Stochastic Lag Time in Nucleated Linear Self-Assembly

TL;DR

This paper investigates how stochastic fluctuations influence the lag time in nucleated linear self-assembly of proteins, revealing that lag time scales inversely with system volume and depends on kinetic pathways.

Contribution

It provides a detailed analysis of stochastic effects on lag time in protein self-assembly, highlighting the inverse relationship with system size and pathway-dependent corrections.

Findings

Lag time inversely proportional to system volume.

Finite-size effects depend on kinetic pathway.

Stochastic fluctuations significantly impact nucleation timing.

Abstract

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerisation reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of the system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerisation commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway.