Regulation and Function of the Caspase-1 in an Inflammatory Microenvironment.

The inflammasome is a complex of proteins that has a critical role in mounting an inflammatory response in reply to a harmful stimulus that compromises the homeostatic state of the tissue. The NLRP3 inflammasome, which is found in a wound-like environment, is comprised of three components: the NLRP3, the adaptor protein ASC and caspase-1. Interestingly, although ASC levels do not fluctuate, caspase-1 levels are elevated in both physiological and pathological conditions. Despite the observation that merely raising caspase-1 levels is sufficient to induce inflammation, the crucial question regarding the mechanism governing its expression is unexplored. We found that, in an inflammatory microenvironment, caspase-1 is regulated by NF-κB. Consistent with this association, the inhibition of caspase-1 activity parallels the effects on wound healing caused by the abrogation of NF-κB activation. Surprisingly, not only does inhibition of the NF-κB/caspase-1 axis disrupt the inflammatory phase of the wound-healing program, but it also impairs the stimulation of cutaneous epithelial stem cells of the proliferative phase. These data provide a mechanistic basis for the complex interplay between different phases of the wound-healing response in which the downstream signaling activity of immune cells can kindle the amplification of local stem cells to advance tissue repair

The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps

The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces

Viscosity Iterative Schemes for Finding Split Common Solutions of Variational Inequalities and Fixed Point Problems

We introduce some new iterative schemes based on viscosity approximation method for finding a split common element of the solution set of a pair of simultaneous variational inequalities for inverse strongly monotone mappings in real Hilbert spaces with a family of infinitely nonexpansive mappings. Some strong convergence theorems are also given. Our results generalize and improve some well-known results in the literature and references therein

New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

We study a nondifferentiable fractional programming problem as follows: (P)minx∈Kf(x)/g(x) subject to x∈K⊆X,  hi(x)≤0,  i=1,2,…,m, where K is a semiconnected subset in a locally convex topological vector space X, f:K→ℝ, g:K→ℝ+ and hi:K→ℝ, i=1,2,…, m. If f, -g, and hi, i=1,2,…,m, are arc-directionally differentiable, semipreinvex maps with respect to a continuous map γ:[0,1]→K⊆X satisfying γ(0)=0 and γ′(0+)∈K, then the necessary and sufficient conditions for optimality of (P) are established