# Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptide

## TL;DR

This paper presents a simple model showing how breaking symmetries in linear chains can lead to various phases, including structures similar to protein secondary structures, with implications for peptide self-assembly.

## Contribution

It introduces a model that links symmetry breaking in biopolymer chains to the emergence of complex phases resembling protein structures.

## Key findings

- Introduction of marginally compact phases with alpha-helix and beta-sheet-like conformations.
- Discovery of a new phase with complex secondary structures due to side-chain symmetry breaking.
- Potential application in designing self-assembling peptides.

## Abstract

We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of $\alpha$-helices and $\beta$-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the negative normal of the chain, to mimic the presence of side chains in real proteins. This leads to the emergence of a novel phase within the previously obtained marginally compact phase, with the appearance of more complex secondary structure assemblies. The potential importance of this new phase in the \textit{de novo} design of self-assembled peptides is highlighted.