Towards functorial chemistry: completeness and universality for reaction representation

Abstract: Organic molecules can be represented mathematically using labelled graphs [1]. Recently, the graph approach to chemistry has been extended to reactions using the techniques of graph rewriting [2,3]. While representing reactions lies at the heart of mathematical chemistry, the focus to date has been on the "forward" direction of reaction prediction and composition. The "reverse" direction of discovering reaction pathways to new compounds is, however, one of the main aims of modern chemical engineering. The methodology of this field, known as retrosynthetic analysis, is well-established and widely practised [4,5,6,7], but has received significantly less mathematical attention.

In this talk, I will suggest taking the basic units of retrosynthetic analysis - disconnection rules - as first-class citizens of reaction representation. The mathematical and conceptual justification for doing so lies in the fact that both disconnection rules and formalised reactions can be arranged into monoidal categories [8], such that there is a monoidal functor taking each (composable) sequence of disconnection rules to a reaction. Our main result shows that, under a certain axiomatisation of the disconnection rules, the functor is faithful and an opfibration. This implies that every reaction can be decomposed into a sequence of disconnection rules (universality) in an essentially unique way (completeness).

[1] D. Bonchev and D.H. Rouvray (eds). Chemical Graph Theory: Introduction and Fundamentals. Abacus Press / Gordon & Breach Science Publishers. 1991.

[2] J.L. Andersen, C. Flamm, D. Merkle, and P.F. Stadler. Inferring chemical reaction patterns using rule composition in graph grammars. J. Syst. Chem. 2013.

[3] J.L. Andersen, C. Flamm, D. Merkle, and P.F. Stadler. An intermediate level of abstraction for computational systems chemistry. Philos. Trans. R. Soc. 2017.

[4] E.J. Corey and X. Cheng. The logic of chemical synthesis. John Wiley. 1989.

[5] S. Warren and P. Wyatt. Organic synthesis: the disconnection approach. Wiley. 2008.

[6] J. Clayden, N. Greeves, and S. Warren. Organic chemistry. OUP. 2012.

[7] Y. Sun and N.V. Sahinidis. Computer-aided retrosynthetic design: fundamentals, tools, and outlook. Curr. Opin. Chem. Eng. 2022.

[8] E. Gale, L. Lobski, and F. Zanasi. A Categorical Approach to Synthetic Chemistry. Theoretical Aspects of Computing - ICTAC. 2023.

game theorylogic in computer scienceprogramming languagescomputer science theorycategory theory

Audience: researchers in the topic

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University of Birmingham theoretical computer science seminar

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