Assembly in Directed Hypergraphs

TL;DR

This paper formalizes assembly theory within directed hypergraphs, linking it to chemical reaction systems and graph rewriting, and introduces ILP-based methods for computing complexity measures.

Contribution

It generalizes assembly theory to chemical systems, connects it with hyperpath problems and rule-based chemistry models, and proposes ILP methods for complexity analysis.

Findings

Assembly pathways correspond to minimal hyperpaths in B-hypergraphs.

Assembly index aligns with cost measures in hyperpath problems.

ILP approaches enable computation of complexity measures in chemical hypergraphs.

Abstract

Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to generalize the notion of assembly to general chemical reaction systems and to make explicit the connection to rule based models of chemistry, in particular DPO graph rewriting. We observe, furthermore, that assembly theory is closely related to retrosynthetic analysis in chemistry. The assembly index fits seamlessly into a large family of cost measures for directed hyperpath problems that also encompasses cost functions used in computational synthesis planning. This allows to devise a generic approach to compute complexity measures derived from minimal hyperpaths in rule-derived directed hypergraphs using integer linear programming.