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

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

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

Identification and structural characterization of FYVE domain-containing proteins of Arabidopsis thaliana

<p>Abstract</p> <p>Background</p> <p>FYVE domains have emerged as membrane-targeting domains highly specific for phosphatidylinositol 3-phosphate (PtdIns(3)<it>P</it>). They are predominantly found in proteins involved in various trafficking pathways. Although FYVE domains may function as individual modules, dimers or in partnership with other proteins, structurally, all FYVE domains share a fold comprising two small characteristic double-stranded β-sheets, and a C-terminal α-helix, which houses eight conserved Zn²⁺ion-binding cysteines. To date, the structural, biochemical, and biophysical mechanisms for subcellular targeting of FYVE domains for proteins from various model organisms have been worked out but plant FYVE domains remain noticeably under-investigated.</p> <p>Results</p> <p>We carried out an extensive examination of all <it>Arabidopsis </it>FYVE domains, including their identification, classification, molecular modeling and biophysical characterization using computational approaches. Our classification of fifteen <it>Arabidopsis </it>FYVE proteins at the outset reveals unique domain architectures for FYVE containing proteins, which are not paralleled in other organisms. Detailed sequence analysis and biophysical characterization of the structural models are used to predict membrane interaction mechanisms previously described for other FYVE domains and their subtle variations as well as novel mechanisms that seem to be specific to plants.</p> <p>Conclusions</p> <p>Our study contributes to the understanding of the molecular basis of FYVE-based membrane targeting in plants on a genomic scale. The results show that FYVE domain containing proteins in plants have evolved to incorporate significant differences from those in other organisms implying that they play a unique role in plant signaling pathways and/or play similar/parallel roles in signaling to other organisms but use different protein players/signaling mechanisms.</p

Handpicking epigenetic marks with PHD fingers

Plant homeodomain (PHD) fingers have emerged as one of the largest families of epigenetic effectors capable of recognizing or ‘reading’ post-translational histone modifications and unmodified histone tails. These interactions are highly specific and can be modulated by the neighboring epigenetic marks and adjacent effectors. A few PHD fingers have recently been found to also associate with non-histone proteins. In this review, we detail the molecular mechanisms and biological outcomes of the histone and non-histone targeting by PHD fingers. We discuss the significance of crosstalk between the histone modifications and consequences of combinatorial readout for selective recruitment of the PHD finger-containing components of chromatin remodeling and transcriptional complexes

The Peripheral Binding of 14-3-3γ to Membranes Involves Isoform-Specific Histidine Residues

Mammalian 14-3-3 protein scaffolds include seven conserved isoforms that bind numerous phosphorylated protein partners and regulate many cellular processes. Some 14-3-3-isoforms, notably γ, have elevated affinity for membranes, which might contribute to modulate the subcellular localization of the partners and substantiate the importance of investigating molecular mechanisms of membrane interaction. By applying surface plasmon resonance we here show that the binding to phospholipid bilayers is stimulated when 14-3-3γ is complexed with its partner, a peptide corresponding to the Ser19-phosphorylated N-terminal region of tyrosine hydroxylase. Moreover, membrane interaction is dependent on salts of kosmotropic ions, which also stabilize 14-3-3γ. Electrostatic analysis of available crystal structures of γ and of the non-membrane-binding ζ-isoform, complemented with molecular dynamics simulations, indicate that the electrostatic potential distribution of phosphopeptide-bound 14-3-3γ is optimal for interaction with the membrane through amphipathic helices at the N-terminal dimerization region. In addition, His158, and especially His195, both specific to 14-3-3γ and located at the convex lateral side, appeared to be pivotal for the ligand induced membrane interaction, as corroborated by site-directed mutagenesis. The participation of these histidine residues might be associated to their increased protonation upon membrane binding. Overall, these results reveal membrane-targeting motifs and give insights on mechanisms that furnish the 14-3-3γ scaffold with the capacity for tuned shuffling from soluble to membrane-bound states.This work was supported by grants from the Norwegian Cancer Society (to ØH), Junta de Andalucía, grant CVI-02483 (to JMSR), The Research Council of Norway (grant 185181 to A.M.), the Western Norway Health Authorities (grant 911618 to A.M.) and The Kristian Gerhard Jebsen Foundation (to AM)

TRAF4 is a novel phosphoinositide-binding protein modulating tight junctions and favoring cell migration

Tumor necrosis factor (TNF) receptor-associated factor 4 (TRAF4) is frequently overexpressed in carcinomas, suggesting a specific role in cancer. Although TRAF4 protein is predominantly found at tight junctions (TJs) in normal mammary epithelial cells (MECs), it accumulates in the cytoplasm of malignant MECs. How TRAF4 is recruited and functions at TJs is unclear. Here we show that TRAF4 possesses a novel phosphoinositide (PIP)-binding domain crucial for its recruitment to TJs. Of interest, this property is shared by the other members of the TRAF protein family. Indeed, the TRAF domain of all TRAF proteins (TRAF1 to TRAF6) is a bona fide PIP-binding domain. Molecular and structural analyses revealed that the TRAF domain of TRAF4 exists as a trimer that binds up to three lipids using basic residues exposed at its surface. Cellular studies indicated that TRAF4 acts as a negative regulator of TJ and increases cell migration. These functions are dependent from its ability to interact with PIPs. Our results suggest that TRAF4 overexpression might contribute to breast cancer progression by destabilizing TJs and favoring cell migration

Identification and Characterization of an Unusual Class I Myosin Involved in Vesicle Traffic in Trypanosoma brucei

Myosins are a multimember family of motor proteins with diverse functions in eukaryotic cells. African trypanosomes possess only two candidate myosins and thus represent a useful system for functional analysis of these motors. One of these candidates is an unusual class I myosin (TbMyo1) that is expressed at similar levels but organized differently during the life cycle of Trypanosoma brucei. This myosin localizes to the polarized endocytic pathway in bloodstream forms of the parasite. This organization is actin dependent. Knock down of TbMyo1 results in a significant reduction in endocytic activity, a cessation in cell division and eventually cell death. A striking morphological feature in these cells is an enlargement of the flagellar pocket, which is consistent with an imbalance in traffic to and from the surface. In contrast TbMyo1 is distributed throughout procyclic forms of the tsetse vector and a loss of ∼90% of the protein has no obvious effects on growth or morphology. These results reveal a life cycle stage specific requirement for this myosin in essential endocytic traffic and represent the first description of the involvement of a motor protein in vesicle traffic in these parasites

Bacteriophage-encoded depolymerases: their diversity and biotechnological applications

Bacteriophages (phages), natural enemies of bacteria, can encode enzymes able to degrade polymeric substances. These substances can be found in the bacterial cell surface, such as polysaccharides, or are produced by bacteria when they are living in biofilm communities, the most common bacterial lifestyle. Consequently, phages with depolymerase activity have a facilitated access to the host receptors, by degrading the capsular polysaccharides, and are believed to have a better performance against bacterial biofilms, since the degradation of extracellular polymeric substances by depolymerases might facilitate the access of phages to the cells within different biofilm layers. Since the diversity of phage depolymerases is not yet fully explored, this is the first review gathering information about all the depolymerases encoded by fully sequenced phages. Overall, in this study, 160 putative depolymerases, including sialidases, levanases, xylosidases, dextranases, hyaluronidases, peptidases as well as pectate/pectin lyases, were found in 143 phages (43 Myoviridae, 47 Siphoviridae, 37 Podoviridae, and 16 unclassified) infecting 24 genera of bacteria. We further provide information about the main applications of phage depolymerases, which can comprise areas as diverse as medical, chemical, or food-processing industry.DPP acknowledges the financial support from the Portuguese Foundation for Science and Technology (FCT) through the grant SFRH/BD/76440/2011. SS is an FCT investigator (IF/01413/2013). The authors also thank FCT for the Strategic Project of the UID/BIO/04469/2013 unit, FCT and European Union funds (FEDER/COMPETE) for the project RECI/BBB-EBI/0179/2012 (FCOMP-01-0124-FEDER027462)