Stochastic Yield Catastrophes and Robustness in Self-Assembly

A guiding principle in macromolecular self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze a generic stochastic model for self-assembly into finite-sized target structures, and investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior even in the limit of small particle numbers, the activation scenario is highly sensitive to stochastic effects, which can completely suppress yield. Our results reveal that stochasticity is an important limiting factor for self-assembling systems and, in general, details of the nucleation process play a significant role for the final yield.