Quantifying Error Correction through a Rule-Based Model of Strand Escape from an [ n]-Rung Ladder

The rational design of 3D structures (MOFs, COFs, etc.) is presently limited by our understanding of how the molecular constituents assemble. The common approach of using reversible interactions (covalent or noncovalent) becomes challenging, especially when the target is made from multivalent building blocks and/or under conditions of slow exchange, as kinetic traps and nonequilibrium product distributions are possible. Modeling the time course of the assembly process is difficult because the reaction networks include many possible pathways and intermediates. Here we show that rule-based kinetic simulations efficiently model dynamic reactions involving multivalent building blocks. We studied "strand escape from an [n]-rung ladder" as an example of a dynamic process characterized by a complex reaction network. The strand escape problem is important in that it predicts the time a dynamic system needs to backtrack from errors involving [n]-misconnections. We quantify the time needed for error correction as a function of the dissociation rate coefficient, strand valency, and seed species. We discuss the simulation results in relation to a simple probabilistic framework that captures the power law dependence on the strand's valency, and the inverse relationship to the rung-opening rate coefficient. The model also tests the synthetic utility of a one-rung (i.e., hairpin) seed species, which, at intermediate times, bifurcates to a long-lived, fully formed [n]-rung ladder and a pair of separated strands. Rule-based models thus give guidance to the planning of a dynamic covalent synthesis by predicting time to maximum yield of persistent intermediates for a particular set of rate coefficients and valency.