1 / 19

A fast Prunning Algorithm for optimal Sequence Alignment

A fast Prunning Algorithm for optimal Sequence Alignment. Linear Space Bounded Dynamic Programming. Overview. An introduction to alignments Dynamic Programming Other approaches to optimal alignment calculation A*-star algorithm LBD and boundaries Results Outlook on coming improvements.

bob
Télécharger la présentation

A fast Prunning Algorithm for optimal Sequence Alignment

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A fast Prunning Algorithm for optimal Sequence Alignment Linear Space Bounded Dynamic Programming

  2. Overview • An introduction to alignments • Dynamic Programming • Other approaches to optimal alignment calculation • A*-star algorithm • LBD and boundaries • Results • Outlook on coming improvements

  3. Alignments • “the holy grail of Bioinformatics“ – Dan Gusfield • sequencing • function of genes and proteins • structure of proteins • evolutionary trees Sequencing gel

  4. Mathematical Formalization • Given k sequences sk over an alphabet Σ and k sequences ask over an extended alphabet Σ΄ = Σ + {-} • The set A = {as1, as2, ..., ask} is a sequence alignment when each of the following three conditions are fullfilled • Each of the sequences in A have the same length • If you remove the gap symbols you arrive at the original sequneces • There is no column of gap symbols AGGTCG AGAC_ G ACGC_ G AGGTCG AGACG ACGCG

  5. Dynamic Programming • Algorithm for finding the optimal sequence alignment: Needleman–Wunsch algorithm AGC_G A_CGG AGCG_ A_CGG

  6. Dynamic Programming • Analysis of the Algorithm • Runtime: O(n*n) (filling a quadratic matrix) • Space consumption: O(n*n) (store n * n entries of the quadratic matrix) • Comparison of the genomes of Yeast, Saccharomyces cerevisiae (20 * 10^6bp) Fruit fly, Drosophila melanogaster (130 * 10^6bp) Space consumption: 20*10^6 * 130 * 10^6 = 26 * 10 ^14 4 Bytes to store an integer => 26 * 10 ^5 Gigabytes Drosophila melanogaster Saccharomyces cerevisiae

  7. Hirschberg‘s Divide & Conquer • Main idea: • Only the row above neccessary to compute the one below that • Problem: Backtracking is not possible anymore • Algorithm: • Divide s1 in s1a and s1b • Align s1a with s2 and s1b with s2 • Search the largest transition (maximum sum) of these rows. • Go in recursion • Extra cell computations but space requirements reduced to O(n^d-1) s1a s1b s2 s1a s1b s2

  8. A*-Algorithm • A classic graph algorithm to find the shortest distance between two locations

  9. A*-Algorithm • Mathematical formalization • Scoring function f*(n) = g*(n) + h*(n) with g* giving the optimal path to node n found so far and the heuristic h* giving an optimistic approximation for the cost of a path from node n to a goal node • h* may never under-/overerstimate the score! • Open list/priority que, close list (avoid circles)

  10. A*- Algorithm • Application • The shortest path problem • Use coordinate frame as the heuristic (shortest connection between to points is a straight line) • Alignments • Problems • Close and open list can easily become large • Not applicable to our problem in the basic version • Extensions • Do not store close list • Do not insert none promising children in open lists

  11. Bounded Dynamic Programming • Main idea: Combine the low overhead of dynamic programming with the pruning capabilities of A* • Algorithm(1) • Only prune where promising • Compute the matrix (anti-)diagonalwise and check for pruning always at the end of the diagonal which means to compare the current upper bound with the lowest lower bound • Good upper and lower bounds are neccessary Diagonal wise computation & pruning pruned matrix

  12. Upper and lower Bounds • Lower Bounds • Diagonal Alignment e.g align the sequences directly without any gaps • Greedy headlight search • Result of several local alignments • Always search the frontier for the largest value • Use this as a fulcrum for the next local alignment step • Only use diagonals for computing as no backtracking is needed • Size of local alignment influences the time consumption drastically Greedy headlight search

  13. Upper and lower Bounds • Upper bound • Simply assume that the remaining characters are aligned perfectly Upper bound: 5 – 3 = 2

  14. Linear space- lbd align • Algorithm(2) • Use Hirschberg‘s Divide & Conquer Algorithm • Shaded areas show the two created subproblems Diagonalwise matrix computation Divide & Conquer step

  15. Results Log(time in secondes) Sequence length Method

  16. Results • Changes in pruning • Strictly penalization leads to more pruning • Using different lower bounds • Estimation of the greedy method comes with far better results and in conclusion more pruning than the diagonal alignment • Affine gap cost greatly reduces pruning as well as sequences with large difference in size • Dissimilar sequences (lengths) Different shaded areas denote different lower bounds Normal and affine gap costs

  17. Extension & Future Work • LBD-Align has limited usage due to high flunctuation in pruning (affine gap costs, lower bounds, differnt sequence length) • use as second-order sequence tool • sort out dissimilar sequences by highly heuristic tools like BLAST • best available optimal sequence alignment tool for similar sequences

  18. Summary • Alignments are still a current topic in bioinformatics because there is still room for improvements

  19. ThankyouforyourAttention

More Related