Lie symmetries of Benjamin-Ono equation.

Lie Symmetry analysis is often used to exploit the conservative laws of nature and solve or at least reduce the order of differential equation. One dimension internal waves are best described by Benjamin-Ono equation which is a nonlinear partial integro-differential equation. Present article focuses on the Lie symmetry analysis of this equation because of its importance. Lie symmetry analysis of this equation has been done but there are still some gaps and errors in the recent work. We claim that the symmetry algebra is of five dimensional. We reduce the model and solve it. We give its solution and analyze them graphically.

Metric basis and metric dimension of 1-pentagonal carbon nanocone networks.

Resolving set and metric basis has become an integral part in combinatorial chemistry and molecular topology. It has a lot of applications in computer, chemistry, pharmacy and mathematical disciplines. A subset S of the vertex set V of a connected graph G resolves G if all vertices of G have different representations with respect to S. A metric basis for G is a resolving set having minimum cardinal number and this cardinal number is called the metric dimension of G. In present work, we find a metric basis and also metric dimension of 1-pentagonal carbon nanocones. We conclude that only three vertices are minimal requirement for the unique identification of all vertices in this network.

Laplacian and signless laplacian spectra and energies of multi-step wheels.

Energies and spectrum of graphs associated to different linear operators play a significant role in molecular chemistry, polymerisation, pharmacy, computer networking and communication systems. In current article, we compute closed forms of signless Laplacian and Laplacian spectra and energies of multi-step wheel networks Wn,m. These wheel networks are useful in networking and communication, as every node is one hoop neighbour to other. We also present our results for wheel graphs as particular cases. In the end, correlation of these energies on the involved parameters m ≥ 3 and n is given graphically. Present results are the natural generalizations of the already available results in the literature.

M-polynomials and topological indices of linear chains of benzene, napthalene and anthracene.

The universality of M-polynomial paves way towards establishing closed forms of many leading degree-based topological indices as it is done by Hosoya polynomial for distance-based indices. The study of topological indices is recently one of the most active research areas in chemical graph theory. The aim of this paper is to establish closed formulas for M-polynomials of Linear chains of benzene, napthalene, and anthracene graphs. From this polynomial we also compute as many as nine degree-based topological indices for these three chains. Our results will potentially play an important role in pharmacy, drug design, and many other applied areas of molecular sciences.

Advances in the role of HCV nonstructural protein 5a (NS5A) of 3a genotype in inducing insulin resistance by possible phosphorylation of AKT/PKB.

HCV genes interfere with host cellular genes and play crucial role in pathogenesis. The mechanism under which HCV genes induce insulin resistance is not much clear. This study is aimed to examine the role of HCV NS5A in inducing insulin resistance by examining its affect in the phosphorylation level of AKT/PKB. In the present study, HepG2 cells were transfected with HCV NS5A and after 24 hours of transfection, protein was extracted from cells that were pre induced with insulin at three different time intervals i.e. 1hour, 2 hours and 3hours. Dot Blot analysis was performed to study the phosphorylation level of AKT. Results showed that there is clear upregulation of serine 473 phosphorylation level of AKT in NS5A transfected cells as compared with control (without NS5A). In conclusion, upregulation of serine 473 phosphorylation by NS5A of HCV genotype 3a suggests that this gene impairs the normal insulin AKT/PKB signaling pathway that leads towards insulin resistance and Type 2 diabetes mellitus. Therefore, HCV non-structural protein NS5A should be considered as promising candidate to be studied in detail for HCV induced insulin resistance and should be regarded as a therapeutically important target for the prevention of chronic liver diseases.

Computational Analysis of topological indices of two Boron Nanotubes.

There has been a recent debate that boron nanotubes can outperform carbon nanotubes on many grounds. The most stable boron nanotubes are made of a hexagonal lattice with an extra atom added to some of the hexagons called ∝-boron nanotubes. Closed forms of M-polynomial of nanotubes produce closed forms of many degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned nanotubes. In this article, we compute and analyze many topological indices of ∝-boron nanotubes correlating with the size of structure of these tubes through the use of M-polynomial. More importantly we make a graph-theoretic comparison of indices of two types of boron nanotubes namely triangular boron and ∝-boron nanotubes.

On Molecular Descriptors of Carbon Nanocones.

Many degree-based topological indices can be obtained from the closed-off M-polynomial of a carbon nanocone. These topological indices are numerical parameters that are associated with a structure and, in combination, determine the properties of the carbon nanocone. In this paper, we compute the closed form of the M-polynomial of generalized carbon nanocone and recover many important degree-based topological indices. We use software Maple 2015 (Maplesoft, Waterloo, ON, Canada) to plot the surfaces and graphs associated with these nanocones, and relate the topological indices to the structure of these nanocones.

Antigenic Peptide Prediction From E6 and E7 Oncoproteins of HPV Types 16 and 18 for Therapeutic Vaccine Design Using Immunoinformatics and MD Simulation Analysis.

Human papillomavirus (HPV) induced cervical cancer is the second most common cause of death, after breast cancer, in females. Three prophylactic vaccines by Merck Sharp & Dohme (MSD) and GlaxoSmithKline (GSK) have been confirmed to prevent high-risk HPV strains but these vaccines have been shown to be effective only in girls who have not been exposed to HPV previously. The constitutively expressed HPV oncoproteins E6 and E7 are usually used as target antigens for HPV therapeutic vaccines. These early (E) proteins are involved, for example, in maintaining the malignant phenotype of the cells. In this study, we predicted antigenic peptides of HPV types 16 and 18, encoded by E6 and E7 genes, using an immunoinformatics approach. To further evaluate the immunogenic potential of the predicted peptides, we studied their ability to bind to class I major histocompatibility complex (MHC-I) molecules in a computational docking study that was supported by molecular dynamics (MD) simulations and estimation of the free energies of binding of the peptides at the MHC-I binding cleft. Some of the predicted peptides exhibited comparable binding free energies and/or pattern of binding to experimentally verified MHC-I-binding epitopes that we used as references in MD simulations. Such peptides with good predicted affinity may serve as candidate epitopes for the development of therapeutic HPV peptide vaccines.

M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori.

V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical properties of the material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of V-Phylenic nanotubes and nanotori. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

Towards peptide vaccines against Zika virus: Immunoinformatics combined with molecular dynamics simulations to predict antigenic epitopes of Zika viral proteins.

The recent outbreak of Zika virus (ZIKV) infection in Brazil has developed to a global health concern due to its likely association with birth defects (primary microcephaly) and neurological complications. Consequently, there is an urgent need to develop a vaccine to prevent or a medicine to treat the infection. In this study, immunoinformatics approach was employed to predict antigenic epitopes of Zika viral proteins to aid in development of a peptide vaccine against ZIKV. Both linear and conformational B-cell epitopes as well as cytotoxic T-lymphocyte (CTL) epitopes were predicted for ZIKV Envelope (E), NS3 and NS5 proteins. We further investigated the binding interactions of altogether 15 antigenic CTL epitopes with three class I major histocompatibility complex (MHC I) proteins after docking the peptides to the binding groove of the MHC I proteins. The stability of the resulting peptide-MHC I complexes was further studied by molecular dynamics simulations. The simulation results highlight the limits of rigid-body docking methods. Some of the antigenic epitopes predicted and analyzed in this work might present a preliminary set of peptides for future vaccine development against ZIKV.