# Geometrical frustration yields fiber formation in self-assembly

## TL;DR

This paper demonstrates that geometrical frustration in irregular particles with short-range interactions naturally leads to the formation of fibers during self-assembly, providing insights into biological and synthetic fiber formation.

## Contribution

It introduces a minimal model showing how geometrical frustration causes fiber formation in self-assembling particles, regardless of particle shape.

## Key findings

- Fibers form robustly across various particle shapes and conditions.
- Geometrical frustration determines the parameter range for fiber formation.
- Fibers exhibit metastable behavior influenced by particle irregularity.

## Abstract

Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined morphologies. This is the case in numerous medical conditions where normally soluble proteins aggregate into fibers. Beyond the diversity of molecular mechanisms involved, we propose that fibers generically arise from the aggregation of irregular particles with short-range interactions. Using a minimal model of ill-fitting, sticky particles, we demonstrate robust fiber formation for a variety of particle shapes and aggregation conditions. Geometrical frustration plays a crucial role in this process, and accounts for the range of parameters in which fibers form as well as for their metastable character.