Global hypoellipticity and global solvability for vector fields on compact Lie groups

We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In view of Greenfield's and Wallach's conjecture, about the non-existence of globally hypoelliptic vector fields on compact manifolds different from tori, we also investigate different notions of regularity weaker than global hypoellipticity and describe completely the global hypoellipticity and global solvability of zero-order perturbations of our vector fields. We also present a class of vector fields with variable coefficients whose operators can be reduced to a normal form, and we prove that the study of the global properties of such operators is equivalent to the study of the respective properties for their normal forms.Comment: 43 page

Transcriptional responses of in vivo praziquantel exposure in schistosomes identifies a functional role for calcium signalling pathway member CamKII

Treatment for clinical schistosomiasis has relied centrally on the broad spectrum anthelmintic praziquantel; however, there is limited information on its mode of action or the molecular response of the parasite. This paper presents a transcriptional and functional approach to defining the molecular responses of schistosomes to praziquantel. Differential gene expression in Schistosoma japonicum was investigated by transcriptome-wide microarray analysis of adult worms perfused from infected mice after 0.5 to 24 hours after oral administration of sub-lethal doses of praziquantel. Genes up-regulated initially in male parasites were associated with "Tegument/Muscle Repair" and "Lipid/Ion Regulation" functions and were followed by "Drug Resistance" and "Ion Regulation" associated genes. Prominent responses induced in female worms included upregulation of "Ca²⁺ Regulation" and "Drug Resistance" genes and later by transcripts of "Detoxification" and "Pathogen Defense" mechanisms. A subset of highly over-expressed genes, with putative drug resistance/detoxification roles or Ca²⁺-dependant/modulatory functions, were validated by qPCR. The leading candidate among these was CamKII, a putative calcium/calmodulin-dependent protein kinase type II delta chain. RNA interference was employed to knockdown CamKII in S. japonicum to determine the role of CamKII in the response to praziquantel. After partial-knockdown, schistosomes were analysed using IC₅₀ concentrations (50% worm motility) and quantitative monitoring of parasite movement. When CamKII transcription was reduced by 50-69% in S. japonicum, the subsequent effect of an IC₅₀ dosage of praziquantel was exacerbated, reducing motility from 47% to 27% in female worms and from 61% to 23% in males. These observations indicated that CamKII mitigates the effects of praziquantel, probably through stabilising Ca²⁺ fluxes within parasite muscles and tegument. Together, these studies comprehensively charted transcriptional changes upon exposure to praziquantel and, notably, identified CamKII as potentially central to the, as yet undefined, mode of action of praziquantel