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

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may appear where there should have been none and small fragments may not be represented
because they float away or merge with neighboring fragments. See Chapter 1 for a detailed
overview of the optical mapping system and Chapter 2 for more on the inherent errors and
statistical features of optical map data.
Alignment: A fundamental computational problem in optical mapping is alignment, i.e.,
given an optical map, trying to identify whether it overlaps with other restriction maps, and if
so, where. Alignments are not particularly valuable individually, but used en masse they are
important components in many procedures. Dynamic Programming (DP) algorithms have
been used extensively in DNA and protein sequence alignment (Durbin et al., 1998), and can
be used to align restriction maps with suitable modifications (Huang and Waterman, 1992).
Dynamic programming is a generic approach to alignment, and its usefulness depends on the
details of how it is applied. There are two important components in such alignment schemes.
The first is a score function, which is the objective function that the algorithm maximizes
(see Appendix A). The second is the strategy for detecting significance, i.e., whether or not
the alignment with the optimum score, which exists even if there is no true alignment, should
be considered a real alignment as opposed to a spurious one. The nature of optical mapping
data makes this problem harder than for sequence alignment.
Significance: Prior to the present work, the detection of significance in optical map alignments
has not been systematically studied. Conceptually, the problem is a test for the null
hypothesis that the maps being aligned are independent, with the optimal score as the test
statistic. Unfortunately, the null distribution, i.e. the distribution of the optimal score under
independence, is not easy to obtain. Rules based on simulated optical maps are possible;
however, they are predicated on the accuracy of the simulation model, which may not truly
reflect all the complexities of optical mapping. Our main contribution, as described in Section
3.2, is to phrase the significance problem in a way that allows us to naturally sample
from the null distribution of optimal scores avoiding any explicit model for optical maps. In
Section 3.3, this framework is used to investigate the properties of a particular score function