BMI/CS 776 Lecture #15: Multiple Alignment - ProbCons. Colin Dewey

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1 BMI/CS 776 Lecture #15: Multiple Alignment - ProbCons Colin Dewey

2 Probabilistic multiple alignment Like Needleman-Wunsch, pair HMMs can be generalized to n > 2 sequences Unfortunately, the complexity of such algorithms is exponential in n However, we can still use pair HMMs to our advantage in multiple alignment ProbCons & AMAP: use pairwise statistics as part of objective function 2

3 ProbCons Do et al., 2005 Progressive multiple alignment with refinement Key ideas: Objective function based on PHMM probabilities - maximum expected accuracy Probabilistic consistency - transitivity of homology 3

4 ProbCons algorithm 1. Compute PHMM posterior probabilities for all pairs of sequences 2. Compute maximum expected accuracy (MEA) between all pairs of sequences 3. Apply probabilistic consistency transformation to posterior probabilities 4. Compute guide tree from MEA values 5. Progressively align sequences using guide tree 6. Iteratively refine multiple alignment 4

5 PHMM posteriors Forward and backward algorithms for PHMMs - use to calculate posterior probabilities of alignment properties Specifically, interested in calculating the posterior probability of being aligned to σj 2 P[σ 1 i σ 2 j σ 1, σ 2 ] = P[σ1, σ 2, σ 1 i σ2 j ] P[σ 1, σ 2 ] σ 1 i = P[σ1 1...i, σ2 1...j, σ1 i σ2 j ]P[σ1 i+1...n, σ2 j+1...m σ1 i σ2 j ] P[σ 1, σ 2 ] = f H (i, j)b H (i, j) f E (n, m) 5

6 Expected accuracy Assume P[h r σ 1, σ 2 ] (according to the PHMM) is the probability of alignment being the true alignment E h r[accuracy(h, h r ) σ 1, σ 2 ] = accuracy(h, h r ) = h H h r H min(n, m) = = = h P[h r σ 1, σ 2 ](h r H h r H ) min(n, m) h r P[h r σ 1, σ 2 ] σ 1 i σ2 j h I h r (i, j) min(n, m) σ 1i σ2j h h P[h r σ 1, σ 2 ]I r h r(i, j) min(n, m) σi 1 σ2 j h P[σ1 i σ2 j σ1, σ 2 ] min(n, m) h r 6

7 Maximum expected accuracy (MEA) Goal: Find h such that expected accuracy is maximized E h r[accuracy(h, h r ) σ 1, σ 2 ] = σ 1 i σ2 j h P[σ1 i σ2 j σ1, σ 2 ] min(n, m) Algorithm: Run Needleman-Wunsch σ 1 i σ 2 j alignment with match score of equal to P[σi 1 σj 2 σ 1, σ 2 ] and with zero gap penalties 7

8 Probabilistic consistency transformation Take into account third sequence in calculating P[σ 1 i σ 2 j σ 1, σ 2, σ 3 ] = P[σ 1 i σ 2 j σ 1, σ 2, σ 3 ] + k P[σ 1 i σ 2 j σ 3 k σ 1, σ 2, σ 3 ] k P[σ 1 i σ 2 j σ 3 k σ 1, σ 2, σ 3 ] = k P[σ 1 i σ 3 k and σ 3 k σ 2 j σ 1, σ 2, σ 3 ] k P[σ 1 i σ 3 k σ 1, σ 3 ]P[σ 3 k σ 2 j σ 2, σ 3 ] where are all heuristic approximations 8

9 Probabilistic consistency transformation Over all possible third sequences P [σ 1 i σ 2 j σ 1, σ 2 ] = σ 3 S k P[σ 1 i σ 3 k σ 1, σ 3 ]P[σ 3 k σ 2 j σ 2, σ 3 ] Implemented as sparse matrix multiplication 9

10 Guide tree construction UPGMA using maximum expected accuracy distances Sequences start out as individual clusters Join clusters x and y with highest E(x, y) into new cluster xy Compute E(xy, z) = (E(x,z) + E(y,z)) / 2 Repeat until all clusters joined 10

11 Progressive alignment Profile alignment Sum-of-pairs with maximal expected accuracy scoring No gap penalities Score for aligning two columns: score(c 1, c 2 ) = P [σ s i σ t j S] σ s i c 1 σ t j c 2 11

12 Iterative refinement Randomly partition sequences into two sets Extract multiple alignments for both sets from current multiple alignment Re-align two multiple alignments to make one No gap penalty - sum-of-pairs scoring guaranteed to increase or stay the same 12

13 Other features Unsupervised learning of PHMM parameters Emission probabilities fixed (BLOSUM62) Learn transitions probs via EM Column reliability ψ(c) = ( ) 1 c 2 σ s i,σt j c P [σ s i σ t j S] 13

14 Performance Table 1. Aligner Performance of aligners on the BAliBASE benchmark alignments database Ref 1 (82) Ref 2 (23) Ref 3 (12) Ref 4 (12) Ref 5 (12) Overall (141) SP CS SP CS SP CS SP CS SP CS SP CS Time (mm:ss) Align-m 76.6 n/a 88.4 n/a 68.4 n/a 91.1 n/a 91.7 n/a 80.4 n/a 19:25 DIALIGN :53 CLUSTALW :07 MAFFT :18 T-Coffee :31 MUSCLE :05 ProbCons :32 ProbCons-ext :02 Columns show the average sum-of-pairs (SP) and column scores (CS) achieved by each aligner for each of the five BAliBASE references. All scores have been multiplied by 100. The number of sequences in each reference is given in parentheses. Overall numbers for the entire database are reported in addition to the total running time of each aligner for all 141 alignments. The best results in each column are shown in bold. Do et al.,

15 Friedman rank test k treatments b blocks Each treatment is ranked within each block Tests whether treatments have identical effects Multiple alignment case: treatment = alignment method block = alignment reference database rank methods based on some score (e.g., sensitivity) 15

16 Comparing ProbCons Table 2. Significance test for differences in BAliBASE performance Align-M DIALIGN CLUSTALW MAFFT T-Coffee MUSCLE ProbCons ProbCons-ext Align-M (0.61) <10 10 <10 10 <10 10 <10 10 <10 10 DIALIGN <10 10 <10 10 <10 10 <10 10 <10 10 CLUSTALW <10 10 MAFFT (0.65) T-Coffee +< (0.92) MUSCLE +< ProbCons +< < ProbCons-ext +< < (0.092) (0.088) Entries show the p-value indicating the significance of a difference in performance between two alignment methods as measured using a Friedman rank test. Nonitalicized values above the diagonal were calculated using SP scores on all alignments, whereas italicized values were computed using CS scores. (+) Method on the left had lower average rank (better performance); ( ) Method on the left had higher average rank (worse performance); parentheses denote (nonsignificant) p-values >0.05. Methods compared pairwise via Friedman rank test Do et al.,