Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Nucleolin is regulated both at the level of transcription and translation

Nucleolin is a multi-functional protein that is located to the nucleolus. In tissue Culture cells, the stability of nucleolin is related to the proliferation status of the cell. During development, rat cardiomyocytes proliferate actively with increases in the mass of the heart being due to both hyperplasia and hypertrophy. The timing of this shift in the phenotype of the myocyte from one capable of undergoing hyperplasia to one that can grow only by hypertrophy occurs within 4 days of post-natal development. Thus, cardiomyocytes are an ideal model system in which to study the regulation of nucleolin during growth in vivo. Using Western blot and quantitative RT-PCR (TaqMan) we found that the amount of nucleolin is regulated both at the level of transcription and translation during the development of the cardiomyocyte. However, in cells which had exited the cell cycle and were subsequently given a hypertrophic stimulus, nucleolin was regulated post-transcriptionally. (c) 2005 Elsevier Inc. All rights reserved.

Calicivirus translation initiation requires an interaction between VPg and eIF4E

Unlike other positive-stranded RNA viruses that use either a 5'-cap structure or an internal ribosome entry site to direct translation of their messenger RNA, calicivirus translation is dependent on the presence of a protein covalently linked to the 50 end of the viral genome (VPg). We have shown a direct interaction of the calicivirus VPg with the cap-binding protein eIF4E. This interaction is required for calicivirus mRNA translation, as sequestration of eIF4E by 4E-BP1 inhibits translation. Functional analysis has shown that VPg does not interfere with the interaction between eIF4E and the cap structure or 4E-BP1, suggesting that VPg binds to eIF4E at a different site from both cap and 4E-BP1. This work lends support to the idea that calicivirus VPg acts as a novel 'cap substitute' during initiation of translation on virus mRNA.