Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

Retroperitoneal Castleman's tumor and paraneoplastic pemphigus: report of a case and review of the literature

BACKGROUND: Castleman's disease is a rare lymphoproliferative syndrome. Its etiology and pathogenesis are unclear. The disease can be occasionally associated with a paraneoplastic pemphigus (PNP), an autoimmune mucocutaneous disorder commonly seen in neoplasms of lymphocytic origin. CASE PRESENTATION: We present a case of a 63-year old male patient who was referred for surgical treatment of a lately diagnosed retroperitoneal pelvic mass. The patient had been already treated for two years due to progressive diffuse cutaneous lesions histologically consistent with lichen ruber verucosus and pemphigus vulgaris. Intraoperatively a highly vascularized solid mass occupying the small pelvis was resected after meticulous vascular ligation and hemostasis. After surgery and following immunosuppressive treatment a clear remission of the skin lesions was observed. CONCLUSION: Castleman's tumor should be always suspected when a retroperitoneal mass is combined with PNP. In a review of the literature we found 37 additional cases. Complete surgical resection of the tumor can be curative in most of the cases

A model-independent approach to infer hierarchical codon substitution dynamics

<p>Abstract</p> <p>Background</p> <p>Codon substitution constitutes a fundamental process in molecular biology that has been studied extensively. However, prior studies rely on various assumptions, e.g. regarding the relevance of specific biochemical properties, or on conservation criteria for defining substitution groups. Ideally, one would instead like to analyze the substitution process in terms of raw dynamics, independently of underlying system specifics. In this paper we propose a method for doing this by identifying groups of codons and amino acids such that these groups imply closed dynamics. The approach relies on recently developed spectral and agglomerative techniques for identifying hierarchical organization in dynamical systems.</p> <p>Results</p> <p>We have applied the techniques on an empirically derived Markov model of the codon substitution process that is provided in the literature. Without system specific knowledge of the substitution process, the techniques manage to "blindly" identify multiple levels of dynamics; from amino acid substitutions (via the standard genetic code) to higher order dynamics on the level of amino acid groups. We hypothesize that the acquired groups reflect earlier versions of the genetic code.</p> <p>Conclusions</p> <p>The results demonstrate the applicability of the techniques. Due to their generality, we believe that they can be used to coarse grain and identify hierarchical organization in a broad range of other biological systems and processes, such as protein interaction networks, genetic regulatory networks and food webs.</p

Low root-to-root transmission of a tobamovirus, yellow tailflower mild mottle virus, and resilience of its virions

Tobamoviruses are serious pathogens because they have extremely stable virions, they are transmitted by contact, and they often induce severe disease in crops. Knowledge of the routes of transmission and resilience of tobamovirus virions is essential in understanding the epidemiology of this group of viruses. We used an isolate of the tobamovirus yellow tailflower mild mottle virus (YTMMV) to examine root-to-root transmission in soil and in a hydroponic growth environment. Root-to-root transmission occurred rarely, and when it occurred plants did not exhibit systemic movement of the virus from the roots to the shoots over a 30-day period. The resilience of YTMMV virions was tested in dried leaf tissue over time periods from one hour to one year under temperatures ranging from -80°C to 160°C. Infectivity was maintained for at least a year when incubated at -80°C, 22°C or at fluctuating ambient temperatures of 0.8°C to 44.4°C, but incubation under dry conditions at 160°C for >4 days eliminated infectivity. Exposure of virions to 0.1 M sodium hydroxide or 20% w/v skim milk solution for 30 min, treatments recommended for tobamovirus inactivation, did not abolish infectivity of YTMMV

Total Synthesis of 11â Saxitoxinethanoic Acid and Evaluation of its Inhibitory Activity on Voltageâ Gated Sodium Channels

11â Saxitoxinethanoic acid (SEA) is a member of the saxitoxin (STX) family of paralytic shellfish poisons, and contains an unusual Câ C bond at the C11 position. Reported herein is a total synthesis of SEA. The key to our synthesis lies in a Mukaiyama aldol condensation reaction of silyl enol ether with glyoxylate in the presence of an anhydrous fluoride reagent, [Bu4N][Ph3SnF2], which directly constructs the crucial Câ C bond at the C11 position in SEA. The NaVChâ inhibitory activities of SEA and its derivatives were evaluated by means of cellâ based assay. SEA showed an IC50 value of (47±12)â nm, which is approximately twice as potent as decarbamoylâ STX (dcSTX).At sea: 11â Saxitoxinethanoic acid (SEA) is a member of the saxitoxin family of paralytic shellfish poisons, and contains an unusual Câ C bond at the C11 position. Direct construction the Câ C bond at the C11 position of the saxitoxin skeleton involved a Mukaiyama condensation reaction an efficient synthesis of SEA.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137544/1/anie201604155-sup-0001-misc_information.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137544/2/anie201604155_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137544/3/anie201604155.pd

Integrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources

We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number of the integrable Rosochatius deformed higher-order constrained flows of some soliton hierarchies, which includes the generalized integrable H$\acute{e}$non-Heiles system, and the integrable Rosochatius deformations of the KdV hierarchy with self-consistent sources, of the AKNS hierarchy with self-consistent sources and of the mKdV hierarchy with self-consistent sources as well as their Lax representations are presented.Comment: 18 pages. to appear in J. Phys. A: Math. Ge

An efficient and scalable pipeline for epitope tagging in mammalian stem cells using Cas9 ribonucleoprotein

AbstractCRISPR/Cas9 can be used for precise genetic knock-in of epitope tags into endogenous genes, simplifying experimental analysis of protein function. However, Cas9-assisted epitope tagging in primary mammalian cell cultures is often inefficient and reliant on plasmid-based selection strategies. Here we demonstrate improved knock-in efficiencies of diverse tags (V5, 3XFLAG, Myc, HA) using co-delivery of Cas9 protein pre-complexed with two-part synthetic modified RNAs (annealed crRNA:tracrRNA) and single-stranded oligodeoxynucleotide (ssODN) repair templates. Knock-in efficiencies of ~5-30%, were achieved without selection in embryonic stem (ES) cells, neural stem (NS) cells, and brain tumour-derived stem cells. Biallelic-tagged clonal lines were readily derived and used to define Olig2 chromatin-bound interacting partners. Using our novel web-based design tool, we established a 96-well format pipeline that enabled V5-tagging of sixty different transcription factors. This efficient, selection-free and scalable epitope tagging pipeline enables systematic surveys of protein expression levels, subcellular localization, and interactors across diverse mammalian stem cells.</jats:p

The ADAMTS (A Disintegrin and Metalloproteinase with Thrombospondin motifs) family

The ADAMTS (A Disintegrin and Metalloproteinase with Thrombospondin motifs) enzymes are secreted, multi-domain matrix-associated zinc metalloendopeptidases that have diverse roles in tissue morphogenesis and patho-physiological remodeling, in inflammation and in vascular biology. The human family includes 19 members that can be sub-grouped on the basis of their known substrates, namely the aggrecanases or proteoglycanases (ADAMTS1, 4, 5, 8, 9, 15 and 20), the procollagen N-propeptidases (ADAMTS2, 3 and 14), the cartilage oligomeric matrix protein-cleaving enzymes (ADAMTS7 and 12), the von-Willebrand Factor proteinase (ADAMTS13) and a group of orphan enzymes (ADAMTS6, 10, 16, 17, 18 and 19). Control of the structure and function of the extracellular matrix (ECM) is a central theme of the biology of the ADAMTS, as exemplified by the actions of the procollagen-N-propeptidases in collagen fibril assembly and of the aggrecanases in the cleavage or modification of ECM proteoglycans. Defects in certain family members give rise to inherited genetic disorders, while the aberrant expression or function of others is associated with arthritis, cancer and cardiovascular disease. In particular, ADAMTS4 and 5 have emerged as therapeutic targets in arthritis. Multiple ADAMTSs from different sub-groupings exert either positive or negative effects on tumorigenesis and metastasis, with both metalloproteinase-dependent and -independent actions known to occur. The basic ADAMTS structure comprises a metalloproteinase catalytic domain and a carboxy-terminal ancillary domain, the latter determining substrate specificity and the localization of the protease and its interaction partners; ancillary domains probably also have independent biological functions. Focusing primarily on the aggrecanases and proteoglycanases, this review provides a perspective on the evolution of the ADAMTS family, their links with developmental and disease mechanisms, and key questions for the future