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

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

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'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

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

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

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

Mobile Regulatory Cassettes Mediate Modular Shuffling in T4-Type Phage Genomes

Coliphage phi1, which was isolated for phage therapy in the Republic of Georgia, is closely related to the T-like myovirus RB49. The ∼275 open reading frames encoded by each phage have an average level of amino acid identity of 95.8%. RB49 lacks 7 phi1 genes while 10 phi1 genes are missing from RB49. Most of these unique genes encode functions without known homologs. Many of the insertion, deletion, and replacement events that distinguish the two phages are in the hyperplastic regions (HPRs) of their genomes. The HPRs are rich in both nonessential genes and small regulatory cassettes (promoterearly stem-loops [PeSLs]) composed of strong σ70-like promoters and stem-loop structures, which are effective transcription terminators. Modular shuffling mediated by recombination between PeSLs has caused much of the sequence divergence between RB49 and phi1. We show that exchanges between nearby PeSLs can also create small circular DNAs that are apparently encapsidated by the virus. Such PeSL “mini-circles” may be important vectors for horizontal gene transfer