The Characteristic Properties of the Minimal Lp-Mean Width

Giannopoulos proved that a smooth convex body K has minimal mean width position if and only if the measure hK(u)σ(du), supported on Sn-1, is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal Lp-mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal Lp-mean width of convex bodies and prove the existence and uniqueness of the minimal Lp-mean width in its SL(n) images. In addition, we establish a characterization of the minimal Lp-mean width, conclude the average Mp(K) with a variation of the minimal Lp-mean width position, and give the condition for the minimum position of Mp(K)

The Characteristic Properties of the Minimal Lp-Mean Width

Giannopoulos proved that a smooth convex body K has minimal mean width position if and only if the measure hK(u)σ(du), supported on Sn-1, is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal Lp-mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal Lp-mean width of convex bodies and prove the existence and uniqueness of the minimal Lp-mean width in its SL(n) images. In addition, we establish a characterization of the minimal Lp-mean width, conclude the average Mp(K) with a variation of the minimal Lp-mean width position, and give the condition for the minimum position of Mp(K)

Dual Orlicz geominimal surface area

Abstract The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski theory. In this paper, based on the concept of the dual Orlicz mixed volume, we extend the dual geominimal surface area to the Orlicz version and give its properties. In addition, the isoperimetric inequality, a Blaschke-Santaló type inequality, and the monotonicity inequality for the dual Orlicz geominimal surface areas are established

Dual Lp-Mixed Geominimal Surface Area and Related Inequalities

The integral formula of dual Lp-geominimal surface area is given and the concept of dual Lp-geominimal surface area is extended to dual Lp-mixed geominimal surface area. Properties for the dual Lp-mixed geominimal surface areas are established. Some inequalities, such as analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for dual Lp-mixed geominimal surface areas, are also obtained

Orlicz difference bodies

In this paper, by the Orlicz-Minkowski combinations of convex bodies, we define the general Orlicz difference bodies and study their properties. Furthermore, we obtain the extreme values of the general Orlicz difference bodies and their polars

Design of pH-responsive antimicrobial peptide melittin analog-camptothecin conjugates for tumor therapy

Melittin, a classical antimicrobial peptide, is a highly potent antitumor agent. However, its significant toxicity seriously hampers its application in tumor therapy. In this study, we developed novel melittin analogs with pH-responsive, cell-penetrating and membrane-lytic activities by replacing arginine and lysine with histidine. After conjugation with camptothecin (CPT), CPT-AAM-1 and CPT-AAM-2 were capable of killing tumor cells by releasing CPT at low concentrations and disrupting cell membranes at high concentrations under acidic conditions. Notably, we found that the C-terminus of the melittin analogs was more suitable for drug conjugation than the N-terminus. CPT-AAM-1 significantly suppressed melanoma growth in vivo with relatively low toxicity. Collectively, the present study demonstrates that the development of antitumor drugs based on pH-responsive antimicrobial peptide-drug conjugates is a promising strategy

Micro Integral Membrane Protein (MIMP), a Newly Discovered Anti-Inflammatory Protein of Lactobacillus Plantarum, Enhances the Gut Barrier and Modulates Microbiota and Inflammatory Cytokines

Background/Aims: Recent studies have demonstrated that the manipulation of the gut microbiome represents a promising treatment for inflammatory bowel disease (IBD). We previously identified micro integral membrane protein (MIMP) as the smallest domain of surface layer protein from Lactobacillus Plantarum. However, the therapeutic relevance of MIMP in IBD remains unknown. Methods: We initially employed a dextran sodium sulphate (DSS)-induced colitis model and evaluated the effect of MIMP on the inflammation response, intestinal barrier and gut microbiota using histological examination, Fluorescein isothiocyanate-Dextran detection and pyrosequencing analysis respectively. We then established peripheral blood mononuclear cells (PBMCs) and an epithelial CaCO-2 co-culture model to investigate the regulatory role of MIMP in inflammatory cytokines. The level changes of inflammatory cytokines were detected using Enzyme-linked immunosorbent and real-time polymerase chain reaction assay. The involved regulatory mechanisms were investigated mainly using dual luciferase reporter and chromatin immunoprecipitation assay. Results: In the DSS-induced colitis model, we observed that MIMP intervention effectively improved the body weight loss, increased the colon length and decreased disease activity index. Consistently, the inflammation scores in the MIMP treatment group were significantly lower than those in the DSS treatment group. Furthermore, MIMP intervention was found to successfully neutralize DSS treatment by decreasing the expression of pro-inflammatory cytokines (IFN-γ, IL-17 and IL-23) and increasing the expression of anti-inflammatory cytokines (IL-4 and IL-10). Notably, the permeability assay demonstrated that the MIMP treatment group was remarkably lower than that in the DSS treatment group. We also showed that MIMP improved gut microbiota dysbiosis caused by DSS-induced inflammation. Additionally, in PBMCs and the CaCO-2 co-culture model, MIMP showed an obvious suppressive effect on lipopolysaccharide-induced inflammation in a time- and dose-dependent manner. Furthermore, we revealed that MIMP could modulate inflammatory cytokine expression through the toll-like receptor 4 pathway and histone acetylation. Conclusions: Our results suggested that MIMP showed a significant anti-inflammatory effect through regulating the gut barrier, microbiota and inflammatory cytokines. MIMP may have translational relevance as clinically relevant therapy for IBD patients