1. Lecture 14 Algorithm Analysis
Arne Kutzner
Hanyang University / Seoul Korea

2. Sequence Alignments

3. Sequence Alignment Problem
Given two sequences a, b over some alphabet Σ.
Problem: Find some scheme so that a and b fit together. Example: a = GATTACATAAGTTTT b = GCATGCUTGCTCTT Possible alignment:
mismatch G - A T T A C A T A A G - T T T T G C A T G - C U T - - G C T C T T
gap
match
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Algorithm Analysis

4. Instances of the Alignment Problem
Global Alignment = end-to-end alignment
Local Alignment = best subsection alignment
Example: Align FTALLLAAV to FTFTALILLAVAV:
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Algorithm Analysis

5. Needleman-Wunsch Algorithm
For global alignments
Input:
Two strings a and b over some alphabet Σ
Scoring system, that defines
bonus and penalty for matches and mismatches
penalty for inserting a gap comprising one symbol into a
penalty for inserting a gap comprising one symbol into b (this is equal to the deletion of one symbol in a)
Technique used by algorithm: Dynamic programming on the foundation of matrix computation
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Algorithm Analysis

6. Matrix Initializationb
Initialize with d * i (d * j), where d is the gap penalty -1 -2 -3 -1 -2 -3 a
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Algorithm Analysis

7. Compute Cell Values T A T T Match (+1) Mismatch (-1)
𝐹 𝑖−1,𝑗−1 3
𝐹 𝑖−1,𝑗 2
𝐹 𝑖−1,𝑗−1 3
𝐹 𝑖−1,𝑗 2
𝐹 𝑖−1,𝑗−1 3
𝐹 𝑖−1,𝑗 2
𝐹 𝑖−1,𝑗−1 3
𝐹 𝑖−1,𝑗 2
𝐹 𝑖,𝑗−1 1
𝐹 𝑖,𝑗 4
𝐹 𝑖,𝑗−1 1
𝐹 𝑖,𝑗 2
𝐹 𝑖,𝑗−1 1
𝐹 𝑖,𝑗 1
𝐹 𝑖,𝑗−1 1
𝐹 𝑖,𝑗 T T
Match (+1)
Mismatch (-1)
Delete (gap in b) (-1)
Insert (gap in a) (-1)
Take the maximum of these values as value of 𝐹 𝑖,𝑗 and store the direction of the blue arrow
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Algorithm Analysis

8. Pseudocode for Matrix Computation
NW-Matrix(A, B, S, d, F)
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Algorithm Analysis

9. Example
match
mismatch
insertion
deletion
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Algorithm Analysis

10. Alignment Computation on the Foundation of the Matrix
Start at the bottom cell in the rightmost column and follow the arrows, until you reach the leftmost column or the topmost row.
Situation can be ambiguous, so we can have more than one best match.
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Algorithm Analysis

11. Pseudocode for Alignment Computation
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Algorithm Analysis

12. Example (cont.) G - A T T A C A G C A T G - C U G - A T T A C A G C A
insertion
mismatch
deletion
mismatch G - A T T A C A G C A T - G C U G - A T T A C A G C A - T G C U
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Algorithm Analysis

13. Complexity Analysis Let m=length(a) and n=length(b)
Matrix computation: θ(𝑚∗𝑛)
Alignment Computation: O(max{𝑚,𝑛})
Together: θ(𝒎∗𝒏)
Practically quite expensive with respect to time as well as space.
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Algorithm Analysis

14. Similarity Matrix
Static values for match and mismatch can be replaced by a similarity matrix:
Example:
In the field of Bio-IT exist several predefined similarity matrices for amino acids:
BLOSUM (BLOcks SUbstitution Matrix)
PAM (Point Accepted Mutation )
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Algorithm Analysis

15. Smith-Waterman Algorithm
For local alignments
Input:
Two strings a and b over some alphabet Σ
Similarity scoring scheme 𝒔 𝒂 𝒊 , 𝒃 𝒋 over the alphabet Σ
𝑾 𝒊 gap-scoring scheme
Ouput:
Scoring Matrix 𝑯
Variation of Needleman-Wunsch Algorithm, so that the NW-Alg. works for local alignments.
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Algorithm Analysis

16. = differences to NW-Alg.
Matrix Computation
The matrix H is build as follows:
where: m is the length of a, and n is the length of b
= differences to NW-Alg.
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Algorithm Analysis

17. Computation of alignments
Backtracking like in the NW-Alg., but with significant difference: Search the cell with the highest score and start over there H
backtracking area
cell with highest score
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Algorithm Analysis

18. Complexity Analysis Same story like for Needleman-Wunsch Alg.:
Let m=length(a) and n=length(b)
Matrix computation: θ(𝑚∗𝑛)
Backtracking (Alignment Computation): O(max{𝑚,𝑛})
Together: θ(𝒎∗𝒏)
Practically quite expensive with respect to time as well as space.
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Algorithm Analysis

19. How to overcome the demanding space-time requirements of NW-Alg
How to overcome the demanding space-time requirements of NW-Alg. and SW-Alg.?
Many solutions … Long story…
Heuristic Approaches:
BLAST (One of the standard tools for sequence alignment nowadays)
BLAT fast but considerably less sensitive than BLAST
BWT-based approaches as e.g. Bowtie or BWA
Many of the above tools/algorithms rely on some form of seeding before starting the core alignment
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Algorithm Analysis

20. Seeding technique
Step 1: Somehow “digest” (break into smaller pieces) sequence b (let us call it query sequence).
Step 2 (seeding): Align these short segments quickly using some form of precomputed dictionary the comprises data for sequence a (let us call a the reference sequence)
Step 3: Take the output of step 2 in order to limit the search space for further alignment activities
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Algorithm Analysis

21. Example: Local alignment by seeding
query sequence
1. digest 1 2 3 4 5
(seeding)
2. align
reference sequence 1 2 4 5 6 3
3. compute area of interest
area of interest
section of reference
query sequence
4. cut and SW align
local alignment
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Algorithm Analysis

22. Efficient seeding technique
Suffix array: Contains the starting positions of suffixes of a string in lexicographical order Example: word banana$
sort
as array
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Algorithm Analysis

23. Search a suffix area … Where is an in banana$? 2016/11
Algorithm Analysis

24. How to search suffix arrays efficiently?
FM-Index:
Makes use of Burrows-Wheeler transform (BWT)
Stores precomputed symbol counts in a tabular form (occurrence table)
Foundation of the aligner Bowtie and BWA
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Algorithm Analysis

25. ITBE working group at Hanyang University
Projects in the joint field of Information Technology (Computer Science) and Microbiology (Genetics)
Analysis of genes/gene families by using/combining available computational tools
Development of special tailored solutions/algorithms for specific kinds of problems
Example (big data analysis): Taxonomic heat diagrams that show the expression/occurrence of some gene with respect to some given taxonomy
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Algorithm Analysis

26. Heat diagram for Gene FAM72
Example
Example
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Algorithm Analysis