Gene Prediction: Similarity-Based Approaches Spliced Alignment

Transcription

1 Gene Prediction: Similarity-Based Approaches Spliced Alignment

2 Gene Prediction introns S exon exon exon he predicted gene November 15 2

3 Outline of Agenda he idea of similarity-based approach to gene prediction Previous Lecture: Exon Chaining Problem (2D Interval Chaining) his Lecture: Spliced Alignment Problem

4 Problem with 2D chaining Sometimes we know the exact chaining (gene sequence) in one of the two sequences would like to utilize this information better.

5 Using Known Genes to Predict New Genes Some genomes may be very well-studied, with many genes having been experimentally verified. Closely-related organisms may have similar genes Unknown genes in one species may be compared to genes in some closely-related species

6 Similarity-Based Approach to Gene Prediction he similarity-based approach uses known genes in one genome to predict (unknown) genes in another genome Problem: Given a known gene sequence and an (unannotated) genomic sequence S, find a set of non overlapping substrings S* of the genomic sequence S whose concatenation yields the highest similarity to (where similarity is measured in terms of an alignment score).

7 Gene Prediction Analogy: Selecting Putative Exons he cell carries DNA as a blueprint for producing proteins, like a manufacturer carries a blueprint for producing a car.

8 Assembling Candidate Exons

9 Using Blueprint

10 Assembling Candidate Exons Guided by known gene sequence

11 Similarity-Based Approach to Gene Prediction he similarity-based approach uses known genes in one genome to predict (unknown) genes in another genome Problem: Given a known gene sequence and an (unannotated) genomic sequence S, find a set of non overlapping substrings S* of the genomic sequence S whose concatenation yields the highest similarity to (where similarity is measured in terms of an alignment score).

12 Spliced Alignment Problem: Formulation Goal: Find a chain of blocks in a genomic sequence that best fits a target sequence Input: Genomic sequences S of size n, target sequence, and a set of candidate exons B. Output: A chain of non overlapping exons S* such that the global alignment score between S* and is maximum among all chains of blocks from B.

13 Gene Prediction Via Spliced Alignment Gelfand, Mironov and Pevzner (96) O(nb + nk) time complexity - n is the length of S - k is the number of candidate exons in B - b denotes the sum of the lengths of the blocks from B

14 Spliced Alignment Algorithm Begins by selecting either all putative exons between potential acceptor (A) and donor (G) sites. his set is further filtered in a such a way that attempts to retain all true exons, with some false ones.

15 Gene Prediction Via Spliced Alignment he Puzzle: find a set of exons in S whose concatenation fits best a known homologous genome. S???? November 15 15

16 Small Example on Board

17 S [Gelfand et al-96 ]: Gene Prediction As a Network Graph

18 Do we really need to compute all possible chains, at the cost of O(n 2 ) each?

19 Spliced Alignment: Idea Compute the best alignment between i-prefix of genomic sequence S and j-prefix of target under the assumption that the alignment uses the block B (i,j,b) (i,j,3) 3

20 [Gelfand et al-96 ]: Gene Prediction As a Network Graph I O I I O I I 8 O 2 O I 3 O O

21 Spliced Alignment Recurrence If i is not the starting vertex of block B: (i, j, B) = max { (i 1, j, B) indel penalty (i, j 1, B) indel penalty (i 1, j 1, B) + δ(g i, t j ) } If i is the starting vertex of block B: (i, j, B) = max { (i, j 1, B) indel penalty max all blocks B preceding block B (end(b ), j, B ) indel penalty max all blocks B preceding block B (end(b ), j 1, B ) + δ(g i, t j ) }

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24 Spliced Alignment Solution After computing the three-dimensional table (i, j, B), the score of the optimal spliced alignment is: max all blocks B (end(b), length(), B)

25 Spliced Alignment: Complications Considering multiple i-prefixes leads to slow down. running time: O(nb + nk 2 ) where n is the target length, b is the sum of the lengths of the blocks from B and k is the number of blocks.

26 Spliced Alignment: Complications Considering multiple i-prefixes leads to slow down. running time: O(nb + nk 2 ) where n is the target length, b is the sum of the lengths of the blocks from B and k is the number of blocks. Can we get rid of one O(k) in the time complexity?

27 Lewis Carroll Example

28 Spliced Alignment: Speedup

29 P(1)= 0 P(2)= 0 P(3)= 0 P(4)= 2 P(5)= 3 1 w(1)= 6 w(2)= 5 w(3)= 4 w(4)= 1 w(5)= 10 M[0] = 0 M[1] = max(6 + 0, 0) = 6 M[2] = max(5+0,6) = 6 M[3] = max(4+0,6) = 6 6( = 7M[4] = max(1+6, M[5] = max(10+6,7)=16 תזכורת: אינטרוולים במימד דוגמת ריצה לאלגוריתם האיטרטיבי: Input: n, s 1,,s n, f 1,,f n, w 1,,w n M: Sort jobs by finish times so that f 1 f 2... f n. Compute p(1), p(2),, p(n) Iterative-Compute-Opt { M[0] = 0 for j = 1 to n M[j] = max(w j + M[p(j)], M[j-1]) } 4

30 Spliced Alignment: Speedup

31 Spliced Alignment: Speedup P(i,j)=max all blocks B preceding position i (end(b), j, B) j S i

32 S I I 2 O I O ime Complexity? I O 3 I 7 O O

33 S I I 2 O I O ime Complexity? O(nb + nk) I O 3 I 7 O O