因為科技的進步，可以使用高產出(high-throughput)裝置來測量DNA、RNA 和蛋白質的濃度，使我們可以得到大量來自於生物動態系統的豐富資訊。因此，我們迫切的需要對這些資料進行反向工程(reverse engineering)以挖掘隱含在這些資料中參數�結構和行為的關係。最後目的是希望可以對組成一個系統的成份之間的交互作用有更佳的了解。 然而，目前在生物資訊反向工程領域探討的議題有：使用的運算法、時序樣本的數量、或輸入資料是連續型或間斷型等，幾乎沒有定位在反向工程有效性問題的研究。我們認為，現實得到的資料是不可能完美，所以反向工程的結果會受到資料誤差影響。如果這論點是對的，那麼知道資料誤差如何影響反面工程的結果以及到什麼程度就是一個重要的議題。我們選擇參數估計做為我們反向工程的題目，並且發展一個新的方法來檢測這一個有效性問題。我們讓使用的資料與真正的資料之間有一個小的誤差，然後把結果與它的目標參數值做比較。我們可以理解到若是資料有較大的誤差時，反向工程將面臨更嚴重的有效性問題。

我們使用三個人造的系統來展示我們的概念。實驗結果顯示，一個小的資料誤差可能會讓求解的參數值有很大偏差，由此我們可以結論不應該忽略資料誤差對反向工程的影響。為了進一步探討此一現象，我們發展出一個分析的程序嘗試來分析動態系統的哪一個特性會是造成此一現象的主因。此一程序包含了敏感度測試、擾動傳遞分析和衝擊因素分析。以上分析歸納出了幾個反向工程結果和系統動態性質之間的描述性規則。

本探索性研究的所有發現還需要有更多的研究來確定它的結果。未來的研究方向包含：若資料誤差造成反向工程結果參數的變異，它在生物演化可能扮演的角色是什麼；它與生物系統的強健性(robustness)的關係是什麼；尋找更好的反向工程演算法以避免此一個有效性問題等。

The high-throughput measurement devices for DNA, RNA, and proteins produce large amount of information-rich data from biological dynamic systems. It is a need to reverse engineering these data to reveal parameters/structure and behavior relationships implicit in the data. Ultimately, complex interactions between its components that make up a system can be better understood.

However, issues of reverse engineering in bioinformatics like algorithms use, the number of temporal sample, continuous or discrete type of input data, etc. are discussed but merely in the validity problem. We argue that, since the data available in reality are not so perfect, the result of reverse engineering is impacted by the un-perfect data. If this is true, to know how this impacts the results of the reverse engineering and to what extent is an important issue. We choose the parameter estimation as our task of reverse engineering and develop a novel method to investigate this validity problem. The data we used has a minor deviation from real data in each data point and then we compare the results of reverse engineering with its target parameters. It can be realized that the more error in data will introduce more serious validity problem in reverse engineering.

Three artificial systems are used as test bed to demonstrate our approach. The results of the experiments show, a minor deviation in data may introduce large parameter deviation in the parameter solutions. We conclude that we should not ignore the data error in reverse engineering. To have more knowledge of this phenomenon, we further develop an analytical procedure to analyze the dynamic of the systems to see which characteristic will contribute to this impact. The sensitivity test, propagation analysis and impact factor analysis are applied to the systems. Some qualitative rules that describe the relationship between the results of reverse engineering and the dynamics of the system are summarized.

All the finding of this exploration research needs more study to confirm its results. Along this line of research, the biological meaning and the possible relationship between robustness and the variation in parameters in reverse engineering is worth to study in the future. The better reverse algorithm to avoid this validity problem is another topic for future work.

中文摘要 II
ABSTRACT II
ABSTRACT III
致謝詞 IV
TABLE OF CONTENTS 1
LIST OF FIGURES 4
LIST OF TABLES 6
CHAPTER 1 INTRODUCTION 8
1. BACKGROUND 8
1.1 THE PROBLEM OF REVERSE ENGINEERING IN DYNAMIC SYSTEM 9
1.2 RESEARCH MOTIVATION AND OBJECTIVES 11
1.4 ORGANIZATION OF THE DISSERTATION 12
CHAPTER 2 LITERATURE REVIEW 13
2.1 REVERSE ENGINEERING IN BIOINFORMATICS 13
2.2 VALIDITY OF REVERSE ENGINEERING IN BIOINFORMATICS 15
2.3 SENSITIVITY ANALYSIS 16
2.4 SYSTEM DYNAMICS MODELS AND LOOP DOMINANCE ANALYSIS 17
2.4.1 System Dynamics Models 17
2.4.2 Loop Dominance Analysis 20
CHAPTER 3 RESEARCH METHODOLOGY 22
3.1 FORMALIZATION OF REVERSE ENGINEERING PROBLEM 22
3.2 THE CHARACTERISTIC OF THE REVERSE PROBLEM IN BIOINFORMATICS 27
3.3 THE PROCEDURES OF ANALYZING VALIDITY OF REVERSE ENGINEERING 28
3.3.1 The Evolution Process 31
3.3.2 Algorithm Implementation 32
3.4 THE SENSITIVITY ANALYSIS 33
3.5 THE ANALYSIS OF SYSTEM DYNAMICS AND IMPACT FACTOR 36
3.6 THE SCOPE OF PROBLEM SPACE 39
3.7 SUMMARY 42
CHAPTER 4 EMPIRICAL STUDY 46
4.1 THE MODEL OF PHOSPHOLIPID CYCLE (KOZA) 47
4.1.1 The Briefing of the Biological Function 47
4.1.2 The state function and the system’s behavior 49
4.1.3 Other Experimental Setting 50
4.1.4 The Reverse Engineering from the Temporal Data 51
4.1.5 The Sensitivity Analysis 53
4.1.6 The System Dynamics and Impact Factor Analysis 54
4.2 MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR (GARDNER) 57
4.2.1 The Briefing of the Biological Function 57
4.2.2 The state function and the system’s behavior 58
4.2.3 Other Experimental Setting 59
4.2.4 The statistics of the results of the reverse function 60
4.2.5 The Sensitivity Analysis 62
4.2.6 The System Dynamics and Impact factor Analysis 64
4.3 THE MODEL OF CELL DIVISION CYCLE 66
4.3.1 The Briefing of the Biological Function 66
4.3.2 The state function and the system’s behavior 67
4.3.3 Other Experimental Setting 69
4.3.4 The Reverse Engineering from the Temporal Data 70
4.3.5 The Sensitivity Analysis 71
4.3.6 The System Dynamics and Impact Factor Analysis 75
4.4 FINDINGS 78
CHAPTER 5 DISCUSSION 84
CHAPTER 6 CONTRIBUTIONS AND FUTURE RESEARCH 93
6.1 CONTRIBUTIONS 93
6.2 FUTURE WORKS 94
REFERENCES 96
CHAPTER 7 APPENDIX 100
CHAPTER 7 APPENDIX 100
APPENDIX 1: THE PARTIAL DERIVATES OF THE DIFFERENTIAL EQUATIONS 100
APPENDIX 2: PROOF OF THE EXPERIMENTAL MODELS FIT THE ASSUMPTION I 103
APPENDIX 3: THE PERTURBATION PROPAGATION OF ALL THE PARAMETERS 106


List of Figures
FIGURE 1.1 THE DIFFERENT SETTING OF REVERSE ENGINEERING. 10
FIGURE 2.1 AN INVENTORY MODEL IN THE FLOW DIAGRAM FORM. 18
FIGURE 3.1 THE MAPPING OF THE SYSTEM AND ITS BEHAVIOR (WOLKENHAUER, 2002) 23
FIGURE 3.2 THE CONCEPT OF THE REVERSE ENGINEERING. 26
FIGURE 3.3 THE SCHEMATIC OF THE VALIDITY PROBLEM IN REVERSE ENGINEERING SYSTEM DYNAMICS. 28
FIGURE 3.4 SAMPLING IN THE MODEL SPACE. 30
FIGURE 3.5 THE FLOW OF REVERSE ENGINEERING EXPERIMENT. 31
FIGURE 3.6 THE GENETIC ALGORITHM (MICHALEWICZ, 1994). 32
FIGURE 3.7 THE THREE BASIC TYPE OF THE BEHAVIOR CHANGE. 35
FIGURE 3.8 THE ODE TO FLOW DIAGRAM TRANSFORMATION. 37
FIGURE 3.9 THE FLOW DIAGRAM OF EQUATION (3.8). 37
FIGURE 3.10 A SIMPLE EXAMPLE OF CAUSAL LINK-BASED ANALYSIS, ADOPTED FROM (TSENG AND TU, 2004). 38
FIGURE 3.11 THE RELATIONSHIP OF DIFFERENT SPACE. 39
FIGURE 3.12 THE THREE PERSPECTIVES OF SYSTEMS. 42
FIGURE 3.13 THE RESEARCH FRAMEWORK. 43
FIGURE 3.14 THE RELATIONSHIP OF THE ANALYSIS STEPS. 45
FIGURE 4.1 THE REACTIONS OF THE PHOSPHOLIPID CYCLE SYSTEM (KOZA, MYDLOWEC ET AL., 2001). 48
FIGURE 4.2 THE TEMPORAL BEHAVIOR OF THE PHOSPHOLIPID CYCLE SYSTEM. 50
FIGURE 4.3 THE DISTRIBUTION OF THE PARAMETERS OF THE KOZA’S SYSTEM. 52
FIGURE 4.4 THE SENSITIVITY TEST OF THE PHOSPHOLIPID CYCLE SYSTEM. 53
FIGURE 4.5 THE PROPAGATION OF PERTURBATIONS (PHOSPHOLIPID CYCLE SYSTEM). 54
FIGURE 4.6 THE FLOW DIAGRAM OF PHOSPHOLIPID CYCLE SYSTEM. 55
FIGURE 4.7 CONTROL OF THE GOLDBETER MODEL WITH A CYCLIN INHIBITOR SYSTEM (GARDNER, DOLNIK ET AL., 1998). 57
FIGURE 4.8 THE TEMPORAL BEHAVIOR OF THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 59
FIGURE 4.9 THE DISTRIBUTION OF THE PARAMETERS OF THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 61
FIGURE 4.10 THE SENSITIVITY TEST OF THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 63
FIGURE 4.11 THE PROPAGATION OF THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 63
FIGURE 4.12 THE FLOW DIAGRAM OF THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 64
FIGURE 4.13 THE RELATIONSHIP BETWEEN CYCLIN AND CDC2 IN THE CELL CYCLE. AA, AMINO ACIDS; ~P, ATP; PI, INORGANIC PHOSPHATE (TYSON, 1991). 67
FIGURE 4.14 THE TEMPORAL BEHAVIOR OF THE CELL DIVISION CYCLE SYSTEM (THREE STATES). 69
FIGURE 4.15 THE SENSITIVITY TEST OF THE CELL DIVISION CYCLE (THREE STATES). 73
FIGURE 4.16 THE PROPAGATION OF PERTURBATION, CELL DIVISION CYCLE SYSTEM. 75
FIGURE 4.17 THE FLOW DIAGRAM OF CELL DIVISION CYCLE SYSTEM. 75
FIGURE 5.1. SIMULATING-ANNEALING ALGORITHM (MICHALEWICZ, 1994) 88
FIGURE 5.2. THE ALGORITHM OF COMBINING GENETIC ALGORITHM AND SIMULATING ANNEALING. 89


List of Tables
TABLE 2.1 THE MEASUREMENTS OF SENSITIVITY TEST (ADAPTED FROM MCRAE ET AL., 1982). 10
TABLE 4.1 THE GENERAL SETTING OF THE EXPERIMENTS. 30
TABLE 4.2 THE EXECUTION PROFILE OF THE PHOSPHOLIPID CYCLE SYSTEM. 33
TABLE 4.3 THE DESCRIPTIVE STATISTICS OF THE INFERRED PARAMETERS. 33
TABLE 4.4 THE IMPACT FACTOR ANALYSIS (KOZA’S SYSTEM). 36
TABLE 4.5 THE EXECUTION PROFILE OF THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 40
TABLE 4.6 THE DESCRIPTIVE STATISTICS OF THE INFERRED PARAMETERS. 41
TABLE 4.7 THE DOMINANT PARAMETER ANALYSIS (GARDNER’S SYSTEM). 44
TABLE 4.8 THE EXECUTION PROFILE OF CELL DIVISION CYCLE. 48
TABLE 4.9 THE DESCRIPTIVE OF CELL DIVISION CYCLE (STEADY STATE). 49
TABLE 4.10 THE DESCRIPTIVE OF CELL DIVISION CYCLE (CYCLIC STATE). 49
TABLE 4.11 THE DESCRIPTIVE OF CELL DIVISION CYCLE (EXCITABLE STATE). 49
TABLE 4.12 THE DOMINANT PARAMETER ANALYSIS (CDC6, STEADY STATE). 54
TABLE 4.13 THE DOMINANT PARAMETER ANALYSIS (CDC6, CYCLIC STATE). 55
TABLE 4.14 THE DOMINANT PARAMETER ANALYSIS (CDC6, EXCITABLE STATE). 56
TABLE 4.15 THE PHOSPHOLIPID CYCLE SYSTEM. 56
TABLE 4.16 THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 57
TABLE 4.17 THE CELL DIVISION CYCLE SYSTEM (STEADY STATE). 58
TABLE 4.18 THE CELL DIVISION CYCLE SYSTEM (STATE CYCLIC). 58
TABLE 4.19 THE CELL DIVISION CYCLE SYSTEM (EXCITABLE STATE). 58
TABLE 4.20 THE PREDICT RANGE OF THE REVERSE ENGINEERING. 59
TABLE 4.21 THE APPLICABLE OF THE RULES. 59
TABLE 5.1 THE RANDOMNESS SAMPLING OF THE SEARCHING SPACE. 61
TABLE 5.2 PHOSPHOLIPID CYCLE SYSTEM. 62
TABLE 5.3 THE MINIMAL MITOTIC OSCILLATOR WITH INHIBITOR SYSTEM. 62
TABLE 5.4 THE ERROR ALLOWED EFFECT (CELL DIVISION CYCLE, STEADY STATE). 62
TABLE 5.5 THE ERROR ALLOWED EFFECT (CELL DIVISION CYCLE, CYCLIC STATE). 62
TABLE 5.6 THE ERROR ALLOWED EFFECT (CELL DIVISION CYCLE, EXCITABLE STATE). 63
TABLE 5.7 THE SETTING OF SIMULATING-ANNEALING ALGORITHM 65
TABLE 5.8 THE COMPARISON OF TWO LEARNING ALGORITHM. 65
TABLE 5.9 PHOSPHOLIPID CYCLE, FULL DATA SET (1). 67
TABLE 5.10 PHOSPHOLIPID CYCLE, FULL DATA SET (2). 67

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