Beck's Conjecture for Power Graphs

Beck's conjecture on coloring of graphs associated to various algebraic objects has generated considerable interest in the community of discrete mathematics and combinatorics since its inception in the year 1988. The version of this conjecture for power-graphs of finite groups has been addressed and partially settled by previous authors. In this paper we answer it in the affirmative in complete generality, and, in effect, we establish a "nicer" statement on a larger class of graphs. We also clear up certain ambiguities present in the way the previous versions of the conjecture were posed

Role of leishmanial glyceraldehyde3-phosphate dehydrogenase in host-parasite interaction

Glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is a classic glycolytic enzyme and is involved in the reversible oxidative phosphorylation of glyceraldehyde-3-phosphate in the presence of inorganic phosphate and nicotinamide adenine dinucleotide (NAD). However, emerging evidence indicates that GAPDH is a multifunctional protein implicated in diverse functions independent of its role in energy metabolism; GAPDH participates in numerous cellular functions, in addition to glycolytic effects, contributes to nuclear tRNA export, DNA replication and repair, endocytosis, exocytosis, cytoskeletal organization, iron metabolism, carcinogenesis, and cell death. It also acts as an mRNA-binding protein, controlling posttranscriptional gene regulation. In the case of Leishmania, apart from glycolysis, no other function of GAPDH is known. Specific post-translational modifications, protein-protein interactions, and subsequent changes in the intracellular distribution of GAPDH in leishmanial species remain unknown. Considering all these facts together, we tried to find out the role of GAPDH in Leishmania other than its role in glycolysis. To understand the non-glycolytic function of LmGAPDH, we have generated control (CT), overexpressed (OE), half-knockout (HKO) and complement (CM) cell lines. HKO cells exhibited reduced virulence compared to control cells when infected with macrophages and BALB/c mice, showing that LmGAPDH plays an important role in Leishmania infection and disease progression. We have demonstrated that LmGAPDH is localized within the extracellular vesicles (EVs) released by Leishmania during infection and, by different molecular biology techniques, established that EV mediated LmGAPDH suppresses the production of pro-inflammatory cytokines like Tumor Necrosis Factor α (TNF-α), which seems to have a primordial role in the process of controlling infection. In vitro protein translation and mRNA binding assays indicate that LmGAPDH binding to the AU-rich 3'-UTR region of TNF-α mRNA is the primary cause for the limitation of its production. Together, these findings confirm that the LmGAPDH found in EVs inhibits TNF-α expression in macrophages via posttranscriptional repression during infection. So, in this project, we attempted to uncover a novel mechanism by which the Leishmania parasite suppresses host immune response, which is critical for developing new drugs and therapeutic strategies against the disease. Here we have illustrated our research in three separate chapters; Chapter1 elucidate mainly the cloning, expression and localization of LmGAPDH from Leishmania major. Chapter2 deals with the functional characterization of LmGAPDH contained within the extracellular vesicles from Leishmania major and its essentiality in disease development and progression. Chapter3 unravels a novel mechanism by which LmGAPDH contained in the extracellular vesicles modulate host immune response through post-transcriptional regulation of TNF-α expression

Recent results on homological properties of binomial edge ideal of graphs

In this article, we give a comprehensive survey of the recent progress of research on binomial edge ideal of a graph since 2018

Cell-Mediated Immune Responses of Healthy Laboratory Volunteers to Sonicate Antigens Prepared from the Most Prevalent Strains of Mycobacterium tuberculosis from South India Harboring a Single Copy of IS6110

Our restriction fragment length polymorphism (RFLP) studies have shown that the most prevalent (40%) strains of Mycobacterium tuberculosis from South India contain a single copy of the IS6110 insertion sequence and are of importance in studying virulence and immunity. Sonicate antigens from seven such strains were used to study in vitro T-cell proliferation and gamma interferon (IFN-�) and interleukin-12 (IL-12) secretion as markers of protective immunity in 25 healthy subjects positive for purified protein derivative (PPD). The standard PPD and heat-killed H37Rv antigens induced the maximum levels of T-cell proliferation and IFN-� secretion but low levels of IL-12. All sonicate antigens induced T-cell proliferation and IFN-� secretion with strong positive correlation. Our results suggest that sonicate antigens from the most prevalent and recent strains of M. tuberculosis from clinical isolates have the potential to induce T-cell activation and may allow newer and specific antigens to be further characterized for diagnosis and vaccine development

Fragility and elastic behavior of a supercooled liquid

A model for the supercooled liquid is considered by taking into account its solidlike properties. We focus on how the long time dynamics is affected due to the coupling between the slowly decaying density fluctuations and the local displacement variables in the frozen liquid. Results from our model agree with the recent observation of Novikov and Sokolov [Nature (London) 431, 961 (2004)] that the fragility index m of a glass forming material is linearly related to the corresponding ratio K/G of the bulk and the shear moduli

Bounds for the regularity of product of edge ideals

Let $I$ and $J$ be edge ideals in a polynomial ring $R = \mathbb{K}[x_1,\ldots,x_n]$ with $I \subseteq J$. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of $IJ$ in terms of certain invariants associated with $I$ and $J$. Using these results, we explicitly compute the regularity of $IJ$ for several classes of edge ideals. Let $J_1,\ldots,J_d$ be edge ideals in a polynomial ring $R$ with $J_1 \subseteq \cdots \subseteq J_d$. Finally, we compute the precise expression for the regularity of $J_1 J_2\cdots J_d$ when $d \in \{3,4\}$ and $J_d$ is the edge ideal of complete graph.Comment: Pages 11, 1 figur

Humoral immune responses of normals and tuberculosis patients to multiple sonicate antigens prepared from the most prevalent strains of Mycobacterium tuberculosis harbouring single copy of IS6110 from South India

The search for newer species-specific antigens from prevalent strains of Mycobacterium tuberculosis (Mtb) associated with active disease will add substantially to improve the presently available diagnostic tools. We studied the protein profiles of 13 sonicate antigens (S1– S13) prepared from the prevalent strains. The humoral immune response was also studied in 30 normal and 30 tuberculosis (TB) patients. The sonicate antigens S10 and S12 showed maximum differential protein bands in low molecular mass region of 10–30 kDa on SDS–PAGE. Our ELISA results showed significant increase in Mtb-specific IgG antibodies in TB plasma for H37Rv, followed by PPD, S1 and S10 antigens. Immunoblot analysis of S10 antigen showed specific recognition pattern at low molecular mass region by TB plasma alone with 12–77% positivity of protein bands. Thus the sonicate antigen S10 was found to be discriminatory by ELISA and Western blot and hence a good candidate for further purification of its individual proteins to be evaluated for diagnosis