Existencia y unicidad de solución y comportamiento asintótico para la ecuación de onda con condición de frontera del tipo Neumann y disipación localmente distribuido

En este trabajo se estudia la existencia y unicidad de solución de la ecuación de la onda con condiciones de frontera del tipo Neumann, con disipación localmente distribuida usando el método de Faedo Galerkin. Además analiza el decaimiento no exponencial de la energía asociado al sistema planteado. Se hacen las estimativas correspondientes basándose en propiedades del espacio donde se encuentra la solución de la ecuación, así como los teoremas correspondientes al sistema estudiado.Tesi

Co-exposure to <i>C. albicans</i> induces Th17 cells in the joint.

<p>The mRNA expression of T-bet, GATA-3, RORγT and FOXP3 in synovial biopsies of the knee joints (n=3 mice/group) were measured by QPCR (A) The mRNA expression of IFNy, IL-17A, IL-17F, IL-21, IL-22 and IL-10 are shown (B). The knee joint synovium was dissected and prepared for enzymatic digestion. The cells were incubated with PMA/ionomycine and Golgiplug for 5 hours before flowcytometric analysis (n=6 mice/group) and stained for CD3, IL-17, and IFN-γ. Representative dot plots of the isolated cells gated on CD3+ are shown (C). The mean percentage of isolated IFN-γ and IL-17 producing T cells (CD3+ population) are shown (D). Results are mean ± SEM; ns=non significant *=P<0.05, **=P<0.01, by one-way ANOVA.</p

<i>Candida albicans</i> and Zymosan A aggravate the inflammation in the chronic SCW model.

<p>On days 0, 7, 14, and 21, streptococcal cell wall (SCW) fragments were injected intra-articularly (i.a.) into the knee joint. Joint swelling (ratio of ^{99 m}Tc uptake in the treated right knee joint to that in the untreated left knee joint) were determined 1 day after every injection (A) and during the chronic phase of the model on day 28 (B; n=6 mice/group). In addition, the inflammatory cell influx (C) on histological slides was quantified on day 28. H&E stained frontal knee sections (original magnification 100×) (D) are shown (n=8 mice/group. Values are the mean ± SEM; ns=non significant, * P<0.05, ** P<0.01, *** P<0.001, by One-way ANOVA.</p

<i>C. albicans</i> skews T-cell cytokine profile.

<p>Serum levels of anti-SCW-specific total IgG, IgG1, and IgG3 antibodies (A). Draining lymph node cells (1*10⁵/well) were stimulated with anti-CD3/anti-CD28 antibodies for 72 hours (n=6/group). Levels of IFN-γ, IL-17 and IL-10 were determined by Luminex in the supernatants of the stimulated lymph node cells (B) and washouts of synovial biopsies of day 22 (C). Results are the mean ± SEM; ns=non significant *=P<0.05; **=P<0.01, ***=P<0.001, by One-Way ANOVA.</p

Exposure to <i>C. albicans</i> increases the cartilage destruction and bone erosion during chronic SCW arthritis.

<p>Analysis of destructive parameters after 4 relapsing flares of arthritis. On day 28, knee joints (n=8/group) were harvested for histological assessment. Knee joint sections were stained using Safranin O to determine the degree of proteoglycan (PG) depletion. H&E staining was used to score the degree of chondrocyte death, cartilage surface erosion and bone erosion (A). QPCR analysis of destructive related genes was performed on synovial biopsies (n=3/group) of day 22, one day after the last injection (B). Representative images of arthritic knee joints showing immunohistochemical staining for VDIPEN after the 4 repeated injections (day 28) (C). Besides, the quantitative measurement of VDIPEN expression (percentage of positively stained area) in the cartilage of the 3 groups of mice (n=8/group) was analyzed. Values are the mean ± SEM; ns=non significant * P<0.05, ** P<0.01, *** P<0.001, by One-way ANOVA.</p

IL-6 and IL-21 play an important role during in vivo Th17 differentiation and antibody production.

<p>AIA was induced in WT, IL-6^-/-, IL-21R^-/-, and IL-6^-/- x IL-21R^-/- mice. Draining lymph node CD4+IL-17+ cell fraction two days after arthritis induction as measured using flow cytometry (A; n = 10/group). Serum IgG1, IgG2b, and total IgG levels as measured by ELISA (B; n = 5/group). *p<0.05, **p<0.01, ***p<0.001 versus WT; ^##p<0.01 versus IL-6^-/-; ^^^p<0.001 versus IL-21R^-/-; A—One-way ANOVA, B—Kruskal-Wallis.</p

Highly reduced Th17 differentiation in the absence of both IL-6 and IL-21 signaling.

<p>WT and IL-21R^-/- naïve T cells were stimulated for four days with a differentiation cocktail either with or without IL-6 as described in <i>Methods</i>. Representative flow cytometry dot plots reflecting the IL-17+ fraction of the CD4+ population. Gates were set at a maximum of 0.3% IL-17-positive cells in the ‘fluorescence minus one’ control per condition, without addition of IL-17A antibodies (A). Summary of the relative proportion of IL-17+ cells within the CD4+ population (B). Culture supernatant levels of IL-17 (C), IL-21 (D), and IL-22 (E). 6–10 mice/group; *p<0.05, **p<0.01, ***p<0.001 versus WT + IL-6; ^###p<0.001 versus WT—IL-6; ^p<0.05, ^^^p<0.001 versus IL-21R^-/- + IL-6; A—Kruskal-Wallis, B-D—One-way ANOVA.</p

Arthritis incidence and severity of mice receiving anti-IL-6 and/or anti-IL-21 treatment late in disease development.

<p>Collagen induced arthritis was initiated in DBA-1 mice, subsequently treated with anti-IL-6R antibodies and/or sIL-21R.Fc from the day of booster injection (d = 21; n = 5/group). Arthritis incidence (A) and severity (B) based on macroscopic scoring. Bone damage as measured using the Faxitron depicted as radiological damage (C). Histologically scored inflammation, bone erosion (both H&E staining, scale bar 500 μM), and cartilage proteoglycan depletion (SafO staining, scale bar 200 μM) (D). *p<0.05 versus Rat IgG1; One-way ANOVA.</p

Effect of anti-IL-6 and/or anti-IL-21 treatment on Th17, Th1, and antibody development in CIA mice.

<p>Th17 (A) and Th1 (B) levels in draining lymph nodes as measured using flow cytometry, and anti-CII antibody level in serum (C) as measured by ELISA of mice with CIA receiving anti-IL-6 and/or anti-IL-21 treatment. n = 5/group; **p<0.01 versus Rat IgG1; A+C—Kruskal-Wallis, B—One-way ANOVA.</p

Antigen-induced arthritis severity is potently reduced by combinatorial blockade of IL-6 and IL-21 signaling pathways.

<p>Joint swelling of WT, IL-6^-/-, IL-21R^-/-, and IL-6^-/- x IL-21R^-/- mice at day 1 (A), day 2 (B), and day 4 (C) after arthritis induction, depicted as ratio between right and left knee joint, measured by ^99mTechnetium pertechnetate uptake in the joint (n = 6/group). Histologically scored inflammation, bone erosion (both H&E staining, scale bar 500 μM), and cartilage proteoglycan depletion (SafO staining, scale bar 200 μM) (D; n = 10/group). *p<0.05, **p<0.01, ***p<0.001 versus WT; ^#p<0.05, ^###p<0.001 versus IL-6^-/-; ^p<0.05 versus IL-21R^-/-; A+B One-way ANOVA, C+D Kruskal-Wallis.</p