BCB 444/544

1
BCB 444/544

• Lecture 6
• Finish Dynamic Programming
• Scoring Matrices
• Alignment Statistics
• 6_Aug31

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Required Reading (before lecture)

• Mon Aug 27 - for Lecture 4
• Pairwise Sequence Alignment
• Chp 3 - pp 31-41
• Wed Aug 29 - for Lecture 5
• Dynamic Programming
• Eddy What is Dynamic Programming? 2004 Nature
  Biotechnol 22909
• http//www.nature.com/nbt/journal/v22/n7/abs/nbt07
  04-909.html
• Thurs Aug 30 - Lab 2
• Databases, ISU Resources Pairwise Sequence
  Alignment
• Fri Aug 31 - for Lecture 6
• Scoring Matrices Alignment Statistics
• Chp 3 - pp 41-49

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Announcements

• Fri Aug 31 - Revised notes for Lecture 5 posted
  online
• Changes? mainly re-ordering, symbols, color
  "coding"
• Mon Sept 3 - NO CLASSES AT ISU (Labor Day)!! -
  Enjoy!!
• Tues Sept 4 - Lab 2 Exercise Writeup Due by 5 PM
  (or sooner!)
• Send via email to Pete Zaback
  petez_at_iastate.edu
• (HW2 assignment will be posted online)
• Fri Sept 14 - HW2 Due by 5 PM (or sooner!)
• Fri Sept 21 - Exam 1

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Chp 3- Sequence Alignment

• SECTION II SEQUENCE ALIGNMENT
• Xiong Chp 3
• Pairwise Sequence Alignment
• vEvolutionary Basis
• vSequence Homology versus Sequence Similarity
• vSequence Similarity versus Sequence Identity
• Methods - cont
• Scoring Matrices
• Statistical Significance of Sequence Alignment

Adapted from Brown and Caragea, 2007, with some
slides from Altman, Fernandez-Baca, Batzoglou,
Craven, Hunter, Page.
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Methods

• vGlobal and Local Alignment
• vAlignment Algorithms
• vDot Matrix Method
• Dynamic Programming Method - cont
• Gap penalities
• DP for Global Alignment
• DP for Local Alignment
• Scoring Matrices
• Amino acid scoring matrices
• PAM
• BLOSUM
• Comparisons between PAM BLOSUM
• Statistical Significance of Sequence Alignment

6
Sequence Homology vs Similarity

• Homologous sequences - sequences that share a
  common evolutionary ancestry
• Similar sequences - sequences that have a high
  percentage of aligned residues with similar
  physicochemical properties
• (e.g., size, hydrophobicity, charge)

• IMPORTANT
• Sequence homology
• An inference about a common ancestral
  relationship, drawn when two sequences share a
  high enough degree of sequence similarity
• Homology is qualitative
• Sequence similarity
• The direct result of observation from a sequence
  alignment
• Similarity is quantitative can be described
  using percentages

7
Goal of Sequence Alignment

• Find the best pairing of 2 sequences, such that
  there is maximum correspondence between residues
• DNA 4 letter alphabet ( gap)
• TTGACAC
• TTTACAC
• Proteins 20 letter alphabet ( gap)
• RKVA-GMA
• RKIAVAMA

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Statement of Problem

• Given
• 2 sequences
• Scoring system for evaluating match (or mismatch)
  of two characters
• Penalty function for gaps in sequences
• Find Optimal pairing of sequences that
• Retains the order of characters
• Introduces gaps where needed
• Maximizes total score

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Avoiding Random Alignments with a Scoring
Function

• Introducing too many gaps generates nonsense
  alignments
• s--e-----qu---en--cesometimesquipsentice
• Need to distinguish between alignments that occur
  due to homology and those that occur by chance
• Define a scoring function that rewards matches
  () and penalizes mismatches (-) and gaps (-)

Scoring Function (S) e.g.
Match ? 1 Mismatch ? 1
Gap ? 0 S ?(matches) -
?(mismatches) - ?(gaps)
Note I changed symbols colors on this slide!
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Not All Mismatches are the Same

• Some amino acids are more "exchangeable" than
  others (physicochemical properties are similar)
• e.g., Ser Thr are more similar than Trp Ala
• Substitution matrix can be used to introduce
  "mismatch costs" for handling different types of
  substitutions
• Mismatch costs are not usually used in aligning
  DNA or RNA sequences, because no substitution is
  "better" than any other (in general)

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Substitution Matrix

• s(a,b) corresponds to score of aligning character
  a with character b
• Match scores are often calculated
• based on frequency of mutations in very similar
  sequences
• (more details later)

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Global vs Local Alignment

• Global alignment
• Finds best possible alignment across entire
  length of 2 sequences
• Aligned sequences assumed to be generally similar
  over entire length

• Local alignment
• Finds local regions with highest similarity
  between 2 sequences
• Aligns these without regard for rest of sequence
• Sequences are not assumed to be similar over
  entire length

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Global vs Local Alignment - example
1 CTGTCGCTGCACG 2 TGCCGTG
Which is better?
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Global vs Local Alignment Which should be used
when?

• It is critical to choose correct method!
• Global Alignment vs Local Alignment?
• Shout out the answers!! Which should we use for?
• Searching for conserved motifs in DNA or protein
  sequences?
• Aligning two closely related sequences with
  similar lengths?
• Aligning highly divergent sequences?
• Generating an extended alignment of closely
  related sequences?
• Generating an extended alignment of closely
  related sequences with very different lengths?
• Hmmm - we'll work on that
• Excellent!

15
Alignment Algorithms

• 3 major methods for pairwise sequence alignment
• Dot matrix analysis
• Dynamic programming
• Word or k-tuple methods (later, in Chp 4)

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Dot Matrix Method (Dot Plots)

• Place 1 sequence along top row of matrix
• Place 2nd sequence along left column of matrix
• Plot a dot each time there is a match between an
  element of row sequence and an element of column
  sequence
• For proteins, usually use more sophisticated
  scoring schemes than "identical match"
• Diagonal lines indicate areas of match
• Contiguous diagonal lines reveal alignment
  "breaks" gaps (indels)

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Interpretation of Dot Plots

• When comparing 2 sequences
• Diagonal lines of dots indicate regions of
  similarity between 2 sequences
• Reverse diagonals (perpendicular to diagonal)
  indicate inversions
• What do such patterns mean when comparing a
  sequence with itself (or its reverse complement)?
  
• e.g. Reverse diagonals crossing diagonals (X's)
  indicate palindromes

Exploring Dot Plots
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Dynamic Programming
For Pairwise sequence alignment
Idea Display one sequence above another with
spaces inserted in both to reveal similarity

• C A T - T C A - C
• C - T C G C A G C

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Global Alignment Scoring
CTGTCG-CTGCACG -TGC-CG-TG----
Reward for matches ? Mismatch penalty
? Space/gap penalty ?
Score ?w ?x - ?y
w matches x mismatches y spaces
Note I changed symbols colors on this slide!
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Global Alignment Scoring
Reward for matches 10 Mismatch penalty
-2 Space/gap penalty -5
C T G T C G C T G C - T G C
C G T G -
-5 10 10 -2 -5 -2 -5 -5 10 10 -5
Total 11
Note I changed symbols colors on this slide!
We could have done better!!
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Alignment Algorithms

• Global Needleman-Wunsch
• Local Smith-Waterman
• Both NW and SW use dynamic programming
• Variations
• Gap penalty functions
• Scoring matrices

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Dynamic Programming - Key Idea

• The score of the best possible alignment that
  ends at a given pair of positions (i, j) is equal
  to
• the score of best alignment ending just
  previous to those two positions (i.e., ending at
  i-1, j-1)
• PLUS
• the score for aligning xi and yj

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Global Alignment DP Problem Formulation
Notations

• Given two sequences (strings)
• X x1x2xN of length N x AGC N 3
• Y y1y2yM of length M y AAAC M 4
• Construct a matrix with (N1) x (M1) elements,
  where
• S(i,j) Score of best alignment of
  x1..ix1x2xi with y1..jy1y2yj

Which means Score of best alignment of a prefix
of X and a prefix of Y
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Dynamic Programming - 4 Steps

1. Define score of optimum alignment, using
   recursion
2. Initialize and fill in a DP matrix for storing
   optimal scores of subproblems, by solving
   smallest subproblems first (bottom-up approach)
3. Calculate score of optimum alignment(s)
4. Trace back through matrix to recover optimum
   alignment(s) that generated optimal score

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1- Define Score of Optimum Alignment using
Recursion
Define
Initial conditions
Recursive definition For 1 ? i ? N, 1 ? j ?
M
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2- Initialize Fill in DP Matrix for Storing
Optimal Scores of Subproblems

• Construct sequence vs sequence matrix

Recursion
Initialization
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2- cont Fill in DP Matrix

• Fill in from 0,0 to N,M (row by row),
  calculating best
• possible score for each alignment including
  residues at i,j
• Keep track of dependencies of scores (in a
  pointer matrix).

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3- Calculate Score S(N,M) of Optimum Alignment
- for Global Alignment

• What happens in last step in alignment of x1..i
  to y1..j?
• 1 of 3 cases applies

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Example
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Fill in the matrix
? C T C G C
A G C
0 -5 -10 -15 -20 -25 -30 -35 -40
?
10
5
C
A
T
T
C
A
C
10 for match, -2 for mismatch, -5 for space
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Calculate score of optimum alignment
? C T C G C
A G C
0 -5 -10 -15 -20 -25 -30 -35 -40
-5 10 5 0 -5 -10 -15 -20 -25
-10 5 8 3 -2 -7 0 -5 -10
-15 0 15 10 5 0 -5 -2 -7
-20 -5 10 13 8 3 -2 -7 -4
-25 -10 5 20 15 18 13 8 3
-30 -15 0 15 18 13 28 23 18
-35 -20 -5 10 13 28 23 26 33
10 for match, -2 for mismatch, -5 for space
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4- Trace back through matrix to recover optimum
alignment(s) that generated the optimal score

• How? "Repeat" alignment calculations in reverse
  order, starting at from position with highest
  score and following path, position by position,
  back through matrix
• Result? Optimal alignment(s) of sequences

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Traceback - for Global Alignment

• Start in lower right corner trace back to upper
  left
• Each arrow introduces one character at end of
  sequence alignment
• A horizontal move puts a gap in left sequence
• A vertical move puts a gap in top sequence
• A diagonal move uses one character from each
  sequence

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Traceback to Recover Alignment
? C T C G C
A G C
0 -5 -10 -15 -20 -25 -30 -35 -40
-5 10 5 0 -5 -10 -15 -20 -25
-10 5 8 3 -2 -7 0 -5 -10
-15 0 15 10 5 0 -5 -2 -7
-20 -5 10 13 8 3 -2 -7 -4
-25 -10 5 20 15 18 13 8 3
-30 -15 0 15 18 13 28 23 18
-35 -20 -5 10 13 28 23 26 33
Can have gt1 optimum alignment this example has 2
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Local Alignment Motivation

• To "ignore" stretches of non-coding DNA
• Non-coding regions (if "non-functional") are more
  likely to contain mutations than coding regions
• Local alignment between two protein-encoding
  sequences is likely to be between two exons
• To locate protein domains or motifs
• Proteins with similar structures and/or similar
  functions but from different species (for
  example), often exhibit local sequence
  similarities
• Local sequence similarities may indicate
  functional modules

Non-coding - "not encoding protein" Exons -
"protein-encoding" parts of genes vs Introns
"intervening sequences" - segments of
eukaryotic genes that "interrupt" exons
Introns are transcribed into RNA, but are later
removed by RNA processing are not translated
into protein
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Local Alignment Example
g g t c t g a g a a a c g a
Match 2 Mismatch or space -1
Best local alignment
g g t c t g a g a a a c g a -
Score 5
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Local Alignment Algorithm

• S i, j Score for optimally aligning a suffix
  of X with a suffix of Y
• Initialize top row leftmost column of matrix
  with "0"

• Recall for Global Alignment,
• S i, j Score for optimally aligning a
  prefix of X with a prefix of Y
• Initialize top row leftmost column of with gap
  penalty

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Traceback - for Local Alignment
? C T C G C
A G C
0 0 0 0 0 0 0 0 0
0 1 0 1 0 1 0 0 1
0 0 0 0 0 0 2 0 0
0 0 1 0 0 0 0 1 0
0 0 1 0 0 0 0 0 0
0 1 0 2 0 1 0 0 1
0 0 0 0 1 0 2 0 0
0 1 0 1 0 2 0 1 1
1 for a match, -1 for a mismatch, -5 for a space
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Some Results re Alignment Algorithms (for
ComS, CprE Math types!)

• Most pairwise sequence alignment problems can be
  solved in O(mn) time
• Space requirement can be reduced to O(mn), while
  keeping run-time fixed Myers88
• Highly similar sequences can be aligned in O (dn)
  time, where d measures the distance between the
  sequences Landau86

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"Scoring" or "Substitution" Matrices

• 2 Major types for Amino Acids PAM BLOSUM
• PAM Point Accepted Mutation
• relies on "evolutionary model" based on
  observed differences in alignments of closely
  related proteins
• BLOSUM BLOck SUbstitution Matrix
• based on aa substitutions observed in blocks
  of conserved sequences within evolutionarily
  divergent proteins

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PAM Matrix

• PAM Point Accepted Mutation
• relies on "evolutionary model" based on observed
  differnces in closely related proteins
• Model includes defined rate for each type of
  sequence change
• Suffix number (n) reflects amount of "time"
  passed rate of expected mutation if n of amino
  acids had changed
• PAM1 - for less divergent sequences (shorter
  time)
• PAM250 - for more divergent sequences (longer
  time)

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BLOSUM Matrix

• BLOSUM BLOck SUbstitution Matrix
• based on aa substitutions observed in blocks
  of conserved sequences within evolutionarily
  divergent proteins
• Doesn't rely on a specific evolutionary model
• Suffix number (n) reflects expected similarity
  average aa identity in the MSA from which the
  matrix was generated
• BLOSUM45 - for more divergent sequences
• BLOSUM62 - for less divergent sequences

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Statistical Significance of Sequence Alignment
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Affine Gap Penalty Functions

• Gap penalty h gk
• where
• k length of gap
• h gap opening penalty
• g gap extension penalty

Can also be solved in O(nm) time using dynamic
programming