Trees, Stars, and Multiple Biological Sequence Alignment

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Trees, Stars, and Multiple Biological Sequence
Alignment

• Jesse Wolfgang
• CSE 497
• February 19, 2004

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Importance?

• Molecular evolution (Dayhoff)

• RNA folding (Trifonov, Bolshoi)

• Gene regulation (Galas et al.)

• Protein structure-function relationships(Wu,
  Kabat)

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Introduction

• Original sequence unknown
• Must consider all possible transformations
• Including insertions, deletions, and replacements

• Choose the most likely set of transformations
• With a given model of protein evolution

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Sequences and Alignments
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Alignments

• Ex sequences DQLF, DNVQ, QGL

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Lattices and Paths
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Paths
2n-1 O(2n)
2 dimensions
3 dimensions
3 possible paths
7 possible paths
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Paths

• Sequences DQLF, DNVQ, QGL

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Paths and Sequence Length

• Sequences ABCD, ABD, BCD

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Paths and Sequence Length

• Sequences ABCD, EFGH, IJK

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Projections

• Sequences DQLF, DNVQ, QGL

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Optimal Paths
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Calculating Optimal Paths
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Problems with This Algorithm

• Calculates a weighted sum of its projected
  pairwise alignments
• Called Sum-of-the-Pairs (SP)
• Other methods fit biological intuition more
  closely

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Tree-Alignment

• Treat sequences as leaves of an evolutionary tree
• Reconstruct ancestral sequences which minimize
  the cost of the tree
• Must assign sequences to internal nodes
• Align the given and reconstructed sequences
• Star-alignment only one internal node

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Tree-Alignment

• Many different methods for calculating tree
  alignments
• Discuss version used by ClustalX

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Tree-Alignment in ClustalX

• Three main parts
• Perform pairwise alignment on all sequences to
  calculate a distance matrix
• Use distance matrix to calculate a guide tree
• Sequences are progressively aligned using the
  branching order in the guide tree

http//bimas.dcrt.nih.gov/clustalw/clustalw.html
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Calculating Distance Matrix

• Use standard dynamic programming to find the best
  alignment
• Gap penalties for opening a gap and continuing a
  gap (possibly different)
• Divide number of matches by total number of
  residues compared (excluding gaps)
• Convert to distances by dividing by 100 and
  subtracting from 1
• Gives one entry in the n by n matrix

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Calculating Distance Matrix

• Ex sequences ATCG, ATCC, AGGC, AGCC

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Calculating Distance Matrix
ATCG ATCT AGGC GCAA
ATCG -- -- -- --
ATCT .9925 -- -- --
AGGC .9975 .9975 -- --
GCAA 1 1 1 --
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Calculating a Guide Tree

• Using Nearest-Neighbor method to group sequences
• Results in an unrooted tree
• Branch lengths proportional to estimated
  divergence
• Mid-point method used to determine root
• Means of the branch lengths to each side of the
  root are equal (or approximately equal)

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Calculating a Guide Tree
AGAA
GCAA
AGCC
AGGC
ATCG
ATCT
ATCG
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Calculating a Guide Tree
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Progressive Alignment

• Perform a series of pairwise alignments
• Slowly align larger and larger groups of
  sequences
• Follow the branching order of the tree
• From leaves to root

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Progressive Alignment
AGCC
ATCG
AGAA
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Alignment Costs
Traditional
A, A, A, C, C
A, A, A, C, C
A, A, A, C, C
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Alignment Inconsistencies

• Different definitions of multiple alignments can
  yield different optimal alignments
• Optimal tree-alignments minimize number of
  mutations from theorized common ancestors
• SP-alignments maximize number of positions where
  aligned sequences agree
• Sometimes makes more biological sense since
  certain regions of proteins more likely to mutate

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Alignment Inconsistencies

• Ex cost of 1 for aligning two different
  letters, cost of 2 for aligning a letter with a
  null
• Sequences ACC, ACC, TCT, ATCT

Input sequences Reconstructedsequences
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ClustalX Demo

• Multiple sequence alignment program
• For more information on ClustalX
• http//www.at.embnet.org/embnet/progs/clustal/clus
  talx.htm