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

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is rejected at level α if S > c α where F 0 (c α |M) = 1 − α. The advantage of this formulation
is that given a choice of P G , we can in principle simulate from F 0 (·|M) to obtain a suitable
cutoff, without requiring any probabilistic model for the optical map M. An effective choice
of P G is given by random permutations of the reference ˜G. This preserves characteristics of
the reference that are known to affect the spurious score distribution, namely the number
and lengths of fragments. Permuting the order of fragments is also reasonable given the
additive nature of score functions, which essentially reward matches in order. Formally, if we
assume that the fragment lengths defining G are i.i.d. from some distribution in a family F,
permutation can be viewed as sampling from P G conditional on the set of fragment lengths in
˜G, which is sufficient for F. Such tests are often called permutation tests (Cox and Hinkley,
1979, Chapter 6). See Figure 3.1 for a graphical justification of the i.i.d. assumption.
3.3 Results
3.3.1 Exploration
We use optical map data from GM07535, a diploid normal human lymphoblastoid cell line,
for illustration. The data consists of 206796 optical maps longer than 300 Kb. These maps
are aligned against an in silico reference map derived from Build 35 of the human genome
sequence (International Human Genome Sequencing Consortium, 2004), with sequence gaps
replaced by their estimated length. We use a score function implemented in the SOMA
software suite with parameters that have been extensively used with optical map data. The
actual score function, henceforth referred to as the SOMA score, is described in Appendix
A. In addition to the best alignment scores against the in silico reference, we consider best
scores for each map against several independent random permutations of the reference. The
permutations are done separately for every chromosome, thus retaining the total length and
number of fragments within each. For the most part, we restrict our attention to ungapped
global alignments.
In theory, we can approximate the conditional null distribution F 0 (·|M) by sampling from
it an arbitrary number of times. In practice, each such sample involves a permutation of