# Stochastic Yield Catastrophes and Robustness in Self-Assembly

## TL;DR

This paper uses mathematical modeling to show that stochastic fluctuations can cause yield failures in self-assembly, especially when nucleation is delayed by slow activation or reduced dimerization, highlighting the importance of stochastic effects.

## Contribution

It demonstrates that demographic fluctuations can lead to stochastic yield catastrophes in self-assembly, emphasizing the role of stochasticity in limiting assembly yield.

## Key findings

- Dimerization delay leads to robust self-assembly.
- Slow activation causes sensitivity to fluctuations.
- Stochastic yield catastrophe is a generic phenomenon.

## Abstract

A guiding principle in 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 self-assembly into finite-sized target structures employing mathematical modeling. We 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, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield.