Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly

TL;DR

This paper introduces a stochastic minimal model to explain the variability in amyloid nucleation and growth, providing analytical tools to predict and understand the initial aggregation phases relevant to diseases and biomaterials.

Contribution

The authors develop a simple stochastic model with mathematical proof of a central limit theorem, offering new insights into amyloid aggregation variability not captured by deterministic models.

Findings

Derived closed-form analytical results for amyloid growth variability

Proved a central limit theorem for nucleated aggregation trajectories

Applied the model to experimental design and interpretation

Abstract

Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic differential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model offers a new perspective and paves the way for a new and efficient approach on extracting vital information regarding the key initial events of amyloid formation.