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

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Gapped alignments: The above description implicitly assumes that given any two cut
sites involved in the alignment, all intermediate cut sites will also be involved. Such alignments
are known as ungapped alignments. One may wish to relax this assumption and allow
gaps, e.g. to represent deletions or insertions. The above notation can be easily generalized
to include such gapped alignments by allowing some index pairs to attain a special value
(
representing a boundary, e.g.
il
) (
j l = NA)
. In principle the requirement that il ’s and j l ’s
be increasing can also be relaxed to allow change in orientation within an alignment (e.g. to
represent inversion) but this is rarely allowed in practice due to difficulty in implementation.
The true orientation of raw optical maps are unknown, so both must be considered during
analysis.
Map types: x and y above denote generic restriction maps. In practice, they can be one
of three types; individual optical maps, reference maps derived in silico from sequence and
intermediate consensus maps derived by combining multiple optical maps. This distinction is
important when comparing two maps. For example, optical maps are noisy whereas in silico
reference maps are generally considered error free. Consensus maps lie somewhere in between,
since they contain information averaged over individual optical maps. Thus, comparing an
optical map with another optical map is a symmetric problem, whereas comparing an optical
map with an in silico reference or a consensus map is not.
Alignment types: Most types of sequence alignment problems have a corresponding map
alignment problem. Terminology regarding the various types of alignment are not standard,
so we refrain from giving a full list and refer the reader to their favorite book on sequence
alignment, e.g. Waterman (1995). Two variants of global alignment have been particularly
useful in recent work: overlap alignment, where a suffix of one map is aligned to a prefix of
another, and fit alignment, where an alignment is desired for a map so that it is completely
contained in another, usually much larger, map. Local alignments are another important
class of alignments that are potentially useful in identifying structural variation, but have
not been studied extensively in this context.