Metrics and spectral triples for Dirichlet and resistance forms

The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the intrinsic metric yields a geodesic space. Given a regular Dirichlet form, we consider Dirac operators within the framework of differential 1-forms proposed by Cipriani and Sauvageot, and comment on its spectral properties. If the Dirichlet form admits a carr\'e operator and the generator has discrete spectrum, then we can construct a related spectral triple, and in the compact and strongly local case the associated Connes distance coincides with the intrinsic metric. We finally give a description of the intrinsic metric in terms of vector fields

An evolving view of the eukaryotic oligosaccharyltransferase

Asparagine-linked glycosylation (ALG) is one of the most common protein modification reactions in eukaryotic cells, as many proteins that are translocated across or integrated into the rough endoplasmic reticulum (RER) carry N-linked oligosaccharides. Although the primary focus of this review will be the structure and function of the eukaryotic oligosaccharyltransferase (OST), key findings provided by the analysis of the archaebacterial and eubacterial OST homologues will be reviewed, particularly those that provide insight into the recognition of donor and acceptor substrates. Selection of the fully assembled donor substrate will be considered in the context of the family of human diseases known as congenital disorders of glycosylation (CDG). The yeast and vertebrate OST are surprisingly complex hetero-oligomeric proteins consisting of seven or eight subunits (Ost1p, Ost2p, Ost3p/Ost6p, Ost4p, Ost5p, Stt3p, Wbp1p, and Swp1p in yeast; ribophorin I, DAD1, N33/IAP, OST4, STT3A/STT3B, Ost48, and ribophorin II in mammals). Recent findings from several laboratories have provided overwhelming evidence that the STT3 subunit is critical for catalytic activity. Here, we will consider the evolution and assembly of the eukaryotic OST in light of recent genomic evidence concerning the subunit composition of the enzyme in diverse eukaryotes

The physical basis of self-organization of the mammalian oocyte spindle

To prepare gametes with the appropriate number of chromosomes, mammalian oocytes undergo two sequential cell divisions. During each division, a large, long-lived, microtubule-based organelle called the meiotic spindle assembles around condensed chromosomes. Although meiotic spindles have been intensively studied for several decades, as force-generating mechanical objects, they remain very poorly understood. In materials physics, coarse-grained theories have been essential in understanding the large-scale behavior of systems composed of many interacting particles. It is unclear, however, if this approach can succeed in capturing the properties of active, biochemically complex, living materials like the spindle. Here, we show that a class of models based on nematic liquid crystal theory can describe important aspects of the organelle-scale structure and dynamics of spindles in living mouse oocytes. Using our models to interpret quantitative polarization microscopy data, we measure for the first time material properties relating to stress propagation in living oocytes, including the nematic diffusivities corresponding to splay and bend deformations. Unlike the reconstituted amphibian spindles that were previously studied in vitro, nematic elastic stress is exponentially screened in the microtubule network of living mammalian oocytes, with a screening length of order one micron. This observation can be explained by the relatively high volume fraction of embedded chromosomes in mammalian meiotic spindles, which cause long voids in the microtubule network and so disrupt orientational stress propagation

Analyzing Self-similar and Fractal Properties of the C. Elegans Neural Network

The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs

Dolichol-linked oligosaccharide selection by the oligosaccharyltransferase in protist and fungal organisms

The dolichol-linked oligosaccharide Glc3Man9GlcNAc2-PP-Dol is the in vivo donor substrate synthesized by most eukaryotes for asparagine-linked glycosylation. However, many protist organisms assemble dolichol-linked oligosaccharides that lack glucose residues. We have compared donor substrate utilization by the oligosaccharyltransferase (OST) from Trypanosoma cruzi, Entamoeba histolytica, Trichomonas vaginalis, Cryptococcus neoformans, and Saccharomyces cerevisiae using structurally homogeneous dolichol-linked oligosaccharides as well as a heterogeneous dolichol-linked oligosaccharide library. Our results demonstrate that the OST from diverse organisms utilizes the in vivo oligo saccharide donor in preference to certain larger and/or smaller oligosaccharide donors. Steady-state enzyme kinetic experiments reveal that the binding affinity of the tripeptide acceptor for the protist OST complex is influenced by the structure of the oligosaccharide donor. This rudimentary donor substrate selection mechanism has been refined in fungi and vertebrate organisms by the addition of a second, regulatory dolichol-linked oligosaccharide binding site, the presence of which correlates with acquisition of the SWP1/ribophorin II subunit of the OST complex