Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities

There was an elegant expression for the volume of hypercube $[0,1]^n$ clipped by a hyperplane. We generalize the formula to the case of more than one hyperplane. Furthermore we derive several combinatorial identities from the volume expressions of clipped hypercubes

Partially abelian representations of knot groups

A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called $w$-variables. In this paper, we consider the case when pinched octahedra appear as a boundary parabolic solution in the decomposition. A $w$-solution with pinched octahedra induces a solution for a new knot obtained by changing the crossing or inserting a tangle at the pinched place. We discuss this phenomenon with corresponding holonomy representations and give some examples including ones obtained from connected sum.Comment: 11 page

Ceramides and Cell Signaling Molecules in Psoriatic Epidermis: Reduced Levels of Ceramides, PKC-α, and JNK

Ceramides are the main lipids in the stratum corneum and are generated during cellular stress and apoptosis by de novo synthesis or by the action of sphingomyelinase. In addition, they are lipid second messengers produced by sphingolipid metabolism and trigger important cell responses, including protein kinase C-alpha (PKC-α) activation and the stimulation of signal transduction pathways with apoptosis and stress-activated protein kinases (SAPK), such as c-jun N-terminal kinase (JNK). Thus, ceramides have anti-proliferative and apoptotic effects. This study measured the changes in the levels of epidermal ceramides and ceramide-related apoptotic signaling molecules in psoriasis patients. Samples from lesional and non-lesional epidermis were obtained from psoriasis patients. Total ceramides were fractionated using thin-layer chromatography, and the levels of PKC-α and JNK expression were measured using Western blot analysis with specific antibodies. The ceramide level was reduced significantly, and this was associated with the downregulation of apoptotic signaling molecules, such as PKC-α and JNK, in the lesional epidermis of psoriasis patients. These results suggest that the decreased level of ceramides downregulates the apoptotic pathway, leading to epidermal proliferation in psoriasis

A Study on Altered Expression of Serine Palmitoyltransferase and Ceramidase in Psoriatic Skin Lesion

Ceramides are the main lipid component maintaining the lamellae structure of stratum corneum, as well as lipid second messengers for the regulation of cellular proliferation and/or apoptosis. In our previous study, psoriatic skin lesions showed marked decreased levels of ceramides and signaling molecules, specially protein kinase C-alpha (PKC-α) and c-jun N-terminal kinase (JNK) in proportion to the psoriasis area and severity index (PASI) scores, which suggested that the depletion of ceramide is responsible for epidermal hyperproliferation of psoriasis via downregulation of proapoptotic signal cascade such as PKC-α and JNK. In this study, we investigated the protein expression of serine palmitoyltransferase (SPT) and ceramidase, two major ceramide metabolizing enzymes, in both psoriatic epidermis and non-lesional epidermis. The expression of SPT, the ceramide generating enzyme in the de novo synthesis in psoriatic epidermis, was significantly less than that of the non-lesional epidermis, which was inversely correlated with PASI score. However, the expression of ceramidase, the degradative enzyme of ceramides, showed no significant difference between the lesional epidermis and the non-lesional epidermis of psoriatic patients. This might suggest that decreased expression of SPT protein is one of the important causative factors for decreased ceramide levels in psoriasis

FULL COMMUNICATION Royal Jelly Protects Against Ultraviolet B-Induced Photoaging in Human Skin Fibroblasts via Enhancing Collagen Production

ABSTRACT Royal jelly (RJ) is a honeybee product containing proteins, carbohydrates, fats, free amino acids, vitamins, and minerals. As its principal unsaturated fatty acid, RJ contains 10-hydroxy-2-decenoic acid (10-HDA), which may have antitumor and antibacterial activity and a capacity to stimulate collagen production. RJ has attracted interest in various parts of the world for its pharmacological properties. However, the effects of RJ on ultraviolet (UV)-induced photoaging of the skin have not been reported. In this study we measured the 10-HDA content of RJ by high-performance liquid chromatography and tested the effects of RJ on UVB-induced skin photoaging in normal human dermal fibroblasts. The effects of RJ and 10-HDA on UVB-induced photoaging were tested by measuring procollagen type I, transforming growth factor (TGF)-b1, and matrix metalloproteinase (MMP)-1 after UVB irradiation. The RJ contained about 0.211% 10-HDA. The UVB-irradiated human skin fibroblasts treated with RJ and 10-HDA had increased procollagen type I and TGF-b1 productions, but the level of MMP-1 was not changed. Thus RJ may potentially protect the skin from UVB-induced photoaging by enhancing collagen production. KEY WORDS: 10-hydroxy-2-decenoic acid matrix metalloproteinase-1 photoaging procollagen type I royal jelly transforming growth factor-b

An Inverse Relationship Between Ceramide Synthesis and Clinical Severity in Patients with Psoriasis

Ceramides play major roles in maintaining the epidermal barrier. It has been sus-pected that the depletion of ceramides, associated with disrupted barrier function in the epidermis, leads to the clinical manifestation of dryness and inflammation seen in patients with psoriasis. The aim of the present study was to determine the relation-ship between the level of ceramide synthesis in the epidermis and the clinical severity in patients with psoriasis. Samples from lesional and unlesional epidermis obtained from psoriasis patients were incubated with [14C]serine, an initiator of ceramide syn-thesis. otal ceramide was fractionated using high performance thin layer chromato-graphy, and the radioactivity was measured. The clinical severity of psoriasis was graded according to the psoriasis area and severity index scoring system. The level of ceramide synthesis in the lesional epidermis of patients was significantly lower than that in the unlesional epidermis and bore a negative correlation with the clinical severity of psoriasis. The present results suggest that the decreased level of ceramide synthesis in the epidermis contributes to the clinical severity of psoriasis

Analysis of ceramide metabolites in differentiating epidermal keratinocytes treated with calcium or vitamin C

Ceramides (Cer) comprise the major constituent of sphingolipids in the epidermis and are known to play diverse roles in the outermost layers of the skin including water retention and provision of a physical barrier. In addition, they can be hydrolyzed into free sphingoid bases such as C18 sphingosine (SO) and C18 sphinganine (SA) or can be further metabolized to C18 So-1-phosphate (S1P) and C18 Sa-1-phosphate (Sa1P) in keratinocytes. The significance of ceramide metabolites emerged from studies reporting altered levels of SO and SA in skin disorders and the role of S1P and Sa1P as signaling lipids. However, the overall metabolism of sphingoid bases and their phosphates during keratinocyte differentiation remains not fully understood. Therefore, in this study, we analyzed these Cer metabolites in the process of keratinocyte differentiation. Three distinct keratinocyte differentiation stages were prepared using 0.07 mM calcium (Ca2+) (proliferation stage), 1.2 mM Ca2+ (early differentiation stage) in serum-free medium, or serum-containing medium with vitamin C (50 µL/mL) (late differentiation stage). Serum-containing medium was also used to determine whether vitamin C increases the concentrations of sphingoid bases and their phosphates. The production of sphingoid bases and their phosphates after hydrolysis by alkaline phosphatase was determined using high-performance liquid chromatography. Compared to cells treated with 0.07 mM Ca2+, levels of SO, SA, S1P, and SA1P were not altered after treatment with 1.2 mM Ca2+. However, in keratinocytes cultured in serum-containing medium with vitamin C, levels of SO, SA, S1P, and SA1P were dramatically higher than those in 0.07- and 1.2-mM Ca2+-treated cells; however, compared to serum-containing medium alone, vitamin C did not significantly enhance their production. Taken together, we demonstrate that late differentiation induced by vitamin C and serum was accompanied by dramatic increases in the concentration of sphingoid bases and their phosphates, although vitamin C alone had no effect on their production