Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.

Short tail stories: the hirudin-like factors HLF6 and HLF7 of the Asian medicinal leech, Hirudinaria manillensis

The leech-derived hirudins and hirudin-like factors (HLFs) share a common molecule structure: a short N-terminus, a central globular domain, and an elongated C-terminal tail. All parts are important for function. HLF6 and HLF7 were identified in the Asian medicinal leech, Hirudinaria manillensis. The genes of both factors encode putative splice variants that differ in length and composition of their respective C-terminal tails. In either case, the tails are considerably shorter compared to hirudins. Here we describe the functional analyses of the natural splice variants and of synthetic variants that comprise an altered N-terminus and/or a modified central globular domain. All natural splice variants of HLF6 and HLF7 display no detectable thrombin-inhibitory potency. In contrast, some synthetic variants effectively inhibit thrombin, even with tails as short as six amino acid residues in length. Our data indicate that size and composition of the C-terminal tail of hirudins and HLFs can vary in a great extent, yet the full protein may still retain the ability to inhibit thrombin.

Soliton molecules in the (2+1)-dimensional Nizhnik–Novikov–Veselov equation

The [Formula: see text]-soliton solution of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation is constructed. The line soliton molecule, the breather and the lump soliton are presented successively for [Formula: see text]. The three-soliton molecule structure, interaction of one-soliton molecule and a line soliton, the soliton molecules consisting of a line soliton and the breather/lump soliton of the solution [Formula: see text] are constructed for [Formula: see text]. Moreover, the four-soliton molecule structure, interaction of the soliton molecule and a line soliton, the soliton molecule consisting of the line soliton molecule and a lump soliton, the elastic interaction between the line soliton molecule and a lump soliton, the soliton molecules consisting of the line soliton molecule and the breather, two breather solitons, the breather soliton and a lump of the variable [Formula: see text] for this equation are also derived for [Formula: see text] by applying the velocity resonance, the module resonance of wave number and the long-wave limit ideas. To illustrate these phenomena, the analysis explicit solutions are all given and their dynamics features are all displayed through figures.

Deep Learning Insights into Lanthanides Complexation Chemistry

Modern structure–property models are widely used in chemistry; however, in many cases, they are still a kind of a “black box” where there is no clear path from molecule structure to target property. Here we present an example of deep learning usage not only to build a model but also to determine key structural fragments of ligands influencing metal complexation. We have a series of chemically similar lanthanide ions, and we have collected data on complexes’ stability, built models, predicting stability constants and decoded the models to obtain key fragments responsible for complexation efficiency. The results are in good correlation with the experimental ones, as well as modern theories of complexation. It was shown that the main influence on the constants had a mutual location of the binding centers.