Sequence alignment algorithms

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Sequence alignment algorithms
Presented By Cary Miller Sastry
Akella Daisuke Yasuda
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Overview

• Biological background / motivation / applications
• Dot matrix / dynamic programming
• FASTA / BLAST

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biology

• Biomolecules are strings from a restricted
  alphabet
• Length4 DNA
• Length20 protein
• Proteins are the working part

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Proteins

• Protein is a linear sequence of 20 characters
  (amino acids)
• Proteins do not maintain linearity
• Folding happens
• Folding determines overall 3-D shape
• Shape determines function

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Sequence Structure Function

• sequence does not reveal structure
• Much less function
• A sequenceARTUVEDYERRWWUHUK

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Structure

• Pic 1
• Pic 2

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Structure
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function

• Protein A is a constituent of muscle, skin,
  cartilage, or
• Protein B catalyzes the transformation of glucose
  to fructose, or
• How do we find proteins with similar function?

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Nature does not solve the same problem twice
(usually)

• Short sequence with a specific function (or
  shape) is called a domain
• The same domain appears in multiple proteins
• If we find the same domain in multiple proteins
  that provides a clue to function and/or structure

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Amino acids

• Each has the same basic chemical configuration
  but has a functional group that makes it
  chemically unique
• They occur in families
• Some functional groups are similar

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How biologists study proteins

• Expensive (NMR, x-ray crystallography)
• Discovery of function is difficult
• Few proteins are understood in detail
• Many are known by sequence
• Sequence is easier to get than structure or
  function

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A biological scenario

• Biologist discovers the sequence of a new protein
  with unknown function
• She has no idea of function
• If sequence can be associated with a known
  protein sequence we have a clue about structure
  and/or function
• Most proteins have unknown function

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Public databases

• Vast quantities of sequence, structure, function
  info is deposited into public databases
• A new sequence should be compared to the database

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Comparing sequences

• Alignment with exact matchABCTUVABUVABCTUVAB
  ----UV

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Alignment with inexact match

• InexactGARUIPPRSTGARVVBUIEEYSTGAR------UIPPRS
  TGARVVBUIEEYST

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Global vs. local alignment

• ABQRTASGGBV
• ABRRRASGVBB
• ABQRTASGGBV
• ABQ------SGGBV

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A real alignment

• MyoglobinPDLRKY FKG-A ENFTA DDVQ KSDRPDTKAY
  FPKFG DLSTA AALK SSPK
• Homology common ancestry

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Real alignment

• Pic 3

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Real alignment
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Scoring pairs of amino acids

• For amino acid pairs assign a score based on
  frequency of substitutionATRGUVXQATRCVVXTATRGV
  VEQAT-----VVEQ

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A substitution matrix

• Pic 4

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A substitution matrix
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Substitution matrices

• Pam and Blosum are standard substitution matrices
• Also include scores for
• Gap opening
• Gap extension

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Scoring amino acid strings

• Sum the individual pair scores
• Database is huge
• Spurious match to random sequence is likely
• Try your name
• E-value is probability of getting a given score
  from a random sequence

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Alignment algorithms

• Dot matrix
• Dynamic programming
• FASTA
• BLAST

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Dot Matrix and DP
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Dot Matrix

• Locating regions of similarity between two DNA or
  protein sequences which provide a great deal of
  information about the function and structure of
  the query sequence.
• Similar structure indicates homology, or similar
  evolution, which provides critical information
  about the functions of these sequences.

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Dot Matrix Contd..

• A dot matrix plot is a method of aligning two
  sequences to provide a picture of the homology
  between them.
• The dot matrix plot is created by designating one
  sequence to be the subject and placing it on the
  horizontal axis and designating the second
  sequence to be the query and placing it on the
  vertical axis of the matrix.

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Dot Matrix Contd..

• At each position within the matrix, a point is
  plotted if the horizontal and vertical elements
  are identical.
• Diagonal lines within the resulting matrix
  indicate regions of similarity. A simple dot
  matrix plot is shown in Figure A.

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Dot Matrix with noise reduction

• A certain percentage of the matches between
  sequence elements can be expected to be the
  result of the random nature of their evolution.
  These random matches are considered noise" and
  are filtered out to enhance the diagonal lines.

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Dot Matrix

• Noise Reduction
• a) Noise reduction in dot matrix can be done
  by centering a substring of elements of the
  query sequence over each element in the
  subject sequence and determining the number of
  corresponding elements within this window.

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Dot Matrix

• b) If the number of corresponding elements
  exceeds a specified threshold then a point is
  plotted for the center element. This is
  demonstrated in figure B.

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Dot Matrix (Figure B)
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Dot Matrix

• Advantages Readily reveals the presence of
  insertions/deletions and direct and inverted
  repeats that are more difficult to find by the
  other, more automated methods.
• DisadvantagesMost dot matrix computer programs
  do not show an actual alignment. Does not return
  a score to indicate how optimal a given
  alignment is.

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Dynamic Programming

• Dynamic programming (DP) algorithms are a general
  class of algorithms typically applied to
  optimization problems.
• For DP to be applicable, an optimization problem
  must have two key ingredients
• a) Optimal substructure an optimal solution
  to the problem contains within it optimal
  solutions to sub-problems.
• b) Overlapping sub-problems the pieces
  of larger problem have a sequential
  dependency.

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Dynamic Programming

• DP works by first solving every sub-sub-problem
  just once, and saves its answer in a table,
  thereby avoiding the work of re- computing the
  answer every time the sub-sub-problem is
  encountered. Each intermediate answer is stored
  with a score, and DP finally chooses the sequence
  of solution that yields the highest score.

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Dynamic Programming

• Path Matrix

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Dynamic Programming

• Both global and local types of alignments may be
  made by simple changes in the basic DP algorithm.
• Alignments depend on the choice of a scoring
  system for comparing character pairs and penalty
  scores (e.g. PAM and BLOSUM matrixes covered
  before)
• Scoring functions example
• w (match) 2 or substitution matrix
• w (mismatch) -1 or substitution matrix
• w (gap) -3

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Dynamic Programming

• Global Alignment (Needleman-Wunsch)
• a) General goal is to obtain optimal global
  alignment between two sequences, allowing
  gaps.b) We construct a matrix F indexed by i
  and j, one index for each sequence, where the
  value F(i,j) is the score of the best
  alignment between the initial segment x1i of x
  up to xi and the initial segment y1j of y up
  to yj. We begin by initializing F(0,0) 0.
  We then proceed to fill the matrix from top
  left to bottom right. If F(i-1, j-1),
  F(i-1,j) and F(i,j-1) are known, it is
  possible to calculate F(i,j).

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Dynamic Programming

• F(i,j) max F(i-1, j-1) s(xi , yj
  )F(i-1,j) dF(i, j-1) d.
• where s(a,b) is the likelihood score
  that residues a and b occur as an aligned
  pair, and d is the gap penalty.
• Once you construct the matrix, you trace back the
  path that leads to F(n,m), which is by definition
  the best score for an alignment of x1n to y1m.

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Dynamic Programming

• Global Dynamic programming matrix

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Dynamic Programming

• Local alignment (Smith-Waterman)Two changes from
  global alignment1. Possibility of taking the
  value 0 if all other options have value less
  than 0. This corresponds to starting a new
  alignment.2. Alignments can end anywhere in
  the matrix, so instead of taking the value
  in the bottom right corner, F(n,m) for the
  best score, we look for the highest value of
  F(i,j) over the whole matrix and start the
  trace-back from there.
• F(i,j) max 0F(i-1, j-1) s(xi , yj
  ) F(i-1,j) dF(i, j-1) d.

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Dynamic Programming

• Local Dynamic programming matrix

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Dynamic Programming

• Advantages Guaranteed in a mathematical
  sense to provide the optimal (very best or
  highest-scoring) alignment for a given set of
  scoringfunctions.
• Disadvantages
• a) Slow due to the very large number of
  computational steps O(n 2).b) Computer
  memory requirement also increases as the square
  of the sequence lengths.
• Therefore, it is difficult to use the
  method for very long sequences.

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FASTA and BLAST
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FASTA - Idea -

• Problem of Dynamic Programming
• D.P. compute the score in a lot of useless
  area for optimal sequence
• FASTA focuses on diagonal area

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FASTA - Heuristic -

• Heuristic
• Good local alignment should have some exact
  match subsequence.

FASTA focus on this area
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FASTA - Hi Level Algorithm -

• Hi level algorithm
• Let q be a query
• max ? 0
• For each sequence, s in DB
• compare q with s and compute a score, y
• if max
• max ? y
• bestSequence ? s
• Return bestSequence

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FASTA - Algorithm -

• Step 1
• Find all hot-spots
• // Hot spots is pairs of words of length k
  that exactly match

Sequence 1
Hot Spots
Sequence 2
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FASTA - Algorithm -

• Step 1 in detail
• Use look-up Table
• Query G A A T T C A G T T A
• Sequence G G A T C G A

DotMatrix
Look-up Table
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FASTA - Algorithm -

• Step 2
• Score the Hot-spot and locate the ten best
  diagonal run.
• // There is some scoring system ex. PAM250

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FASTA - Algorithm -

• Step 3
• Combine sub-alignments into one alignment
  with GAP

GAP
One of local alignment
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FASTA - Algorithm -

• Step 4
• Consider weighted direct graph.
• Let node be a sub-alignment found in step 1
• Let u and v be nodes
• Edge (u,v) exists if alignment u is before
  in the sequence.
• Each edge has gap penalty (negative)
• Find the maximum weight path

Sub-sequence
Edge
One Sequence
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FASTA - Algorithm -

• Step 4 in detail

GAP
Sub-alignment
Gap
-5
-3
-3
Max Weight Path
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FASTA - Algorithm -

• Step 5
• Use the dynamic programming in restricted area
  around the best-score alignment to find out the
  higher-score alignment than the best-score
  alignment

Width of this band is a parameter
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FASTA - Algorithm -

• Summary of Algorithm
• 1 Find all hot-spots
• // Hot spots is pairs of words of length k
  that exactly match
• 2 Score the Hot-spot and locate the ten best
  diagonal run.
• 3 Combine sub-alignments into one alignment
• 4 Score Each alignment with gap penalty and
  pick up the best-score alignment
• 5 Use the dynamic programming in restricted
  area around the best-score alignment to find out
  the alignment greater than the best-score
  alignment.

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FASTA - Complexity -

• Complexity
• Step 1 and 2 // select the best 10
  diagonal run
• Let n be a sequence from DB
• O(n) because Step 1 just uses look up the
  table
• O(n)

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FASTA - Complexity -

• Step 3 and 4 // compute the MAX Weight Path
• Let r be the number of sub-alignments. (r
  10)
• Lets be the number of edges
• O(r2)
• n1 n2 n3
• n1
• n2
• n3
• ? 1 of D.P because r2 102
• and mn 104

Positive Weight
-5
-3
-3
Max Weight Path
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FASTA - Complexity -

• Step 5 // compute partial D.P.
• Depends on the restricted area
• Therefore, FASTA is faster than D.P.

Width of this band is a parameter
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BLAST - Heuristic -

• Another Heuristic algorithm
• Heuristic but evaluating the result
  statistically.
• Homologous sequence are likely to contain a
  short high scoring word pair, a hit.
• BLAST tries to extend it on the both sides to
  get optimal sequence.

A T T A G .
Sequence
Short high score Word
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BLAST - Algorithm -
Neighborhood Word

• Step 1 preprocessing Query
• Compile the short-hit scoring word list from
  query.
• The length of query word,w, is 3 for brosom
  scoring
• Threshold T is 13

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BLAST - Algorithm -

• Step 1 2
• Create neighborhood words for each query word

Query Word
Neighborhood words
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BLAST - Algorithm -

• Step 2 Scanning DB
• For each words list, identify all exact matches
  with DB sequences

Query Word
Neighborhood Word list
Sequences in DB
Sequence 1
Sequence 2
Step 2
Step 1
The purpose of Step 1 and 2 is as same as FASTA
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BLAST - Algorithm -

• Step 2-2
• Method 1 Hash Table
• Query LAALLNKCKTPQGQRLVNQWIKQPLMD

Hash Table
Word list
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BLAST - Algorithm -

• Step 2-3
• Method 2 Finite Automata

A,G
L
A
G
A
A
A
I
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BLAST Algorithm -

• Step 3 (Search optimal alignment)
• Let S be a score of hit-word
• For each hit-word, extend ungapped alignmentin
  both directions.
• Step 4 (Evaluate the alignment statistically)
• Stop extension when E-value (depending on score
  S) become less than threshold. The hit-word is
  called High Scoring Segment Pair. BLAST return it
• E-value the number of HSPs having score S
  (or higher) expected to
• occur only by chance.
• ? Smaller E-value, more significant in
  statistics
• Bigger E-value , by chance

A T T A G .
Sequence
Hit Word
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BLAST - Algorithm -

• Step 3 -2
• Definition of E-Value
• The expected number of HSP with the score at
  least S is
• E Knme-?S
• K, ? is constant depending on model
• n, m are the length of query and sequence
• The probability of finding at least one such HSP
  is
• P 1 - eE
• ? If a word is hit by chance
  (E-value is bigger),
• P become smaler.

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BLAST - Running Time -

• Running Time
• The length of Query 153
• DB size 5997 sequences
• PC Pentium 4
• By Dr. Takeshi Kawabata
• Nara Sentan Gijyutu University

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Comparison of Algorithm

• Dynamic Programming
• 1. most sensitive result
• ? D.P uses all information of two sequence
• 2. Running time is slow
• ? D.P compute the useless area for computing
  the optimal sequence.

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Comparison of Algorithm

• FASTA
• 1. Less sensitive than D.P and BLAST
• ? FASTA uses partial information to speed up
  the computaiotn.
• ? FASTA does not evaluate the result
  statistically.
• 2. Running time is faster D.P
• ? the same reason as the above.

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Comparison of Algorithms

• BLAST
• 1. Sensitive than FASTA
• ? BLAST evaluate the result statistically.
• 2.Faster than FASTA
• ? Because BLAST evaluate the entire DB with
  the same threshold based on statistics. BLAST
  eliminate noises and reduces the running time.

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FASTA vs BLAST

• BLAST
• Compare the query and sequences in DB
• with the same threshold.
• FASTA
• compare the query and a sequence one by one
• And compare the each result.

DB
DB
Query
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Conclusion