Quantum Molecular Dynamics, Topological, Group Theoretical and Graph Theoretical Studies of Protein-Protein Interactions

Graph Theoretical Description of Phase Transitions in Complex Multiscale Phases with Supramolecular Assemblies

Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems- thermotropic liquid crystals and a lyotropic water/surfactant mixtures-graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node-based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.

Bioinformatic investigation of Nipah virus surface protein mutations: Molecular docking with Ephrin B2 receptor, molecular dynamics simulation, and structural impact analysis

The SARS-CoV-2 outbreak resulted in significant challenges and loss of life. The Nipah virus, known for its high infectivity and severity, was designated an emergency concern by the World Health Organization. To understand its mutations, the Nipah virus proteins were analyzed extensively, with a focus on the essential G and F proteins responsible for viral entry into host cells. Our bioinformatics analysis unveiled multiple mutations, including simultaneous mutations within a single sequence. Notably, the G273S mutation in the F protein was identified as a potential cause of structural damage, which carries significant implications for vaccine development. Comparing the docking scores of G and F proteins with the Ephrin B2 receptor, it was found that the Y228H mutation in the G protein and the D252G mutation in the F protein likely affect virus entry into host cells. Moreover, our investigation into stability and deformability highlighted the impact of the Y228H mutation in the G protein complex. Molecular dynamics simulations revealed increased flexibility and conformational changes in the G protein complex with the Y228H mutation compared with the known complex. Furthermore, evaluating the root mean square deviation variation demonstrated greater dynamic behavior in the G protein complex and the Ephrin B2 receptor complex. This comprehensive study provides valuable insights into Nipah virus mutations, their significance for vaccine development, and the importance of understanding protein complex behavior in drug discovery. The identified mutations, especially G273S and Y228H, hold crucial implications for future research and potential interventions against the Nipah virus.

Symmetry and Combinatorial Concepts for Cyclopolyarenes, Nanotubes and 2D-Sheets: Enumerations, Isomers, Structures Spectra & Properties

This review article highlights recent developments in symmetry, combinatorics, topology, entropy, chirality, spectroscopy and thermochemistry pertinent to 2D and 1D nanomaterials such as circumscribed-cyclopolyarenes and their heterocyclic analogs, carbon and heteronanotubes and heteronano wires, as well as tessellations of cyclopolyarenes, for example, kekulenes, septulenes and octulenes. We establish that the generalization of Sheehan’s modification of Pólya’s theorem to all irreducible representations of point groups yields robust generating functions for the enumeration of chiral, achiral, position isomers, NMR, multiple quantum NMR and ESR hyperfine patterns. We also show distance, degree and graph entropy based topological measures combined with techniques for distance degree vector sequences, edge and vertex partitions of nanomaterials yield robust and powerful techniques for thermochemistry, bond energies and spectroscopic computations of these species. We have demonstrated the existence of isentropic tessellations of kekulenes which were further studied using combinatorial, topological and spectral techniques. The combinatorial generating functions obtained not only enumerate the chiral and achiral isomers but also aid in the machine construction of various spectroscopic and ESR hyperfine patterns of the nanomaterials that were considered in this review. Combinatorial and topological tools can become an integral part of robust machine learning techniques for rapid computation of the combinatorial library of isomers and their properties of nanomaterials. Future applications to metal organic frameworks and fullerene polymers are pointed out.

Discovery of Novel Small Molecule Inhibitors Disrupting the PCSK9-LDLR Interaction

Proprotein convertase subtilisin kexin 9 (PCSK9) has been identified as a reliable therapeutic target for hypercholesterolemia and coronary artery heart diseases since the monoclonal antibodies of PCSK9 have launched. Disrupting the protein-protein interaction (PPI) between PCSK9 and the low-density lipoprotein receptor (LDLR) has been considered as a promising approach for developing PCSK9 inhibitors. However, PPIs have been traditionally considered difficult to target by small molecules since the PPI surface is usually large, flat, featureless, and without a "pocket" or "groove" for ligand binding. The PCSK9-LDLR PPI interface is such a typical case. In this study, a potential binding pocket was generated on the PCSK9-LDLR PPI surface of PCSK9 through induced-fit docking. On the basis of this induced binding pocket, virtual screening, molecular dynamics (MD) simulation, and biological evaluations have been applied for the identification of novel small molecule inhibitors of PCSK9-LDLR PPI. Among the selected compounds, compound 13 exhibited certain PCSK9-LDLR PPI inhibitory activity (IC₅₀: 7.57 ± 1.40 μM). The direct binding affinity between 13 and PCSK9 was determined with a K_D value of 2.50 ± 0.73 μM. The LDLR uptake function could be also restored to a certain extent by 13 in HepG2 cells. This well-characterized hit compound will facilitate the further development of novel small molecule inhibitors of PCSK9-LDLR PPI.

Symmetry, Combinatorics, Artificial Intelligence, Music and Spectroscopy

Symmetry forms the foundation of combinatorial theories and algorithms of enumeration such as Möbius inversion, Euler totient functions, and the celebrated Pólya’s theory of enumeration under the symmetric group action. As machine learning and artificial intelligence techniques play increasingly important roles in the machine perception of music to image processing that are central to many disciplines, combinatorics, graph theory, and symmetry act as powerful bridges to the developments of algorithms for such varied applications. In this review, we bring together the confluence of music theory and spectroscopy as two primary disciplines to outline several interconnections of combinatorial and symmetry techniques in the development of algorithms for machine generation of musical patterns of the east and west and a variety of spectroscopic signatures of molecules. Combinatorial techniques in conjunction with group theory can be harnessed to generate the musical scales, intensity patterns in ESR spectra, multiple quantum NMR spectra, nuclear spin statistics of both fermions and bosons, colorings of hyperplanes of hypercubes, enumeration of chiral isomers, and vibrational modes of complex systems including supergiant fullerenes, as exemplified by our work on the golden fullerene C150,000. Combinatorial techniques are shown to yield algorithms for the enumeration and construction of musical chords and scales called ragas in music theory, as we exemplify by the machine construction of ragas and machine perception of musical patterns. We also outline the applications of Hadamard matrices and magic squares in the development of algorithms for the generation of balanced-pitch chords. Machine perception of musical, spectroscopic, and symmetry patterns are considered.

On Extremal Graphs of Degree Distance Index by Using Edge-Grafting Transformations Method

BACKGROUND

Topological indices have numerous implementations in chemistry, biology and in lot of other areas. It is a real number associated to a graph, which provides information about its physical and chemical properties and their correlations. For a connected graph H, the degree distance defined as DD(H)=∑_(\{h_1,h_2}⊆V(H))〖(〖deg〗_H (h_1 )+〖deg〗_H (h_2 )) d_H (h_1,h_2 ) 〗, where 〖deg〗_H (h_1 ) is the degree of vertex h_1and d_H (h_1,h_2 ) is the distance between h_1and h_2in the graph H.

AIM AND OBJECTIVE

In this article, we characterize some extremal trees with respect to degree distance index which has a lot of applications in theoretical and computational chemistry.

MATERIALS AND METHODS

A novel method of edge-grafting transformations is used. We discuss the behavior of DD index under four edge-grafting transformations.

RESULTS

By the help of those transformations, we derive some extremal trees under certain parameters including pendant vertices, diameter, matching and domination numbers. Some extremal trees for this graph invariant are also characterized.

CONCLUSION

It is shown that balanced spider approaches to the smallest DD index among trees having given fixed leaves. The tree Cn,d has the smallest DD index, among the all trees of diameter d. It is also proved that the matching number and domination numbers are equal for trees having minimum DD index.

Combinatorics of Supergiant Fullerenes: Enumeration of Polysubstituted Isomers, Chirality, Nuclear Magnetic Resonance, Electron Spin Resonance Patterns, and Vibrational Modes from C70 to C150000

We have developed combinatorial techniques for the enumeration of isomers of polysubstituted giant fullerenes through icosahedral C₁₅₀₀₀₀ and applied the techniques to chirality of the isomers, NMR spectroscopy, and group theoretical analysis of the vibrational modes of supergiant fullerenes. We have employed a combination of distance-degree vectorial sequences, self-returning walk sequences followed by our generalization of Sheehan's version of Pólya's theorem, and Möbius inversion technique extended to all irreducible representations of the point groups of giant fullerenes. The concept of shell equivalence classes was utilized to analyze supergiant fullerenes. We have applied these techniques to golden fullerenes in the series C_60m² for m of up to 50 or C₁₅₀₀₀₀ as well as giant fullerenes in the series C_180m² and C₇₀(D_5h). We have employed computational and combinatorial tools to enumerate both chiral and achiral isomers of substituted and hetero giant fullerenes as well as NMR-generating functions for the giant fullerenes. The techniques also provide efficient tools to enumerate all of the vibrational modes of giant fullerenes in terms of the shell partitions. General combinatorial formulae are obtained for larger polysubstituted golden fullerenes of the series C_60m² for any m, and thus the techniques are applied to larger fullerenes such as C₁₅₀₀₀₀. New insights into chirality measures, NMR, ESR hyperfine structures, and vibrational modes of supergiant fullerenes are provided using the novel combinatorial techniques.

Topological and Thermodynamic Entropy Measures for COVID-19 Pandemic through Graph Theory

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part of artificial intelligence are designed for contact tracing, genetic network analysis for uncovering the biological evolution of the virus, understanding the underlying mechanisms of the observed disease dynamics, evaluating mitigation strategies, and predicting the COVID-19 pandemic dynamics. This paper describes mathematical techniques to exploit and understand the progression of the pandemic through a topological characterization of underlying graphs. We have obtained several topological indices for various graphs of biological interest such as pandemic trees, Cayley trees, Christmas trees, and the corona product of Christmas trees and paths. We have also obtained an analytical expression for the thermodynamic entropies of pandemic trees as a function of R0, the reproduction number, and the level of spread, using the nested wreath product groups. Our plots of entropy and logarithms of topological indices of pandemic trees accentuate the underlying severity of COVID-19 over the 1918 Spanish flu pandemic.

The Universal Soldier: Enzymatic and Non-Enzymatic Antioxidant Functions of Serum Albumin

As a carrier of many biologically active compounds, blood is exposed to oxidants to a greater extent than the intracellular environment. Serum albumin plays a key role in antioxidant defence under both normal and oxidative stress conditions. This review evaluates data published in the literature and from our own research on the mechanisms of the enzymatic and non-enzymatic activities of albumin that determine its participation in redox modulation of plasma and intercellular fluid. For the first time, the results of numerous clinical, biochemical, spectroscopic and computational experiments devoted to the study of allosteric modulation of the functional properties of the protein associated with its participation in antioxidant defence are analysed. It has been concluded that it is fundamentally possible to regulate the antioxidant properties of albumin with various ligands, and the binding and/or enzymatic features of the protein by changing its redox status. The perspectives for using the antioxidant properties of albumin in practice are discussed.

Computations of Colorings 7D-Hypercube's Hyperplanes for All Irreducible Representations

In the present study, we compute and enumerate the colorings of 7D-hypercube for all of its hyperplanes (q = 1-7) for all 110 irreducible representations (IRs) of the seventh-dimensional hyperoctahedral group consisting of 645,120 symmetry operations. The computations of colorings of the 7D-hypercube are motivated by a number of chemical and biological applications such as the 7D-hypercube representation of the periodic table, hypercube representations of water heptamer clusters, genetic regulatory networks, isomerization graphs, massively large data representations, and so forth. We have employed the Möbius inversion technique combined with generalized character cycle indices for 110 IRs to compute the generating functions for colorings of seven different types of hyperplanes of the 7D-hypercube varying from the vertices (q = 7) to hexeracts (q = 1) of the 7D-hypercube. Explicit computed tables are provided for 110 IRs from q = 1 to q = 7 for the 7D-hypercube. © 2019 Wiley Periodicals, Inc.

Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons

In this study we consider relatively new bond-additive Mostar indices that appear to provide quantitative measures of peripheral shapes of molecules. We have computed weighted Mostar, edge-Mostar and total-Mostar indices of graphene, [Formula: see text]-types of graphyne and graphdiyne, which are of considerable interest owing to their novel properties and thus find applications in a number of areas such as sensors, catalysis, chemisorption and nanomedicine. We have implemented the results to analyse the weighted Mostar indices and have obtained exact analytical expressions for the title molecules. We propose that Mostar indices together with frontier molecular orbitals, and HOMO-LUMO gaps can provide measures of chemical reactivity and analysis of peripheral molecular shapes.

Edge Distance-based Topological Indices of Strength-weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO2 Nanostructures

The edge-Wiener index is conceived in analogous to the traditional Wiener index and it is defined as the sum of distances between all pairs of edges of a graph G. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the techniques to compute the edge-Wiener and vertex-edge-Wiener indices of G by dissecting the original graph G into smaller strength-weighted quotient graphs with respect to Djoković-Winkler relation. These techniques have been applied to compute the exact analytic expressions for the edge-Wiener and vertex-edge-Wiener indices of coronoid systems, carbon nanocones and SiO₂ nanostructures. In addition, we have reduced these techniques to the subdivision of partial cubes and applied to the circumcoronene series of benzenoid systems.