蛋白質在生物化學中扮演非常重要的角色，蛋白質的化學構造非常複雜，然而大多數生物學家相信蛋白質的摺疊方式是唯一的：將蛋白質拆解拉成一長串胺機酸序列後，蛋白質會在數微秒到數毫秒間恢復原狀。這個問題也一直是生物學家、化學家、物理學家爭論的焦點，然而一直得不到令各方信服的說法。近年來，數學家想以數學模型來模擬此一問題：”蛋白質摺疊的唯一性”。 本論文採用Dill於1985年依據能量觀點所提出的二維HP模型為基礎，討論蛋白質摺疊的唯一性的問題(Crescenzi等人已於1998年證明此一問題在二維HP模型下為NP-complete)。本論文分為三章：第一章，簡介蛋白質構造及摺疊問題。第二章，針對Norman於2002年所提出的演算法做出細部修正。第三章，討論由Brian Hayes於1998年所提出的問題：在二維HP模型下，什麼樣的蛋白質序列有唯一摺疊？本文以迥異於Brian Hayes的想法，提出並證明長度為4k+5時的序列型態。並推測長度為4k+3時，具唯一摺疊的序列。 There are three chapters in this paper. In chapter1, we introduce the structures of proteins and the HP model suggest by Dill in 1985. In chapter2, we consider a algorithm suggested by Alanthan Newman in 2002: It is a 1/3-approximation linear-time algorithm for the protein folding problem on the 2D square lattice. Unfortunately his proof was not sound and had gaps. We claim that there are a few blemishes in his analysis of the algorithm, and we are going to fix it. In chapter3, we consider a problem suggested by Brian Hayes in 1998: what proteins in the two-dimensional HP model have unique optimal foldings? In particular, we prove that there are (open chains) with the property for all lengths of the form 4k+5.
