Strong and safe Nash equilibrium in some repeated 3-player games

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players' payoffs do not exceed the non-deviating player payoff more than a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale's good strategies described in \cite{smale}, where the repeated Prisoner's Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.Comment: 19 page

Trastuzumab deruxtecan in the treatment of adult patients with HER2-positive breast cancer

In 2020, approximately 18,000 women in Poland were diagnosed with breast cancer, and 6,000 of them died. In recent years, we have witnessed significant progress in the diagnosis and treatment of breast cancer patients. When detected early and treated appropriately, the prognosis is very good, and even some patients with distant metastases have experienced long-term survival. The most common biological subtype is hormone receptor-positive breast cancer, accounting for about 70% of diagnoses, showing expression of estrogen and progesterone receptors. Triple-negative breast cancer and HER2-positive breast cancer each make up approximately 15% of all cases. In the treatment of advanced HER2-positive breast cancer, a combination of docetaxel with pertuzumab and trastuzumab is used in the first line. In subsequent lines of treatment, options include trastuzumab deruxtecan (T-DXd), trastuzumab emtansine, lapatinib, tucatinib, margetuximab, and trastuzumab. Trastuzumab derukstekan is an immunoconjugate that, upon entering the cell, releases a cytostatic agent that destroys its genetic material and neighboring cells (the “bystander effect”). It significantly prolongs the time to disease progression and overall survival compared to standard treatments used in the second and subsequent lines of treatment. It represents an effective and valuable therapeutic option for patients with early-stage HER2- positive metastatic breast cancer

Should perioperative chemotherapy in triple negative breast cancer routinely comprise platinum salts? A vote for no

Breast cancer is the most common female neoplasm in Poland and worldwide, its mortality rate ranking second only to lung cancer. There are several biological subtypes, differing, among other parameters, as to prognosis and perioperative treatment recommendations. Triple negative breast cancer is one of the worst prognoses and systemic preoperative treatment is recommended as early as of II TNM stage. Pathological complete response (pCR) may result in an improved prognosis. Most patients respond well to standard chemotherapy and there is no need to include platinum derivatives in perioperative therapies. One should remember that platinum salts use not only increases the percentage of pCRs, but also results in an increased therapeutic toxicity; it does not, however, have an impact on disease free survival (DFS) an overall survival (OS)

Efficient termination of transcription by RNA polymerase I requires the 5 ' exonuclease Rat1 in yeast

During transcription termination by RNA polymerase II on protein-coding genes, the nuclear 5′ exonuclease Rat1/Xrn2 degrades the nascent transcript downstream from the polyadenylation site and “torpedoes” the polymerase. We report that the activity of Rat1 is also required for efficient termination by RNA polymerase I (Pol I) on the rDNA. In strains lacking catalytically active Rat1 or its cofactor Rai1, Pol I reads through the major, “Reb1-dependent” terminator (T1) but stops downstream at the “fail-safe” terminator (T2) and replication fork barrier (RFB). The absence of both Rat1 and the RFB-binding protein Fob1 increased Pol I read-through of T2 and the RFB. We propose that cotranscriptional cleavage of the pre-rRNA by the endonuclease Rnt1 generates a loading site for the Rat1/Rai1 complex, which then degrades the nascent transcript. When Rat1 catches Pol I, which is predicted to be paused at T1, transcription is terminated

Substrate discrimination in RNase P RNA-mediated cleavage: importance of the structural environment of the RNase P cleavage site

Like the translational elongation factor EF-Tu, RNase P interacts with a large number of substrates where RNase P with its RNA subunit generates tRNAs with matured 5′ termini by cleaving tRNA precursors immediately 5′ of the residue at +1, i.e. at the position that corresponds to the first residue in tRNA. Most tRNAs carry a G(+1)C(+72) base pair at the end of the aminoacyl acceptor-stem whereas in tRNA(Gln) G(+1)C(+72) is replaced with U(+1)A(+72). Here, we investigated RNase P RNA-mediated cleavage as a function of having G(+1)C(+72) versus U(+1)A(+72) in various substrate backgrounds, two full-size tRNA precursors (pre-tRNA(Gln) and pre-tRNA(Tyr)Su3) and a model RNA hairpin substrate (pATSer). Our data showed that replacement of G(+1)C(+72) with U(+1)A(+72) influenced ground state binding, cleavage efficiency under multiple and single turnover conditions in a substrate-dependent manner. Interestingly, we observed differences both in ground state binding and rate of cleavage comparing two full-size tRNA precursors, pre-tRNA(Gln) and pre-tRNA(Tyr)Su3. These findings provide evidence for substrate discrimination in RNase P RNA-mediated cleavage both at the level of binding, as previously observed for EF-Tu, as well as at the catalytic step. In our experiments where we used model substrate derivatives further indicated the importance of the +1/+72 base pair in substrate discrimination by RNase P RNA. Finally, we provide evidence that the structural architecture influences Mg(2+) binding, most likely in its vicinity

Diagnosis and treatment of patients with breast cancer and mutation in the BRCA1/2 genes

Breast cancer is the most common cancer among women in Poland and worldwide, second only to lung cancer in terms of mortality. Germline mutations account for approximately 5–10% of all breast cancer cases, with mutations in the BRCA1/2 genes being the most frequently identified. The presence of pathogenic variants in the BRCA1/2 genes is associated with a more than 60% risk of developing breast cancer, a 40–60% risk of ovarian cancer in women with a BRCA1 mutation, and a 13–30% risk in women with a BRCA2 variant. Breast cancer is often diagnosed at a younger age in BRCA1/2 mutation carriers. The prevalence and increased accessibility of genetic testing, especially next-generation sequencing, lead to a higher number of diagnosed individuals and healthy family members. Identifying a pathogenic variant in the BRCA1/2 genes, analyzing a family history, and genetic counseling enables the development of individual recommendations for further management. This article aims to present the diagnostic and therapeutic approach in breast cancer patients with a pathogenic variant in the BRCA1/2 genes

Microarray detection of novel nuclear RNA substrates for the exosome

Microarray analyses were performed on yeast strains mutant for the nuclear-specific exosome components Rrp6p and Rrp47p/Lrp1p or the core component Rrp41p/Ski6p, at permissive temperature and following transfer to 37 degrees C. 339 mRNAs showed clearly altered expression levels, with an unexpectedly high degree of heterogeneity in the different exosome mutants. In contrast, no clear alterations were seen in strains lacking the cytoplasmic exosome component Ski7p. 27 mRNAs that were overexpressed in each strain defective in the nuclear exosome are good candidates for regulation by nuclear turnover. These included the mRNA for the autoregulated RNA-binding protein Nrd1p. Northern and primer extension analyses confirmed the elevated NRD1 mRNA levels in exosome mutants, and revealed the accumulation of truncated 5' fragments of the mRNA. These contain a predicted Nrd1p-binding site, potentially sequestering the protein and disrupting its autoregulation. Several genes located immediately downstream of independently transcribed snoRNA genes were overexpressed in exosome mutants, presumably due to stabilization of the products of transcription termination read-through. Further analyses indicated that many snoRNA and snRNA genes are inefficiently terminated, but read-through transcripts into downstream ORFs are normally rapidly degraded by the exosome. Copyright (c) 2006 John Wiley & Sons, Ltd

Kiedy powiedzieć „nie” chorej w złym stanie ogólnym z nowotworem jajnika?

Nowotwory neuroendokrynne (NET) jajnika występują bardzo rzadko, stanowiąc około 0,52–1,7% wszystkich NET. Pierwotne rakowiaki stanowią około 0,1% nowotworów jajnika oraz 0,3% wszystkich rakowiaków. Rzadko wykazują czynność hormonalną. Rozpoznawane są najczęściej pooperacyjnie, na podstawie badania patomorfologicznego z wykorzystaniem metod immunohistochemicznych. Ze względu na niewielką liczbę przypadków większość informacji dotyczących postępowania u chorych z tym rozpoznaniem pochodzi z badań retrospektywnych i opisów przypadków. W niniejszej pracy przedstawiono opis przypadku 63-letniej chorej, która trafiła na oddział ginekologii operacyjnej z rozpoznaniem 15-centymetrowego guza jajnika prawego, w bardzo złym stanie ogólnym z powodu nasilonej niewydolności oddechowej i ciężkiej niewydolności zastawki trójdzielnej. Obraz kliniczny oraz wykonane badanie echokardiograficzne budziły podejrzenie rakowiakowej choroby serca (zespołu Hedingera — kardiologicznego zespołu rakowiaka). Dzięki zdeterminowaniu i współpracy wielospecjalistycznego zespołu medycznego, mimo bardzo złego rokowania, u chorej przeprowadzono operację. Bezpośrednio po operacji stan chorej był krytyczny, ale ulegał stopniowej poprawie. W pooperacyjnym badaniu patomorfologicznym rozpoznano nowotwór neuroendokrynny wysokozróżnicowany (G1) w stopniu zaawansowania IA według klasyfikacji FIGO. Chorą przekazano do kliniki endokrynologii, gdzie wykonano scyntygrafię receptorową, nie stwierdzając innych ognisk nowotworu. Chora nie wymagała leczenia uzupełniającego. Podjęcie decyzji o leczeniu operacyjnym chorej w stanie ciężkim z prawdopodobnie odwracalną przyczyną niewydolności serca było słuszne i umożliwiło jej powrót do normalnej sprawności fizycznej

When to say “no” to a patient with an ovarian tumour and in poor general condition?

Neuroendocrine tumours (NET) originating from the ovary are very rare, constituting about 0.52–1.7% of all NETs. Primary carcinoids constitute about 0.1% of ovarian tumours and 0.3% of all carcinoids. They rarely show hormonal activity. They are most often diagnosed post-operatively, based on pathomorphological examination using immunohistochemical methods. Due to the small number of cases, most information on the management of patients with this diagnosis comes from retrospective studies and case reports. This paper presents a case report of a 63-year-old woman who was admitted to the department of surgical gynaecology with the diagnosis of a 15-cm right ovary tumour. Her general condition was poor due to severe respiratory failure and severe tricuspid valve insufficiency. The clinical picture and the performed echocardiographic examination aroused the suspicion of carcinoid heart disease (Hedinger syndrome — a cardiological syndrome of carcinoids). Due to the determination and cooperation of a multidisciplinary medical team, despite a very bad prognosis, the patient underwent surgery. Immediately after the operation, the patient’s condition was critical, but it gradually improved. In the postoperative pathomorphological examination, a highly differentiated neuroendocrine tumour (grade 1 – G1) was diagnosed at stage IA according to the FIGO classification. The patient was referred to the endocrinology department, where receptor scintigraphy was performed without revealing other tumour changes. The patient did not require adjuvant therapy. Making a decision about surgical treatment of a patient in poor physical condition with a possibly reversible cause of heart failure was the right thing to do, and it allowed her to return to normal physical activity