Proper Mergings of Stars and Chains are Counted by Sums of Antidiagonals in Certain Convolution Arrays -- The Details

A proper merging of two disjoint quasi-ordered sets $P$ and $Q$ is a quasi-order on the union of $P$ and $Q$ such that the restriction to $P$ or $Q$ yields the original quasi-order again and such that no elements of $P$ and $Q$ are identified. In this article, we determine the number of proper mergings in the case where $P$ is a star (i.e. an antichain with a smallest element adjoined), and $Q$ is a chain. We show that the lattice of proper mergings of an $m$-antichain and an $n$-chain, previously investigated by the author, is a quotient lattice of the lattice of proper mergings of an $m$-star and an $n$-chain, and we determine the number of proper mergings of an $m$-star and an $n$-chain by counting the number of congruence classes and by determining their cardinalities. Additionally, we compute the number of Galois connections between certain modified Boolean lattices and chains.Comment: 27 pages, 7 figures, 1 table. Jonathan Farley has solved Problem 4.18; added Section 4.4 to describe his solutio

Understanding cisplatin resistance using cellular models

Many mechanisms of cisplatin resistance have been proposed from studies of cellular models of resistance including changes in cellular drug accumulation, detoxification of the drug, inhibition of apoptosis and repair of the DNA adducts. A series of resistant models were developed from CCRF-CEM leukaemia cells with increasing doses of cisplatin from 100 ng/ml. This produced increasing resistance up to 7-fold with a treatment dose of 1.6 microg/ml. Cisplatin resistance in these cells correlated with increases in the antioxidant glutathione, yet treatment with buthionine sulphoximine, an inhibitor of glutathione synthesis, had no effect on resistance, suggesting that the increase in glutathione was not directly involved in cisplatin resistance. Two models were developed from H69 SCLC cells, H69-CP and H69CIS200 using 100 ng/ml or 200 ng/ml cisplatin respectively. Both cell models were 2-4 fold resistant to cisplatin, and have decreased expression of p21 which may increase the cell's ability to progress through the cell cycle in the presence of DNA damage. Both the H69-CP and H69CIS200 cells showed no decrease in cellular cisplatin accumulation. However, the H69-CP cells have increased levels of cellular glutathione and are cross resistant to radiation whereas the H69CIS200 cells have neither of these changes. This suggests that increases in glutathione may contribute to cross-resistance to other drugs and radiation, but not directly to cisplatin resistance. There are multiple resistance mechanisms induced by cisplatin treatment, even in the same cell type. How then should cisplatin-resistant cancers be treated? Cisplatin-resistant cell lines are often more sensitive to another chemotherapeutic drug paclitaxel (H69CIS200), or are able to be sensitized to cisplatin with paclitaxel pre-treatment (H69-CP). The understanding of this sensitization by paclitaxel using cell models of cisplatin resistance will lead to improvements in the clinical treatment of cisplatin resistant tumours

A systematic review of genes involved in the inverse resistance relationship between cisplatin and paclitaxel chemotherapy: role of BRCA1

A systematic review of cell models of acquired drug resistance not involving genetic manipulation showed that 80% of cell models had an inverse resistance relationship between cisplatin and paclitaxel. Here we systematically review genetically modified cell lines in which the inverse cisplatin/paclitaxel resistance phenotype has resulted. This will form a short list of genes which may play a role in the mechanism of the inverse resistance relationship as well as act as potential markers for monitoring the development of resistance in the clinical treatment of cancer. The literature search revealed 91 genetically modified cell lines which report toxicity or viability/apoptosis data for cisplatin and paclitaxel relative to their parental cell lines. This resulted in 26 genes being associated with the inverse cisplatin/paclitaxel phenotype. The gene with the highest number of genetically modified cell lines associated with the inverse resistance relationship was BRCA1 and this gene is discussed in detail with reference to chemotherapy response in cell lines and in the clinical treatment of breast, ovarian and lung cancer. Other genes associated with the inverse resistance phenotype included dihydrodiol dehydrogenase (DDH) and P-glycoprotein. Genes which caused cross resistance or cross sensitivity between cisplatin and paclitaxel were also examined, the majority of these genes were apoptosis associated genes which may be useful for predicting cross resistance. We propose that BRCA1 should be the first of a panel of cellular markers to predict the inverse cisplatin/paclitaxel resistance phenotype

ERCC1 expression and RAD51B activity correlate with cell cycle response to platinum drug treatment not DNA repair

Background: The H69CIS200 and H69OX400 cell lines are novel models of low-level platinum-drug resistance. Resistance was not associated with increased cellular glutathione or decreased accumulation of platinum, rather the resistant cell lines have a cell cycle alteration allowing them to rapidly proliferate post drug treatment. Results: A decrease in ERCC1 protein expression and an increase in RAD51B foci activity was observed in association with the platinum induced cell cycle arrest but these changes did not correlate with resistance or altered DNA repair capacity. The H69 cells and resistant cell lines have a p53 mutation and consequently decrease expression of p21 in response to platinum drug treatment, promoting progression of the cell cycle instead of increasing p21 to maintain the arrest. Conclusion: Decreased ERCC1 protein and increased RAD51B foci may in part be mediating the maintenance of the cell cycle arrest in the sensitive cells. Resistance in the H69CIS200 and H69OX400 cells may therefore involve the regulation of ERCC1 and RAD51B independent of their roles in DNA repair. The novel mechanism of platinum resistance in the H69CIS200 and H69OX400 cells demonstrates the multifactorial nature of platinum resistance which can occur independently of alterations in DNA repair capacity and changes in ERCC1

A 39 kDa fragment of endogenous ASK1 suggests specific cleavage not degradation by the proteasome

Transfected human apoptosis signal-regulating kinase 1 (ASK1) produces a 150 kDa protein. However, we have detected endogenous ASK1 predominantly as 39 and 50 kDa C-terminal and 75 and 110 kDa N-terminal fragments in a panel of nontransfected cancer cell lines and HUVEC endothelial cells. This suggests that in nonapoptotic cells, endogenous ASK1 protein is normally cleaved at a number of specific sites, some of which are in the kinase domain. Transfected ASK1 protein is known to be degraded by the proteasome. In contrast, the cleavage of endogenous ASK1 is independent of the proteasome as treatment with the proteasome inhibitor, lactacystin did not inhibit cleavage. Cisplatin treatment decreased the amount of 39 kDa C-terminal ASK1 fragments in mutant p53 cell lines suggesting a decrease in cleavage associated with apoptosis. Transfected ASK1 may, therefore, not accurately reflect the role of endogenous ASK1

Platinum resistance needs the mythbusters

Letter to the Edito

Further thoughts on precision

Background: There has been much discussion amongst automated software defect prediction researchers regarding use of the precision and false positive rate classifier performance metrics. Aim: To demonstrate and explain why failing to report precision when using data with highly imbalanced class distributions may provide an overly optimistic view of classifier performance. Method: Well documented examples of how dependent class distribution affects the suitability of performance measures. Conclusions: When using data where the minority class represents less than around 5 to 10 percent of data points in total, failing to report precision may be a critical mistake. Furthermore, deriving the precision values omitted from studies can reveal valuable insight into true classifier performancePeer reviewedFinal Accepted Versio