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Sequence alignment algorithms

Sequence alignment algorithms . Presented By Cary Miller Sastry Akella Daisuke Yasuda. Overview. Biological background / motivation / applications Dot matrix / dynamic programming FASTA / BLAST. biology. Biomolecules are strings from a restricted alphabet Length=4 DNA

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Sequence alignment algorithms

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  1. Sequence alignment algorithms Presented By Cary Miller Sastry Akella Daisuke Yasuda

  2. Overview • Biological background / motivation / applications • Dot matrix / dynamic programming • FASTA / BLAST

  3. biology • Biomolecules are strings from a restricted alphabet • Length=4 DNA • Length=20 protein • Proteins are the working part

  4. Proteins • Protein is a linear sequence of 20 characters (amino acids) • Proteins do not maintain linearity • Folding happens • Folding determines overall 3-D shape • Shape determines function

  5. Sequence => Structure => Function • sequence does not reveal structure • Much less function • A sequenceARTUVEDYERRWWUHUK…

  6. Structure • Pic 1 • Pic 2

  7. Structure

  8. function • Protein A is a constituent of muscle, skin, cartilage, or … • Protein B catalyzes the transformation of glucose to fructose, or … • How do we find proteins with similar function?

  9. Nature does not solve the same problem twice (usually) • Short sequence with a specific function (or shape) is called a domain • The same domain appears in multiple proteins • If we find the same domain in multiple proteins that provides a clue to function and/or structure

  10. Amino acids • Each has the same basic chemical configuration but has a functional group that makes it chemically unique • They occur in families • Some functional groups are similar

  11. How biologists study proteins • Expensive (NMR, x-ray crystallography) • Discovery of function is difficult • Few proteins are understood in detail • Many are known by sequence • Sequence is easier to get than structure or function

  12. A biological scenario • Biologist discovers the sequence of a new protein with unknown function • She has no idea of function • If sequence can be associated with a known protein sequence we have a clue about structure and/or function • Most proteins have unknown function

  13. Public databases • Vast quantities of sequence, structure, function info is deposited into public databases • A new sequence should be compared to the database

  14. Comparing sequences • Alignment with exact matchABCTUVABUVABCTUVAB----UV

  15. Alignment with inexact match • InexactGARUIPPRSTGARVVBUIEEYSTGAR------UIPPRSTGARVVBUIEEYST

  16. Global vs. local alignment • ABQRTASGGBV • ABRRRASGVBB • ABQRTASGGBV • ABQ------SGGBV

  17. A real alignment • MyoglobinPDLRKY FKG-A ENFTA DDVQ KSDRPDTKAY FPKFG DLSTA AALK SSPK • Homology: common ancestry

  18. Real alignment • Pic 3

  19. Real alignment

  20. Scoring pairs of amino acids • For amino acid pairs assign a score based on frequency of substitutionATRGUVXQATRCVVXTATRGVVEQAT-----VVEQ

  21. A substitution matrix • Pic 4

  22. A substitution matrix

  23. Substitution matrices • Pam and Blosum are standard substitution matrices • Also include scores for • Gap opening • Gap extension

  24. Scoring amino acid strings • Sum the individual pair scores • Database is huge • Spurious match to random sequence is likely • Try your name • E-value is probability of getting a given score from a random sequence

  25. Alignment algorithms • Dot matrix • Dynamic programming • FASTA • BLAST

  26. Dot Matrix and DP

  27. Dot Matrix • Locating regions of similarity between two DNA or protein sequences which provide a great deal of information about the function and structure of the query sequence. • Similar structure indicates homology, or similar evolution, which provides critical information about the functions of these sequences.

  28. Dot Matrix Contd.. • A dot matrix plot is a method of aligning two sequences to provide a picture of the homology between them. • The dot matrix plot is created by designating one sequence to be the subject and placing it on the horizontal axis and designating the second sequence to be the query and placing it on the vertical axis of the matrix.

  29. Dot Matrix Contd.. • At each position within the matrix, a point is plotted if the horizontal and vertical elements are identical. • Diagonal lines within the resulting matrix indicate regions of similarity. A simple dot matrix plot is shown in Figure A.

  30. B A S K E T B A L L BASEBALL * * * * * ** * * * * * * *

  31. Dot Matrix with noise reduction • A certain percentage of the matches between sequence elements can be expected to be the result of the random nature of their evolution. These random matches are considered “noise" and are filtered out to enhance the diagonal lines.

  32. Dot Matrix • Noise Reduction a) Noise reduction in dot matrix can be done by centering a substring of elements of the query sequence over each element in the subject sequence and determining the number of corresponding elements within this “window”.

  33. Dot Matrix b) If the number of corresponding elements exceeds a specified threshold then a point is plotted for the center element. This is demonstrated in figure B.

  34. B A S E BB A S K E T B A L L BASEBALL * Dot Matrix (Figure B)

  35. Dot Matrix • Advantages: Readily reveals the presence of insertions/deletions and direct and inverted repeats that are more difficult to find by the other, more automated methods. • Disadvantages:Most dot matrix computer programs do not show an actual alignment. Does not return a score to indicate how ‘optimal’ a given alignment is.

  36. Dynamic Programming • Dynamic programming (DP) algorithms are a general class of algorithms typically applied to optimization problems. • For DP to be applicable, an optimization problem must have two key ingredients: • a) Optimal substructure – an optimal solution to the problem contains within it optimal solutions to sub-problems. b) Overlapping sub-problems – the pieces of larger problem have a sequential dependency.

  37. Dynamic Programming • DP works by first solving every sub-sub-problem just once, and saves its answer in a table, thereby avoiding the work of re- computing the answer every time the sub-sub-problem is encountered. Each intermediate answer is stored with a score, and DP finally chooses the sequence of solution that yields the highest score.

  38. Dynamic Programming • Path Matrix

  39. Dynamic Programming • Both global and local types of alignments may be made by simple changes in the basic DP algorithm. • Alignments depend on the choice of a scoring system for comparing character pairs and penalty scores (e.g. PAM and BLOSUM matrixes – covered before) Scoring functions – example: w (match) = +2 or substitution matrix w (mismatch) = -1 or substitution matrix w (gap) = -3

  40. Dynamic Programming • Global Alignment (Needleman-Wunsch) a) General goal is to obtain optimal global alignment between two sequences, allowing gaps.b) We construct a matrix F indexed by i and j, one index for each sequence, where the value F(i,j) is the score of the best alignment between the initial segment x1…i of x up to xi and the initial segment y1…j of y up to yj. … We begin by initializing F(0,0) = 0. We then proceed to fill the matrix from top left to bottom right. If F(i-1, j-1), F(i-1,j) and F(i,j-1) are known, it is possible to calculate F(i,j).

  41. Dynamic Programming F(i,j) = max { F(i-1, j-1) + s(xi , yj );F(i-1,j) – d;F(i, j-1) – d. } where s(a,b) is the likelihood score that residues a and b occur as an aligned pair, and d is the gap penalty. • Once you construct the matrix, you trace back the path that leads to F(n,m), which is by definition the best score for an alignment of x1…n to y1…m.

  42. Dynamic Programming • Global Dynamic programming matrix

  43. Dynamic Programming • Local alignment (Smith-Waterman)Two changes from global alignment:1. Possibility of taking the value 0 if all other options have value less than 0. This corresponds to starting a new alignment.2. Alignments can end anywhere in the matrix, so instead of taking the value in the bottom right corner, F(n,m) for the best score, we look for the highest value of F(i,j) over the whole matrix and start the trace-back from there. F(i,j) = max { 0;F(i-1, j-1) + s(xi , yj ); F(i-1,j) – d;F(i, j-1) – d.}

  44. Dynamic Programming • Local Dynamic programming matrix

  45. Dynamic Programming • Advantages:Guaranteed in a mathematical sense to provide the optimal (very best or highest-scoring) alignment for a given set of scoringfunctions. • Disadvantages: a) Slow due to the very large number of computational steps: O(n 2).b) Computer memory requirement also increases as the square of the sequence lengths. Therefore, it is difficult to use the method for very long sequences.

  46. FASTA and BLAST

  47. G A A T T C A G T T A G 1 1 1 1 1 1 1 1 1 1 1 G 1 1 1 1 1 1 1 2 2 2 2 A 1 2 2 2 2 2 2 2 2 2 2 T 1 2 2 3 3 3 3 3 3 3 3 C 1 2 2 3 3 4 4 4 4 4 4 G 1 2 2 3 3 4 4 5 5 5 5 A 1 2 3 3 3 4 5 5 5 5 6 FASTA - Idea - • Problem of Dynamic Programming D.P. compute the score in a lot of useless area for optimal sequence • FASTA focuses on diagonal area

  48. FASTA - Heuristic - • Heuristic Good local alignment should have some exact match subsequence. FASTA focus on this area

  49. FASTA - Hi Level Algorithm - Hi level algorithm Let q be a query max  0 For each sequence, s in DB compare q with s and compute a score, y if max < y max  y; bestSequence  s ; Return bestSequence

  50. FASTA - Algorithm - • Step 1 Find all hot-spots // Hot spots is pairs of words of length k that exactly match Sequence 1 Hot Spots Sequence 2

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