Self-assembly, modularity and physical complexity

TL;DR

This paper introduces a quantitative measure of physical complexity based on information needed for self-assembly, applicable to various structures, and highlights its utility in analyzing symmetry, modularity, and biological assembly processes.

Contribution

It proposes a novel information-based measure of physical complexity adaptable to any geometry, enabling analysis of symmetry, modularity, and structural relationships in physical systems.

Findings

Symmetric and modular structures are favored in biological self-assembly.

The measure effectively quantifies complexity in molecules and protein complexes.

Introduces joint, mutual, and conditional complexity as structural distance metrics.

Abstract

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favoured in biological self-assembly, for example of protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful distance measure between physical structures.