Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Translation termination and protein folding pathway genes are not correlated in gastric cancer

Background: The eukaryotic release factor 3 (eRF3) has been shown to affect both tubulin and actin cytoskeleton, suggesting a role in cytoskeleton assembly, mitotic spindle formation and chromosome segregation. Also, direct interactions between eRF3 and subunits of the cytosolic chaperonin CCT have been described. Moreover, both eRF3a and CCT subunits have been described to be up-regulated in cancer tissues. Our aim was to evaluate the hypothesis that eRF3 expression levels are correlated with the expression of genes encoding proteins involved in the tubulin folding pathways. Methods: Relative expression levels of eRF1, eRF3a/GSPT1, PFDN4, CCT2, CCT4, and TBCA genes in tumour samples relative to their adjacent normal tissues were investigated using real time-polymerase chain reaction in 20 gastric cancer patients. Results: The expression levels of eRF3a/GSPT1 were not correlated with the expression levels of the other genes studied. However, significant correlations were detected between the other genes, both within intestinal and diffuse type tumours. Conclusions: eRF3a/GSPT1 expression at the mRNA level is independent from both cell translation rates and from the expression of the genes involved in tubulin-folding pathways. The differences in the patterns of expression of the genes studied support the hypothesis of genetically independent pathways in the origin of intestinal and diffuse type gastric tumours.

Modulation of translation factor's gene expression by histone deacetylase inhibitors in breast cancer cells

The histone deacetylase inhibitors sodium butyrate (NaBu) and trichostatin A (TSA) exhibit anti-proliferative activity by causing cell cycle arrest and apoptosis. The mechanisms by which NaBu and TSA cause apoptosis and cell cycle arrest are not yet completely clarified, although these agents are known to modulate the expression of several genes including cell-cycle- and apoptosis-related genes. The enzymes involved in the process of translation have important roles in controlling cell growth and apoptosis, and several of these translation factors have been described as having a causal role in the development of cancer. The expression patterns of the translation mechanism, namely of the elongation factors eEF1A1 and eEF1A2, and of the termination factors eRF1 and eRF3, were studied in the breast cancer cell line MCF-7 by real-time quantitative reverse transcription-polymerase chain reaction after a 24-h treatment with NaBu and TSA. NaBu induced inhibition of translation factors' transcription, whereas TSA caused an increase in mRNA levels. Thus, these two agents may modulate the expression of translation factors through different pathways. We propose that the inhibition caused by NaBu may, in part, be responsible for the cell cycle arrest and apoptosis induced by this agent in MCF-7 cells.