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

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16 Software: The SOMA software suite can be used to perform restriction map alignments. As in sequence alignment, one is often interested in sub-optimal alignments as well, i.e. highscoring alignments in addition to the top-scoring one. SOMA is able to find such alignments. Genspect can be used to visualize alignments reported by SOMA. Figure 1.5 shows a typical visualization of optical map alignments. Assembly The assembly problem can be viewed as a multiple alignment problem, with an additional step of producing an inferred consensus map. The most successful optical map assembly software to date is Gentig, based on ideas described in Anantharaman et al. (1997) (for clones) and Anantharaman et al. (1999) (for genomic DNA). Briefly, they develop a Bayesian approach where a prior model for the unknown restriction map and a conditional distribution for optical maps given the true map are used to derive the posterior density for an hypothesized map. The inferred restriction map is, in principle, the one that maximizes this posterior density. Due to the complexities of the problem, a complete search is infeasible, and various heuristics are employed to enable an efficient implementation. We have little to add on the assembly problem, and refer the reader to the original papers for further details. Gentig results can also be visualized using Genspect, as shown in Figure 1.6. 1.3.5 Example (continued) The goal of an optical mapping project is to infer the underlying restriction map of the genome being studied. For small genomes, Gentig serves this purpose well. However, for large genomes such as GM07535 and CHM (Table 1.1), the sizes of the data sets exceeds its capacity, and new algorithms are required. Fortunately, additional information is available for these data sets in the form of an in silico reference map, derived from the human genome sequence by locating instances of the SwaI recognition pattern. The genomes being studied are largely similar to this reference, so we are primarily interested in how their restriction maps differ from the reference.
Figure 1.5 A visualization of alignments of optical maps to an in silico reference. The alignments were done using SOMA, and Genspect was used to visualize the results. The top row represents a segment of the in silico map derived from the human genome, to which optical maps were aligned. The optical map fragments are color coded to indicate cut differences and jittered vertically to emphasize fragment boundaries. 17
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: 15 Gapped alignments: The above des
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
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
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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
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85 Appendix A: Score functions for
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87 Appendix B: Hidden Markov Model
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89 which can be shown to have highe
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