我們考慮胺基酸中側鏈化學原子的空間位置，提出六個新的結構參數，以輔助蛋白質結構的描述，文末一併附上計算這些參數的程式。
本文主要探討長鏈α神經毒蛋白家族中Ophiophagus hannah神經毒蛋白及α-bungarotoxin兩大類蛋白質中二環座標結構的11個座標結構參數分佈（包括phi角、psi角、C-N、C-O、Cα-C和N-Cα等化學鍵的鍵長，及C-N-Cα、Cα-C-N、Cα-C-O、N-Cα-C和O-C-N化學鍵的夾角等），分別對兩類之phi及psi角配適二維von Mises分佈，並利用Ward’s群集分析、LIBSVM討論這些參數對群集和分類工作的適切度。最後更進一步探討這些神經毒蛋白二環中Trp胺基酸的座標結構參數分佈，尋找鑑定毒姓強弱的因子。

Six new structural parameters ψB, φB, ψC, φC, ψS, and φS are proposed to enhance the side chain actions in protein structures. Programs for calculating these new parameters based on phi and psi torsion angles vector algebra calculation method are established. A bivariate model with von Mises marginal distributions are applied to establish models of phi and psi in protein class Ophiophagus hannah neurotoxins and alpha-bungarotoxins respectively. 11 global structural parameters include phi and psi torsion angles, bond lengths of C-N, C-O, Cα -C, and N-Cα, and bond angles of C-N-Cα, Cα-C-N, Cα-C-O, N-Cα-C, and O-C-N are considered to classify long alpha-neurotoxins by Ward's cluster method and LIBSVM program package. Those global structural parameters of loop II Trp residues of alpha-neurotoxins are discussed.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature Review . . . . . . . . . . . . . . . . . .. . . . . . . 5
2.1 Protein Structure Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Torsion Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Von Mises Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Cluster and Classification Tools . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Ward's Hierarchical Method . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 LIBSVM: A Library For Support Vector Machines (Version 2.33) . 13
3 Data Manipulation 14
3.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 New Torsion Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Results and Discussions 18
4.1 Correlations of Torsion Angles . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Fitting Von Mises Distributions to Phi and Psi Angles . . . . . . . . . . . . . 33
4.3 Cluster and Classification Results . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Structural Parameters of Trp . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 Conclusions 44
Acknowledgments 45
References 46
Appendices 49
A Procheck v.3.5.4 Install Process 49
B Programs of Proposed New Parameters 50
B.1 Basic.cpp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
B.2 Centroid.cpp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
B.3 Short.cpp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
C Sequence Details 62
D i ProClass Cross-References 63

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