由於密碼子的簡併性，胺基酸序列可以被多種mRNA序列轉譯產生。密碼子優化的目標在於在不改變目標胺基酸序列的情況下，去設計出一些mRNA序列，來改善蛋白質表現或轉譯的效率。事實上，有許多因素可以來影響蛋白質表現和轉譯的效率，如密碼子偏好性、RNA二級結構與模體等。在本篇研究論文中，我們藉由考慮密碼子偏好性和RNA二級結構的穩定度，定義了一個多目標的密碼子優化問題。如果需要最大化 (或最小化) RNA二級結構的穩定度，則我們將這個問題表示為 PMCO_max (或 PMCO_min)。對於 PMCO_max 問題，我們首先提出了一個動態規劃 (DP) 演算法來找出這個問題的柏拉圖最佳解。接下來，我們設計一個整數線性規劃的演算法，來得到這個問題的近似解。另一方面， PMCO_min 是一個NP-hard 的問題，因此我們設計一個ILP-based演算法來有效解決這個問題。對於 PMCO_max 問題，我們的實驗結果顯示出對於RNA二級結構的穩定性而言，我們的ILP-based演算法的表現是略遜於我們的DP演算法，但我們的ILP-based演算法的執行時間表現卻遠勝於我們的DP演算法。對於 PMCO_min 問題，我們的ILP-based演算法在RNA二級結構不穩定性的表現比另一個已被設計出來的ILP-based演算法來得更好。

Due to degeneracy of codons, the amino acid sequence can be translated from a variety of mRNA sequence. Codon optimization aims to improve the protein expression or translation efficiency by designing mRNA sequences without changing the target amino acid sequence. In fact, there are many factors that can affect protein expression or translation efficiency, such as codon usage bias, RNA secondary structure, motifs, etc. In this thesis, we define a multi-objective codon optimization problem by considering codon usage bias and stability of RNA secondary structure. If the stability of RNA secondary structure needs to be maximized (respectively, minimized), then we denote this problem as PMCO_max (respectively, PMCO_min). For the PMCO_max problem, we first propose a dynamic programming (DP) algorithm to find Pareto-optimal solutions of this problem. We next design an integer linear programming (ILP) based algorithm to obtain approximate solutions of this problem. On the other hand, PMCO_min is an NP-hard problem and therefore we design an ILP-based algorithm to efficiently solve this problem. Our experimental results show that for the PMCO_max problem, the performance of our ILP-based algorithm for the stability of RNA secondary structure is slightly inferior to that of our DP algorithm, but the performance of its running time is much superior to that of our DP algorithm. For the PMCO_min problem, our ILP-based algorithm performs much better than the other existing ILP-based algorithm for the instability of RNA secondary structure.

摘要 1
Abstract 2
Contents 3
List of figures 4
Chapter 1 Introduction 8
Chapter 2 Methods 14
2.1 DP Algorithm for PMCOmax 14
2.1.1 Preliminaries 14
2.1.2 Recursive Formula 15
2.1.3 Optimiality 25
2.1.4 Time Complexity 28
2.2 ILP-based Algorithm for PMCOmax 29
2.2.1 Preliminaries 30
2.2.2 ILP Variables 33
2.2.3 ILP Constraints 33
2.2.4 ILP Objective Function 35
2.3 ILP-based Algorithm for PMCOmin 35
2.3.1 Preliminaries 36
2.3.2 ILP Variables 38
2.3.3 ILP Constraints 38
2.3.4 ILP Objective Function 39
Chapter 3 Experiment Results and Discussion 40
3.1 Datasets 40
3.2 Experiments 40
Chapter 4 Conclusion 48
Reference 49

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