Resonances of the cusp family

We study a family of chaotic maps with limit cases-the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius-Perron operator in different function spaces including spaces of analytical functions and study numerically the eigenvalues and eigenfunctions.

AINT/ERIC/TACC: an expanding family of proteins with C-terminal coiled coil domains:an expanding family of proteins with C-terminal coiled coil domains

The AINT/ERIC/TACC genes encode novel proteins with a coiled coil domain at their C-terminus. The founding member of this expanding family of genes, transforming acidic coiled coil 1 (TACC1), was isolated from a BAC contig spanning the breast cancer amplicon-1 on 8p11. Transfection of cells in vitro with TACC1 resulted in anchorage-independent growth consistent with a more "neoplastic" phenotype. Database searches employing the human TACC1 sequence revealed other novel genes, TACC2 and TACC3, with substantial sequence homology particularly in the C-terminal regions encoding the coiled coil domains. TACC2, located at 10q26, is similar to anti-zuai-1 (AZU-1), a candidate breast tumour suppressor gene, and ECTACC, an endothelial cell TACC which is upregulated by erythropoietin (Epo). The murine homologue of TACC3, murine erythropoietin-induced cDNA (mERIC-1) was also found to be upregulated by Epo in the Friend virus anaemia (FVA) model by differential display-PCR. Human ERIC-1, located at 4p16.3, has been cloned and encodes an 838-amino acid protein whose N- and C-terminal regions are highly homologous to the shorter 558-amino acid murine protein, mERIC-1. In contrast, the central portions of these proteins differ markedly. The murine protein contains four 24 amino acid imperfect repeats. ARNT interacting protein (AINT), a protein expressed during embryonic development in the mouse, binds through its coiled coil region to the aryl hydrocarbon nuclear translocator protein (ARNT) and has a central portion that contains seven of the 24 amino acid repeats found in mERIC-1. Thus mERIC-1 and AINT appear to be developmentally regulated alternative transcripts of the gene. Most members of the TACC family discovered so far contain a novel nine amino acid putative phosphorylation site with the pattern [R/K]-X(3)-[E]-X(3)-Y. Genes with sequence homology to the AINT/ERIC/TACC family in other species include maskin in Xenopus, D-TACC in Drosophila and TACC4 in the rabbit. Maskin contains a peptide sequence conserved among eIF-4E binding proteins that is involved in oocyte development. D-TACC cooperates with another conserved microtubule-associated protein Msps to stabilise spindle poles during cell division. The diversity of function already attributed to this protein family, including both transforming and tumour suppressor properties, should ensure that a new and interesting narrative is about to unfold.