The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

Human twinning is not linked to the region of chromosome 4 syntenic with the sheep twinning gene FecB

The tendency to dizygotic (DZ) twinning is inherited in both humans and sheep, and a fecundity gene in sheep (FecB) maps to sheep chromosome 6, syntenic with human 4q21-25. Our aim was to see whether a gene predisposing to human DZ twinning mapped to this region. DNA was collected from 169 pairs and 17 sets of 3 sisters (trios) from Australia and New Zealand who had each had spontaneous DZ twins, mostly before the age of 35, and from a replication sample of 111 families (92 affected sister pairs) from The Netherlands. Exclusion mapping was carried out after typing 26 markers on chromosome 4, of which 8 spanned the region Likely to contain the human homologue of the sheep FecB gene. We used nonparametric affected sib pair methods for linkage analysis [ASPEX 2.2, Hinds and Risch, 1999]. Complete exclusion of linkage (lod < -2) of a gene conferring a relative risk for sibs as low as 1.5 ((s) > 1.5) was obtained for all but the p terminus region on chromosome 4. Exclusion in the syntenic region was stronger, down to lambda (s) = 1.3. We concluded that if there is a gene influencing DZ twinning on chromosome 4, its effect must be minor. (C) 2001 Wiley-Liss, Inc.

No significant association between progesterone receptor exon 4 Val660Leu G/T polymorphism and risk of ovarian cancer

Epidemiological studies suggest that ovarian cancer is an endocrine-related tumour, and progesterone exposure specifically may decrease the risk of ovarian cancer. To assess whether the progesterone receptor (PR) exon 4 valine to leucine amino acid variant is associated with specific tumour characteristics or with overall risk of ovarian cancer, we examined 551 cases of epithelial ovarian cancer and 298 unaffected controls for the underlying G-->T nucleotide substitution polymorphism. Stratification of the ovarian cancer cases according to tumour behaviour (low malignant potential or invasive), histology, grade or stage failed to reveal any heterogeneity with respect to the genotype defined by the PR exon 4 polymorphism. Furthermore, the genotype distribution did not differ significantly between ovarian cancer cases and unaffected controls. Compared with the GG genotype, the age-adjusted odds ratio (95% confidence interval) for risk of ovarian cancer was 0.78 (0.57-1.08) for the GT genotype, and 1.39 (0.47-4.14) for the TT genotype. In conclusion, the PR exon 4 codon 660 leucine variant encoded by the T allele does not appear to be associated with ovarian tumour behaviour, histology, stage or grade. This variant is also not associated with an increased risk of ovarian cancer, and is unlikely to be associated with a large decrease in ovarian cancer risk, although we cannot rule out a moderate inverse association between the GT genotype and ovarian cancer.

Conversion of glucosamine to galactosamine and allosamine derivatives: Control of inversions of stereochemistry at C-3 and C-4

The reactions of sodium benzoate with a series of trimesylates derived from glucosamine have been examined in an attempt to gain facile access to galactosamine analogues. Trimesylate 17, in which the amino group was protected as a phthalimide, underwent double displacement at positions 4 and 6 to give the dibenzoate 18 with the desired galactosamine configuration. In contrast, trimesylates 21 and 27, in which the amino groups were protected as acetamides, unexpectedly underwent double displacement at positions 3 and 6, giving products 22 and 28, respectively, with allosamine configurations.