RNA或蛋白質的比較方法為分子生物研究中之重要基本工具。到目前為止，大部分比較方法僅適用在RNA或蛋白質之一級結構，也就是一般常見到的序列比對與序列對齊方法。從生物的角度來看，結構與功能有著非常密切的關係。目前對於結構探知的方法，主要有核磁共振法、X光繞射法以及透過電腦程式來預測，因此有許多分子是已知其結構但功能尚未被發掘。RNA二級結構的對齊問題，是想要知道兩個RNA二級結構整個對齊之後的情況，以及它們之間的相似程度。另一方面，可以藉由RNA二級結構對齊的方法來協助預測其功能，並加以分類。在本論文中，我們針對兩個RNA二級結構的對齊問題加以研究，在我們的方法中，所處理的二級結構並不包含假扭結。我們設計一個動態規劃演算法來解兩個RNA二級結構的對齊問題，此演算法的時間複雜度為O(N4)，其中N為兩個RNA結構的最大區塊個數。我們亦將此演算法應用於人類腺粒體tRNA，藉以評估其實用性。從實驗結果顯示，我們的方法可以有效地評估兩個RNA之結構相似程度，不論其序列是否相似。

The comparison methods for RNA or protein molecules are important basic tools in molecular biology. So far, most comparison methods are only applicable to the primary structures of biomolecules, such as the sequence alignment and comparison methods. The functions of biomolecules have close relationship with their structures. The recent methods for finding the structures of biomolecules are NMR spectroscopy, X-ray crystallography, and prediction with computational simulation. There are many biomolecules with known structures, but their functions are unknown. The RNA secondary structure alignment problem is to align two RNA molecules to get the structure similarity, where their secondary structures are given. In addition, it is also helpful to predict the functions of biomolecules and to classify them. In this thesis, we design a dynamic programming method for aligning two RNA secondary structures which do not contain any pseudoknot. The time complexity of our algorithm is O(N4), where N is the number of blocks contained in the given RNA sequences. We also apply our algorithm to the real biomolecules, the tRNAs of Homo sapiens mitochondrion, to evaluate the practicability our method. We take three tRNA genes, TRNG, TRNA and TRNV, to test the performance of our algorithm. From the view point of human eyes, in fact, the structure of TRNG is more similar to TRNA. Our algorithm also gets this result. Hence, our algorithm provides an effective method to measure the similarity of two RNA secondary structures.

LIST OF FIGURES ............................................................. 4
LIST OF TABLES .............................................................. 7
ABSTRACT .................................................................... 0
Chapter 1. Introduction .................................................... 1
Chapter 2. Preliminaries ................................................... 9
2.1 RNA and cDNA ........................................................... 9
2.2 The Stem .............................................................. 12
Chapter 3. Prediction Methods for the RNA Secondary Structure ............. 17
Chapter 4. The Sequence Alignment ......................................... 24
4.1 The Longest Common Subsequence Problem ................................ 24
4.2 The Sequence Alignment Problem ........................................ 28
4.3 The Local Alignment Problem ........................................... 35
4.4 The Affine Gap Penalty ................................................ 38
Chapter 5. Sequence Alignment for RNA Secondary Structure .................. 43
5.1 Terminologies ......................................................... 43
5.2 An Alignment Algorithm for RNA Secondary Structures ................... 46
5.3 Improvement on Space .................................................. 72
5.4 The Stem Alignment Problem ............................................ 78
5.5 The RNA Secondary Structure Alignment Algorithm ....................... 83
5.6 Analysis of Time Complexity ........................................... 85
Chapter 6. Experimental Results ............................................ 87
Chapter 7. Conclusion ..................................................... 110
BIBLIOGRAPHY .............................................................. 112

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