Collective deformation modes promote fibrous self-assembly in protein-like particles

TL;DR

This study explores how collective deformation modes in ill-fitting, deformable particles promote the formation of fibrous, self-limited aggregates, providing insights into protein aggregation and design principles for artificial structures.

Contribution

It analytically and numerically demonstrates that collective deformations in deformable particles lead to fibrous self-assembly, revealing a link between particle properties and aggregate structure.

Findings

Moderately sticky particles form self-limited aggregates.

Soft internal deformation modes lead to large aggregates.

Incompressible particles tend to form anisotropic, fiber-like structures.

Abstract

The self-assembly of particles into organized structures is a key feature of living organisms and a major engineering challenge. While it may proceed through the binding of perfectly matched, puzzle-pieces-like particles, many other instances involve ill-fitting particles that must deform to fit together. These include some pathological proteins, which have a known propensity to form fibrous aggregates. Despite this observation, the general relationship between the individual characteristics of the particles and the overall structure of the aggregate is not understood. To elucidate it, we analytically and numerically study the self-assembly of two-dimensional, deformable ill-fitting particles. We find that moderately sticky particles tend to form equilibrium self-limited aggregates whose size is set by an elastic boundary layer associated with collective deformations that may extend over many particles. Particles with a soft internal deformation mode thus give rise to large aggregates. Besides, when the particles are incompressible, their aggregates tend to be anisotropic and fiber-like. Our results are preserved in a more complex particle model with randomly chosen elastic properties. This indicates that generic protein characteristics such as allostery and incompressibility could favor the formation of fibers in protein aggregation, and suggests design principles for artificial self-assembling structures.