Types of Discrete molecular models

Question

It is often assumed in cheminformatics that molecules with similar physical structure tend to have similar chemical properties [1].

Based on this, our group has used discrete graphs as a model for the physical structure of molecules [2][3].

What other types of molecular models are out there? My interest is mainly simple, discrete models, but I'm hoping to find something that offers more insight than the nodes and edges of discrete graph models.

1. Joerg Kurt Wegner, Aaron Sterling, Rajarshi Guha, Andreas Bender, Jean-Loup Faulon, Janna Hastings, Noel O’Boyle, John Overington, Herman Van Vlijmen, and Egon Willighagen. 2012. Cheminformatics. Commun. ACM 55, 11 (November 2012), 65–75. DOI: 10.1145/2366316.2366334

2. Kyousuke Yamashita, Ryuji Masui, Xiang Zhou, Chenxi Wang, Aleksandar Shurbevski, Hiroshi Nagamochi, & Tatsuya Akutsu. (2020). Enumerating Chemical Graphs with Two Disjoint Cycles Satisfying Given Path Frequency Specifications. arXiv: 2004.08381 [cs.DS]

3. Yuui Tamura, Yuhei Nishiyama, Chenxi Wang, Yanming Sun, Aleksandar Shurbevski, Hiroshi Nagamochi, & Tatsuya Akutsu. (2020). Enumerating Chemical Graphs with Mono-block 2-Augmented Tree Structure from Given Upper and Lower Bounds on Path Frequencies. arXiv: 2004.06367 [cs.DS]

Answer 1

One place to start is just altering how you form your graphs or their corresponding matrix representation. The simplest representation is probably an unweighted graph, which corresponds to an adjacency matrix and just tells you what atoms neighbor each other. Depending on your interest, this description can be improved by using the bond order to weight the edges.

Alternatively, you can include information related to distance, whether that is simply encoding the shortest number of bonds between two atoms. If you are willing to use a continuous model, the actual Euclidean distances can be used. More general versions of this idea have been developed in the context of machine learning to create simplified molecular descriptors. This page gives a basic summary of some commonly used continuous models, such as the Coulomb matrix, which includes both distance and charge information about the atoms/bonds of molecule. Again, these are continuous, but I would expect that it would be possible to include some notion of charge in a graph model as well. This is just to say perhaps you could still use a graph, but encode different information than you are currently.

Machine learning and cheminformatics have also inspired the development of molecular fingerprints, which encode certain features of a molecule (e.g. number of rings, aromaticity, presence/absence of some substructure or functional group) rather than the exact arrangement of atoms. These are often expressed as simple bits strings, which makes comparisons very simple to perform. The choice of the features to include is an area of active study, but has generally been along the lines of manually choosing them using chemical intuition about the intended property to be studied or automatic generation of features through some type of learning process.