1. #7 Still more DP, Scoring Matrices
BCB 444/544
9/5/07
Lecture 7
Still more: Dynamic Programming
Global vs Local Alignment
Scoring Matrices & Alignment Statistics
BLAST nope
#7_Sept5
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

2. Required Reading (before lecture)
#7 Still more DP, Scoring Matrices
Required Reading (before lecture)
9/5/07
√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
Chp 4 - pp 51-62
Fri Sept - for Lecture 8
BLAST variations; BLAST vs FASTA
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

3. Assignments & Announcements
#7 Still more DP, Scoring Matrices
Assignments & Announcements
9/5/07
√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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

4. Chp 3- Sequence Alignment
#7 Still more DP, Scoring Matrices
9/5/07
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.
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

5. #7 Still more DP, Scoring Matrices
Methods
9/5/07
√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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

6. Global vs Local Alignment
#7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

7. Global vs Local Alignment - example
#7 Still more DP, Scoring Matrices
9/5/07
Global vs Local Alignment - example
1 = CTGTCGCTGCACG
2 = TGCCGTG
CTGTCGCTGCACG
-TGCCG-T----G
Global alignment
-TG-C-C-G--TG
CTGTCGCTGCACG
-TGCCG-TG----
Local alignment
Which is better?
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

8. Global vs Local Alignment Which should be used when?
#7 Still more DP, Scoring Matrices
9/5/07
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!
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

9. Global vs Local Alignment Which should be used when?
#7 Still more DP, Scoring Matrices
9/5/07
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? Local
Aligning two closely related sequences with similar lengths? Global
Aligning highly divergent sequences? Local (at least initially)
Generating an extended alignment of closely related sequences? Global
Generating an extended alignment of closely related sequences with very different lengths? Hmmm - we'll work on that
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

10. #7 Still more DP, Scoring Matrices
9/5/07
Alignment Algorithms
3 major methods for pairwise sequence alignment:
Dot matrix analysis √ - practice in HW2
Dynamic programming - more today & in HW2
Word or k-tuple methods (later, in Chp 4)
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

11. #7 Still more DP, Scoring Matrices
Dynamic Programming
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

12. Global Alignment: Scoring
#7 Still more DP, Scoring Matrices
Global Alignment: Scoring
9/5/07
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!
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

13. Global Alignment: Scoring
#7 Still more DP, Scoring Matrices
9/5/07
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 -
Total = 11
Note: I changed symbols & colors on this slide!
We could have done better!!
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

14. #7 Still more DP, Scoring Matrices
Alignment Algorithms
9/5/07
Global: Needleman-Wunsch
Local: Smith-Waterman
Both NW and SW use dynamic programming
Variations:
Gap penalty functions
Scoring matrices
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

15. Dynamic Programming - Key Idea:
#7 Still more DP, Scoring Matrices
Dynamic Programming - Key Idea:
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

16. Global Alignment: DP Problem Formulation & Notations
#7 Still more DP, Scoring Matrices
Global Alignment: DP Problem Formulation & Notations
9/5/07
Given two sequences (strings)
X = x1x2…xN of length N x = AGC N = 3
Y = y1y2…yM of length M y = AAAC M = 4
Construct a matrix with (N+1) x (M+1) elements, where
S(i,j) = Score of best alignment of x[1..i]=x1x2…xi with y[1..j]=y1y2…yj
S(2,3) = score of best alignment
of AG (x1x2) to AAA (y1y2y3) x1 x2 x3 y1 y2 y3 y4
Which means:
S(i,j) = Score of best alignment of
a prefix of X and a prefix of Y
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

17. Dynamic Programming - 4 Steps:
#7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

18. 1- Define Score of Optimal Alignment using Recursion
#7 Still more DP, Scoring Matrices
1- Define Score of Optimal Alignment using Recursion
9/5/07
Define:
Initial conditions:
 = Match Reward
= Mismatch Penalty
 = Gap penalty
Recursive definition:
For 1  i  N, 1  j  M:
(xi,yj) =  or 
 = Gap penalty
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

19. #7 Still more DP, Scoring Matrices
9/5/07
2- Initialize & Fill in DP Matrix for Storing Optimal Scores ofSubproblems
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

20. #7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

21. #7 Still more DP, Scoring Matrices
9/5/07
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 C
Mismatch Penalty
j - 1 j
Case 2: Line up xi with space
i - 1 i
x: C A T T C A - C
y: C - T T C A G -
Space Penalty j
Case 3: Line up yj with space i
x: C A T T C A C -
y: C - T T C A - G
Space Penalty
j -1 j
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

22. #7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

23. #7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

24. 3- Calculate Score S(N,M) of Optimal Alignment - for Global Alignment
#7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

25. #7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

26. Traceback - for Global Alignment
#7 Still more DP, Scoring Matrices
Traceback - for Global Alignment
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

27. Traceback to Recover Alignment
#7 Still more DP, Scoring Matrices
Traceback to Recover Alignment
9/5/07
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 d v 1 d h d d h d h 2
Can have >1 optimal alignment; this example has 2
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

28. What are the 2 Global Alignments with Optimal Score = 33?
#7 Still more DP, Scoring Matrices
9/5/07
What are the 2 Global Alignments with Optimal Score = 33?
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:
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

29. Local Alignment: Motivation
#7 Still more DP, Scoring Matrices
Local Alignment: Motivation
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

30. Local Alignment: Example
#7 Still more DP, Scoring Matrices
Local Alignment: Example
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

31. Local Alignment: Algorithm
#7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

32. Traceback - for Local Alignment
#7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

33. What are the 4 Local Alignments with Optimal Score = 2?
#7 Still more DP, Scoring Matrices
9/5/07
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:
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

34. Some Results re: Alignment Algorithms (for ComS, CprE & Math types!)
#7 Still more DP, Scoring Matrices
9/5/07
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]
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

35. Affine Gap Penalty Functions
#7 Still more DP, Scoring Matrices
Affine Gap Penalty Functions
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

36. #7 Still more DP, Scoring Matrices
Methods
9/5/07
√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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

37. "Scoring" or "Substitution" Matrices
#7 Still more DP, Scoring Matrices
9/5/07
"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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

38. #7 Still more DP, Scoring Matrices
9/5/07
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)
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

39. #7 Still more DP, Scoring Matrices
9/5/07
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
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs

40. BLOSUM62 Substitution Matrix
#7 Still more DP, Scoring Matrices
BLOSUM62 Substitution Matrix
9/5/07
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)
BCB 444/544 F07 ISU Dobbs #7 - Still more DP, Scoring Matrices
BCB 444/544 Fall 07 Dobbs