Algorithms for Multiple Alignment

1
Algorithms for Multiple Alignment

• Christian E. Loza and Joseph Sheinberg
• University of North Texas - 2005

2
The Task

• Given N sequences, provide an optimal sequence
  alignment

C T T G T A T
C
C T
A T
T C
C T
T T
C T
C G T G T A C
C
3
Brute Force approach

• For 3 sequences ( k 3 )

O( nk! )
4
Dynamic Programming
O( 2nk )
5
Pairwise algorithm (Bains)
C T T G T A T
C
C T
A T
T C
C T
O( k n2 )
T T
C
T
Problems initial errors are chaotic
C G T G T A C
C
6
Clustal (Higgins and Sharp)

• Alignments are done in four steps.
• Pairwise alignments
• Similarity matrix
• Cluster similar sequences based on their
  similarity score
• Progressive multiple alignment

O( k n2 ) or faster, depending on pairwise
algorithms
7
Discrete Alignment (Loza, Shneirder)

• Discrete alignment
• Calculate window size
• Calculation of relative frequencies
• Alignment and consensus

8
1. Window Size

• One sequence of codons has the following
  probability to appear in a n sequence.
• 4w n, ? w (0.5) lg n
• Where 4 is the number of symbols, in this case,
  ACTG.

9
2. Calculation of frequencies

• We divide each of the sequences in the window
  size, and store the occurrences of the different
  sub sequences.
• ACTCGTGCGT
• with a window size of three will return
• ACT, CTC, TCG, CGT(2), GTG, TGC, GCG
• We store not only the frequencies, but also the
  positions to be used in the next step.

10
2. (Biased Option)

• We divide each of the sequences in the window
  size, and store the occurrences of the different
  sub sequences.
• ACTCGTGCGT
• with a window size of three will return
• ACT, CTC, TCG, CGT(2), GTG, TGC, GCG
• we do this for the frequencies of all
  sequences except the one we want to be biased to.
• In the Biased Option, we store just the
  frequencies relative to one of the sequences.

11
3. Final alignment

• We proceed to use the same cluster algorithm as
  Higgins and Sharp to align in a hierarchal
  approach the result subsequences. We cluster them
  and do a incremental global alignment.
• Note that in the case of the biased algorithm, we
  proceed in the same way, but the result is going
  to be biased to one of the sequences.
• This is a greedy approach

12
3. Final alignment

• The final alignment resembles the pairwise
  alignment, with the difference that is between
  one sequence and globally the rest of the
  sequences.
• Therefore, the time complexity is the same as in
  pairwise alignment O(kn2).

13
Time Complexity

• This approximation algorithm has the complexity
  of O(kn2).
• The biased algorithm has a time complexity of
  O(k2n2).
• It is less vulnerable to initial bad choices.
• The biased alignment shows us how we can align
  all of the sequences considering one of the
  sequences more important than the others.

14
Questions?

• Thank you )