On the Analysis of Optical Mapping Data - University of Wisconsin ...

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iii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v vi viii 1 Overview of Optical Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Elements of optical mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.2 Optical map data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.3 Goals and challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.4 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.5 Example (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Modeling Optical Map Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 A stochastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.1 Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.2 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1 Desorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.2 Length errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.3 Cut errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 Significance of Optical Map Alignments . . . . . . . . . . . . . . . . . . . . 37 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
iv Page 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3.1 Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3.2 Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.3.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3.4 Improving assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4.1 Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4.2 Information measure . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.4.3 Other topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4 Detecting Copy Number Polymorphism . . . . . . . . . . . . . . . . . . . . 60 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.1 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.1.1 Score function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.1.2 Scale errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Other topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 APPENDICES Appendix A: Score functions for alignment . . . . . . . . . . . . . . . . . . . . . 85 Appendix B: Hidden Markov Model calculations . . . . . . . . . . . . . . . . . . 87
Page 1 and 2: ON THE ANALYSIS OF OPTICAL MAPPING
Page 3 and 4: To my parents. i
Page 5: DISCARD THIS PAGE
Page 9 and 10: v LIST OF TABLES Table Page 1.1 Sum
Page 11 and 12: vi LIST OF FIGURES Figure Page 1.1
Page 13 and 14: ON THE ANALYSIS OF OPTICAL MAPPING
Page 15 and 16: 1 Chapter 1 Overview of Optical Map
Page 17 and 18: 3 hard, do not always have a unique
Page 19 and 20: 5 for microbial and other small gen
Page 21 and 22: 7 Figure 1.2 Close-up of a typical
Page 23 and 24: 9 0.96 0.98 1.00 1.02 1.04 Offset a
Page 25 and 26: 11 direct glimpse at the underlying
Page 27 and 28: 13 which is not surprising since we
Page 29 and 30: 15 Gapped alignments: The above des
Page 31 and 32: Figure 1.5 A visualization of align
Page 33 and 34: 19 Assembly: For these examples, th
Page 35 and 36: 21 Chapter 2 Modeling Optical Map D
Page 37 and 38: 23 Alternatively, it can be thought
Page 39 and 40: 25 and V (X i ) = E(V (Y i R i |R i
Page 41 and 42: 27 affect inference. If necessary,
Page 43 and 44: 29 Quantiles of fragment lengths (K
Page 45 and 46: 31 as a function of the parameters.
Page 47 and 48: 33 by rejecting maps that do not al
Page 49 and 50: 35 30 0.700 − 0.005 0 50 100 150
Page 51 and 52: 37 Chapter 3 Significance of Optica
Page 53 and 54: 39 using optical mapping data from
Page 55 and 56: 41 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8
Page 57 and 58:
43 3.3.2 Simplifications Direct app
Page 59 and 60:
45 Mean spurious score 0 −10 −2
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47 3.3.3 Simulation Given a generat
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49 3.4 Discussion 3.4.1 Uses Alignm
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51 The ability to simulate from the
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53 maps, where the separation betwe
Page 69 and 70:
Figure 3.10 Schematic representatio
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57 especially a short noisy one, to
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59 Test statistics: Variability due
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61 in sequence assembly and validat
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63 1988). However, due to sampling
Page 79 and 80:
65 and rate parameters Λ i = E(N i
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67 with mean µ k for the k th stat
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69 Estimated Copy Number in simulat
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71 Posterior probabilities 1.0 0.8
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73 (a) Observed counts and decoded
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75 Conclusion: Copy number alterati
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77 well in its current form, but th
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79 Change in score 15 10 5 0 0.9 1.
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81 will rarely be homozygous. It ma
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83 E.T. Dimalanta, A. Lim, R. Runnh
Page 99 and 100:
85 Appendix A: Score functions for
Page 101 and 102:
87 Appendix B: Hidden Markov Model
Page 103 and 104:
89 which can be shown to have highe
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