Distance Optimization and the Extremal Variety of the Grassmann Variety

The approximation of a multivector by a decomposable one is a distance-optimization problem between the multivector and the Grassmann variety of lines in a projective space. When the multivector diverges from the Grassmann variety, then the approximate solution sought is the worst possible. In this paper, it is shown that the worst solution of this problem is achieved, when the eigenvalues of the matrix representation of a related two-vector are all equal. Then, all these pathological points form a projective variety. We derive the equation describing this projective variety, as well as its maximum distance from the corresponding Grassmann variety. Several geometric and algebraic properties of this extremal variety are examined, providing a new aspect for the Grassmann varieties and the respective projective spaces

Palmitate-induced ER stress and inhibition of protein synthesis in cultured myotubes does not require Toll-like receptor 4

Saturated fatty acids, such as palmitate, are elevated in metabolically dysfunctional condi- tions like type 2 diabetes mellitus. Palmitate has been shown to impair insulin sensitivity and suppress protein synthesis while upregulating proteolytic systems in skeletal muscle. Increased sarco/endoplasmic reticulum (ER) stress and subsequent activation of the unfolded protein response may contribute to the palmitate-induced impairment of muscle protein synthesis. In some cell types, ER stress occurs through activation of the Toll-like receptor 4 (TLR4). Given the link between ER stress and suppression of protein synthesis, we investigated whether palmitate induces markers of ER stress and protein synthesis by activating TLR4 in cultured mouse C2C12 myotubes. Myotubes were treated with vehicle, a TLR4-specific ligand (lipopolysaccharides), palmitate, or a combination of palmitate plus a TLR4-specific inhibitor (TAK-242). Inflammatory indicators of TLR4 activation (IL-6 and TNFα) and markers of ER stress were measured, and protein synthesis was assessed using puromycin incorporation. Palmitate substantially increased the levels of IL-6, TNF-α, CHOP, XBP1s, and ATF 4 mRNAs and augmented the levels of CHOP, XBP1s, phospho- PERK and phospho-eIF2α proteins. The TLR4 antagonist attenuated both acute palmitate and LPS-induced increases in IL-6 and TNFα, but did not reduce ER stress signaling with either 6 h or 24 h palmitate treatment. Similarly, treating myotubes with palmitate for 6 h caused a 43% decline in protein synthesis consistent with an increase in phospho-eIF2α, and the TLR4 antagonist did not alter these responses. These results suggest that palmitate does not induce ER stress through TLR4 in muscle, and that palmitate impairs protein syn- thesis in skeletal muscle in part by induction of ER stress

Functional Roles of the N- and C-Terminal Regions of the Human Mitochondrial Single-Stranded DNA-Binding Protein

Biochemical studies of the mitochondrial DNA (mtDNA) replisome demonstrate that the mtDNA polymerase and the mtDNA helicase are stimulated by the mitochondrial single-stranded DNA-binding protein (mtSSB). Unlike Escherichia coli SSB, bacteriophage T7 gp2.5 and bacteriophage T4 gp32, mtSSBs lack a long, negatively charged C-terminal tail. Furthermore, additional residues at the N-terminus (notwithstanding the mitochondrial presequence) are present in the sequence of species across the animal kingdom. We sought to analyze the functional importance of the N- and C-terminal regions of the human mtSSB in the context of mtDNA replication. We produced the mature wild-type human mtSSB and three terminal deletion variants, and examined their physical and biochemical properties. We demonstrate that the recombinant proteins adopt a tetrameric form, and bind single-stranded DNA with similar affinities. They also stimulate similarly the DNA unwinding activity of the human mtDNA helicase (up to 8-fold). Notably, we find that unlike the high level of stimulation that we observed previously in the Drosophila system, stimulation of DNA synthesis catalyzed by human mtDNA polymerase is only moderate, and occurs over a narrow range of salt concentrations. Interestingly, each of the deletion variants of human mtSSB stimulates DNA synthesis at a higher level than the wild-type protein, indicating that the termini modulate negatively functional interactions with the mitochondrial replicase. We discuss our findings in the context of species-specific components of the mtDNA replisome, and in comparison with various prokaryotic DNA replication machineries

Early Steps of HIV-1 Fusion Define the Sensitivity to Inhibitory Peptides That Block 6-Helix Bundle Formation

The HIV envelope (Env) glycoprotein mediates membrane fusion through sequential interactions with CD4 and coreceptors, followed by the refolding of the transmembrane gp41 subunit into the stable 6-helix bundle (6HB) conformation. Synthetic peptides derived from the gp41 C-terminal heptad repeat domain (C-peptides) potently inhibit fusion by binding to the gp41 pre-bundle intermediates and blocking their conversion into the 6HB. Our recent work revealed that HIV-1 enters cells by fusing with endosomes, but not with the plasma membrane. These studies also showed that, for the large part, gp41 pre-bundles progress toward 6HBs in endosomal compartments and are thus protected from external fusion inhibitors. Here, we examined the consequences of endocytic entry on the gp41 pre-bundle exposure and on the virus' sensitivity to C-peptides. The rates of CD4 and coreceptor binding, as well as the rate of productive receptor-mediated endocytosis, were measured by adding specific inhibitors of these steps at varied times of virus-cell incubation. Following the CD4 binding, CCR5-tropic viruses recruited a requisite number of coreceptors much faster than CXCR4-tropic viruses. The rate of subsequent uptake of ternary Env-CD4-coreceptor complexes did not correlate with the kinetics of coreceptor engagement. These measurements combined with kinetic analyses enabled the determination of the lifetime of pre-bundle intermediates on the cell surface. Overall, these lifetimes correlated with the inhibitory potency of C-peptides. On the other hand, the basal sensitivity to peptides varied considerably among diverse HIV-1 isolates and ranked similarly with their susceptibility to inactivation by soluble CD4. We conclude that both the longevity of gp41 intermediates and the extent of irreversible conformational changes in Env upon CD4 binding determine the antiviral potency of C-peptides

Step-wise evolution of complex chemical defenses in millipedes: a phylogenomic approach

With fossil representatives from the Silurian capable of respiring atmospheric oxygen, millipedes are among the oldest terrestrial animals, and likely the first to acquire diverse and complex chemical defenses against predators. Exploring the origin of complex adaptive traits is critical for understanding the evolution of Earth’s biological complexity, and chemical defense evolution serves as an ideal study system. The classic explanation for the evolution of complexity is by gradual increase from simple to complex, passing through intermediate “stepping stone� states. Here we present the first phylogenetic-based study of the evolution of complex chemical defenses in millipedes by generating the largest genomic-based phylogenetic dataset ever assembled for the group. Our phylogenomic results demonstrate that chemical complexity shows a clear pattern of escalation through time. New pathways are added in a stepwise pattern, leading to greater chemical complexity, independently in a number of derived lineages. This complexity gradually increased through time, leading to the advent of three distantly related chemically complex evolutionary lineages, each uniquely characteristic of each of the respective millipede groups

Computational Refinement of Functional Single Nucleotide Polymorphisms Associated with ATM Gene

gene are the most common forms of genetic variations that account for various forms of cancer. However, the extent to which SNPs interferes with the gene regulation and affects cancer susceptibility remains largely unknown. gene. gene function can aid in better understanding of genetic differences in disease susceptibility

The neurobiology of mouse models syntenic to human chromosome 15q

Autism is a neurodevelopmental disorder that manifests in childhood as social behavioral abnormalities, such as abnormal social interaction, impaired communication, and restricted interest or behavior. Of the known causes of autism, duplication of human chromosome 15q11–q13 is the most frequently associated cytogenetic abnormality. Chromosome 15q11–q13 is also known to include imprinting genes. In terms of neuroscience, it contains interesting genes such as Necdin, Ube3a, and a cluster of GABAA subunits as well as huge clusters of non-coding RNAs (small nucleolar RNAs, snoRNAs). Phenotypic analyses of mice genetically or chromosomally engineered for each gene or their clusters on a region of mouse chromosome seven syntenic to human 15q11–q13 indicate that this region may be involved in social behavior, serotonin metabolism, and weight control. Further studies using these models will provide important clues to the pathophysiology of autism. This review overviews phenotypes of mouse models of genes in 15q11–q13 and their relationships to autism

Conserved Genes Act as Modifiers of Invertebrate SMN Loss of Function Defects

Spinal Muscular Atrophy (SMA) is caused by diminished function of the Survival of Motor Neuron (SMN) protein, but the molecular pathways critical for SMA pathology remain elusive. We have used genetic approaches in invertebrate models to identify conserved SMN loss of function modifier genes. Drosophila melanogaster and Caenorhabditis elegans each have a single gene encoding a protein orthologous to human SMN; diminished function of these invertebrate genes causes lethality and neuromuscular defects. To find genes that modulate SMN function defects across species, two approaches were used. First, a genome-wide RNAi screen for C. elegans SMN modifier genes was undertaken, yielding four genes. Second, we tested the conservation of modifier gene function across species; genes identified in one invertebrate model were tested for function in the other invertebrate model. Drosophila orthologs of two genes, which were identified originally in C. elegans, modified Drosophila SMN loss of function defects. C. elegans orthologs of twelve genes, which were originally identified in a previous Drosophila screen, modified C. elegans SMN loss of function defects. Bioinformatic analysis of the conserved, cross-species, modifier genes suggests that conserved cellular pathways, specifically endocytosis and mRNA regulation, act as critical genetic modifiers of SMN loss of function defects across species