Fire

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FireµSatAn Algorithm to Detect Tandem
Repeats in DNA
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Introduction

• What are tandem repeats in DNA?
• How are we going to detect tandem repeats in DNA?
• Why would anybody want to detect tandem repeats
  in DNA?

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Genetic sequences

• DNA consists of four different nucleotides,
  namely
• Adenine (A) Guanine (G)
• Cytosine (C) Thiamine (T)
• Genetic databanks e.g. Genbank, Emboss and Entrez
  stores DNA sequences as concatenated single
  letter codes in FASTA format.

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Tandem Repeats (TRs) in genome sequences

• DNA molecules are subject to numerous mutational
  events. One of the consequences of these events
  that can be detected by computationally analyzing
  genome sequences is tandem duplication.
• A TR or TR-zone is a string of DNA molecules that
  is characterized by a certain motif that
  introduces the string, contiguously followed by a
  number of copies of the motif, e.g.,
  ACGACGACGACGACG

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Tandem Repeats

• Perfect tandem repeat (PTR) if the copies are
  exact e.g. ACGACGACGACGACG, hence five copies of
  the motif ACG.
• Approximate tandem repeat (ATR) if the copies of
  the motif include non-exact copies, thus
  mutational events have, most likely occurred e.g.
  ACGACACGAGGACGAG.
• In the absence of further qualification,
  reference to a tandem repeat should be construed
  as a reference to either a PTR or an ATR.

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Tandem Repeat Elements

• A PTR element (PTRE) is a TR element that matches
  the motif. If the motif is for example ACG then
  the PTRE will also be ACG.
• An ATR element (ATRE) is a TR element similar to
  the motif but not an exact copy thereof. If the
  motif is ACG then an ATRE may for example be AC.

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Microsatellites

• The length of PTREs may vary satellites,
  minisatellites and microsatellites
• Microsatellites is a subset of TRs
• (conforming to Benson, Delgrange, Rivals
  Abajian)

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Formal problem statement

• A PTR whose motif is ? is repeated p times where
  p 1, is denoted by ?p. An ATR u that is
  derived from this PTR ?p must always have the
  motif (?) as its prefix. It therefore has the
  form ?u2up where each ATRE, uk(k 2p), is the
  result of at most e mutations on ?. Here e is the
  so called motif error.
• Besides the restrictions applicable to the motif
  error threshold values are also introduced that
  manipulate the attributes of the detected TR.

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Tolerated error types

• Errors regarding the motif or PTRE (motif
  errors)
• deletions
• mismatches
• insertions
• Errors related to the detected TR (TR errors)
• in terms of the ratio between PTREs and ATREs
• the minimum number TREs to be reported
• the maximum number of ATREs consecutively

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Motif errors

• Maximum of 50 error toleration
• If ? 2 or ? 3 then ? 0 or ? 1
• (default 1)
• If ? 4 or ? 5 then ? 0 ? 1 or ? 2
• (default 2)
• Consider ACGTT then ACT will be an ATRE where two
  deletions have occurred.

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Motif errors Types of Mutations

• Deletion
• Refers to the absence of a base pair in the
  motif.
• Insertion
• An ATRE with up to e base pairs inserted
  into any position of the PTRE.
• Mismatch
• Refers to the replacement of a base pair in
  the motif by another.

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Detected TR errors the substring error

• The substring error
• where is the maximum substring error allowed
  and
• (n_d x p_d) (n_i x p_i) (n_m x p_m)
  n_ptre
• where
• n_d number of deletions
• n_i number of insertions
• n_m number of mismatches
• p_d penalty allocated to deletions
• p_i penalty allocated to insertions
• p_m penalty allocated to mismatches

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Detected TR errors the minimum number of TREs

• tn_tre tn_ptre tn_atre
• tn_tre
• the default value for 2
• to prevent the output of unwanted data

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Detected TR errors the maximum number of
consecutive ATREs

• tn_atreC
• tn_atreC is incremented for every ATRE read
• tn_atreC is set to zero whenever a PTRE is read
• the default of tn_atreC is 0

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DeletionRefers to the absence of a base pair in
the motif
FAD(ACG,1)
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MismatchRefers to the replacement of a base pair
in the motif by another.
FAm(ACG,1)
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High-level Descriptionof FireµSat

• generateWords(?,e) generates a set of all words
• of length ?Length from the alphabet
• S A,C,G,T.
• createFATR(?,e) returns FATR(?,e) as discussed.
• findIndices(gSeq, FATR, t, a, ß, p_m, p_d, p_i)
  returns a set of index pairs in gSeq of an
  identified TR.
• the TR is such that it complies with the
  constraints specified by t, a, ß. Various
  counters have to be updated to ensure correct
  output.

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Why does anybody want to detect TRs in DNA?

• The cause of several human diseases can be traced
  to having too many copies of a certain nucleotide
  triplet.
• TRs play a role in the development of immune
  system cells.
• TRs serves as genetic markers in plant and
  animal species.
• Tandem repeats play a role in gene regulation and
  contribute to the breeding of disease resistant
  cultivars.

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Conclusion

• A new theoretical approach to detect TRs in DNA
  has been introduced. The time complexity of
  FireµSat is linear in gSeq.
• The practical implementation of FireµSat is in
  progress. The following matters constitute a
  future research agenda
• the performance of FireµSat
• the possibility of reducing FATR
• and, if successful, the latter results could
  suggest ways of adapting FireµSat to detect
  minisatellites and satellites as well.