It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorphic to the complement of the trefoil knot in S. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given by the Rademacher symbol, which is a homogenization of the classical Dedekind symbol. The Dedekind symbol arose historically in the transformation formula of the logarithm of Dedekind’s eta function...

It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorhic to the complement of the trefoil knot in S3. As is shown by E. Ghys the linking number of the trefoil with a modular knot associated to a hyperbolic conjugacy is related to the classical Dedekind symbol. These symbols arose historically in the transformation property of the logarithm of Dedekind’s eta function. In this paper we st...

The reaction of cis-Pt(NH3)2Cl2(cis-DDP)-closed circular DNA adducts with DNA topoisomerse I(topo I) were studied by electron microscopy. We identified unique topoisomers such as a singly-linked catenane (2(1)2), trefoil (3(1), and dimetric catenane (2(1)2), etc., by analysis with electron micrographs. These unique recombination products resulted from cis-DDP-intra-twisting looped DNA adducts b...

We report the stereoselective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer with six chiral centers using a lanthanide(III) ion template. The oligomer folds around the lanthanide ion to form an overhand knot complex of single handedness. Subsequent joining of the overhand knot end groups by ring-closing olefin metathesis affords a single enantiomer of t...

IL-12-mediated type 1 inflammation confers host protection against the parasitic protozoan Toxoplasma gondii. However, production of IFN-γ, another type 1 inflammatory cytokine, also drives lethality from excessive injury to the intestinal epithelium. As mechanisms that restore epithelial barrier function following infection remain poorly understood, this study investigated the role of trefoil ...

In the barley (Hordeum vulgare) Hooded (Kap) mutant, the duplication of a 305-bp intron sequence leads to the overexpression of the Barley knox3 (Bkn3) gene, resulting in the development of an extra flower in the spikelet. We used a one-hybrid screen to identify four proteins that bind the intron-located regulatory element (Kap intron-binding proteins). Three of these, Barley Ethylene Response ...

Trefoil factor family (TFF)-domain peptides (formerly P-domain peptides, trefoil factors) represent major mucin-associated peptides of the gastrointestinal tract. Here, the first localization studies on TFF3 in the lower respiratory tract of human material are presented. Immunohistochemistry revealed significant accumulation of TFF3 to mucous cells in the acini of submucosal glands and varying ...

Models of symmetric protein evolution typically invoke gene duplication and fusion events, in which repetition of a structural motif generates foldable, stable symmetric protein architecture. Success of such evolutionary processes suggests that the duplicated structural motif must be capable of nucleating protein folding. If correct, symmetric expansion of a folding nucleus sequence derived fro...