“Social” Network of Isomers Based on Bond Count Distance: Algorithms

Abstract

This paper introduces the concept of an isomer network based on the reaction step counts between pairs of isomers as an alternative means to view and analyze isomer space. The computation of isomer networks is computationally expensive with respect to both run time and memory. Accordingly, this paper focuses on the design of algorithms to compute isomer networks and their analysis on structurally diverse subsets of isomers of nicotine, tyrosine, and phenmetrazine generated using molecular quantum number nearest neighbors. An analysis correlating isomer networks to extended connectivity fingerprints is also provided.

Faster Algorithms for Isomer Network Generation

“…Figure 2 shows the resulting isomer network. 1 Definition: A complete isomer network 1 defined on a set of M isomers is a complete weighted graph on M vertices (each corresponding to an isomer) with edge weights equal to the bond count distances between the corresponding isomers.…”

“…In addition, an improved algorithm (called the Simultaneous All−All algorithm 1 ) resulted in a 15fold improvement in runtime over the naive approach described above for an isomer network consisting of 20 nicotine isomers. Using a combination of these two strategies, we have in previous work 1 Even though this is an improvement, this approach is clearly not scalable to the complete set of isomers. For example, the runtime to compute the 10-isomer network for 2934 nicotine (without small rings) isomers is approximately 59 h (first row of Table 1).…”

“…The concept of an isomer network was invented by our group in collaboration with Dr. Jean-Louis Reymond's group at the University of Berne. 1 On one hand, this work can be viewed as a continuation of a long line of mathematical research related to isomers dating back to the 1920s that is concerned with the counting, generation, and sampling of isomers. Isomer networks extend this by providing a graph-theoretic mechanism to express the relationship between isomers.…”

Random Models and Analyses for Chemical Graphs

“…DN was used to speed up automated reaction mapping (an important tool in bioinformatics and cheminformatics) computations [23][24][25]. The automated reaction mapping algorithms which utilize the DN were tested on a variety of mechanisms, including a Colorado School of Mines (CSM) mechanism, a Lawrence Livermore National Laboratory (LLNL) [18] mechanism and the KEGG/LIGAND v57 database [16].…”

Improved methods to compare distance metrics in networks using uniform random spanning trees (DIMECOST)

“…• Le Corre et al [9] use the Mantel test to find the similarity between geographical distances among populations and chloroplast DNA restriction polymorphism in the same populations. • In our own research group's previous work in cheminformatics, we used the Mantel test to study the relationship between bond count distances and Tanimoto distances between extended connectivity fingerprints corresponding in isomer networks [8].…”