Tandem repeats are a common polymorphism in the genome.
This wiki talks about its representation - and compiles from previous work -especially by Gary Benson's tandem repeat finder's output.
A series of repeats that are contiguous
Motif Canonical Class
Using the concepts of shifting, the canonical class of a set of motifs can be defined as a equivalence relationship.
ACG ~ CGA if there exists a shift that allows s(ACG, i) = CGA
This relationship can be show to be reflexive, symmetric and transitive. And a equivalence class can be defined on this.
This is a distribution of motifs without collapsing
A C G T AA CC GG TT AC AG AT CG CT GT CA GA
show all permutations show acyclic show shift show reverse complement
Consider the motifs ACTT, TACT and TTAC, the following stretches can be observed in the genome
GGGGGGACTTACTTACTTACTTACTTAGGGGG GGGGGGTACTTACTTACTTACTTACTTGGGGG GGGGGGTTACTTACTTACTTACTTACTGGGGG
but looking from the right flank, they can easily be CTTA, ACTT and TACT respectively.
The concept of shifting the sequence is useful for grouping such like motifs together.
We define shift as follow
A shift of a sequence is the sliding of the sequence with the alleles wrapped to the front?
Reverse complement is is a common concept in sequence analysis.
Motifs are required to be acyclic. For example, a motif ACACAC should just be represented by AC as it is 3 copies of AC.
A sequence is cyclic if and only if there exists a sub sequence in which it is a multiple copy of.
The definition can be more explicit as follows:
A sequence is cyclic if and only if there exists a non trivial shift of the sequence that is equivalent to the sequence.
Take for example, the sequence ACACA, is this a bona fide motif? After it seems like it is 2.5 copies of AC and AC might be more appropriate.
shift 0: ACACA shift 1: CACAA shift 2: ACAAC shift 3: CAACA shift 4: AACAC
So ACACA is a bona fide motif.
While it is natural to think of a stretch of repeat as a integer, it is useful to consider fractional counts of a repeat especially in large repeat tracts. This is done in Tandem Repeat Finder.
This is 5.5 copies of the repeat GGGTTAA
You can use a score bounded by one.
By random matching -
A nice useful scheme is +2 for matches and -7 for indels and mismatches, and it provides a convenient way of scoring for purity.
- motif length
- motif basis
- repeat tract lengfth
Algorithm for Detection
Exact alignment algorithm
Fuzzy alignment algorithm
Detection of a motif in a sequence
Model free left alignment and right alignment
Model based fuzzy left alignment and right alignment
Model free fuzzy left alignment and right alignment
This is implemented in vt.
This page is maintained by Adrian.