Multiple Sequence Alignments Craig A. Struble, Ph.D. Department of Mathematics, Statistics, and Computer Science Marquette University

MSCS 230: Bioinformatics I - Multiple Sequence Alignment2 Overview

MSCS 230: Bioinformatics I - Multiple Sequence Alignment3 Example Multiple sequence alignment of 7 neuroglobins using clustalx

MSCS 230: Bioinformatics I - Multiple Sequence Alignment4 Example Searching for domains with RPS-BLAST

MSCS 230: Bioinformatics I - Multiple Sequence Alignment5 Applications of Multiple Sequence Alignment Identify conserved domains/elements in sequences Compare regions of similarity among multiple organisms Identify probes for similar sequences in other organisms Develop PCR primers Phylogenetic analysis

MSCS 230: Bioinformatics I - Multiple Sequence Alignment6 Definition A multiple alignment of strings S 1, … S k is a series of strings with spaces S 1 ’, …, S k ’ such that |S 1 ’| = … = |S k ’| S j ’ is an extension of S j by insertion of spaces Goal: Find an optimal multiple alignment.

MSCS 230: Bioinformatics I - Multiple Sequence Alignment7 Scoring Alignments In order to find an optimal alignment, we need to be able to measure how good an alignment is Sum of pairs (SP) method: in a column, score each pair of letters and total the scores. Pairs of gaps score 0. Total up scores for each column

MSCS 230: Bioinformatics I - Multiple Sequence Alignment8 SP Method Example Using BLOSUM62 matrix, gap penalty -8 In column 1, we have pairs -,S S,S k(k-1)/2 pairs per column -IK SIK SSE = -12

MSCS 230: Bioinformatics I - Multiple Sequence Alignment9 Dynamic Programming The dynamic programming approach can be adapted to MSA For simplicity, assume k sequences of length n The dynamic programming array F is k- dimensional of length n+1 (including initial gaps) The entry F(i 1, …, i k ) represents score of optimal alignment for s 1 [1..i 1 ], … s k [1..i k ]

MSCS 230: Bioinformatics I - Multiple Sequence Alignment10 Dynamic Programming Letting i represent the vector (i 1,…,i k ) and b represent a nonzero binary vector of length k, we fill in the array with the formula where (selecting a column to score)

MSCS 230: Bioinformatics I - Multiple Sequence Alignment11 Example Let i=(1,1,1,1), b=(1,0,0,0) Checking F(0,1,1,1) (i-b) Column(s,i,b) is SP-score is -24 (assuming gap penalty of -8) s 1 : MPE s 2 : MKE s 3 : MSKE s 4 : SKE M---M---

MSCS 230: Bioinformatics I - Multiple Sequence Alignment12 Analysis O(n k ) entries to fill Each entry combines O(2 k ) other entries Costs O(k 2 ) to calculate each SP score Overall cost is O(k 2 2 k n k ), or exponential in the number of sequences! MSA with SP-score shown NP-complete

MSCS 230: Bioinformatics I - Multiple Sequence Alignment13 Star Alignments Heuristic method for multiple sequence alignments Select a sequence sc as the center of the star For each sequence s 1, …, s k such that index i  c, perform a Needleman-Wunsch global alignment Aggregate alignments with the principle “once a gap, always a gap.”

MSCS 230: Bioinformatics I - Multiple Sequence Alignment14 Star Alignments Example s2s2 s1s1 s3s3 s4s4 s 1 : MPE s 2 : MKE s 3 : MSKE s 4 : SKE MPE | MKE MSKE - || MKE SKE || MKE MPE MKE -MPE -MKE MSKE -MPE -MKE MSKE -SKE

MSCS 230: Bioinformatics I - Multiple Sequence Alignment15 Choosing a center Try them all and pick the one with the best score Calculate all O(k 2 ) alignments, and pick the sequence s c that maximizes

MSCS 230: Bioinformatics I - Multiple Sequence Alignment16 Analysis Assuming all sequences have length n O(n 2 ) to calculate global alignment O(k) global alignments to calculate Using a reasonable data structure for joining alignments, no worse than O(kl), where l is upper bound on alignment lengths O(kn 2 +k 2 l) overall cost

MSCS 230: Bioinformatics I - Multiple Sequence Alignment17 Tree Alignments Model the k sequences with a tree having k leaves (1 to 1 correspondence) Compute a weight for each edge, which is the similarity score Sum of all the weights is the score of the tree Find tree with maximum score

MSCS 230: Bioinformatics I - Multiple Sequence Alignment18 Tree alignment example Match +1, gap -1, mismatch 0 If x=CT and y=CG, score of 6 CAT GT CTG CG x y

MSCS 230: Bioinformatics I - Multiple Sequence Alignment19 Analysis The tree alignment problem is NP- complete Hence, phylogenetic tree generation is NP- complete Again, likely only exponential time solution available (for optimal answers)

MSCS 230: Bioinformatics I - Multiple Sequence Alignment20 Progressive Approaches CLUSTALW Perform pairwise alignments Construct a tree, joining most similar sequences first (guide tree) Align sequences sequentially, using the phylogenetic tree PILEUP Similar to CLUSTALW Uses UPGMA to produce tree (chapter 6)

MSCS 230: Bioinformatics I - Multiple Sequence Alignment21 Progressive Approaches

MSCS 230: Bioinformatics I - Multiple Sequence Alignment22 Problems with Progressive Alignments MSA depends on pairwise alignments If sequences are very distantly related, much higher likelihood of errors Care must be made in choosing scoring matrices and penalties Other approaches using Bayesian methods such as hidden Markov models

MSCS 230: Bioinformatics I - Multiple Sequence Alignment23 When Craig Talks Next Introduction to Bayesian Statistics Profile and Block analysis Expectation Maximization (MEME) Introduction to HMMs Multiple sequence alignments using HMMs