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

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70 States d.f. AIC BIC 1 2 9775.9 9786.7 2 5 9731.3 9758.1 3 10 9729.9 9783.5 Table 4.1 In comparing the GM07535 and CHM genomes, AIC and BIC values for HMM fits with 1, 2 and 3 states serve as a guide to choose the number of states. In this case, we choose the model with 2 states. optical maps represent a population that has 6 known sites each of decreased (1:2) and elevated (3:2) copy number. Figure 4.2 shows the results of fitting a 3-state negative binomial HMM to one such data set. Figure 4.3 summarizes the results from multiple instances of this simulation. For each simulation, models were fitted using the full data sets as well as smaller subsets. Copy number changes larger that 1 Mb were detected more or less consistently, while smaller regions were not. Surprisingly, the results obtained from the smaller data sets were not much different, except in a couple of runs which had more false positives. Presumably, these details will vary depending on the size of the genome and the number and magnitude of the copy number alterations. Example: GM07535 and CHM: We next considered optical map data from two human genomes, GM07535 and CHM (Section 1.2), restricting our attention to alignments to the first 6 chromosomes. 23424 GM07535 and 43502 CHM optical maps aligned to these chromosomes. Alignments of CHM maps were used as the normalizing genome to detect relative copy number changes in GM07535. Both genomes are believed to be “normal”, so not much variation is expected. AIC and BIC values given in Table 4.1 provide some guidance in selecting an appropriate number of states, and a model with 2 states seems appropriate. Some regions of mild copy number differences are indicated by the graph of posterior probabilities in Figure 4.4. The reason for the differences is not clear, but could in part reflect heterozygous differences in GM07535.
71 Posterior probabilities 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1 2 3 4 5 6 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 Location (Mb) 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 Figure 4.4 Coverage of the GM07535 genome normalized by CHM. Both are “normal” genomes, so we do not expect to see much variation. The HMM fit has two states, with a target normal state with 15 hits expected per interval. The estimated mean states are approximately 11.66 and 16.31, with the higher state having a probability of 0.69 in the stationary distribution. Green bars represent posterior probabilities of the low state and grey rectangles represent sequence gaps.
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ON THE ANALYSIS OF OPTICAL MAPPING
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To my parents. i
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DISCARD THIS PAGE
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iv Page 3.3 Results . . . . . . . .
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v LIST OF TABLES Table Page 1.1 Sum
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vi LIST OF FIGURES Figure Page 1.1
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ON THE ANALYSIS OF OPTICAL MAPPING
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1 Chapter 1 Overview of Optical Map
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3 hard, do not always have a unique
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5 for microbial and other small gen
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7 Figure 1.2 Close-up of a typical
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9 0.96 0.98 1.00 1.02 1.04 Offset a
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11 direct glimpse at the underlying
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13 which is not surprising since we
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15 Gapped alignments: The above des
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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
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: 69 Estimated Copy Number in simulat
Page 87 and 88: 73 (a) Observed counts and decoded
Page 89 and 90: 75 Conclusion: Copy number alterati
Page 91 and 92: 77 well in its current form, but th
Page 93 and 94: 79 Change in score 15 10 5 0 0.9 1.
Page 95 and 96: 81 will rarely be homozygous. It ma
Page 97 and 98: 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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