# Geometric constraints in protein folding

## TL;DR

This paper presents a simple geometric model of protein folding that captures key structural features of real proteins, suggesting geometry alone influences protein structure formation.

## Contribution

The study introduces a minimal model based solely on geometric constraints that reproduces several statistical properties of actual protein structures.

## Key findings

- Model reproduces degree distribution of amino acid interactions
- Structure size scales with chain length similarly to real proteins
- Eigenvalue spectrum matches that of biological protein networks

## Abstract

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.