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Unformatted text preview: 1 3 F 2 2 2 4 2 3 3 3 3 3 1 3 3 0 0 0 1 6 3 Y 2 2 2 3 2 3 2 3 2 1 2 2 2 1 1 1 1 3 7 2 W 2 3 3 4 3 2 4 4 3 2 2 3 3 1 3 2 3 1 2 11 1 Patterns on DotPlot Internal Repeat Inser<on (Dele<on) Divergence 6 1/28/14 Patterns on DotPlot Sequence 1 Sequence 2 Patterns on DotPlot With many details! Overall view  no details! What is sequence alignment? Given two sequences of letters and a scoring scheme for evaluating
letter matching, find the optimal pairing of letters from one
sequence to the other. 7 1/28/14 Ungapped Alignment (From Biochemistry, Stryer, ﬁ=h edi6on) Alignment with gap(s) How do we generate the “best” gapped alignment ?
min( N , M ) Total number of possible gapped alignment: ∑
k =1 " N %" M %
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# k &# k & € Sequence Analysis
1. Why do we compare sequences?
2. Sequence comparison: from qualitative to quantitative methods
3. Deterministic methods: Dynamic programming
1. Concept
2. Global Alignment
3. Statistics
4. Local Alignment
4. Heuristics: BLAST
5. Multiple Sequence Alignment 8 1/28/14 DP and Sequence Alignment Key idea: The score of the optimal alignment that ends at a given
pair of positions in the sequences is the score of the best
alignment previous to these positions plus the score of
aligning these two positions. DP and Sequence Alignment
Test all alignments that can lead to i aligned with j
i ?
j DP and Sequence Alignment
Test all alignments that can lead to i aligned with j
i ?
j 3 possibilities:
1) i 1 aligned with j 1 i1 j1 i j 9 1/28/14 DP and Sequence Alignment
Test all alignments that can lead to i aligned with j
i ?
j 3 possibilities:
1) i 1 aligned with j 1 i1 j1 2) i 1 aligned with k, 1≤k ≤j 2 i i1 i k j j > Choose alignment yielding best score DP and Sequence Alignment
Test all alignments that can lead to i aligned with j
i ?
j 3 possibilities:
1) i 1 aligned with j 1 i1 j1 2) i 1 aligned with k, 1≤k ≤j 2 i j i1 k 3) j 1 aligned with l, 1≤l ≤i 2 i l i j j1 j > Choose alignment yielding best score Implementing the DP algorithm for sequences
Aligning 2 sequence S1 and S2 of lengths N and M:
1) Build a NxM alignment matrix A such that
A(i,j) is the optimal score for alignments
up to the pair (i,j)
2) Find the best score in A
3) Track back through the matrix to get
the optimal alignment of S1 and S2. 10 1/28/14 Example
Sequence 1: AWVCDEC
Sequence 2: AWEC
Score(i,j) = 10 if i=j, 0 otherwise
no gap penalty Example
1) Initialize
A W V C D E C A 10 0 0 0 0 0 0 W 0 E 0 C 0 Example
2) Propagate
A W V C D E C A 10 0 0 0 0 0 0 W 0 20 E 0 C 0 11 1/28/14 Example
2) Propagate
A W V C D E C A 10 0 0 0 0 0 0 W 0 20 10 E 0 C 0 Example
2) Propagate
A W V C D E C A 10 0 0 0 0 0 0 W 0 20 10 10 10 10 10 E 0 10 20 20 20 30 20 C 0 10 20 30 20 Example
3) Trace back
A W V C D E C A 10 0 0 0 0 0 0 W 0 20 10 10 10 10 10 E 0 10 20 20 20 30 20 C 0 10 20 30 20 20 40 Alignment: AWVCDEC
AWEC Total score: 40 12 1/28/14 Example 2 A A T G C A 10 10 0 0 0 G 0 10 10 20 10 G 0 10 10 20 20 C 0 10 10 10 30 High Score: 30 Alignments:
AATGC
AG GC AATGC
A GGC AATGC
AGGC AATG C
A GGC AATG C
A GGC Example 2 with Gap Gap cost: 2
A A T G C A 10 8 2 2 2 G 2 10 8 18 8 G 2 8 10 18 16 C 2 8 8 10 28 High Score: 28 Alignments:
AATGC
AG GC AATGC...
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This document was uploaded on 03/12/2014 for the course CSCI 129 at UC Davis.
 Winter '14
 PatriceKoehl
 C Programming

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