Stochastic yield catastrophes and robustness in self-assembly.

Area of Science:

• Physical Chemistry
• Materials Science
• Biophysics

Background:

• A core principle in self-assembly for high production yield is that nucleation must be significantly slower than growth.
• The specific mechanisms impeding nucleation are often overlooked, despite their potential impact on self-assembly outcomes.

Purpose of the Study:

• To analyze the impact of different nucleation delay mechanisms on self-assembly into finite-sized target structures using mathematical modeling.
• To investigate how stochasticity, particularly demographic fluctuations, affects self-assembly yield under various nucleation control strategies.

Main Methods:

• Mathematical modeling of self-assembly processes.
• Analysis of two distinct scenarios for delaying nucleation: slow constituent activation and decreased dimerization rate.
• Investigation of the role of demographic fluctuations and stochasticity in self-assembly yield.

Main Results:

• Decreasing the dimerization rate provides a robust method for delaying nucleation.
• Introducing a slow activation step for constituents leads to sensitivity to demographic fluctuations.
• Demographic fluctuations can disfavor growth over nucleation, leading to a 'stochastic yield catastrophe' and complete yield suppression.

Conclusions:

• Stochasticity is a critical limiting factor in self-assembly processes.
• The specific implementation of the nucleation mechanism significantly influences self-assembly yield, with activation-based delays being particularly susceptible to yield failure.
• Understanding and controlling nucleation dynamics, including stochastic effects, is crucial for optimizing self-assembly production.