Dynamic Programming Multiple Alignment

1
Lecture 10

• Dynamic Programming - Multiple Alignment Gene
  Finding
• Jones Pevzner,
• Secs. 6.10-6.16

2
Multiple Alignment

• We are often interested in simultaneously
  aligning a collection of sequence so as to best
  highlight the similarities within a family.
• We can handle this with a dynamic programming
  approach.
• Construct a graph analogous to that used for
  pair-wise alignment, but corresponding to a
  matrix of dimension k, with k the number of
  sequences.
• Have strings v1,,vk, each with character counts
  ni.
• The maximum length of the alignment is the
  maximum among the ni.

3
Constructing the graph

• Each cell now has 2k - 1 predecessors (can we
  show that?)
• We have characters drawn from an extended
  alphabet A, which includes a gap character.
• If we follow the original DP approach, our
  scoring matrix also needs to be k dimensional.

4
Recurrence relations for three sequences
5
Performance of rigorous multiple alignment

• Very slow, runs in O((2n)k), where n is the
  typical sequence length and k the number of
  sequences.
• Not practical for anything other than a small
  family of sequences
• An active area of research to find more efficient
  algorithms, often using heuristics.

6
Progressive alignment

• One approach that doesnt work - making all
  possible pair-wise alignments and then assembling
  them at the end.
• Typically the individual alignments will not be
  compatible with a multiple alignment
• In progressive alignment (ala CLUSTAL), the
  strongest pair-wise alignment is used as a seed
  to build up a profile, which is progressively
  extended by adding more sequences.

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The problem with progressive alignment

• The strongest initial alignment may be a bad
  seed that spoils the multiple alignment.
• This can be circumvented (somewhat) by
  considering all possible initial pairs as seeds,
  no matter their score.

8
Scoring multiple alignments

• A k-dimensional scoring matrix is not practical!
• One useful measure is the sum of the entropies
  computed for the columns
• Another measure is to score using all unique
  pairs of comparisons within a column, and
  applying a conventional scoring matrix (e.g.
  PAM-250)

9
Gene Prediction

• Genomic sequences are translated into peptide
  sequences by the mechanism of codons. One codon
  is a triple of three consecutive nucleotides.
• There are 43 64 codons. 61 of these map to one
  of the twenty amino acids, while 3 of them (TAA,
  TAG, TGA) are stop codons which terminate a
  protein coding sequence. They are like periods at
  the end of a sentence
• Note that U (uracil) substitutes for T (thymine)
  in the messenger RNA copies of genomic sequences.

10
Reading frames
Frame1 A T G C T T A G T C T G Frame2 A T G
C T T A G T C T G Frame3 A T G C T T A G T C
T G
Translations Met Leu Ser Leu Cys Leu Val Va
l STOP
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Open Reading Frames (ORFs) are clues for finding
genes

• Based on random chance alone, the average length
  of an ORF is about 21 codons.
• Translated peptides are typically 300 amino acids
  in length
• Long ORFs can be an indication of the presence of
  a coding region