1. #8 Finish DP, Scoring Matrices, Stats & BLAST
BCB 444/544
9/7/07
Lecture 8
Finish: Dynamic Programming
Global vs Local Alignment
Scoring Matrices & Alignment Statistics
BLAST
#8_Sept7
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2. Required Reading (before lecture)
#8 Finish DP, Scoring Matrices, Stats & BLAST
Required Reading (before lecture)
9/7/07
√Last week: - for Lectures 4-7
Pairwise Sequence Alignment, Dynamic Programming,
Global vs Local Alignment, Scoring Matrices, Statistics
Xiong: Chp 3
Eddy: What is Dynamic Programming? 2004 Nature Biotechnol 22:909
√Wed Sept 5 - for Lecture 7 & Lab 3
Database Similarity Searching: BLAST (nope, more DP)
Chp 4 - pp 51-62
Fri Sept - for Lecture 8 (will finish on Monday)
BLAST variations; BLAST vs FASTA
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3. Assignments & Announcements
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Assignments & Announcements
9/7/07
√Tues Sept 4 - Lab #2 Exercise Writeup due by 5 PM Send via to Pete Zaback
(For now, no late penalty - just send ASAP)
√Wed Sept 5 - Notes for Lecture 5 posted online
- HW#2 posted online & sent via
& handed out in class
Fri Sept HW#2 Due by 5 PM
Fri Sept Exam #1
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4. Chp 3- Sequence Alignment
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9/7/07
Chp 3- Sequence Alignment
SECTION II SEQUENCE ALIGNMENT
Xiong: Chp 3
Pairwise Sequence Alignment
√Evolutionary Basis
√Sequence Homology versus Sequence Similarity
√Sequence 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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5. #8 Finish DP, Scoring Matrices, Stats & BLAST
Methods
9/7/07
√Global and Local Alignment
√Alignment Algorithms
√Dot 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
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6. Dynamic Programming - 4 Steps:
#8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
Dynamic Programming - 4 Steps:
Define score of optimal alignment, using recursion
Initialize and fill in a DP matrix for storing optimal scores of subproblems, by solving smallest subproblems first (bottom-up approach)
Calculate score of optimal alignment(s)
Trace back through matrix to recover optimal alignment(s) that generated optimal score
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7. 1- Define Score of Optimal Alignment using Recursion
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1- Define Score of Optimal Alignment using Recursion
9/7/07
Define:
Initial conditions:
 = Match Reward
= Mismatch Penalty
 = Gap penalty
Recursive definition:
For 1  i  N, 1  j  M:
(xi,yj) =  or 
 = Gap penalty
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8. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
2- Initialize & Fill in DP Matrix for Storing Optimal Scores of Subproblems
Construct sequence vs sequence matrix
Fill in from [0,0] to [N,M] (row by row), calculating best
possible score for each alignment ending at residues at [i,j] 1 N
S(0,0)=0 1
S(i,j)
S(N,M) M
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9. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
How do we calculate S(i,j)? i.e., Score for alignment of x[1..i] to y[1..j]?
1 of 3 cases  optimal score for this subproblem:
x1 x xi-1 xi
y1 y yj-1 yj
S(i-1,j-1) + (xi,yj)
x1 x xi-1 xi
y1 y yj —
S(i-1,j) 
x1 x xi —
S(i,j-1) 
xi aligns to yj
xi aligns to a gap
yj aligns to a gap
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10. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
Specific Example:
Note: I changed sequences on this slide (to match the rest of DP example)
Scoring Consequence?
Case 1: Line up xi with yj
i - 1 i
x: C - T C G C A
y: C A T - T C A
Match Bonus
j - 1 j
Case 2: Line up xi with space
i - 1 i
x: C - T C G C - A
y: C A T - T C A -
Space Penalty j
Case 3: Line up yj with space i
x: C - T C G C A -
y: C A T - T C - A
Space Penalty
j -1 j
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11. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
Ready? Fill in DP Matrix
Keep track of dependencies of scores (in a pointer matrix) 1 N
S(0,0)=0
+ (xi,yj) =  or  1
S(i-1,j-1)
S(i-1,j)
 = Match Reward
= Mismatch Penalty
 = Gap penalty
- 
S(i,j-1)
S(i,j)
- 
S(N,M) M
Initialization
Recursion
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12. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
Fill in the DP matrix !!
λ C T C G C A G C λ C -5
-10
-15
-20
-25
-30
-35 10 5 A T T C
We first compute T[i, j] for the smallest possible values of i and j, then for increasing values of i and j
Usually performed with a table of size
(n + 1) X (m + 1) A C
+10 for match, -2 for mismatch, -5 for space
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13. 3- Calculate Score S(N,M) of Optimal Alignment - for Global Alignment
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3- Calculate Score S(N,M) of Optimal Alignment - for Global Alignment
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
We first compute T[i, j] for the smallest possible values of i and j, then for increasing values of i and j
Usually performed with a table of size
(n + 1) X (m + 1)
+10 for match, -2 for mismatch, -5 for space
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14. 3- Calculate Score S(N,M) of Optimal Alignment - for Global Alignment
#8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
3- Calculate Score S(N,M) of Optimal Alignment - for Global Alignment
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
We first compute T[i, j] for the smallest possible values of i and j, then for increasing values of i and j
Usually performed with a table of size
(n + 1) X (m + 1)
+10 for match, -2 for mismatch, -5 for space
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15. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
4- Trace back through matrix to recover optimal 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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16. Traceback - for Global Alignment
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Traceback - for Global Alignment
9/7/07
Start in lower right corner & trace back to upper left
Each arrow introduces one character at end of 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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17. Traceback to Recover Alignment
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Traceback to Recover Alignment
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
Can have >1 optimal alignment; this example has 2
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18. Traceback to Recover Alignment
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Traceback to Recover Alignment
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
Where did red arrows come from?
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19. Traceback to Recover Alignment
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Traceback to Recover Alignment
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
+10 for match, -2 for mismatch, -5 for space
Where did 33 come from? Match = 10, so 33-10= 23
Must have come from diagonal
Where did 23 come from? (Not a match)
Left? 28-5= 23; Diag? 13-2= 11; Top? 8-5= 3
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20. Traceback to Recover Alignment
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Traceback to Recover Alignment
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
+10 for match, -2 for mismatch, -5 for space
Where did 8 come from?
Two possibilities: = 8 or 10-2=8
Then, follow both paths
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21. Traceback to Recover Alignment
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Traceback to Recover Alignment
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
C with C
- with A
T with T
C with -
G with T
C with C
A with A
G with -
C with C
Great - but what are the alignments? #1
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22. Traceback to Recover Alignment
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Traceback to Recover Alignment
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33
C with C
- with A
T with T
C with T
G with -
C with C
A with A
G with -
C with C
Great - but what are the alignments? #2
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23. What are the 2 Global Alignments with Optimal Score = 33?
#8 Finish DP, Scoring Matrices, Stats & BLAST
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What are the 2 Global Alignments with Optimal Score = 33?
Top: C T C G C A G C
Left: C A T T C A C
C T C G C A G C 1:
C T C G C A G C 2:
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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24. What are the 2 Global Alignments with Optimal Score = 33?
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What are the 2 Global Alignments with Optimal Score = 33?
Top: C T C G C A G C
Left: C A T T C A C
C T C G C A G C
C A T T C A C 1:
C T C G C A G C
C A T T C A C 2:
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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25. #8 Finish DP, Scoring Matrices, Stats & BLAST
Check Traceback?
9/7/07
λ C T C G C A G C C A T λ -5
-10
-15
-20
-25
-30
-35
-40 10 5 8 3 -2 -7 15 13 -4 20 18 28 23 26 33 v d 1 d h d h 2 d h
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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26. Local Alignment: Motivation
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Local Alignment: Motivation
9/7/07
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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27. Local Alignment: Example
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Local Alignment: Example
9/7/07
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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28. Local Alignment: Algorithm
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9/7/07
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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29. Filling in DP Matrix for Local Alignment
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Filling in DP Matrix for Local Alignment
λ C T C G C A G C A C T λ 1 2
+1 for a match, -1 for a mismatch, -5 for a space
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30. Traceback - for Local Alignment
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9/7/07
Traceback - for Local Alignment
λ C T C G C A G C A C T λ 1 2
+1 for a match, -1 for a mismatch, -5 for a space
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31. What are the 4 Local Alignments with Optimal Score = 2?
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What are the 4 Local Alignments with Optimal Score = 2?
C T C G C A G C
C A T T C A C
C T C G C A G C 1:
C T C G C A G C 2:
C T C G C A G C 3:
C T C G C A G C 4:
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32. Some Results re: Alignment Algorithms (for ComS, CprE & Math types!)
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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(m+n), 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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33. Affine Gap Penalty Functions
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Affine Gap Penalty Functions
9/7/07
Affine Gap Penalties = Differential Gap Penalties used to reflect cost differences between opening a gap and extending an existing gap
Total Gap Penalty is linear function of gap length:
W =   X (k - 1)
where  = gap opening penalty
 = gap extension penalty
k = length of gap
Sometimes, a Constant Gap Penalty is used, but it is usually least realistic than the Affine Gap Penalty
Can also be solved in
O(nm) time using DP
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34. #8 Finish DP, Scoring Matrices, Stats & BLAST
Methods
9/7/07
√Global and Local Alignment
√Alignment Algorithms
√Dot 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
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35. "Scoring" or "Substitution" Matrices
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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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36. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
PAM Matrix
PAM = Point Accepted Mutation
relies on "evolutionary model" based on observed differences 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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37. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
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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38. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
PAM250 vs BLOSUM 62
See Text
Fig 3.5 = PAM250
Fig 3.6= BLOSUM62
Usually only 1/2 of matrix is displayed (it is symmetric)
Here:
s(a,b) corresponds to score of aligning character a with character b
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39. Which is Better? PAM or BLOSUM
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9/7/07
Which is Better? PAM or BLOSUM
PAM matrices
derived from evolutionary model
often used in reconstructing phylogenetic trees - but, not very good for highly divergent sequences
BLOSUM matrices
based on direct observations
more 'realistic" - and outperform PAM matrices in terms of accuracy in local alignment
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40. Which Type of Matrix Should You Use?
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9/7/07
Which Type of Matrix Should You Use?
Several other types of matrices available:
Gonnet & Jones-Taylor-Thornton:
very robust in tree construction
"Best" matrix depends on task:
different matrices for different applications
ADVICE: if unsure, try several different matrices & choose the one that gives best alignment result
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41. Sequence Alignment Statistics
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Sequence Alignment Statistics
9/7/07
Distribution of similarity scores in sequence alignment is not a simple "normal" distribution
"Gumble extreme value distribution" - a highly skewed normal distribution with a long tail
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42. How Assess Statistical Significance of an Alignment?
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How Assess Statistical Significance of an Alignment?
9/7/07
Compare score of an alignment with distribution of scores of alignments for many 'randomized' (shuffled) versions of the original sequence
If score is in extreme margin, then unlikely due to random chance
P-value = probability that original alignment is due to random chance (lower P is better)
P = sequences have clear homology
P > no better than random
Check out: PRSS (Probability of Random Shuffles)
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43. Chp 4- Database Similarity Searching
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9/7/07
Chp 4- Database Similarity Searching
SECTION II SEQUENCE ALIGNMENT
Xiong: Chp 4
Database Similarity Searching
Unique Requirements of Database Searching
Heuristic Database Searching
Basic Local Alignment Search Tool (BLAST)
FASTA
Comparison of FASTA and BLAST
Database Searching with Smith-Waterman Method
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44. Exhaustive vs Heuristic Methods
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Exhaustive vs Heuristic Methods
Exhaustive - tests every possible solution
guaranteed to give best answer
(identifies optimal solution)
can be very time/space intensive!
e.g., Dynamic Programming
as in Smith-Waterman algorithm
Heuristic - does NOT test every possibility
no guarantee that answer is best
(but, often can identify optimal solution)
sacrifices accuracy (potentially) for speed
uses "rules of thumb" or "shortcuts"
e.g., BLAST & FASTA
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45. Today's Lab: focus on BLAST Basic Local Alignment Search Tool
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9/7/07
Today's Lab: focus on BLAST Basic Local Alignment Search Tool
STEPS:
Create list of very possible "word" (e.g., 3-11 letters) from query sequence
Search database to identify sequences that contain matching words
Score match of word with sequence, using a substitution matrix
Extend match (seed) in both directions, while calculating alignment score at each step
Continue extension until score drops below a threshold (due to mismatches)
Contiguous aligned segment pair (no gaps) is called:
High Scoring Segment Pair (HSP)
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46. Lab3: focus on BLAST Basic Local Alignment Search Tool
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9/7/07
Lab3: focus on BLAST Basic Local Alignment Search Tool
BLAST Results?
Original version of BLAST?
List of HSPs = Maximum Scoring Pairs
More recent, improved version of BLAST?
Allows gaps: Gapped Alignment
How? Allows score to drop below threshold,
(but only temporarily)
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47. #8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
BLAST - a few details
Developed by Stephen Aultschul at NCBI in 1990
Word length?
Typically: 3 aa for protein sequence
11 nt for DNA sequence
Substitution matrix?
Default is BLOSUM62
Can change under Algorithm Parameters
Choose other BLOSUM or PAM matrices
Stop-Extension Threshold?
Typically: for proteins
20 for DNA
BCB 444/544 F07 ISU Dobbs #8 - Finish DP, Scoring Matrices, Stats & BLAST
BCB 444/544 Fall 07 Dobbs

48. BLAST - Statistical Significance?
#8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
BLAST - Statistical Significance?
E-value: E = m x n x P
m = total number of residues in database
n = number of residues in query sequence
P = probability that an HSP is result of random chance
lower E-value, less likely to result from random change, thus higher significance
Bit Score: S'
normalized score, to account for differences in sequence length & size of database
3. Low Complexity Masking
remove repeats that confound scoring
BCB 444/544 F07 ISU Dobbs #8 - Finish DP, Scoring Matrices, Stats & BLAST
BCB 444/544 Fall 07 Dobbs

49. BLAST - a Family of Programs: Several different BLAST "flavors"
#8 Finish DP, Scoring Matrices, Stats & BLAST
9/7/07
BLAST - a Family of Programs: Several different BLAST "flavors"
BLASTN -
BLASTP -
BLASTX -
TBLASTN -
BCB 444/544 F07 ISU Dobbs #8 - Finish DP, Scoring Matrices, Stats & BLAST
BCB 444/544 Fall 07 Dobbs