CS262 Lecture 4, Win07, Batzoglou Heuristic Local Alignerers 1.The basic indexing & extension technique 2.Indexing: techniques to improve sensitivity Pairs of Words, Patterns 3.Systems for local alignment

CS262 Lecture 4, Win07, Batzoglou Indexing-based local alignment Dictionary: All words of length k (~10) Alignment initiated between words of alignment score  T (typically T = k) Alignment: Ungapped extensions until score below statistical threshold Output: All local alignments with score > statistical threshold …… query DB query scan

CS262 Lecture 4, Win07, Batzoglou Indexing-based local alignment— Extensions A C G A A G T A A G G T C C A G T C T G A T C C T G G A T T G C G A Gapped extensions until threshold Extensions with gaps until score < C below best score so far Output: GTAAGGTCCAGT GTTAGGTC-AGT

CS262 Lecture 4, Win07, Batzoglou Sensitivity-Speed Tradeoff long words (k = 15) short words (k = 7) Sensitivity Speed Kent WJ, Genome Research 2002 Sens. Speed X%

CS262 Lecture 4, Win07, Batzoglou Sensitivity-Speed Tradeoff Methods to improve sensitivity/speed 1.Using pairs of words 2.Using inexact words 3.Patterns—non consecutive positions ……ATAACGGACGACTGATTACACTGATTCTTAC…… ……GGCACGGACCAGTGACTACTCTGATTCCCAG…… ……ATAACGGACGACTGATTACACTGATTCTTAC…… ……GGCGCCGACGAGTGATTACACAGATTGCCAG…… TTTGATTACACAGAT T G TT CAC G

CS262 Lecture 4, Win07, Batzoglou Measured improvement Kent WJ, Genome Research 2002

CS262 Lecture 4, Win07, Batzoglou Non-consecutive words—Patterns Patterns increase the likelihood of at least one match within a long conserved region 3 common 5 common 7 common Consecutive PositionsNon-Consecutive Positions 6 common On a 100-long 70% conserved region: Consecutive Non-consecutive Expected # hits: Prob[at least one hit]:

CS262 Lecture 4, Win07, Batzoglou Advantage of Patterns 11 positions 10 positions

CS262 Lecture 4, Win07, Batzoglou Multiple patterns K patterns  Takes K times longer to scan  Patterns can complement one another Computational problem:  Given: a model (prob distribution) for homology between two regions  Find: best set of K patterns that maximizes Prob(at least one match) TTTGATTACACAGAT T G TT CAC G T G T C CAG TTGATT A G Buhler et al. RECOMB 2003 Sun & Buhler RECOMB 2004 How long does it take to search the query?

CS262 Lecture 4, Win07, Batzoglou Variants of BLAST NCBI BLAST: search the universe MEGABLAST:  Optimized to align very similar sequences Works best when k = 4i  16 Linear gap penalty WU-BLAST: (Wash U BLAST)  Very good optimizations  Good set of features & command line arguments BLAT  Faster, less sensitive than BLAST  Good for aligning huge numbers of queries CHAOS  Uses inexact k-mers, sensitive PatternHunter  Uses patterns instead of k-mers BlastZ  Uses patterns, good for finding genes Typhon  Uses multiple alignments to improve sensitivity/speed tradeoff

CS262 Lecture 4, Win07, Batzoglou Example Query: gattacaccccgattacaccccgattaca (29 letters) [2 mins] Database: All GenBank+EMBL+DDBJ+PDB sequences (but no EST, STS, GSS, or phase 0, 1 or 2 HTGS sequences) 1,726,556 sequences; 8,074,398,388 total letters >gi| |gb|AC | Oryza sativa chromosome 3 BAC OSJNBa0087C10 genomic sequence, complete sequence Length = Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plusgi| |gb|AC | Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: tacacccagattacaccccga Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: tacacccagattacaccccga >gi| |gb|AC | Oryza sativa chromosome 3 BAC OSJNBa0052F07 genomic sequence, complete sequence Length = Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plusgi| |gb|AC | Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 3891 tacacccagattacaccccga 3911

CS262 Lecture 4, Win07, Batzoglou Example Query: Human atoh enhancer, 179 letters[1.5 min] Result: 57 blast hits 1. gi| |gb|AF |AF Homo sapiens ATOH1 enhanc e-95 gi| |gb|AF |AF gi| |gb|AC | Mus musculus Strain C57BL6/J ch e-68gi| |gb|AC |264 3.gi| |gb|AF |AF Mus musculus Atoh1 enhanc e-66gi| |gb|AF |AF gi| |gb|AF | Gallus gallus CATH1 (CATH1) gene e-12gi| |gb|AF |78 5.gi| |emb|AL | Zebrafish DNA sequence from clo e-05gi| |emb|AL |54 6.gi| |gb|AC | Oryza sativa chromosome 10 BAC O gi| |gb|AC |44 7.gi| |ref|NM_ | Mus musculus suppressor of Ty gi| |ref|NM_ |42 8.gi| |gb|BC | Mus musculus, Similar to suppres gi| |gb|BC |42 gi| |gb|AF |AF218258gi| |gb|AF |AF Mus musculus Atoh1 enhancer sequence Length = 1517 Score = 256 bits (129), Expect = 9e-66 Identities = 167/177 (94%), Gaps = 2/177 (1%) Strand = Plus / Plus Query: 3 tgacaatagagggtctggcagaggctcctggccgcggtgcggagcgtctggagcggagca 62 ||||||||||||| ||||||||||||||||||| |||||||||||||||||||||||||| Sbjct: 1144 tgacaatagaggggctggcagaggctcctggccccggtgcggagcgtctggagcggagca 1203 Query: 63 cgcgctgtcagctggtgagcgcactctcctttcaggcagctccccggggagctgtgcggc 122 |||||||||||||||||||||||||| ||||||||| |||||||||||||||| ||||| Sbjct: 1204 cgcgctgtcagctggtgagcgcactc-gctttcaggccgctccccggggagctgagcggc 1262 Query: 123 cacatttaacaccatcatcacccctccccggcctcctcaacctcggcctcctcctcg 179 ||||||||||||| || ||| |||||||||||||||||||| ||||||||||||||| Sbjct: 1263 cacatttaacaccgtcgtca-ccctccccggcctcctcaacatcggcctcctcctcg

CS262 Lecture 4, Win07, Batzoglou The Four-Russian Algorithm brief overview A (not so useful) speedup of Dynamic Programming [ Arlazarov, Dinic, Kronrod, Faradzev 1970 ]

CS262 Lecture 4, Win07, Batzoglou Main Observation Within a rectangle of the DP matrix, values of D depend only on the values of A, B, C, and substrings x l...l’, y r…r’ Definition: A t-block is a t  t square of the DP matrix Idea: Divide matrix in t-blocks, Precompute all possible t-blocks Speedup: O(t) A B C D xlxl x l’ yryr y r’ t

CS262 Lecture 4, Win07, Batzoglou Main Observation—Shifts Observation: In Needleman-Wunsch alignment: Decreasing A, B, and C all by same constant Q, Results in D decreased by Q Observation: Each nbr pair of cells cannot have “too different” values Idea: Divide matrix in t-blocks, Precompute all possible t-blocks (Possible, because we keep all A, B, C within a fixed range.) Speedup: O(t) A B C D xlxl x l’ yryr y r’ t

CS262 Lecture 4, Win07, Batzoglou The Four-Russian Algorithm Main structure of the algorithm: 1.Build lookup table of all possible t- blocks 2.Divide N  N DP matrix into t-blocks that overlap by 1 column & 1 row 3.For i = 1……K 4. For j = 1……K 5. Compute D i,j as a function of A i,j, B i,j, C i,j, x[l i …l’ i ], y[r j …r’ j ] Theoretically optimal: t = log N Time: O(N 2 / log 2 N) times the cost of step 4 t t t

CS262 Lecture 4, Win07, Batzoglou The Four-Russian Algorithm t t t

CS262 Lecture 4, Win07, Batzoglou Hidden Markov Models 1 2 K … 1 2 K … 1 2 K … … … … 1 2 K … x1x1 x2x2 x3x3 xKxK 2 1 K 2

CS262 Lecture 4, Win07, Batzoglou Outline for our next topic Hidden Markov models – the theory Probabilistic interpretation of alignments using HMMs Later in the course: Applications of HMMs to biological sequence modeling and discovery of features such as genes

CS262 Lecture 4, Win07, Batzoglou Example: The Dishonest Casino A casino has two dice: Fair die P(1) = P(2) = P(3) = P(5) = P(6) = 1/6 Loaded die P(1) = P(2) = P(3) = P(5) = 1/10 P(6) = 1/2 Casino player switches back-&-forth between fair and loaded die once every 20 turns Game: 1.You bet $1 2.You roll (always with a fair die) 3.Casino player rolls (maybe with fair die, maybe with loaded die) 4.Highest number wins $2

CS262 Lecture 4, Win07, Batzoglou Question # 1 – Evaluation GIVEN A sequence of rolls by the casino player QUESTION How likely is this sequence, given our model of how the casino works? This is the EVALUATION problem in HMMs Prob = 1.3 x

CS262 Lecture 4, Win07, Batzoglou Question # 2 – Decoding GIVEN A sequence of rolls by the casino player QUESTION What portion of the sequence was generated with the fair die, and what portion with the loaded die? This is the DECODING question in HMMs FAIRLOADEDFAIR

CS262 Lecture 4, Win07, Batzoglou Question # 3 – Learning GIVEN A sequence of rolls by the casino player QUESTION How “loaded” is the loaded die? How “fair” is the fair die? How often does the casino player change from fair to loaded, and back? This is the LEARNING question in HMMs Prob(6) = 64%

CS262 Lecture 4, Win07, Batzoglou The dishonest casino model FAIRLOADED P(1|F) = 1/6 P(2|F) = 1/6 P(3|F) = 1/6 P(4|F) = 1/6 P(5|F) = 1/6 P(6|F) = 1/6 P(1|L) = 1/10 P(2|L) = 1/10 P(3|L) = 1/10 P(4|L) = 1/10 P(5|L) = 1/10 P(6|L) = 1/2