Search results for "Trefoil"
showing 4 items of 14 documents
A synthetic molecular pentafoil knot
2011
Knots are being discovered with increasing frequency in both biological and synthetic macromolecules and have been fundamental topological targets for chemical synthesis for the past two decades. Here, we report on the synthesis of the most complex non-DNA molecular knot prepared to date: the self-assembly of five bis-aldehyde and five bis-amine building blocks about five metal cations and one chloride anion to form a 160-atom-loop molecular pentafoil knot (five crossing points). The structure and topology of the knot is established by NMR spectroscopy, mass spectrometry and X-ray crystallography, revealing a symmetrical closed-loop double helicate with the chloride anion held at the centre…
Feynman diagrams as a weight system: four-loop test of a four-term relation
1996
At four loops there first occurs a test of the four-term relation derived by the second author in the course of investigating whether counterterms from subdivergence-free diagrams form a weight system. This test relates counterterms in a four-dimensional field theory with Yukawa and $\phi^4$ interactions, where no such relation was previously suspected. Using integration by parts, we reduce each counterterm to massless two-loop two-point integrals. The four-term relation is verified, with $ = 0 - 3\zeta_3 + 6\zeta_3 - 3\zeta_3 = 0$, demonstrating non-trivial cancellation of the trefoil knot and thus supporting the emerging connection between knots and counterterms, via transcendental number…
Insulin-like growth factor 1 differentially regulates estrogen receptor-dependent transcription at estrogen response element and AP-1 sites in breast…
2007
Cross-talk between insulin-like growth factor 1 (IGF-1) and estrogen receptor alpha (ER) regulates gene expression in breast cancer cells, but the underlying mechanisms remain unclear. Here, we studied how 17-beta-estradiol (E2) and IGF-1 affect ER transcriptional machinery in MCF-7 cells. E2 treatment stimulated ER loading on the estrogen response element (ERE) in the pS2 promoter and on the AP-1 motif in the cyclin D1 promoter. On ERE, similar amounts of liganded ER were found at 1-24-h time points, whereas on AP-1, ER binding fluctuated over time. At 1 h, liganded ER was recruited to ERE together with histone acetyltransferases SRC-1 and p300, ubiquitin ligase E6-AP, histone methyltransf…