Abstract. We study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type. We prove a one-to-one relation between the long time behavior of the solution and the limit value of its energy for symmetric decreasing initial data in L 2 under minimal assumptions on the nonlinearities. The obtained relation allows to establish sharp threshold results between propagation and extinction for monotone families of initial data in the considered general setting. Mathematics Subject Classification (2010). 35K57, 35K15, 35A15.

We study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in R N with bistable, ignition or monostable nonlinearities that exhibit threshold behavior. For L 2 initial data that are radial and non-increasing as a function of the distance to the origin, we characterize the ignition behavior in terms of the long time behavior of the energy associated with the solution. We then use this characterization to establish existence of a sharp threshold for monotone families of initial data in the considered class under various assumptions on the nonlinearities and spatial dimension. We also prove that for more general initial data that are sufficiently localized the solutions that exhibit ignition behavior propagate in all directions with the asymptotic speed equal to that of the unique one-dimensional variational traveling wave.Here u = u(x, t) ∈ [0, ∞), and the nonlinearity f is of monostable, ignition or bistable type (for a review, see, e.g., [52]). For all three nonlinearity types, f satisfies

No abstract

Toll-like receptor (TLR) signaling pathways need to be tightly controlled to avoid excessive inflammation and unwanted damage to the host. Myeloid differentiation primary response gene 88 (MyD88) is a critical adaptor of TLR signaling. Here, we identified the speckle-type POZ protein (SPOP) as a MyD88-associated protein. SPOP was recruited to MyD88 following TLR4 activation. TLR4 activation also caused the translocation of SPOP from the nucleus to the cytoplasm. SPOP depletion promoted the aggregation of MyD88 and recruitment of the downstream signaling kinases IRAK4, IRAK1 and IRAK2. Consistently, overexpression of SPOP inhibited the TLR4-mediated activation of NF-κB and production of inflammatory cytokines, whereas SPOP depletion had the opposite effects. Furthermore, knockdown of SPOP increased MyD88 aggregation and inflammatory cytokine production upon TLR2, TLR7 and TLR9 activation. Our findings reveal a mechanism by which MyD88 is regulated and highlight a role for SPOP in limiting inflammatory responses.

Mounting evidence indicates that gut microbiome may be involved in the pathogenesis of type 2 diabetes mellitus (T2DM). However, there is no consensus on whether there is a causal link between gut microbiome and T2DM risk. In the present study, the Mendelian randomization (MR) analysis was performed to investigate whether gut microbiome was causally linked to T2DM risk. The single nucleotide polymorphisms (SNPs) that were significantly related to exposure from published available genome-wide association study (GWAS) were selected as instrumental variables (IVs). The robust methods including inverse variance weighting (IVW), MR Egger, and weighted median were conducted to infer the causal links. Mendelian randomization pleiotropy residual sum and outlier (MR-PRESSO) and MR-Egger regression were used to test whether there was horizontal pleiotropy and identify outlier SNPs. The estimates of IVW suggested that Streptococcaceae (odds ratio (OR) = 1.17, 95% confidence interval (CI), 1.04–1.31, p = 0.009) was associated with higher risk of T2DM in European population. In Asian population, the MR IVW estimates revealed that there was a causal link between Acidaminococcaceae and T2DM risk (OR = 1.17, 95% CI, 1.04–1.31, p = 0.008). There was no evidence of notable heterogeneity and horizontal pleiotropy. However, after false discovery rate (FDR) correction, the causal link between gut microbiome and T2DM was absent (FDR, p > 0.05). In summary, using genetic instruments, this study does not find evidence of association between the 28 gut microbiome families and T2DM risk. However, Streptococcaceae and Acidaminococcaceae may have a borderline positive correlation with T2DM risk.