Minimal model of self-assembly: emergence of diversity and complexity.

Molecular self-assembly is ubiquitous in nature, yet prediction of assembly pathways from fundamental interparticle interactions has yet to be achieved. Here, we introduce a minimal self-assembly model with two attractive and two repulsive beads bound into a tetrahedron. The model is associated with a single parameter η defined as the repulsive to attractive interaction ratio. We explore self-assembly pathways and resulting assembly morphologies for different η values by discrete molecular dynamics. Our results demonstrate that η governs the assembly dynamics and resulting assembly morphologies, revealing an unexpected diversity and complexity for 0.5 ≤ η < 1. One of the key processes that governs the assembly dynamics is assembly breakage, which emerges spontaneously at η > 0 with the breakage rate increasing with η. The observed assembly pathways display a broad variety of assembly structures characteristic of aggregation of amyloidogenic proteins, including quasi-spherical oligomers that coassemble into elongated protofibrils, followed by a conversion into ordered polymorphic fibril-like aggregates. We further demonstrate that η can be meaningfully mapped onto amyloidogenic protein sequences, with the majority of amyloidogenic proteins characterized by 0.5 ≤ η < 1. Prion proteins, which are known to form highly breakage-prone fibrils, are characterized by η > 1, consistent with the model predictions. Our model thus provides a theoretical basis for understanding the universal aspects of aggregation pathways of amyloidogenic proteins relevant to human disease. As the model is not specific to proteins, these findings represent an important step toward understanding and predicting assembly dynamics of not only proteins but also viruses, colloids, and nanoparticles.