Can topological indices transmit information on properties but not on structures?

Network-Based Modeling of the Molecular Topology of Fuchsine Acid Dye with Respect to Some Irregular Molecular Descriptors

Fuchsine acid is one of the supramolecular dyes used in Masson’s trichrome stain and has enormous applications in histology. It is also used in Van Gieson’s method with picric acid to show red collagen fibers and in Masson’s trichrome to show smooth muscle in contrast to collagen. In addition to these, it has several other important applications in electronic fields and photonic devices as an organic semiconductor. Therefore, it is of utmost importance to investigate and predict the complex molecular topology of fuchsine acid, which serves as a foundation for the link with its physicochemical properties. In this article, the supramolecular sheet of fuchsine acid is modeled topologically based on the edge partition, and closed formulae are derived for some of its important irregular molecular descriptors, with the ultimate object of throwing some light on the effectiveness of the computed molecular descriptors for QSAR and QSPR analyses.

On the zagreb connection indices of hex and honeycomb networks

Regular plane tessellations can easily be constructed by repeating regular polygons. This design is of extreme importance for direct interconnection networks as it yields high overall performance. The honeycomb and the hexagonal networks are two such popular mesh-derived parallel networks. The first and second Zagreb indices are among the most studied topological indices. We now consider analogous graph invariants, based on the second degrees of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the Hex, Hex derived and some honeycomb networks.

M-Polynomial and Degree Based Topological Indices of Some Nanostructures

The association of M-polynomial to chemical compounds and chemical networks is a relatively new idea, and it gives good results about the topological indices. These results are then used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. In this paper, an effort is made to compute the general form of the M-polynomials for two classes of dendrimer nanostars and four types of nanotubes. These nanotubes have very nice symmetries in their structural representations, which have been used to determine the corresponding M-polynomials. Furthermore, by using the general form of M-polynomial of these nanostructures, some degree-based topological indices have been computed. In the end, the graphical representation of the M-polynomials is shown, and a detailed comparison between the obtained topological indices for aforementioned chemical structures is discussed.

The Sanskruti index of trees and unicyclic graphs

The Sanskruti index of a graphGis defined as$$\begin{align*}S(G)=\sum_{uv\in{}E(G)}{\left(\frac{s_G(u)s_G(v)}{s_G(u)+s_G(v)-2}\right)}^3, \end{align*}$$wheresG(u) is the sum of the degrees of the neighbors of a vertexuinG. LetPn,Cn,SnandSn+ebe the path, cycle, star and star plus an edge ofnvertices, respectively. The Sanskruti index of a molecular graph of a compounds can model the bioactivity of compounds, has a strong correlation with entropy of octane isomers and its prediction power is higher than many existing topological descriptors.

In this paper, we investigate the extremal trees and unicyclic graphs with respect to Sanskruti index. More precisely, we show that

(1)$\frac{512}{27}n-\frac{172688}{3375}\leq{}S(T)\leq{}\frac{(n-1)^7}{8(n-2)^3}$for ann-vertex treeTwithn≤ 3, with equalities if and only ifT ≌Pn(left) andT≌Sn(right);

(2)$ \frac{512}{27}n\leq{}S(G)\leq{}\frac{(n-3)(n+1)^3}{8}+\frac{3(n+1)^6}{8n^3}$for ann-vertex unicyclic graph withn≥ 4, with equalities if and only ifG ≌Cn(left) andG≌Sn+e(right).

The inverse Wiener polarity index problem for chemical trees

The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by W_p) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index W_p of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n − 3, n − 2,…,3n − 16, 3n − 15}, n ≥ 6, there exists an n-vertex chemical tree T such that W_p(T) = t.

Bigger data, collaborative tools and the future of predictive drug discovery

Over the past decade we have seen a growth in the provision of chemistry data and cheminformatics tools as either free websites or software as a service commercial offerings. These have transformed how we find molecule-related data and use such tools in our research. There have also been efforts to improve collaboration between researchers either openly or through secure transactions using commercial tools. A major challenge in the future will be how such databases and software approaches handle larger amounts of data as it accumulates from high throughput screening and enables the user to draw insights, enable predictions and move projects forward. We now discuss how information from some drug discovery datasets can be made more accessible and how privacy of data should not overwhelm the desire to share it at an appropriate time with collaborators. We also discuss additional software tools that could be made available and provide our thoughts on the future of predictive drug discovery in this age of big data. We use some examples from our own research on neglected diseases, collaborations, mobile apps and algorithm development to illustrate these ideas.

Sharing chemical relationships does not reveal structures

In this study, we propose a new, secure method of sharing useful chemical information from small-molecule libraries, without revealing the structures of the libraries' molecules. Our method shares the relationship between molecules rather than structural descriptors. This is an important advance because, over the past few years, several groups have developed and published new methods of analyzing small-molecule screening data. These methods include advanced hit-picking protocols, promiscuous active filters, economic optimization algorithms, and screening visualizations, which can identify patterns in the data that might otherwise be overlooked. Application of these methods to private data requires finding strategies for sharing useful chemical data without revealing chemical structures. This problem has been examined in the context of ADME prediction models, with results from information theory suggesting it is impossible to share useful chemical information without revealing structures. In contrast, we present a new strategy for encoding the relationships between molecules instead of their structures, based on anonymized scaffold networks and trees, that safely shares enough chemical information to be useful in analyzing chemical data, while also sufficiently blinding structures from discovery. We present the details of this encoding, an analysis of the usefulness of the information it conveys, and the security of the structures it encodes. This approach makes it possible to share data across institutions, and may securely enable collaborative analysis that can yield insight into both specific projects and screening technology as a whole.

Crowd computing: using competitive dynamics to develop and refine highly predictive models

A recent application of a crowd computing platform to develop highly predictive in silico models for use in the drug discovery process is described. The platform, Kaggle™, exploits a competitive dynamic that results in model optimization as the competition unfolds. Here, this dynamic is described in detail and compared with more-conventional modeling strategies. The complete and full structure of the underlying dataset is disclosed and some thoughts as to the broader utility of such 'gamification' approaches to the field of modeling are offered.

Structural discrimination of networks by using distance, degree and eigenvalue-based measures

In chemistry and computational biology, structural graph descriptors have been proven essential for characterizing the structure of chemical and biological networks. It has also been demonstrated that they are useful to derive empirical models for structure-oriented drug design. However, from a more general (complex network-oriented) point of view, investigating mathematical properties of structural descriptors, such as their uniqueness and structural interpretation, is also important for an in-depth understanding of the underlying methods. In this paper, we emphasize the evaluation of the uniqueness of distance, degree and eigenvalue-based measures. Among these are measures that have been recently investigated extensively. We report numerical results using chemical and exhaustively generated graphs and also investigate correlations between the measures.

Novel graph distance matrix

We have introduced novel distance matrix for graphs, which is based on interpretation of columns of the adjacency matrix of a graph as a set of points in n-dimensional space, n being the number of vertices in the graph. Numerical values for the distances are based on the Euclidean distance between n points in n-dimensional space. In this way, we have combined the traditional representation of graphs (drawn as 2D object of no fixed geometry) with their representation in n-dimensional space, defined by a set of n-points that lead to a representation of definite geometry. The novel distance matrix, referred to as natural distance matrix, shows some structural properties and offers novel graph invariants as molecular descriptors for structure-property-activity studies. One of the novel graph descriptors is the modified connectivity index in which the bond contribution for (m, n) bond-type is given by 1/ radical(m + n), where m and n are the valence of the end vertices of the bond. The novel distance matrix (ND) can be reduced to sparse distance-adjacency matrix (DA), which can be viewed as specially weighted adjacency matrix of a graph. The quotient of the leading eigenvalues of novel distance-adjacency matrix and novel distance matrix, as illustrated on a collection of graphs of chemical interest, show parallelism with a simple measure of graph density, based on the quotient of the number of edges in a graph and the maximal possible number of edges for graphs of the same size.

Complexity of chemical graphs in terms of size, branching, and cyclicity

Chemical graph complexity depends on many factors, but the main ones are size, branching, and cyclicity. Some molecular descriptors embrace together all these three parameters, which cannot then be disentangled. The topological index J (and its refinements that include accounting for bond multiplicity and the presence of heteroatoms) was designed to compensate in a significant measure for graph size and cyclicity, and therefore it contains information mainly on branching. In order to separate these factors, two new indices (F and G) related with J are proposed, which allow to group together graphs with the same size into families of constitutional formulas differing in their branching and cyclicity. A comparison with other topological indices revealed that a few other topological indices vary similarly with index G, notably DN2S4 among the triplet indices, and TOTOP among the indices contained in the Molconn-Z program. This comparison involved all possible chemical graphs (i.e. connected planar graphs with vertex degrees not higher than four) with four through six vertices, and all possible alkanes with four through nine carbon atoms.