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Dynamic programming with more complex models

This article explores dynamic programming with more complex models, including gaps longer than one residue. It discusses adjustments to recurrence relations and the alignment of two sequences with potential precursors. It also introduces alignment with affine gap scores and heuristic alignment algorithms like BLAST.

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Dynamic programming with more complex models

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  1. Dynamic programming with more complex models • When gaps do occur, they are often longer than one residue.(biology) • We can still use all the dynamic programming versions described in Section2.3,with adjustments to recurrence relations as typified by the following:

  2. k=0,…,j-1 (i-1,j-1) (i,k) +s +r(i-k) (k,j) (i,j) +r(j-k) k=0,…,i-1 Dynamic programming with more complex models • That gives a replacement for the basic global dynamic relation.

  3. Dynamic programming with more complex models • This procedure now requires operations to align two sequences of length . • In each cell (i,j) we have to look at i+j+1 potential precursor,not just three as previously.

  4. Dynamic programming with more complex models • Prohibitively costly increase in computational time in many case. • Under some conditions computational time to ,although the constant of proportionality is higher in these case. • In each cell have to look at 2K+1 potential precursors.

  5. Alignment with affine gap scores • Assume an affine gap cost structure as : . • . • To keep track of multiple values for each pair of residue coefficients (i,j) in place of the single value F(i,j).

  6. Alignment with affine gap scores • M(i,j) Ix(i,j) Iy(i,j)

  7. Alignment with affine gap scores • This will be true for the optimal path if (-d-e) is less then the lowest mismatch score.

  8. Alignment with affine gap scores • The new value for a state variable at (i,j) is maximum of the scores corresponding to the transitions coming into the state. • Each transition score is given by the value of the source state at the offsets specified by the (i,j) pair of the target state, plus the specified score increment.

  9. Alignment with affine gap scores • FAS(finite state automaton)

  10. Alignment with affine gap scores • It is in fact frequent practice to implement an affine gap cost algorithm using only two states, M and I.

  11. Alignment with affine gap scores • This is only guaranteed to provide the correct result if the lowest mismatch score is >= -2e. • For those interested in pursuing the subject, the simpler state-based automata are called Moore machine, and the transition-emitting systems are called Mealy machines.

  12. More complex FSA models • four-state FSA with two match states • There may be high fidelity regions of alignment without gaps, corresponding to match state A.

  13. More complex FSA models • Separated by lower fidelity regions with gaps, corresponding to match state B and gap states Ix and Iy. • (feature)given an alignment path, there is also an implicit attachment of labels to the symbols in the original sequences, indicating which state was used to match them.

  14. Exercise 2.10 • Calculate the score of the example alignment in Figure 2.10, with d=12, e=2.

  15. 實作

  16. Heuristic alignment algorithms • Speed • The current protein database contains of the order of 10^8 residues, so far a sequence of length 10^3, approximately 10^11 matrix cells must be evaluated to search the complete database.

  17. Heuristic alignment algorithms • The goal of these method is to search as small a fraction as possible of cells in dynamic programming matrix ,while still looking at all the high scoring alignment. • For the scoring matrices used to find distant matches, that exact methods become intractable, and we must use heuristic approaches that sacrifice some sensitivity.

  18. Heuristic alignment algorithms-BLAST • The package provides programs for finding high scoring local alignment between a query sequence and a target database. • (idea)true match alignments are vary likely to contain somewhere within them a short stretch of identities, or vary high scoring matches.

  19. Heuristic alignment algorithms-BLAST • Look initially for such short stretches and use them as ‘seeds’, from which to extend out in search of a good longer alignment. • By keeping the seed segments short, it is possible to pre-process the query sequence to make a table of all possible seeds with their corresponding start point.

  20. Heuristic alignment algorithms-BLAST • Make a list of all ‘neighbourhood words’ of a fixed length. • Scan through the database->whenever it finds a word in the set -> starts a ‘hit extension’ process to extend the possible match as an ungapped alignment in both directions->stopping at a maximum scoring extension.

  21. Heuristic alignment algorithms-BLAST • Only find ungapped alignments • restricting to ungapped alignments misses only a small proportion of significant matches. • Can find and report more than one high scoring match per sequence pair and can give significance values for combined scores.

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