Multiple Sequence Alignment

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Multiple Sequence Alignment

• VIBE Education Edition (VIBE-Ed) Initiative

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• The time will come, I believe, though I shall
  not live to see it, when we shall have fairly
  true genealogical trees of each great kingdom of
  Nature.
• Charles Darwin

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Overview

• Why Multiple Sequence Alignment
• Scoring Functions
• Multiple Sequence Alignment Methods
• Dynamic Programming
• Progressive Alignments
• Motif Alignments

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Multiple alignment

• Pairwise alignment
• Infer biological relationships from string
  similarity
• Multiple alignment
• Infer string similarity from biological
  relationships

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Why do we care about multiple sequence alignment?

• Allows us to infer phylogenetic relationships
  evolution of organisms
• Can help us to elucidate biological facts about
  proteins most conserved regions are usually
  biologically significant.
• Formulate test hypotheses about protein 3-D
  structure (based on conserved regions)
• Formulate test hypotheses about protein
  function (see which regions of a gene, or its
  derived protein, are susceptible to mutation and
  which can have one residue replaced by another
  without changing function)

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Multiple Sequence Alignment (MSA) Defined

• MSA is the alignment of N sequences
  (Protein/Nucleotide) simultaneously, where N gt
  2 .
• Let Si denote a sequence. Then the Global
  Multiple Sequence Alignment of N gt 2 sequences
  
• S S1 , , SN
• is obtained by inserting gaps denoted by -.
• The new set of N sequences denoted by
• S S1 , , SN
• will all have length L

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Scoring Function

• In order to find an optimal alignment, we need to
  be able to measure how good an alignment is
• Scoring should take into account
• 1. Some positions are more conserved than others
  (position-specific scoring)
• 2. Sequences are not independent,
• but related by a phylogenetic tree
• (alignment should maximize
• possibility for finding
• common ancestor)

x
y
z
?
w
v
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Scoring Functions

• Columns are statistically independent
• S(m) ?i S(mi)
• mi is column i of multiple alignment m

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Scoring Function Definitions

• Define m
• AC-GCGG-C
• m AC-GC-GAG
• GCACC-GAG
• mij symbol in column i for sequence j
• m42 G
• cia observed counts for residue a in column i
• c1A 2, c1C 0, c1G 1, c1T 0, c1- 0

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Scoring FunctionMinimum Entropy

• Probability of column mi
• P(mi) ?a (pia)cia
• Define column score as
• S(mi) - log P(mi)
• - log ?a (pia)cia
• - cia log ?a (pia)
• - ?a cia log (pia)
• Measures variability observed in an aligned
  columns of residue
• cia
• Estimate for pia
• ?a cia
• Good alignment minimizes total entropy ?i S(mi)

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Scoring FunctionMinimum Entropy Example

• For alignment m
• AC-GCGG-C
• m AG-GC-GAG
• GAACC-GAG
• P(m1) ?a (pia)cia (p1A)c1A (p1C)c1C
  (p1G)c1G (p1T)c1T
• (p1A)2
  (p1C)0 (p1G)1 (p1T)0 (p1A)2 (p1G)
• p1A c1A / ?a c1a 2/3 p1G 1/3
• S(m1) - ?a c1a log (p1a) - 2 log (2/3)
  log (1/3) 0.82
• S(m2) - ?a c2a log (p2a) - log (1/3)
  log (1/3) log(1/3) 1.43
• S(m4) - ?a c1a log (p1a) - 3 log (1) 0

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Scoring Function Sum Of Pairs

• The sum-of-pairs (SP) score of a multiple
  alignment m is the sum of the scores of all
  induced pairwise alignments.
• SP score for column mi is
• S(mi) ?kltl s(mik,mil)
• s(a,b) is obtained from substitution matrix

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Notation

• ?k,l (k,l) ?k ?l (k,l)
• ?4k,l1(k,l) ?k (k,1) (k,2) (k,3)
  (k,4)
• ?4k,l1(k,l) (1,1) (1,2) (1,3) (1,4)
• (2,1) (2,2) (2,3) (2,4)
• (3,1) (3,2) (3,3) (3,4)
• (4,1) (4,2) (4,3) (4,4)

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Notation

• ?kltl (k,l) ?k ?l (k,l) (for all kltl)
• ?4kltl1(k,l) ?k (k,1) (k,2) (k,3) (k,4)
  
• ?4kltl1(k,l) (1,1) (1,2) (1,3) (1,4)
• (2,1) (2,2) (2,3) (2,4)
• (3,1) (3,2) (3,3) (3,4)
• (4,1) (4,2) (4,3) (4,4)

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Notation

• ?kltl (k,l) ?k ?l (k,l) (for all kltl)
• ?4kltl1(k,l) ?k (k,1) (k,2) (k,3) (k,4)
  
• ?4kltl1(k,l) (1,2) (1,3) (1,4)
• (2,3) (2,4)
• 
  (3,4)

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Scoring Function Sum Of Pairs Example

• L-PE
• m L-KE
• ASKE
• -SKE
• S(m1) ?kltl s(m1k,m1l)
• s(m11,m12) s(m11,m13) s(m11,m14)
• s(m12,m13) s(m12,m14)
• s(m13,m14)
• s(L,L) s (L,A) s(L,-)
• s (L,A) s(L,-)
• s(A,-)
• 5 (-2) (-8) (-2) (-8) (-8) -23

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Multiple Alignment Methods

• Now that we have a scoring scheme, lets consider
  methods that use those schemes
• Dynamic Programming (Optimal Solution)
• Heuristic (MSA)
• Progressive
• Progressive - Refinement
• Model (Profile) Alignment

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Dynamic Programming(Optimal Solution)

• Assume N sequences of length k
• Generalization of pair-wise alignment (N2) to
  multiple dimensions (Ngt2)
• The dynamic programming array then becomes an
  N-dimensional hyper-lattice of length k1
  (including initial gaps)
• The entry F(i1, , iN) represents score of
  optimal alignment for s11..i1, sN1..ik

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Dynamic Programming (2 sequences)
Complexity O(n2)
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Dynamic Programming (3 sequences)
Complexity O(n3)
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Dynamic Programming

• Complexity
• O(nk), for k sequences, each n residues long
• Assume sequences of length 300
• 2 sequences 300300 comparisons (9104)
• 3 sequences 300300300 comparisons (2.7 107)
• 4 sequences 8.1 109
• 5 sequences 2.4 1012
• 10 sequences 5.9 1024
• 20 sequences 3.5 1049
• 30 sequences 2.1 1074

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Optimal Solution Path
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MSA Algorithm (Carillo-Lipman Bound)
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MSA Algorithm (CarilloLipman, 1988)

• A Heuristic for Reducing the Search Space in
  Dynamic Programming
• Consider the pair-wise alignments of each pair of
  sequences.
• Create a phylogenetic tree from these scores
  (best scores paired first)
• Produce a draft multiple sequence alignment
  built incrementally from the phylogenetic tree.
• The pair-wise alignments and the draft MSA
  circumscribe a solution space within which a
  full dynamic programming search is performed
  (computationally intensive)
• Does not guarantee an optimal alignment of all
  the sequences in the group.
• Does get an optimal alignment within the space
  chosen.

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Progressive Methods

• First steps similar to dynamic programming
• Consider the pair-wise alignments of each pair of
  sequences.
• Create a phylogenetic tree from these scores
  (best scores paired first)
• Produce a draft multiple sequence alignment
  built incrementally from the phylogenetic tree
• But does NOT refine the draft MSA by doing a
  full search through the reduced search space.
• Does not guarantee an optimal alignment

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Progressive MethodsProblems

• Highly sensitive to choice of initial aligned
  pairs, i.e. initial alignments are frozen even
  when presented with new evidence in subsequent
  steps.
• Example
• x GAAGTT
• y GAC-TT
• z GAACTG
• w GTACTG
• Choice of scoring matrices and gap penalties is
  not straightforward

Frozen!
Now clear that correct y GA-CTT
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Progressive MethodsIterative Refinement

• Attempts to circumvent the problem of error
  propagation from frozen initial pair-wise
  alignments
• Generate initial alignment
• Remove one sequence and realign to the new
  alignment of the remaining sequences, recalculate
  score
• Iterate with different sequences until the
  alignment does not change (score does not
  increase)
• Guaranteed to converge to a local maximum of the
  score.

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Profile Alignment

• Once an alignment has been produced, it is
  advantageous to use position-specific information
  from the groups multiple sequence alignment when
  aligning a new sequence to it.
• Essentially, perfoms a pairwise sequence
  alignment using the profile as a scoring matrix
• HMMs can be used for profiles in progressive or
  iterative refinement methods
• Many progressive alignments use pairwise
  alignment of sequences to profiles, and profiles
  to profiles
• ClustalW

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ClustalW

• Most popular multiple sequence alignment
  algorithm
• Perform pairwise alignment between sequences,
  determine degrees of similarity between each
  pair, construct distance matrix
• Construct a phylogenetic tree using the distance
  matrix and nearest-neighbor algorithm.
• Combine the alignments starting from the most
  closely related groups to the most distantly
  related groups. The most closely-related pairs
  of sequences are aligned using dynamic
  programming
• Includes additional heuristics

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ClustalW
Perform All Pairwise Alignments
Dendrogram
Similarity Matrix
Cluster Analysis
From Higgins(1991) and Thompson(1994).
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Summary

• Scoring scheme critical (similarity matrix, gap
  scores)
• Dynamic programming methods
• too computationally expensive to use for even a
  moderate number of sequences, can use heuristics
  to reduce search space
• Progressive methods
• Much less computationally intensive, but
  sensitive to initial alignments
• Iterative refinement
• Decent approach to address a shortcoming of PM,
  but only guarantees local maximum of score
• Profile methods
• Allows integration of position-specific
  information and profile-profile alignments
• Most computational methods use large number of
  heuristics to obtain the optimum alignment