Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Thyroid hormone can increase estrogen-mediated transcription from a consensus estrogen response element in neuroblastoma cells

Thyroid hormones (T) and estrogens (E) are nuclear receptor ligands with at least two molecular mechanisms of action: (i) relatively slow genomic effects, such as the regulation of transcription by cognate T receptors (TR) and E receptors (ER); and (ii) relatively rapid nongenomic effects, such as kinase activation and calcium release initiated at the membrane by putative membrane receptors. Genomic and nongenomic effects were thought to be disparate and independent. However, in a previous study using a two-pulse paradigm in neuroblastoma cells, we showed that E acting at the membrane could potentiate transcription from an E-driven reporter gene in the nucleus. Because both T and E can have important effects on mood and cognition, it is possible that the two hormones can act synergistically. In this study, we demonstrate that early actions of T via TRalpha1 and TRbeta1 can potentiate E-mediated transcription (genomic effects) from a consensus E response element (ERE)-driven reporter gene in transiently transfected neuroblastoma cells. Such potentiation was reduced by inhibition of mitogen-activated protein kinase. Using phosphomutants of ERalpha, we also show that probable mitogen-activated protein kinase phosphorylation sites on the ERalpha, the serines at position 167 and 118, are important in TRbeta1-mediated potentiation of ERalpha-induced transactivation. We suggest that crosstalk between T and E includes potential interactions through both nuclear and membrane-initiated molecular mechanisms of hormone signaling.