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

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maps, where the separation between spurious and real scores is much more clear. Comparison
with Figure 3.8 reveals an interesting point, namely that for a fair proportion of real optical
maps with high information content, the optimal score with the real reference is more likely
to have risen from the spurious score distribution than the real one. This could be due to
the maps being of low quality, but could also be a reflection of real differences between the
reference map and the actual genome. Maps of the latter type are of particular interest as
they contain possibly novel information about the underlying genome. This fact can be used
to develop a filter to obtain a smaller subset of maps relatively richer in “interesting” maps.
One possible approach to calibrate such a filter is described below. The usefulness of such
filters is yet to be explored.
Thinning: Even if all declared alignments were correct, the set of inferred locations would
only be a subset of the full set of true shotgun locations because not all maps are successfully
aligned. The probability that a map will be successfully aligned depends on the origin of the
map, its length and the errors involved (Figure 3.10). Averaging out the length and error
distributions, this probability can be expressed as a location specific truncation probability.
This random truncation can be thought of as a thinning of the true coverage process, which is
usually modeled as a homogeneous Poisson process (Lander and Waterman, 1988). A good
estimate of the thinning rate is necessary to normalize observed coverage, which can, for
example, be used to study copy number alterations in the underlying genome (Chapter 4).
This estimation has traditionally been done by Monte Carlo simulation of noisy maps from
a normal reference map, followed by alignment, thus replicating the pipeline actual optical
maps go through. The most time consuming step in this process is alignment. In view of the
discussion above, we may expect to be able to model the probability of a map being aligned
as a function of ψ(M). In particular, for the SOMA score and ungapped global alignment,
we fit the following logistic regression model to the alignments of simulated maps used in
Figure 3.9:
P ( aligned | M ) =
eα+β
log ψ(M)
1 + e α+β log ψ(M) (3.2)