by large triglyceride and protein increases without changes in total phospholipids both in E2F2(+/+) and E2F2(-/-) mice. Remarkably, we found that the phenotype of quiescent liver tissue from E2F2(-/-) mice resembles the phenotype of proliferating E2F2(+/+) liver tissue, characterized by a decreased phosphatidylcholine to phosphatidylethanolamine ratio and a reprogramming of genes involved in generation of choline and ethanolamine derivatives. The diversity of fatty acids in total lipid, triglycerides and phospholipids was essentially preserved on E2F2 loss both in proliferating and non-proliferating liver tissue, although notable exceptions in inflammation-related fatty acids of defined phospholipid classes were detected. Overall, our results indicate that E2F2 activity sustains the hepatic homeostasis of major membrane glycerolipid components while it is dispensable for storage glycerolipid balance.
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The far-field intensity distribution of hollow Gaussian beams was investigated based on scalar diffraction theory. An analytical expression of the M-2 factor of the beams was derived on the basis of the second-order moments. Moreover, numerical examples to illustrate our analytical results are given. (c) 2005 Optical Society of America.