We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, in the contractive as well as in the isometric case, we prove that a σ-Henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference group) are NTP2.

Caused by a polyglutamine expansion in the huntingtin protein, Huntington's disease leads to stnatal degeneration via the transcriptional dysregulation of a number of genes, including those involved in mitochondnal biogenesis. Here we show that transglutaminase 2, which is upregulated in HD, exacerbates transcriptional dysregulation by acting as a selective corepressor of nuclear genes; transglutaminase 2 interacts directly with histone H3 in the nucleus. In a cellular model of HD, transglutaminase inhibition de-repressed two established regulators of mitochondrial function, PGC-l alpha and cytochrome c and reversed susceptibility of human HD cells to the mitochondrial toxin, 3-nitroproprionic acid; however, protection mediated by transglutaminase inhibition was not associated with improved mitochondnal bioenergetics. A gene microarray analysis indicated that transglutaminase inhibition normalized expression of not only mitochondrial genes but also 40% of genes that are dysregulated in HD striatal neurons, including chaperone and histone genes. Moreover, transglutaminase inhibition attenuated degeneration in a Drosophila model of HD and protected mouse HD stnatal neurons from excitotoxicity. Altogether these findings demonstrate that selective TG inhibition broadly corrects transcriptional dysregulation in HD and defines a novel HDAC-independent epigenetic strategy for treating neurodegeneration.