Stochastic yield catastrophes and robustness in self-assembly
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.
All data was generated from stochastic simulations in C++ and deterministic simulations in Matlab. The Source File Codes are uploaded with the manuscript files.
Article and author information
Deutsche Forschungsgemeinschaft (GRK2062)
- Patrick Wilke
Deutsche Forschungsgemeinschaft (QBM)
- Florian M Gartner
- Isabella R Graf
Aspen Center for Physics (PHY-160761)
- Erwin Frey
Deutsche Forschungsgemeinschaft (EXC-2094 - 390783311)
- Erwin Frey
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
- Frank Jülicher, Max Planck Institute for the Physics of Complex Systems, Germany
- Received: August 12, 2019
- Accepted: February 4, 2020
- Accepted Manuscript published: February 5, 2020 (version 1)
- Version of Record published: March 23, 2020 (version 2)
© 2020, Gartner et al.
This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.
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