Quantifying Directedness in Chemical Reaction Networks Using Assembly Theory

Abstract

There is currently no general experimental framework for determining whether an open-ended reaction network explores chemical space undirectedly or with some level of directedness. Assembly Theory (AT) provides a quantitative framework for mapping experimentally observed molecular ensembles into assembly space. Here we show that directedness in chemical systems can be quantified using two experimentally accessible observables, the exploration ratio (ER) and ensemble assembly (A). ER measures the fraction of the inferred joint assembly space sampled, while A integrates the molecular assembly index with the observed copy number. Together, these quantities distinguish undirected from directed exploration and, when applied to time-resolved data or matched controls, provide a quantitative measure of transitions associated with selection. By analyzing peptide ensembles generated under diverse polymerization conditions, we find that nonspecific activation conditions yield exploration ratios of 0.77–0.96, whereas sequence-selective proteases yield lower ratios of 0.51–0.75 and elevated A. These differences are consistent across multiple environments and amino-acid combinations. The results establish ER and A as experimentally tractable metrics for directedness in chemical reaction networks and provide a route to quantify selection when the relevant temporal or causal context is defined, with implications for reaction-network analysis, combinatorial synthesis, and chemical evolution.