Leibnizian, Robinsonian, and Boolean Valued Monads

This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities.Comment: This is a talk prepared for the 20th St. Petersburg Summer Meeting in Mathematical Analysis, June 24-29, 201

3′-Hydroxymethyl 2′-deoxynucleoside 5′-triphosphates are inhibitors highly specific for reverse transcriptase

AbstractdNTP(3′-OCH3), a 3′-O-methyl derivative of dNTP, is a chain terminator substrate for DNA synthesis catalyzed by AMV reverse transriptase. The enzyme seems to be the only DNA polymerase susceptible to the inhibitor while all the other DNA polymerases tested are fully resistant to the nucleotide analog. The resistant polymerases are: E. coli DNA polymerase I, Klenow's fragment of DNA polymerase I, phage T4 DNA polymerase, calf thymus DNA polymerase α, rat liver DNA polymerase β and calf thymus terminal deoxyribonucleotidyl transferase

Cauchy, infinitesimals and ghosts of departed quantifiers

Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for the procedures of the classical masters. Thus, Leibniz's distinction between assignable and inassignable numbers finds a proxy in the distinction between standard and nonstandard numbers in Robinson's framework, while Leibniz's law of homogeneity with the implied notion of equality up to negligible terms finds a mathematical formalisation in terms of standard part. It is hard to provide parallel formalisations in a Weierstrassian framework but scholars since Ishiguro have engaged in a quest for ghosts of departed quantifiers to provide a Weierstrassian account for Leibniz's infinitesimals. Euler similarly had notions of equality up to negligible terms, of which he distinguished two types: geometric and arithmetic. Euler routinely used product decompositions into a specific infinite number of factors, and used the binomial formula with an infinite exponent. Such procedures have immediate hyperfinite analogues in Robinson's framework, while in a Weierstrassian framework they can only be reinterpreted by means of paraphrases departing significantly from Euler's own presentation. Cauchy gives lucid definitions of continuity in terms of infinitesimals that find ready formalisations in Robinson's framework but scholars working in a Weierstrassian framework bend over backwards either to claim that Cauchy was vague or to engage in a quest for ghosts of departed quantifiers in his work. Cauchy's procedures in the context of his 1853 sum theorem (for series of continuous functions) are more readily understood from the viewpoint of Robinson's framework, where one can exploit tools such as the pointwise definition of the concept of uniform convergence. Keywords: historiography; infinitesimal; Latin model; butterfly modelComment: 45 pages, published in Mat. Stu

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

A triple action CDK4/6-PI3K-BET inhibitor with augmented cancer cell cytotoxicity

National Institutes of Health GM125195, GM135671, CA192656, FD00511

An Acetyl-Methyl Switch Drives a Conformational Change in p53

Individual posttranslational modifications (PTMs) of p53 mediate diverse p53-dependent responses, however much less is known about the combinatorial action of adjacent modifications. Here, we describe crosstalk between the early DNA damage response mark p53K382me2 and the surrounding PTMs that modulate binding of p53 co-factors, including 53BP1 and p300. The 1.8 Å resolution crystal structure of the tandem Tudor domain (TTD) of 53BP1 in complex with p53 peptide acetylated at K381 and dimethylated at K382 (p53K381acK382me2) reveals that the dual PTM induces a conformational change in p53. The α-helical fold of p53K381acK382me2 positions the side chains of R379, K381ac, and K382me2 to interact with TTD concurrently, reinforcing a modular design of double PTM mimetics. Biochemical and NMR analyses show that other surrounding PTMs, including phosphorylation of serine/threonine residues of p53, affect association with TTD. Our findings suggest a novel PTM-driven conformation switch-like mechanism that may regulate p53 interactions with binding partners

Molecular basis for chromatin binding and regulation of MLL5

The human mixed-lineage leukemia 5 (MLL5) protein mediates hematopoietic cell homeostasis, cell cycle, and survival; however, the molecular basis underlying MLL5 activities remains unknown. Here, we show that MLL5 is recruited to gene-rich euchromatic regions via the interaction of its plant homeodomain finger with the histone mark H3K4me3. The 1.48-Å resolution crystal structure of MLL5 plant homeodomain in complex with the H3K4me3 peptide reveals a noncanonical binding mechanism, whereby K4me3 is recognized through a single aromatic residue and an aspartate. The binding induces a unique His–Asp swapping rearrangement mediated by a C-terminal α-helix. Phosphorylation of H3T3 and H3T6 abrogates the association with H3K4me3 in vitro and in vivo, releasing MLL5 from chromatin in mitosis. This regulatory switch is conserved in the Drosophila ortholog of MLL5, UpSET, and suggests the developmental control for targeting of H3K4me3. Together, our findings provide first insights into the molecular basis for the recruitment, exclusion, and regulation of MLL5 at chromatin

Proteomic Identification of S-Nitrosylated Golgi Proteins: New Insights into Endothelial Cell Regulation by eNOS-Derived NO

<div><h3>Background</h3><p>Endothelial nitric oxide synthase (eNOS) is primarily localized on the Golgi apparatus and plasma membrane caveolae in endothelial cells. Previously, we demonstrated that protein S-nitrosylation occurs preferentially where eNOS is localized. Thus, in endothelial cells, Golgi proteins are likely to be targets for S-nitrosylation. The aim of this study was to identify S-nitrosylated Golgi proteins and attribute their S-nitrosylation to eNOS-derived nitric oxide in endothelial cells.</p> <h3>Methods</h3><p>Golgi membranes were isolated from rat livers. S-nitrosylated Golgi proteins were determined by a modified biotin-switch assay coupled with mass spectrometry that allows the identification of the S-nitrosylated cysteine residue. The biotin switch assay followed by Western blot or immunoprecipitation using an S-nitrosocysteine antibody was also employed to validate S-nitrosylated proteins in endothelial cell lysates.</p> <h3>Results</h3><p>Seventy-eight potential S-nitrosylated proteins and their target cysteine residues for S-nitrosylation were identified; 9 of them were Golgi-resident or Golgi/endoplasmic reticulum (ER)-associated proteins. Among these 9 proteins, S-nitrosylation of EMMPRIN and Golgi phosphoprotein 3 (GOLPH3) was verified in endothelial cells. Furthermore, S-nitrosylation of these proteins was found at the basal levels and increased in response to eNOS stimulation by the calcium ionophore A23187. Immunofluorescence microscopy and immunoprecipitation showed that EMMPRIN and GOLPH3 are co-localized with eNOS at the Golgi apparatus in endothelial cells. S-nitrosylation of EMMPRIN was notably increased in the aorta of cirrhotic rats.</p> <h3>Conclusion</h3><p>Our data suggest that the selective S-nitrosylation of EMMPRIN and GOLPH3 at the Golgi apparatus in endothelial cells results from the physical proximity to eNOS-derived nitric oxide.</p> </div

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems