Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants

We continue the discussion of the fermion models on graphs that started in the first paper of the series. Here we introduce a Graphical Gauge Model (GGM) and show that : (a) it can be stated as an average/sum of a determinant defined on the graph over $\mathbb{Z}_{2}$ (binary) gauge field; (b) it is equivalent to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the model allows an explicit expression in terms of a series over disjoint directed cycles, where each term is a product of local contributions along the cycle and the determinant of a matrix defined on the remainder of the graph (excluding the cycle). We also establish a relation between the MD model on the graph and the determinant series, discussed in the first paper, however, considered using simple non-Belief-Propagation choice of the gauge. We conclude with a discussion of possible analytic and algorithmic consequences of these results, as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

Robustness and Generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work

A La Autoantigen Homologue Is Required for the Internal Ribosome Entry Site Mediated Translation of Giardiavirus

Translation of Giardiavirus (GLV) mRNA is initiated at an internal ribosome entry site (IRES) in the viral transcript. The IRES localizes to a downstream portion of 5′ untranslated region (UTR) and a part of the early downstream coding region of the transcript. Recent studies indicated that the IRES does not require a pre-initiation complex to initiate translation but may directly recruit the small ribosome subunit with the help of a number of trans-activating protein factors. A La autoantigen homologue in the viral host Giardia lamblia, GlLa, was proposed as one of the potential trans-activating factors based on its specific binding to GLV-IRES in vitro. In this study, we further elucidated the functional role of GlLa in GLV-IRES mediated translation in Giardia by knocking down GlLa with antisense morpholino oligo, which resulted in a reduction of GLV-IRES activity by 40%. An over-expression of GlLa in Giardia moderately stimulated GLV-IRES activity by 20%. A yeast inhibitory RNA (IRNA), known to bind mammalian and yeast La autoantigen and inhibit Poliovirus and Hepatitis C virus IRES activities in vitro and in vivo, was also found to bind to GlLa protein in vitro and inhibited GLV-IRES function in vivo. The C-terminal domain of La autoantigen interferes with the dimerization of La and inhibits its function. An over-expression of the C-terminal domain (200–348aa) of GlLa in Giardia showed a dominant-negative effect on GLV-IRES activity, suggesting a potential inhibition of GlLa dimerization. HA tagged GlLa protein was detected mainly in the cytoplasm of Giardia, thus supporting a primary role of GlLa in translation initiation in Giardiavirus

Novel ATP-Independent RNA Annealing Activity of the Dengue Virus NS3 Helicase

The flavivirus nonstructural protein 3 (NS3) bears multiple enzymatic activities and represents an attractive target for antiviral intervention. NS3 contains the viral serine protease at the N-terminus and ATPase, RTPase, and helicase activities at the C-terminus. These activities are essential for viral replication; however, the biological role of RNA remodeling by NS3 helicase during the viral life cycle is still unclear. Secondary and tertiary RNA structures present in the viral genome are crucial for viral replication. Here, we used the NS3 protein from dengue virus to investigate functions of NS3 associated to changes in RNA structures. Using different NS3 variants, we characterized a domain spanning residues 171 to 618 that displays ATPase and RNA unwinding activities similar to those observed for the full-length protein. Interestingly, we found that, besides the RNA unwinding activity, dengue virus NS3 greatly accelerates annealing of complementary RNA strands with viral or non-viral sequences. This new activity was found to be ATP-independent. It was determined that a mutated NS3 lacking ATPase activity retained full-RNA annealing activity. Using an ATP regeneration system and different ATP concentrations, we observed that NS3 establishes an ATP-dependent steady state between RNA unwinding and annealing, allowing modulation of the two opposing activities of this enzyme through ATP concentration. In addition, we observed that NS3 enhanced RNA-RNA interactions between molecules representing the ends of the viral genome that are known to be necessary for viral RNA synthesis. We propose that, according to the ATP availability, NS3 could function regulating the folding or unfolding of viral RNA structures

Endemic Dengue Associated with the Co-Circulation of Multiple Viral Lineages and Localized Density-Dependent Transmission

Dengue is one of the most important infectious diseases of humans and has spread throughout much of the tropical and subtropical world. Despite this widespread dispersal, the determinants of dengue transmission in endemic populations are not well understood, although essential for virus control. To address this issue we performed a phylogeographic analysis of 751 complete genome sequences of dengue 1 virus (DENV-1) sampled from both rural (Dong Thap) and urban (Ho Chi Minh City) populations in southern Viet Nam during the period 2003–2008. We show that DENV-1 in Viet Nam exhibits strong spatial clustering, with likely importation from Cambodia on multiple occasions. Notably, multiple lineages of DENV-1 co-circulated in Ho Chi Minh City. That these lineages emerged at approximately the same time and dispersed over similar spatial regions suggests that they are of broadly equivalent fitness. We also observed an important relationship between the density of the human host population and the dispersion rate of dengue, such that DENV-1 tends to move from urban to rural populations, and that densely populated regions within Ho Chi Minh City act as major transmission foci. Despite these fluid dynamics, the dispersion rates of DENV-1 are relatively low, particularly in Ho Chi Minh City where the virus moves less than an average of 20 km/year. These low rates suggest a major role for mosquito-mediated dispersal, such that DENV-1 does not need to move great distances to infect a new host when there are abundant susceptibles, and imply that control measures should be directed toward the most densely populated urban environments

Dengue Virus Capsid Protein Usurps Lipid Droplets for Viral Particle Formation

Dengue virus is responsible for the highest rates of disease and mortality among the members of the Flavivirus genus. Dengue epidemics are still occurring around the world, indicating an urgent need of prophylactic vaccines and antivirals. In recent years, a great deal has been learned about the mechanisms of dengue virus genome amplification. However, little is known about the process by which the capsid protein recruits the viral genome during encapsidation. Here, we found that the mature capsid protein in the cytoplasm of dengue virus infected cells accumulates on the surface of ER-derived organelles named lipid droplets. Mutagenesis analysis using infectious dengue virus clones has identified specific hydrophobic amino acids, located in the center of the capsid protein, as key elements for lipid droplet association. Substitutions of amino acid L50 or L54 in the capsid protein disrupted lipid droplet targeting and impaired viral particle formation. We also report that dengue virus infection increases the number of lipid droplets per cell, suggesting a link between lipid droplet metabolism and viral replication. In this regard, we found that pharmacological manipulation of the amount of lipid droplets in the cell can be a means to control dengue virus replication. In addition, we developed a novel genetic system to dissociate cis-acting RNA replication elements from the capsid coding sequence. Using this system, we found that mislocalization of a mutated capsid protein decreased viral RNA amplification. We propose that lipid droplets play multiple roles during the viral life cycle; they could sequester the viral capsid protein early during infection and provide a scaffold for genome encapsidation