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

23
Alternatively, it can be thought of as the realization of a random process; in particular,
recognition sites along the genome have been modeled as the realizations of a homogeneous
Poisson point process, or equivalently the fragment lengths as i.i.d. exponential variates. This
model is supported by Figure 2.1, derived from Build 35 of the human genome sequence.
The rate of this process depends on the restriction enzyme being used, as well as the genome
being mapped. In some cases, it may vary across, or even within, chromosomes. Genomic
differences within a species usually involve only a fraction of the genome, and corresponding
restriction maps are expected to be largely similar. In any case, we are chiefly interested in
modeling the generative process of data conditional on the underlying restriction map. It
should be noted that the notion of a ‘true’ map is somewhat simplified. Diploid genomes
have two versions of the map, largely similar but not identical. Cancer samples are usually
a mixture of several cell populations that each contribute a slightly different genome.
Shotgun breaks: Before they are passed into micro-channels, chromosomal DNA is randomly
broken up into smaller molecules, usually by subjecting the DNA to vibration. This
shearing is often referred to as a whole genome shotgun process. The origin of each observed
optical map molecule is characterized by its location in the coordinate system defined by the
underlying true (unknown) restriction map, as well as its length. The distribution of the
location (e.g. midpoint) is assumed to be uniform over the underlying genome. It is typical
to consider only optical maps longer than a predetermined threshold, usually 300 Kb. The
distribution of lengths of the filtered maps is usually consistent with a truncated exponential
distribution.
2.1.2 Errors
Cut site errors: A restriction site in the true restriction map may fail to show up in a
corresponding optical map. These missing cuts can be due to either incomplete digestion
by the restriction enzyme or noise in the optical map image. Whether true cut sites are
identified (success) or not (failure) is modeled as independent Bernoulli trials, with some