Curious congruences for cyclotomic polynomials

Let $\Phi_n^{(k)}(x)$ be the $k$-th derivative of $n$-th cyclotomic polynomial. Extending a work of D.~H.~Lehmer, we show some curious congruences: $2\Phi^{(3)}_n(1)$ is divisible by $\phi(n)-2$ and $\Phi^{(2k+1)}_n(1)$ is divisible by $\phi(n)-2k$ for $k\ge 2$. The congruence stems from a general property of self-reciprocal polynomials.Comment: See remarks we recieved afterwards in the appendix. To appear in Research in Number Theor

cDNA cloning of rat major AP endonuclease (APEX nuclease) and analyses of its mRNA expression in rat tissues.

APEX nuclease is a mammalian DNA repair enzyme having apurinic/apyrimidinic (AP) endonuclease, 3'-5'-exonuclease, DNA 3' repair diesterase and DNA 3'-phosphatase activities. It is also a redox factor (Ref-1), stimulating DNA binding activity of AP-1 binding proteins such as Fos and Jun. In the present paper, a cDNA for the enzyme was isolated from a rat brain cDNA library using mouse Apex cDNA as a probe and sequenced. The rat Apex cDNA was 1221 nucleotides (nt) long, with a 951-nt coding region. The amino acid sequence of rat APEX nuclease has 98.4% identity with mouse APEX nuclease. Using the rat Apex cDNA as a probe for Northern blot analysis, the size of rat Apex mRNA was shown to be approximately 1.5 kb. Its expression was compared in 9 rat organs on postnatal days 7 and 28. Although Apex mRNA was expressed ubiquitously, the levels varied significantly, suggesting organ- or tissue-specific expression of the Apex gene. The highest level was observed in the testis, relatively high levels in the thymus, spleen, kidney and brain, and the lowest level in the liver. The level of expression at postnatal day 28, with the exception of the testis, was almost the same as or lower in respective organs than that at postnatal day 7. Postnatal developmental changes of Apex mRNA expression in the testis and thymus were further studied. The expression in testis was markedly increased on postnatal days 21 and 28. The expression in thymus increased once at postnatal day 14, and then decreased. The developmental changes of Apex mRNA expression in testis and thymus suggest that APEX nuclease is involved in processes such as recombinational events.</p

Decreased Deiminated Keratin K1 in Psoriatic Hyperproliferative Epidermis

Citrulline-containing proteins, mainly originating from keratin K1 and formed by enzymatic deimination of arginine residues, have been identified in the cornified layers of human epidermis. We analyzed the localization and nature of the deiminated proteins in psoriatic epidermis. Immunostaining based on chemical modification of citrulline residues showed that the normal and psoriatic uninvolved epidermis contained deiminated proteins diffusely in the cornified cell layer, whereas the involved epidermis had no detectable or markedly reduced levels of deiminated proteins. Immunolabeling with polyclonal antibodies against a synthetic citrulline-containing peptide corresponding to a deiminated sequence of mouse K1 also suggested markedly decreased deiminated K1 in psoriatic involved lesions. Keratin analyses indicated that deiminated K1 present in normal and psoriatic uninvolved epidermis was not detected in the psoriatic involved epidermis. Double staining with a monoclonal antibody, 34βB4, and the polyclonal antibodies demonstrated that epidermis with low suprabasal keratin expression was negative for deiminated K1. In contrast, intralesional acrosyringia showing decreased suprabasal keratin immunoreactivity like that of the surrounding psoriatic epidermis showed strong deiminated K1 staining. This suggests that abnormal keratin deimination is restricted to the psoriatic hyperproliferative epidermis, without affecting sweat ductal epithelia

Production of unnatural glucosides of curcumin with drastically enhanced water solubility by cell suspension cultures of Catharanthus roseus

AbstractCatharanthus roseus cell suspension cultures converted exogenously supplied curcumin to a series of glucosides, none of which has been found in nature so far. The efficiency of glucosylation was dependent on culture stage of the cells and medium sucrose concentration. Methyl jasmonate and salicylic acid enhanced the glucoside formation only when they were added to the cultures prior to the addition of curcumin. The glucoside yield was 2.5 μmol/g fresh weight of the cells at an optimal culture condition. The water solubility of curcumin-4′,4″-O-β-D-digentiobioside was 0.65 mmol/ml, which was 20 million-fold higher than that of curcumin