臺灣博碩士論文加值系統

在1985及1996年，Miyazawa 和Jernigan 兩人共同使用統計的方法，從蛋白質資料庫中統計分析全部已知
結構的蛋白質內部不同種類氨基酸間相互接觸的數目，然後推導出一個20×20的Miyazawa-Jernigan (MJ)
矩陣，這個矩陣的每個元素值就代表蛋白質結構中，任兩種氨基酸間互相接觸所需的平均能量。藉由分
析MJ矩陣的主要成份(Principal Component)，我們定性及定量的解釋了驅動蛋白質折疊的作用力主要是來
自氨基酸旁鏈分子和水分子間以及氨基酸旁鏈分子間電偶極的相互作用。這同時也解釋了為什麼MJ矩陣
可以自然的被化約成由李浩等人所導出的簡單主要成份。最後我們更進一步解釋了氨基酸旁鏈的電偶極
矩和氨基酸的疏水性、由Keskin等人另外從MJ矩陣導出的一體作用，以及李浩等人從MJ矩陣導出的主要
成份間的親密關聯。我們給了MJ 矩陣一個自恰的物理詮釋，這個新的詮釋或許可以幫忙應用在蛋白質早
期折疊的粗粒化分子動力模擬。

In 1985 and 1996 Miyazawa and Jernigan used a statistical
approach to derive a 20 by 20 matrix of inter-residue
contact energies between different types of amino acids. We show
that the 20 by 20 Miyazawa- Jernigan statistical potential
matrix for protein folding may be quantitatively understood in
terms of classical dipole-dipole interactions involving the
side-chains of amino acids and water molecules. This explains why
the MJ matrix naturally reduces to the simple principal component
from first noticed by Li et al. We also note and explain the
close relations between : the principal eigenvector of Li et al., the
one-body potentials deduced from the MJ matrix by Keskin
et al., the hydrophobicities of the amino acids and the electric
dipole moments of the amino acid side chains. We were able to give
a new self-consistent physical interpretation to the statistically
derived MJ matrix. This interpretation may properly support the
use of MJ matrix for a coarse-grained molecular dynamical
simulation of early protein folding.

1 Introduction 1
2 Background and Theory 3
2.1 Protein folding and amino acids . . . . . . . . . . . . . . . 3
2.2 MJ matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Principal component decomposition of MJ matrix . 8
2.4 Dipole-dipole interactions between amino acids . . . 12
2.5 Hydrophobicities of amino acids . . . . . . . . . . . . . . . 14
2.6 One-body & two-body interactions for MJ matrix . . 15
3 Data 19
3.1 MJ matrix & its principal components . . . . . . . . . . 19
3.2 Dipole moments of amino acids . . . . . . . . . . . . . . . 22
3.3 Hydrophobicities of amino acids . . . . . . . . . . . . . . 23
3.4 One-body potential deduced from MJ matrix . . . . 24
4 Discussion 25
4.1 One-body and two body terms . . . . . . . . . . . . . . . 25
4.1.1 Dipole-dipole interaction of water-residue
coupling for hydrophobicity . . . . . . . . . . . 26
4.1.1.1 Hydrophobicity . . . . . . . . . . . . . . . 26
4.1.1.2 Relations between qi and Qi
(and hydrophobicity scale - Pi) . . . . 28
4.1.1.3 Percentage of residues shielded
from water . . . . . . . . . . . . . . . . . . . 32
4.1.1.4 Water-residue coupling . . . . . . . . . 33
4.1.2 Dipole-dipole interaction of residue-residue
coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Representation of MJ matrix . . . . . . . . . . . . . . . . . 38
5 Conclusion 42
Bibliography 46

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