Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

TL;DR

This paper introduces a simple chain model that exhibits a first order phase transition, spontaneous dimensional reduction, and highly degenerate ground states with secondary motifs, revealing new insights into polymer and protein-like structures.

Contribution

The study presents a novel homopolymer chain model demonstrating spontaneous dimensional reduction and highly degenerate ground states with secondary motifs, supported by analytic and simulation methods.

Findings

First order transition from coil to low-temperature phase

Ground states show spontaneous dimensional reduction

Ground states exhibit secondary motifs like helices and strands

Abstract

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM -- Planar Structures with Secondary Motifs) in the novel phase and protein native state structures.