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

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Example: MCF-7: A more interesting example is provided by the MCF-7 breast cancer
cell line, which is known to exhibit copy number polymorphism (Pollack et al., 2002;
Volik et al., 2003). Figure 4.5 shows results for chromosomes 17 and 20, which have been
shown by other methods to contain short regions of strongly elevated copy number. 10540
MCF-7 optical maps align to these chromosomes. The combined alignments from GM07535
and CHM, totalling 7532, are used as the normalizing data set. For comparison, the figure
also shows data from the same cell line obtained using a completely different technology for
measuring array-based comparative genomic hybridization (CGH), namely the Affymetrix
Xba 50k chip (data provided by Prof. Paul Lizardi, Yale). A visual comparison shows that
the unsmoothed coverage counts track well with the raw CGH data. After smoothing using
the HMM for optical map data and the CBS algorithm (Olshen and Venkatraman, 2002) for
the Affymetrix data, the copy number estimates are also similar. Both methods detect the
short but prominent spikes in copy number.
4.4 Discussion
In this chapter, we have outlined an approach that uses optical map alignments to detect
copy number alterations in a genome. A key step in this process was to summarize alignments
of optical maps to an in silico reference by a single number (midpoint) representing location.
These locations were modeled as realizations of a non-homogeneous Poisson process. We
account for the non-homogeneity using alignment data from a normal genome, which are used
to define random intervals with counts that follow a negative binomial distribution. These
counts were then modeled by a Hidden Markov Model, incorporating spatial dependence in
the data and allowing more natural estimation of certain parameters.
Model building: In HMM’s, as in many other statistical techniques, model selection and
in particular the choice of the number of states, is more an art than a science. A small
number of states may not completely reflect reality, especially if the genome being studied is
a mixture, which would not be unusual in tumor samples. On the other hand, allowing many