Eigenvalues of Dirichlet Laplacian within the class of open sets with constant diameter

This paper is about a shape optimization problem related to the Dirichlet Laplacian eingevalues in the Euclidean plane. More precisely we study the shape of the minimizer in the class of open sets of constant width. We prove that the disk is not a local minimizer except for a limited number of eigenvalues

Additional file 1: of The plasma biomarker soluble SIGLEC-1 is associated with the type I interferon transcriptional signature, ethnic background and renal disease in systemic lupus erythematosus

Table S1. Custom NanoString probe sequences used to measure expression of the 56 IFN-regulated genes defining the transcriptional IFN signature in this study and eight housekeeping genes used to normalise expression levels between donors. (XLSX 13 kb

Functional <i>IL6R</i> 358Ala Allele Impairs Classical IL-6 Receptor Signaling and Influences Risk of Diverse Inflammatory Diseases

<div><p>Inflammation, which is directly regulated by interleukin-6 (IL-6) signaling, is implicated in the etiology of several chronic diseases. Although a common, non-synonymous variant in the IL-6 receptor gene (<i>IL6R</i> Asp358Ala; rs2228145 A>C) is associated with the risk of several common diseases, with the 358Ala allele conferring protection from coronary heart disease (CHD), rheumatoid arthritis (RA), atrial fibrillation (AF), abdominal aortic aneurysm (AAA), and increased susceptibility to asthma, the variant's effect on IL-6 signaling is not known. Here we provide evidence for the association of this non-synonymous variant with the risk of type 1 diabetes (T1D) in two independent populations and confirm that rs2228145 is the major determinant of the concentration of circulating soluble IL-6R (sIL-6R) levels (34.6% increase in sIL-6R per copy of the minor allele 358Ala; rs2228145 [C]). To further investigate the molecular mechanism of this variant, we analyzed expression of IL-6R in peripheral blood mononuclear cells (PBMCs) in 128 volunteers from the Cambridge BioResource. We demonstrate that, although 358Ala increases transcription of the soluble <i>IL6R</i> isoform (<i>P</i> = 8.3×10⁻²²) and not the membrane-bound isoform, 358Ala reduces surface expression of IL-6R on CD4+ T cells and monocytes (up to 28% reduction per allele; <i>P</i>≤5.6×10⁻²²). Importantly, reduced expression of membrane-bound IL-6R resulted in impaired IL-6 responsiveness, as measured by decreased phosphorylation of the transcription factors STAT3 and STAT1 following stimulation with IL-6 (<i>P</i>≤5.2×10⁻⁷). Our findings elucidate the regulation of IL-6 signaling by IL-6R, which is causally relevant to several complex diseases, identify mechanisms for new approaches to target the IL-6/IL-6R axis, and anticipate differences in treatment response to IL-6 therapies based on this common <i>IL6R</i> variant.</p> </div

The 358Ala allele is associated with decreased levels of membrane-bound IL-6R.

<p>Surface expression of IL-6R was quantified by flow cytometry in cryopreserved PBMCs from 128 volunteers from the Cambridge BioResource. Donors were sampled according to rs2228145 genotype. IL-6R surface expression was measured in four distinct immune cell subsets: CD4+ naïve and memory T cells, CD4+ regulatory T cells (Treg) and monocytes. Scatter plots depict the individual normalized IL-6R fluorescence intensity values measured as molecules of equivalent fluorochrome (MEF; see Methods for details). Error bars represent the standard error of the mean as shown by the middle horizontal line. The horizontal grey dotted reference line represents the average background fluorescence signal of the isotype control group. Differences in the mean expression levels, relative to the common homozygote group (Asp/Asp) are indicated above the horizontal black lines. <i>P</i>-values represent test for an association of rs2228145 with surface IL-6R levels, using an additive allelic effects model (see Methods for details).</p

The 358Ala allele is associated with reduced IL-6 signaling potential.

<p>(A) Frequency of pSTAT3 and (B) pSTAT1 positive cells following stimulation of PBMCs with 0, 0.1, 1 or 10 ng/ml of IL-6. Intracellular levels of pSTAT3 and pSTAT1 were measured by flow cytometry in three distinct immune cell subsets: CD4+ naïve T cells, CD4+ memory T cells and monocytes in 14 Asp/Asp and 14 Ala/Ala volunteers from the Cambridge BioResource. Median and interquartile range of the distribution of the frequency of pSTAT3 and pSTAT1 positive events in the two genotype groups for each dose of IL-6 stimulation are plotted. <i>P</i>-values represent tests for differences between rs2228145 genotype groups in pSTAT activation compared to control across doses. (see Methods and <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1003444#pgen.1003444.s006" target="_blank">Figure S6</a> for details).</p

Phenotypes of the residual circulating regulatory T cells at day 1.

<p>(A and B) CD25 expression was increased on mTregs (average baseline CD25 MFI on mTreg = 7,412, SE = 181, range 5,119–9,393, <i>n</i> = 37). (C and D) Concurrently, there was a dose-dependent reduction in CD122 on mTregs in blood (baseline CD122 MFI on mTreg = 444.2, SE = 14.0, range 288.0–616.0, <i>n</i> = 33). (E) There was a reduction in pSTAT5 levels in mTregs incubated with a saturating concentration of aldesleukin (1,000 IU/ml) in vitro when assessing blood obtained 90 min after dosing of aldesleukin. (F) At day 1 post-dosing, there was a dose-dependent reduction in the percentage of mTregs that were pSTAT5⁺ following incubation with 0.4 IU/ml aldesleukin in vitro (percent of pretreatment time point mTregs that were pSTAT5⁺ following aldesleukin incubation: 56.25%, SE = 1.60%, range 43.23%–71.03%, <i>n</i> = 22). (G) There was a reduction in pSTAT5 levels in nTregs assessed 90 min post-dosing when the cells were incubated with a saturating dose of aldesleukin (1,000 IU/ml) in vitro. (H) At day 1 post-dosing, there was not a consistent change from baseline in the percentage of nTregs that were pSTAT5⁺ following incubation with 0.4 IU/ml aldesleukin in vitro (baseline percent of nTregs that were pSTAT5⁺ following incubation with 0.4 IU/ml aldesleukin: 58.01%, SE = 1.65%, range 40.83%–69.88%, <i>n</i> = 21). (A) and (C) show averaged response plots across the five dose groups. (B), (D), and (E) show the best fitted models with 95% CIs. MFI, mean fluorescence intensity; mTreg, memory regulatory T cell; nTreg, naïve regulatory T cell.</p

Effects of aldesleukin on NK CD56^bright cell number, phenotypes, and proliferation.

<p>(A and B) NK CD56^bright cells showed a rapid dose-dependent decline, with the majority of cells not in circulation at 90 min (NK CD56^bright cells percent of lymphocytes: 0.41%, SE = 0.03%, range 0.09%–0.96%, <i>n</i> = 38). (C) Concurrent with this decline is a dose-dependent increase in NK CD56^bright cell pSTAT5 levels (baseline pSTAT5 MFI = 16.55, SE = 0.70, range 9.51–27.87, <i>n</i> = 37). (D and E) There was a sustained dose-dependent reduction in expression of CD25 (MFI = 642, SE = 32, range 255–1,148, <i>n</i> = 38) on NK CD56^bright cells and (F) a transient reduction in CD122 at 90 min (G) followed by a linear dose-dependent increase on day 1 (baseline CD122 MFI = 6,605, SE = 213, range 3,786–9,554, <i>n</i> = 38). (H) The outcome of treatment was increased proliferation of NK CD56^bright cells (baseline percentage of Ki-67⁺ NK CD56^bright cells = 9.9%, SE = 0.9%, range 3.35%–25.9%, <i>n</i> = 30). MFI, mean fluorescence intensity; NK, natural killer.</p

Lymphocyte responses to a dose of aldesleukin.

<p>(A) Average response curves of the absolute change in lymphocyte count across the five dose groups (average baseline lymphocyte count 1.78 × 10⁹/l, SE = 0.08, range 0.95–3.84, <i>n</i> = 39). (B) Three-dimensional plot of dose, baseline lymphocyte count, and change in lymphocyte count on day 1, with lines representing the vertical projections of points (coloured by dose) on the dose/baseline lymphocyte count axis. The surface grid represents the regression model for change in lymphocyte count on day 1 (colour scale), showing that the decrease in lymphocytes depends both on dose and pretreatment count.</p

Regulatory T cell primary endpoint.

<p>(A) Percentage of Tregs was defined as the percentage of CD3⁺CD4⁺CD25^highCD127^low cells within the CD3⁺CD4⁺ gate measured. (B) Individual participant dose allocations and dose groups showing convergence of the study to doses that achieve the two defined Treg targets. (C) A cubic model described the Treg dose response to aldesleukin best, with dashed lines showing the 10% and 20% Treg targets and doses. The shaded areas represent 95% CIs. Baseline, or pretreatment, Treg (percent of CD4⁺ T cells): 6.60% (SE = 0.25%, range 3.50%–10.70%, <i>n</i> = 39). SSC-A, side-scattered light-A; Treg, regulatory T cell.</p

Eosinophil response depends on baseline counts and aldesleukin dose.

<p>(A) Eosinophil counts showed an initial transient decrease at 90 min in a hyperacute response to aldesleukin followed by a dose-dependent increase on day 1, with a return to baseline by day 3–4 (average baseline eosinophil count 0.15 × 10⁹/l, SE = 0.03, range 0.04–0.86, <i>n</i> = 39). (B) Three-dimensional plot of dose, baseline eosinophil count, and change in eosinophil count on day 1, with lines representing the vertical projections of points (coloured by dose) on the dose/baseline eosinophil count axis. The change in eosinophil count is affected by both dose and baseline eosinophil count using a linear dose-response model, with the grid showing the regression model (colour scale) for increase in eosinophils on day 1 (colour scale) (absolute change in eosinophil count on day 1 = −0.0058 + [0.0693 × dose] + [0.1748 × baseline]).</p