Optimizing kinetics of hetero-subunit assembly using differentiable models

In macromolecular assemblies ranging from ribosomes to viral capsids, kinetic trapping produces long-lived intermediates that reduce yield of the target, functional products. Cells can exploit energy-consuming pathways to prevent trapping, but this comes at a cost. Here, we quantify how the threat of kinetic trapping expands with complexity due to topology, size, or heterogeneity of assemblies, from trimers and hetero-tetramers to larger assemblies. We exploit efficient automatic differentiation of kinetic models to 'discover' assembly pathways that can maximize yield while avoiding errors and traps. We show how assemblies can use distinct strategies for avoiding traps, where hierarchies of rates (and binding energies) for dimerization steps offers in some ways a simpler and more flexible evolutionary strategy than pathways that require cooperativity. Our results further show which highly connected subunits must be most severely constrained. We use these results to assess how active control by enzymes could provide more robust strategies to optimize yield than perfect optimization of stochastic interactions. Our results provide strategies for reducing trapping and maximizing assembly yield at minimal cost, borrowing techniques used in machine learning to find optimal assembly pathways despite fixed topologies and energetics.