Disconnection Rules are Complete for Chemical Reactions

Abstract

We provide a category theoretical framework capturing two approaches to graph-based models of chemistry: formal reactions and disconnection rules. We model a translation from the latter to the former as a functor, which is faithful, and full up to isomorphism. This allows us to state, as our main result, that the disconnection rules are sound, complete and universal with respect to the reactions. Concretely, this means that every reaction can be decomposed into a sequence of disconnection rules in an essentially unique way. This provides a uniform way to store reaction data, and gives an algorithmic interface between (forward) reaction prediction and (backward) reaction search or retrosynthesis.

Figures (4)

• Figure 1: A simple retrosynthetic sequence. A molecule (far left) is disconnected at the O-COPh bond giving rise to two synthons (left) which can be mapped to precursor molecules (right) which can react to give the product (far right).
• Figure 2: The four disconnection rules
• Figure 3: The disconnection rules defined as partial functions
• Figure 4: The equivalence relation $\approx$ inducing the identities in the disconnection category. Here $d$ and $h$ range over $\{E,C,I\}$, while $S^U$ stands for the sequence $S^u;S^w$ if $U=uw$. Given vertex names $a,b\in\mathbf{VN}$, the notation $D[a]$ means $a$ occurs in $D$, and $D[b/a]$ means the occurrence of $a$ in $D$ is replaced with $b$. Note that we use the shorthand relations $\lesssim$ and $\simeq$: these are strictly speaking not part of the definition, but we use them to provide the extra information of when well-typedness of one side of an identity implies well-typedness of the other.

Theorems & Definitions (63)

• Remark 1
• Definition 1: Chemically labelled graph
• Example 1
• Definition 2: Neighbours
• Definition 3: Chemical graph
• Example 2
• Definition 4: Category of reactions
• Example 3
• Definition 5: Disconnection rules
• Definition 6: Terms