---
title: Long Proteins with Unique Optimal Foldings in the H-P Model
url: https://www.emergentmind.com/papers/0201018
type: paper
arxiv_id: '0201018'
arxiv_url: https://arxiv.org/abs/0201018
published: '2002-01-21'
categories:
- cs.CG
- q-bio.BM
---

# Long Proteins with Unique Optimal Foldings 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.