# Towards a theory of assembly of protein complexes: lessons from equilibrium statistical physics

## TL;DR

This paper develops an equilibrium thermodynamic model to understand how cells reliably assemble diverse protein complexes despite physical and cellular noise, identifying key conditions for error-free assembly.

## Contribution

It introduces a theoretical framework with four assembly regimes and identifies conditions for error-free complex formation, supported by analysis of real protein data.

## Key findings

- Four distinct assembly behaviors identified
- Heterogeneity and sparsity are key for error-free assembly
- Cellular protein systems likely evolved to meet these conditions

## Abstract

Cellular functions are established through biological evolution, but are constrained by the laws of physics. For instance, the physics of protein folding limits the lengths of cellular polypeptide chains. Consequently, many cellular functions are carried out not by long, isolated proteins, but rather by multi-protein complexes. Protein complexes themselves do not escape physical constraints, one of the most important being the difficulty to assemble reliably in the presence of cellular noise. In order to lay the foundation for a theory of reliable protein complex assembly, we study here an equilibrium thermodynamic model of self-assembly that exhibits four distinct assembly behaviors: diluted protein solution, liquid mixture, "chimeric assembly" and "multifarious assembly". In the latter regime, different protein complexes can coexist without forming erroneous chimeric structures. We show that two conditions have to be fulfilled to attain this regime: (i) the composition of the complexes needs to be sufficiently heterogeneous, and (ii) the use of the set of components by the complexes has to be sparse. Our analysis of publicly available databases of protein complexes indicates that cellular protein systems might have indeed evolved so to satisfy both of these conditions.