Long Proteins with Unique Optimal Foldings in the H-P Model

TL;DR

This paper investigates the uniqueness of optimal foldings in the 2D H-P protein model, proving the existence of chains with unique minimal energy conformations for various lengths, enhancing understanding of protein folding behavior.

Contribution

It demonstrates the existence of both open and closed chains with unique optimal foldings in the 2D H-P model for all relevant lengths, a novel theoretical result.

Findings

Existence of closed chains with unique optimal foldings for all even lengths.

Existence of open chains with unique optimal foldings for lengths divisible by four.

Provides theoretical proof of unique minimal energy conformations in the H-P model.

Abstract

It is widely accepted that (1) the natural or folded state of proteins is a global energy minimum, and (2) in most cases proteins fold to a unique state determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic) model is a simple combinatorial model designed to answer qualitative questions about the protein folding process. In this paper we consider a problem suggested by Brian Hayes in 1998: what proteins in the two-dimensional H-P model have unique optimal (minimum energy) foldings? In particular, we prove that there are closed chains of monomers (amino acids) with this property for all (even) lengths; and that there are open monomer chains with this property for all lengths divisible by four.