RNA analysis by ion-pair reversed-phase high performance liquid chromatography

Ion-pair reversed-phase high performance liquid chromatography (IP RP HPLC) is presented as a new, superior method for the analysis of RNA. IP RP HPLC provides a fast and reliable alternative to classical methods of RNA analysis, including separation of different RNA species, quantification and purification. RNA is stable under the analysis conditions used; degradation of RNA during the analyses was not observed. The versatility of IP RP HPLC for RNA analysis is demonstrated. Components of an RNA ladder, ranging in size from 155 to 1770 nt, were resolved. RNA transcripts of up to 5219 nt were analyzed, their integrity determined and they were quantified and purified. Purification of mRNA from total RNA is described, separating mouse rRNA from poly(A)+ mRNA. IP RP HPLC is also suitable for the separation and purification of DIG-labeled from unlabeled RNA. RNA purified by IP RP HPLC exhibits improved stability.

Inferring phylogenies from DNA sequences of unequal base compositions.

A new method for computing evolutionary distances between DNA sequences is proposed. Contrasting with classical methods, the underlying model does not assume that sequence base compositions (A, C, G, and T contents) are at equilibrium, thus allowing unequal base compositions among compared sequences. This makes the method more efficient than the usual ones in recovering phylogenetic trees from sequence data when base composition is heterogeneous within the data set, as we show by using both simulated and empirical data. When applied to small-subunit ribosomal RNA sequences from several prokaryotic or eukaryotic organisms, this method provides evidence for an early divergence of the microsporidian Vairimorpha necatrix in the eukaryotic lineage.

Zeta functions and Eisenstein series on classical groups

We construct an Euler product from the Hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a CM field and the eigenform is holomorphic. We also prove analytic continuation of an Eisenstein series on another unitary group, containing the group just mentioned defined with such an eigenform. As an application of our methods, we prove an explicit class number formula for a totally definite hermitian form over a CM field.