Superreflexivity and J-convexity of Banach spaces

A Banach space X is superreflexive if each Banach space Y that is finitely representable in X is reflexive. Superreflexivity is known to be equivalent to J-convexity and to the non-existence of uniformly bounded factorizations of the summation operators S_n through X. We give a quantitative formulation of this equivalence. This can in particular be used to find a factorization of S_n through X, given a factorization of S_N through [L_2,X], where N is `large' compared to n

Ideal norms and trigonometric orthonormal systems

In this article, we characterize the $UMD$--property of a Banach space $X$ by ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of that numerical parameters can be used to decide whether or not $X$ is a $UMD$--space. Moreover, in the negative case, we obtain a measure that shows how far $X$ is from being a $UMD$--space. The main result is, that all described parameters are equivalent also in the quantitative setting

An IFN-Associated Cytotoxic Cellular Immune Response against Viral, Self-, or Tumor Antigens Is a Common Pathogenetic Feature in “Interface Dermatitis”

The term “interface dermatitis” (ID) involves a specific histological inflammatory pattern that is characterized by a cytotoxic lymphocytic infiltration and a hydropic degeneration of the basal epidermal layer. ID is typically seen in autoimmune skin disorders such as lichen planus (LP), cutaneous lupus erythematosus (CLE), and may also appear during immune reactions against drugs, viruses, and tumors. Recent studies have shown that the type-I IFN system is involved in cutaneous autoimmune diseases characterized by ID. IFNs induce the expression of proinflammatory cytokines and chemokines, which support the cellular immune response. The role of IFNs in ID is supported by a close morphological association between the expression pattern of IFN-inducible proteins and the distribution of CXCR3+ lymphocytes. The IFN-inducible chemokine CXCL10 is expressed in exactly those areas where cytotoxic lymphocytes invade the basal epidermis and cause keratinocyte death. A similar picture can be found in early herpes simplex viral skin lesions and viral warts, but also in “lichenoid” actinic keratosis and invasive squamous cell carcinoma. These data suggest that ID morphologically reflects a common IFN-driven cytotoxic attack affecting the basal keratinocytes under different conditions, which is important for antiviral and antitumor immune response, but is inappropriately activated in autoimmune skin disorders

Interleukin-36 in Infectious and Inflammatory Skin Diseases

Interleukin-36 (IL-36) comprises to a cytokine family consisting of four isoforms IL-36α, IL-36β, IL-36γ, and IL-36 receptor antagonist (IL-36 Ra). These IL-36 cytokines, in turn, belong to the IL-1 superfamily. The IL-36 receptor (IL-1R6) is functional as a heterodimer formed of IL-1R6 and IL-1 receptor accessory protein (IL-1RAcP). IL-36α, IL-36β, and IL-36γ are regarded as pro-inflammatory ligands and IL-36 Ra as well as IL-38 as anti-inflammatory ligands of IL-1R6. IL-36 cytokines are mainly expressed on the barrier sites of the body e.g., bronchial, intestinal, and dermal epithelium. One of their most important biological functions is the bridging of innate and adaptive immune responses. A disturbed balance between pro-inflammatory and anti-inflammatory branches easily leads to inflammation of the corresponding tissue. The most prominent example for an altered IL-36 expression is the spectrum of psoriasis. In addition to inflammatory dermatoses, IL-36 also seems to play a role in infectious dermatoses. Microbial triggers, especially Staphylococcus aureus infection, increase the production of pro-inflammatory IL-36 cytokines and initiate/promote the inflammation of skin lesions. Due to the discovery of IL-36 as an important immune mediator, it has already been possible to develop important diagnostic tools for dermatitis. Not only in the field of inflammatory skin diseases, but also in pulmonary and intestinal inflammation, there is evidence that IL-36 cytokines might have diagnostic and/or therapeutic relevance

Aberrant inflammasome activation as a driving force of human autoimmune skin disease

Autoimmune skin diseases are understood as conditions in which the adaptive immune system with autoantigen-specific T cells and autoantibody-producing B cells reacting against self-tissues plays a crucial pathogenic role. However, there is increasing evidence that inflammasomes, which are large multiprotein complexes that were first described 20 years ago, contribute to autoimmune disease progression. The inflammasome and its contribution to the bioactivation of interleukins IL-1β and IL-18 play an essential role in combating foreign pathogens or tissue damage, but may also act as a pathogenic driver of myriad chronic inflammatory diseases when dysfunctionally regulated. Inflammasomes containing the NOD-like receptor family members NLRP1 and NLRP3 as well as the AIM2-like receptor family member AIM2 have been increasingly investigated in inflammatory skin conditions. In addition to autoinflammatory diseases, which are often associated with skin involvement, the aberrant activation of the inflammasome has also been implied in autoimmune diseases that can either affect the skin besides other organs such as systemic lupus erythematosus and systemic sclerosis or are isolated to the skin in humans. The latter include, among others, the T-cell mediated disorders vitiligo, alopecia areata, lichen planus and cutaneous lupus erythematosus as well as the autoantibody-driven blistering skin disease bullous pemphigoid. Some diseases are characterized by both autoinflammatory and autoimmune responses such as the chronic inflammatory skin disease psoriasis. Further insights into inflammasome dysregulation and associated pathways as well as their role in forming adaptive immune responses in human autoimmune skin pathology could potentially offer a new field of therapeutic options in the future