Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

Abstract:The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.

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.