The determinism and boundedness of self-assembling structures

TL;DR

This paper introduces a graph theoretical method to analyze the determinism and boundedness of self-assembling structures, improving accuracy and speed over traditional approaches, with applications in biological and physical systems.

Contribution

The authors develop a novel graph-based approach to determine self-assembly properties across various geometries, enhancing analysis efficiency and accuracy.

Findings

The method accurately predicts determinism in self-assembly.

The approach efficiently assesses boundedness in complex systems.

Applications extend to biological protein structures.

Abstract

Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems