Stochastic yield catastrophes and robustness in self-assembly

  1. Florian M Gartner
  2. Isabella R Graf
  3. Patrick Wilke
  4. Philipp M Geiger
  5. Erwin Frey  Is a corresponding author
  1. Ludwig-Maximilians-Universität München, Germany

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.

Data availability

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

Author details

  1. Florian M Gartner

    Arnold-Sommerfeld-Center for Theoretial Physics, Ludwig-Maximilians-Universität München, Munich, Germany
    Competing interests
    The authors declare that no competing interests exist.
  2. Isabella R Graf

    Arnold-Sommerfeld-Center for Theoretial Physics, Ludwig-Maximilians-Universität München, Munich, Germany
    Competing interests
    The authors declare that no competing interests exist.
  3. Patrick Wilke

    Arnold-Sommerfeld-Center for Theoretial Physics, Ludwig-Maximilians-Universität München, Munich, Germany
    Competing interests
    The authors declare that no competing interests exist.
  4. Philipp M Geiger

    Arnold-Sommerfeld-Center for Theoretial Physics, Ludwig-Maximilians-Universität München, Munich, Germany
    Competing interests
    The authors declare that no competing interests exist.
  5. Erwin Frey

    Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, München, Germany
    For correspondence
    frey@lmu.de
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8792-3358

Funding

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.

Reviewing Editor

  1. Frank Jülicher, Max Planck Institute for the Physics of Complex Systems, Germany

Publication history

  1. Received: August 12, 2019
  2. Accepted: February 4, 2020
  3. Accepted Manuscript published: February 5, 2020 (version 1)
  4. Version of Record published: March 23, 2020 (version 2)

Copyright

© 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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  1. Florian M Gartner
  2. Isabella R Graf
  3. Patrick Wilke
  4. Philipp M Geiger
  5. Erwin Frey
(2020)
Stochastic yield catastrophes and robustness in self-assembly
eLife 9:e51020.
https://doi.org/10.7554/eLife.51020

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