Quantifying Pairwise Similarity for Complex Polymers

Abstract

Defining the similarity between chemical entities is an essential task in polymer informatics, enabling ranking, clustering, and classification. Despite its importance, the pairwise chemical similarity of polymers remains an open problem. Here, a similarity function for polymers with well-defined backbones is designed based on polymers’ stochastic graph representations generated from canonical BigSMILES, a structurally based line notation for describing macromolecules. The stochastic graph representations are separated into three parts: repeat units, end groups, and polymer topology. The earth mover’s distance is utilized to calculate the similarity of the repeat units and end groups, while the graph edit distance is used to calculate the similarity of the topology. These three values can be linearly or nonlinearly combined to yield an overall pairwise chemical similarity score for polymers that is largely consistent with the chemical intuition of expert users and is adjustable based on the relative importance of different chemical features for a given similarity problem. This method gives a reliable solution to quantitatively calculate the pairwise chemical similarity score for polymers and represents a vital step toward building search engines and quantitative design tools for polymer data.

Calculating Pairwise Similarity of Polymer Ensembles via Earth Mover’s Distance

“…To map GED(g 1 , g 2 ) onto a distance d ( g 1 , g 2 ) that is 0 and 1, first the GED is normalized to be G E D false( g 1 , g 2 false) false( N 1 + N 2 false) / 2 and then an exponential decay function is used: , d false( g 1 , g 2 false) = 1 − exp true( prefix− α · normalG normalE normalD ( g 1 , g 2 ) ( N 1 + N 2 ) / 2 true) where N i denotes the number of nodes of g i and α is a tunable parameter with the default value being 1. d ( g 1 , g 2 ) is 0 when g 1 and g 2 are identical. d ( g 1 , g 2 ) is also symmetric, so d ( g 1 , g 2 ) = d ( g 2 , g 1 ).…”

“…Aldeghi et al developed a graph-based representation with “stochastic” edges to describe the average structure of repeat units . These existing text-based and graph-based stochastic representations can be used to calculate the pairwise similarity score, which captures the chemical and topological features contained in a polymer chemical structure diagram . However, these stochastic representations do not specify the weight or probability of each polymer molecule within the ensemble.…”

“…46 These existing text-based and graph-based stochastic representations can be used to calculate the pairwise similarity score, which captures the chemical and topological features contained in a polymer chemical structure diagram. 56 However, these stochastic representations do not specify the weight or probability of each polymer molecule within the ensemble. This probability information can include chain length, composition gradient, stereochemistry, and molecular mass distribution.…”

Navigating the Expansive Landscapes of Soft Materials: A User Guide for High-Throughput Workflows

“…In addition to string notation, molecular graphs, where atoms and bonds can be represented as nodes and edges in graphs, have been successful (Figure b). − Extended-connectivity fingerprints (ECFPs), also known as “Morgan fingerprints”, are generated through a circular approach, where the “extended connectivity” of atoms is described with increasingly large radii centered around non-hydrogen atoms . PolyGrammar is a polymer specific graph-type approach that is designed to support architecture and monomer chemistries .…”