The interaction between caveolin-1 and Rho-GTPases promotes metastasis by controlling the expression of alpha5-integrin and the activation of Src, Ras and Erk

Proteins containing a caveolin-binding domain (CBD), such as the Rho-GTPases, can interact with caveolin-1 (Cav1) through its caveolin scaffold domain. Rho-GTPases are important regulators of p130Cas, which is crucial for both normal cell migration and Src kinase-mediated metastasis of cancer cells. However, although Rho-GTPases (particularly RhoC) and Cav1 have been linked to cancer progression and metastasis, the underlying molecular mechanisms are largely unknown. To investigate the function of Cav1–Rho-GTPase interaction in metastasis, we disrupted Cav1–Rho-GTPase binding in melanoma and mammary epithelial tumor cells by overexpressing CBD, and examined the loss-of-function of RhoC in metastatic cancer cells. Cancer cells overexpressing CBD or lacking RhoC had reduced p130Cas phosphorylation and Rac1 activation, resulting in an inhibition of migration and invasion in vitro. The activity of Src and the activation of its downstream targets FAK, Pyk2, Ras and extracellular signal-regulated kinase (Erk)1/2 were also impaired. A reduction in α5-integrin expression, which is required for binding to fibronectin and thus cell migration and survival, was observed in CBD-expressing cells and cells lacking RhoC. As a result of these defects, CBD-expressing melanoma cells had a reduced ability to metastasize in recipient mice, and impaired extravasation and survival in secondary sites in chicken embryos. Our data indicate that interaction between Cav1 and Rho-GTPases (most likely RhoC but not RhoA) promotes metastasis by stimulating α5-integrin expression and regulating the Src-dependent activation of p130Cas/Rac1, FAK/Pyk2 and Ras/Erk1/2 signaling cascades

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations

On the arithmetic of Knuth’s powers and some computational results about their density

The object of the paper are the so-called “unimaginable numbers”. In particular, we deal with some arithmetic and computational aspects of the Knuth’s powers notation and move some first steps into the investigation of their density. Many authors adopt the convention that unimaginable numbers start immediately after 1 googol which is equal to, and G.R. Blakley and I. Borosh have calculated that there are exactly 58 integers between 1 and 1 googol having a nontrivial “kratic representation”, i.e., are expressible nontrivially as Knuth’s powers. In this paper we extend their computations obtaining, for example, that there are exactly 2 893 numbers smaller than with a nontrivial kratic representation, and we, moreover, investigate the behavior of some functions, called krata, obtained by fixing at most two arguments in the Knuth’s power