BCB 444544 F07 ISU Dobbs

1
BCB 444/544

• Lecture 8
• Finish Dynamic Programming
• Global vs Local Alignment
• Scoring Matrices Alignment Statistics
• BLAST
• 8_Sept7

2
Required Reading (before lecture)

• vLast 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 22909
• http//www.nature.com/nbt/journal/v22/n7/abs/nbt
  0704-909.html
• vWed 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
• Chp 4 - pp 51-62

3
Assignments Announcements

• vTues Sept 4 - Lab 2 Exercise Writeup due by 5
  PM Send via email to Pete Zaback
  petez_at_iastate.edu
• (For now, no late penalty - just send ASAP)
• vWed Sept 5 - Notes for Lecture 5 posted online
• - HW2 posted online sent via email
• handed out in class
• Fri Sept 14 - HW2 Due by 5 PM
• Fri Sept 21 - Exam 1

4
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.
5
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
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

7
1- Define Score of Optimal Alignment using
Recursion
Define

• ? Match Reward
• Mismatch Penalty
• ? Gap penalty

Recursive definition For 1 ? i ? N, 1 ? j ?
M
?(xi,yj) ? or ?
? Gap penalty
8
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

0
1
N
0
S(0,0)0
1
S(i,j)
S(N,M)
M
9
How do we calculate S(i,j)? i.e., Score for
alignment of x1..i to y1..j?

• 1 of 3 cases ? optimal score for this subproblem

10
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
11
Ready? Fill in DP Matrix
Keep track of dependencies of scores (in a
pointer matrix)
0
1
N
0
S(0,0)0
1
S(i-1,j)
S(i-1,j-1)

• ? Match Reward
• Mismatch Penalty
• ? Gap penalty

S(i,j-1)
S(i,j)
S(N,M)
M
12
Fill in the DP matrix !!
? C T C G C
A G C
0 -5 -10 -15 -20 -25 -30 -35 -40
?
C
10
5
A
T
T
C
A
C
10 for match, -2 for mismatch, -5 for space
13
3- Calculate Score S(N,M) of Optimal Alignment -
for Global Alignment
? C T C G C
A G C
10 for match, -2 for mismatch, -5 for space
14
3- Calculate Score S(N,M) of Optimal Alignment -
for Global Alignment
? C T C G C
A G C
10 for match, -2 for mismatch, -5 for space
15
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

16
Traceback - for Global Alignment

• 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

17
Traceback to Recover Alignment
? C T C G C
A G C
Can have 1 optimal alignment this example has 2
18
Traceback to Recover Alignment
? C T C G C
A G C
Where did red arrows come from?
19
Traceback to Recover Alignment
? C T C G C
A G C
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

20
Traceback to Recover Alignment
? C T C G C
A G C
10 for match, -2 for mismatch, -5 for space

• Where did 8 come from?
• Two possibilities 13-5 8 or 10-28
  
• Then, follow both paths

21
Traceback to Recover Alignment
? C T C G C
A G C
C with C
- with A
T with T
C with -
G with T
C with C
G with -
A with A
C with C
Great - but what are the alignments? 1
22
Traceback to Recover Alignment
? C T C G C
A G C
C with C
- with A
T with T
C with T
C with C
G with -
G with -
A with A
C with C
Great - but what are the alignments? 2
23
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
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

24
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
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

25
Check Traceback?
? C T C G C
A G C

• 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

26
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
27
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
28
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

29
Filling in DP Matrix for Local Alignment
? C T C G C
A G C
1 for a match, -1 for a mismatch, -5 for a space
30
Traceback - for Local Alignment
? C T C G C
A G C
1 for a match, -1 for a mismatch, -5 for a space
31
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
32
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

33
Affine Gap Penalty Functions

• 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
34
Methods

• vGlobal and Local Alignment
• vAlignment Algorithms
• vDot Matrix Method
• vDynamic 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

35
"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

36
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)

37
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

38
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

39
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

40
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

41
Sequence Alignment Statistics

• 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

42
How Assess Statistical Significance of an
Alignment?

• 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 10-5 - 10-50 sequences have clear homology
• P 10-1 no better than random

Check out PRSS (Probability of Random
Shuffles) http//www.ch.embnet.org/software/PRSS_f
orm.html
43
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

44
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

45
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)

46
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)

47
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 22 for proteins
• 20 for DNA

48
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

49
BLAST - a Family of Programs Several different
BLAST "flavors"

• BLASTN -
• BLASTP -
• BLASTX -
• TBLASTN -
• TBLASTN -