The infimum, supremum and geodesic length of a braid conjugacy class

Algorithmic solutions to the conjugacy problem in the braid groups B_n were given by Elrifai-Morton in 1994 and by the authors in 1998. Both solutions yield two conjugacy class invariants which are known as `inf' and `sup'. A problem which was left unsolved in both papers was the number m of times one must `cycle' (resp. `decycle') in order to increase inf (resp. decrease sup) or to be sure that it is already maximal (resp. minimal) for the given conjugacy class. Our main result is to prove that m is bounded above by n-2 in the situation of the second algorithm and by ((n^2-n)/2)-1 in the situation of the first. As a corollary, we show that the computation of inf and sup is polynomial in both word length and braid index, in both algorithms. The integers inf and sup determine (but are not determined by) the shortest geodesic length for elements in a conjugacy class, as defined by Charney, and so we also obtain a polynomial-time algorithm for computing this geodesic length.Comment: 15 pages. Journa

Stabilization in the braid groups II: Transversal simplicity of knots

The main result of this paper is a negative answer to the question: are all transversal knot types transversally simple? An explicit infinite family of examples is given of closed 3-braids that define transversal knot types that are not transversally simple. The method of proof is topological and indirect.Comment: This is the version published by Geometry & Topology on 4 October 2006. Part I (arXiv:math/0310279) is also published in this volum

Distinct GSDMB protein isoforms and protease cleavage processes differentially control pyroptotic cell death and mitochondrial damage in cancer cells

Gasdermin (GSDM)-mediated pyroptosis is functionally involved in multiple diseases, but Gasdermin-B (GSDMB) exhibit cell death-dependent and independent activities in several pathologies including cancer. When the GSDMB pore-forming N-terminal domain is released by Granzyme-A cleavage, it provokes cancer cell death, but uncleaved GSDMB promotes multiple pro-tumoral effects (invasion, metastasis, and drug resistance). To uncover the mechanisms of GSDMB pyroptosis, here we determined the GSDMB regions essential for cell death and described for the first time a differential role of the four translated GSDMB isoforms (GSDMB1-4, that differ in the alternative usage of exons 6-7) in this process. Accordingly, we here prove that exon 6 translation is essential for GSDMB mediated pyroptosis, and therefore, GSDMB isoforms lacking this exon (GSDMB1-2) cannot provoke cancer cell death. Consistently, in breast carcinomas the expression of GSDMB2, and not exon 6-containing variants (GSDMB3-4), associates with unfavourable clinical-pathological parameters. Mechanistically, we show that GSDMB N-terminal constructs containing exon-6 provoke cell membrane lysis and a concomitant mitochondrial damage. Moreover, we have identified specific residues within exon 6 and other regions of the N-terminal domain that are important for GSDMB-triggered cell death as well as for mitochondrial impairment. Additionally, we demonstrated that GSDMB cleavage by specific proteases (Granzyme-A, Neutrophil Elastase and caspases) have different effects on pyroptosis regulation. Thus, immunocyte-derived Granzyme-A can cleave all GSDMB isoforms, but in only those containing exon 6, this processing results in pyroptosis induction. By contrast, the cleavage of GSDMB isoforms by Neutrophil Elastase or caspases produces short N-terminal fragments with no cytotoxic activity, thus suggesting that these proteases act as inhibitory mechanisms of pyroptosis. Summarizing, our results have important implications for understanding the complex roles of GSDMB isoforms in cancer or other pathologies and for the future design of GSDMB-targeted therapies.This study has been supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación (MICINN-AEI, PID2019-104644RB-I00, PDC2022-133252-I00) -GMB-, (PID2021-126625OB-I00-MCIN/AEI/10.13039/501100011033 FEDER, EU.2022- and DTS20-00024 -ISCIII-) -PGP-, the Instituto de Salud Carlos III (CIBERONC, CB16/12/00295 -GMB- and CB16/12/00241 -JA-, and AC21_2/00020 ERA PerMed ERA-NET, PMP22/00054 Immune4ALL Personalized Medicine -GMB-, cofunded by NextGenerationEU), I “Semilla” CIBERONC-GEICAM Grant -GMB- and the AECC Scientific Foundation (FCAECC PROYE19036MOR and GCTRA18014MATI -GMB-), the National Institutes of Health (NIH, USA) (R01-DK123475) -J-KK- and it has been also supported by a startup fund to -J-KK- from the Ohio State University, the College of Medicine, Department of Surgery. DS contract is funded by CIBERONC partly supported by FEDER funds. SO is funded by the FCAECC (POSTD20028OLTR), SC is funded by the MICINN-AEI PRE2020-095658

A unifying hypothesis for PNMZL and PTFL: morphological variants with a common molecular profile

Pediatric nodal marginal zone lymphoma (PNMZL) is an uncommon B-cell neoplasm affecting mainly male children and young adults. This indolent lymphoma has distinct characteristics that differ from those of conventional nodal marginal zone lymphoma (NMZL). Clinically, it exhibits overlapping features with pediatric-type follicular lymphoma (PTFL). To explore the differences between PNMZL and adult NMZL and its relationship to PTFL, a series of 45 PNMZL cases were characterized morphologically and genetically by using an integrated approach; this approach included whole-exome sequencing in a subset of cases, targeted next-generation sequencing, and copy number and DNA methylation arrays. Fourteen cases (31%) were diagnosed as PNMZL, and 31 cases (69%) showed overlapping histologic features between PNMZL and PTFL, including a minor component of residual serpiginous germinal centers reminiscent of PTFL and a dominant interfollicular B-cell component characteristic of PNMZL. All cases displayed low genomic complexity (1.2 alterations per case) with recurrent 1p36/TNFRSF14 copy number-neutral loss of heterozygosity alterations and copy number loss (11%). Similar to PTFL, the most frequently mutated genes in PNMZL were MAP2K1 (42%), TNFRSF14 (36%), and IRF8 (34%). DNA methylation analysis revealed no major differences between PTFL and PNMZL. Genetic alterations typically seen in conventional NMZL were absent in PNMZL. In summary, overlapping clinical, morphologic, and molecular findings (including low genetic complexity; recurrent alterations in MAP2K1, TNFRSF14, and IRF8; and similar methylation profiles) indicate that PNMZL and PTFL are likely part of a single disease with variation in the histologic spectrum. The term "pediatric-type follicular lymphoma with and without marginal zone differentiation" is suggested.Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0), permitting only noncommercial, nonderivative use with attribution. All other rights reserved

Mediator of DNA Damage Checkpoint 1 (MDC1) Contributes to High NaCl-Induced Activation of the Osmoprotective Transcription Factor TonEBP/OREBP

Background: Hypertonicity, such as induced by high NaCl, increases the activity of the transcription factor TonEBP/OREBP whose target genes increase osmoprotective organic osmolytes and heat shock proteins. Methodology: We used mass spectrometry to analyze proteins that coimmunoprecipitate with TonEBP/OREBP in order to identify ones that might contribute to its high NaCl-induced activation. Principal Findings: We identified 20 unique peptides from Mediator of DNA Damage Checkpoint 1 (MDC1) with high probability. The identification was confirmed by Western analysis. We used small interfering RNA knockdown of MDC1 to characterize its osmotic function. Knocking down MDC1 reduces high NaCl-induced increases in TonEBP/OREBP transcriptional and transactivating activity, but has no significant effect on its nuclear localization. We confirm six previously known phosphorylation sites in MDC1, but do not find evidence that high NaCl increases phosphorylation of MDC1. It is suggestive that MDC1 acts as a DNA damage response protein since hypertonicity reversibly increases DNA breaks, and other DNA damage response proteins, like ATM, also associate with TonEBP/OREBP and contribute to its activation by hypertonicity. Conclusions/Significance: MDC1 associates with TonEBP/OREBP and contributes to high NaCl-induced increase of tha

Measuring the positive psychological well-being of people with rheumatoid arthritis: a cross-sectional validation of the subjective vitality scale

Introduction: People with rheumatoid arthritis (RA) frequently suffer from compromised physical and psychological health, however, little is known about positive indicators of health, due to a lack of validated outcome measures. This study aims to validate a clinically relevant outcome measure of positive psychological well-being for people with RA. The first study examined the reliability and factorial validity of the Subjective Vitality Scale (SVS), whilst study 2 tested the instruments convergent validity. Methods: In study 1, National Rheumatoid Arthritis Society members (N = 333; M age = 59.82 years SD = 11.00) completed a postal questionnaire. For study 2, participants (N = 106; M age = 56 years, SD = 12 years) were those recruited to a randomized control trial comparing two physical activity interventions who completed a range of health-related questionnaires. Results: The SVS had a high level of internal consistency (α = .93, Rho = .92). Confirmatory factor analysis supported the uni-dimensional factor structure of the questionnaire among RA patients [χ = 1327 (10), CFI = 1.0, SRMSR = .01 and RMSEA = .00 (.00 - .08)]. Support for the scales convergent validity was revealed by significant (p < .05) relationships, in expected directions, with health related quality of life (r = .59), physical function (r = .58), feelings of fatigue (r = −.70), anxiety (r = −.57) and depression (r = −.73). Conclusions: Results from two studies have provided support for the internal consistency, factorial structure and convergent validity of the Subjective Vitality Scale. Researchers and healthcare providers may employ this clinically relevant, freely available and brief assessment with the confidence that it is a valid and reliable measure of positive psychological well-being for RA patients

European research priorities for intracerebral haemorrhage

Over 2 million people are affected by intracerebral haemorrhage (ICH) worldwide every year, one third of them dying within 1 month, and many survivors being left with permanent disability. Unlike most other stroke types, the incidence, morbidity and mortality of ICH have not declined over time. No standardised diagnostic workup for the detection of the various underlying causes of ICH currently exists, and the evidence for medical or surgical therapeutic interventions remains limited. A dedicated European research programme for ICH is needed to identify ways to reduce the burden of ICH-related death and disability. The European Research Network on Intracerebral Haemorrhage EURONICH is a multidisciplinary academic research collaboration that has been established to define current research priorities and to conduct large clinical studies on all aspects of ICH. Copyright (C) 2011 S. Karger AG, Base