Quantifying Directedness in Chemical Reaction Networks Using Assembly Theory

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.