Stochastic Yield Catastrophes and Robustness in Self-Assembly

Time efficiency of self-assembly is crucial for many biological processes. Moreover, with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. While structural determinants and the final assembly yield are increasingly well understood, kinetic aspects concerning the time efficiency, however, remain much more elusive. In computer science, the concept of time complexity is used to characterize the efficiency of an algorithm and describes how the algorithm’s runtime depends on the size of the input data. Here we characterize the time complexity of nonequilibrium self-assembly processes by exploring how the time required to realize a certain, substantial yield of a given target structure scales with its size. We identify distinct classes of assembly scenarios, i.e., “algorithms” to accomplish this task, and show that they exhibit drastically different degrees of complexity. Our analysis enables us to identify optimal control strategies for nonequilibrium self-assembly processes. Furthermore, we suggest an efficient irreversible scheme for the artificial self-assembly of nanostructures, which complements the state-of-the-art approach using reversible binding reactions and requires no fine-tuning of binding energies.

show abstract

“…C++ code for simulations and data have been deposited in GitHub ( https://github.com/FloGat88/Self_Assembly.git ) ( 45 ).…”

Section: Data Availabilitymentioning

confidence: 99%

The time complexity of self-assembly

Gartner

Graf

Frey

2022

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

View full text Add to dashboard Cite

show abstract

Stochastic Yield Catastrophes and Robustness in Self-Assembly

Gartner

Graf

Wilke

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Stochastic Yield Catastrophes and Robustness in Self-Assembly

Cited by 2 publications

References 38 publications

The time complexity of self-assembly

The time complexity of self-assembly

Stochastic Yield Catastrophes and Robustness in Self-Assembly

Contact Info

Product

Resources

About