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

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48 Constant (4.5 / 10) Constant (2.75 / 10) Regression (99.9 %) Regression (99.0 %) 14000 Number Input 2 10000 Number in assembly 2 0.95 Ratio 2 12000 9000 0.90 0.85 10000 8000 0.80 8000 7000 0.75 0.70 Bases Covered (Mb) 2 Number of Gaps 2 Proportion Unaligned 2 232 30 0.012 0.010 230 25 0.008 228 20 0.006 0.004 226 15 1 2 3 1 2 3 Iteration 1 2 3 Figure 3.6 Comparison of various significance strategies through the iterative assembly procedure of Reslewic et al., where pairwise alignment is used as a filtering step before assembly. Chromosome 2 is assembled using the CHM data and the SOMA score. Two versions of the regression-based cutoff, with nominal specificities of 99.9% and 99.0%, are compared with a previously used scheme of declaring significance when the alignment has more than 10 aligned restriction sites and score above 4.5. To investigate whether performance is only affected by the number of maps allowed in by the filter, a similar scheme with the constant cutoff lowered to 2.75 is also used, where the cutoff is selected to allow roughly the same number of maps in the first step as the 99.0% regression cutoff. To allow partial alignments at the boundary of the reference, “aligned length” and “count” are used as surrogates for length and number of fragments, which effectively make the regression cutoffs more conservative than their nominal specificities would suggest. The first row reports the number of maps fed into the assembly step and the number (and proportion) of these assembled into contigs. In the second row, we attempt to assess the quality of the assembly by aligning the consensus contigs to the original in silico reference. The first two panels graph the number of bases in the reference covered and the numbers of gaps. The third panel shows a crude measure of the false positive rate, namely the proportion of bases in the assembled contigs that do not align to the reference.
49 3.4 Discussion 3.4.1 Uses Alignment is a fundamental problem in optical mapping. From a statistical perspective, optical map alignment is more challenging than DNA sequence alignment because optical map data are more noisy. Prior work in this area has mostly focused on developing score functions that can be used in DP algorithms. Here we have proposed a general framework to study the null distributions of optimal scores for an arbitrary score function. Its most obvious use is to derive significance tests with direct control over error rates. We have demonstrated the usefulness of such tests in improving assembly of large genomes. Evaluating score functions: The methods described above are applicable to any score function and provide a natural mechanism to evaluate them. We consider here the modelbased likelihood ratio (LR) score proposed by Valouev et al. (2006) for aligning optical maps to an in silico reference. Figure 3.7 plots the best spurious ungapped global alignment score against two replications from P G using this score. The correlation is weaker, but a map specific cutoff is still more appropriate than a constant cutoff. We apply the direct approach as before with n = 4 replications to estimate µ(M). The results, shown in table 3.2, indicate that at least for the particular sets of parameters used, the SOMA score is more sensitive at a comparable specificity. This is somewhat surprising, since the LR score is based on a formal likelihood ratio test whereas the SOMA score is largely heuristic. Informal experiments suggest that this is at least in part due to the sizing model used by Valouev et al. (2006), which does not consider scaling errors and consequently underestimates the marginal sizing variance for large fragments. More generally, this framework can be used for exploratory purposes, e.g. to compare the performance of different scores, or to guide the choice of parameters for a given score. It is helpful, particularly for overlap alignments (required in iterative assembly to extend flanks of a contig), if the distribution of the optimal score under the null does not depend strongly on the map, since otherwise significant alignments can be masked by spurious alignments.
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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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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
Page 61: 47 3.3.3 Simulation Given a generat
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
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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