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

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1.3.2 Optical map data
Representation: An optical map identified by image processing is essentially an ordered
sequence of fragment lengths. Thus, an optical map with n fragments may be denoted as
x = (x 1 , . . .,x n )
where x i is the measured length of the i th fragment. Another natural representation of an
optical map is as a sequence of recognition sites. An optical map x is easily converted into a
sequence of cut sites by accumulating the lengths, noting that the cut sites are only defined
up to location. Denoting the conversion from fragment lengths to cut site locations by S,
we may write
S(x) =
{0 = s 0 < s 1 < · · · < s n = ∑ }
x i
where x i = s i −s i−1 for i = 1, . . ., n are fragment lengths and s i = ∑ i
j=0 x j are locations of cut
sites. The endpoints s 0 and s n are not treated as cut site locations since they represent breaks
that define the original molecule as a segment of the whole genome (from shearing) rather
than breaks created by the restriction enzyme. The first representation, being invariant to
origin, has the advantage of being unambiguous, but the second is often more useful, e.g.
for defining alignments between two or more optical maps. Of course, both representations
apply to any physical map. Optical maps may have additional meta-data associated with
them (e.g. confidence scores from image processing), but most existing algorithms ignore
such attributes.
Characteristics: Optical map molecules are generally regarded as random snapshots obtained
from the underlying genome, i.e., their locations are assumed to be uniformly distributed
within the genome. Their orientation is not known a priori. The lengths of the
molecules vary; a typical molecule may be around 500 Kb long, and 1000 Kb molecules are
not uncommon. Unlike sequence reads that are obtained as averages over many copies of a
clone, optical maps represent single molecules derived from genomic DNA, providing a more