Hierarchical self-assembly for high-yield addressable complexity at fixed conditions

There is evidence that the self-assembly of complex molecular systems often proceeds hierarchically, by first building subunits that later assemble in larger entities, in a process that can repeat multiple times. Yet, our understanding of this phenomenon and its performance is limited. Here we introduce a simple model for hierarchical addressable self-assembly, where interactions between particles can be optimised to maximise the fraction of a well-formed target structure, or yield. We find that a hierarchical strategy leads to an impressive yield up to at least five generations of the hierarchy, and does not require a cycle of temperatures as used in previous methods. High yield is obtained when the microscopic interaction decreases with the scale of units considered, such that the total interaction between intermediate structures remains identical at all scales. We provide thermodynamic and dynamical arguments constraining the interaction strengths where this strategy is effective. Overall, our work characterizes an alternative strategy for addressable self-assembly at a fixed temperature, and provides insight into the mechanisms sustaining hierarchical assembly in biology.