All Small Nuclear RNAs (snRNAs) of the [U4/U6.U5] Tri-snRNP Localize to Nucleoli; Identification of the Nucleolar Localization Element of U6 snRNA

Previously, we showed that spliceosomal U6 small nuclear RNA (snRNA) transiently passes through the nucleolus. Herein, we report that all individual snRNAs of the [U4/U6.U5] tri-snRNP localize to nucleoli, demonstrated by fluorescence microscopy of nucleolar preparations after injection of fluorescein-labeled snRNA into Xenopus oocyte nuclei. Nucleolar localization of U6 is independent from [U4/U6] snRNP formation since sites of direct interaction of U6 snRNA with U4 snRNA are not nucleolar localization elements. Among all regions in U6, the only one required for nucleolar localization is its 3′ end, which associates with the La protein and subsequently during maturation of U6 is bound by Lsm proteins. This 3′-nucleolar localization element of U6 is both essential and sufficient for nucleolar localization and also required for localization to Cajal bodies. Conversion of the 3′ hydroxyl of U6 snRNA to a 3′ phosphate prevents association with the La protein but does not affect U6 localization to nucleoli or Cajal bodies

Extended Crystal PDE's

In this paper we show that between PDE's and crystallographic groups there is an unforeseen relation. In fact we prove that integral bordism groups of PDE's can be considered extensions of crystallographic subgroups. In this respect we can consider PDE's as {\em extended crystals}. Then an algebraic-topological obstruction ({\em crystal obstruction}), characterizing existence of global smooth solutions for smooth boundary value problems, is obtained. Applications of this new theory to the Ricci-flow equation and Navier-Stokes equation are given that solve some well-known fundamental problems. These results, are also extended to singular PDE's, introducing ({\em extended crystal singular PDE's}). An application to singular MHD-PDE's, is given following some our previous results on such equations, and showing existence of (finite times stable smooth) global solutions crossing critical nuclear energy production zone