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

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Figure 1.6 A visualization, using Genspect, of an assembled consensus map, along with optical maps that support it. The assembly was produced by Gentig. The visualization is similar to that in Figure 1.5, with the exception that the top row represents the assembled consensus map rather than the predefined alignment target. 18
19 Assembly: For these examples, the assembly problem was approached using a two-step procedure. In the first step, each individual optical map was aligned to the reference map. The reference genome was then tiled by overlapping “windows” and maps that aligned were grouped together according to membership in these windows. In the second step, the maps in each group were assembled using Gentig, giving a local snapshot of the target map. This strategy can be expected to work in regions where the differences are minor, and use of gapped alignments can reveal certain larger-scale variations. For regions of more severe differences, an initial consensus map can be extended into its flanks by iteratively aligning optical maps to it, allowing partial overlap at the boundaries, followed by assembly. This procedure is revisited in Section 3.3.4. Differences: The next task was to identify the differences between the assembled consensus maps (contigs) and the reference map. Once again, this was approached in two steps, starting with alignments of the consensus contigs to the reference. This induces inferred alignments of single optical maps to the reference. Individual differences between the assembled consensus and the reference, specifically in restriction sites and fragment lengths, can then be assigned confidence in the form of p-values of simple hypothesis tests. In practice, the initial alignment is often problematic in regions with small fragments, and some automated and manual curation is currently required. Larger indels and translocations are usually identified manually. Table 1.2 summarizes the structural variations identified in the CHM and GM07535 genomes. See Reslewic et al. for more details of the analysis. Genome Insertions Deletions Extra cuts Missing cuts Others CHM 221 217 449 466 14 GM07535 109 52 132 254 10 Table 1.2 Summary of “Optical Structural Variations” (OSV) identified in the CHM and GM07535 data sets. The events included are those that were significant at a nominal False Discovery Rate of 90%.
Page 1 and 2: ON THE ANALYSIS OF OPTICAL MAPPING
Page 3 and 4: To my parents. i
Page 5 and 6: DISCARD THIS PAGE
Page 7 and 8: iv Page 3.3 Results . . . . . . . .
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: Figure 1.5 A visualization of align
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
Page 61 and 62: 47 3.3.3 Simulation Given a generat
Page 63 and 64: 49 3.4 Discussion 3.4.1 Uses Alignm
Page 65 and 66: 51 The ability to simulate from the
Page 67 and 68: 53 maps, where the separation betwe
Page 69 and 70: Figure 3.10 Schematic representatio
Page 71 and 72: 57 especially a short noisy one, to
Page 73 and 74: 59 Test statistics: Variability due
Page 75 and 76: 61 in sequence assembly and validat
Page 77 and 78: 63 1988). However, due to sampling
Page 79 and 80: 65 and rate parameters Λ i = E(N i
Page 81 and 82: 67 with mean µ k for the k th stat
Page 83 and 84:
69 Estimated Copy Number in simulat
Page 85 and 86:
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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