Computational Biology, Part 2 Sequence Comparison with Dot Matrices Robert F. Murphy Copyright  1996, All rights reserved.

Sequence Alignment Definition: Procedure for comparing two or more sequences by searching for a series of individual characters or character patterns that are in the same order in the sequences Definition: Procedure for comparing two or more sequences by searching for a series of individual characters or character patterns that are in the same order in the sequences  Pair-wise alignment: compare two sequences  Multiple sequence alignment: compare more than two sequences

Example sequence alignment Task: align “abcdef” with “abdgf” Task: align “abcdef” with “abdgf” Write second sequence below the first Write second sequence below the firstabcdefabdgf Move sequences to give maximum match between them Move sequences to give maximum match between them Show characters that match using vertical bar Show characters that match using vertical bar

Example sequence alignment abcdef||abdgf Insert gap between b and d on lower sequence to allow d and f to align Insert gap between b and d on lower sequence to allow d and f to align

Example sequence alignment abcdef || | | ab-dgf

Example sequence alignment abcdef || | | ab-dgf Note e and g don’t match Note e and g don’t match

Matching Similarity vs. Identity Alignments can be based on finding only identical characters, or (more commonly) can be based on finding similar characters Alignments can be based on finding only identical characters, or (more commonly) can be based on finding similar characters More on how to define similarity later More on how to define similarity later

Global vs. Local Alignment We distinguish We distinguish  Global alignment algorithms which optimize overall alignment between two sequences  Local alignment algorithms which seek only relatively conserved pieces of sequence  Alignment stops at the ends of regions of strong similarity  Favors finding conserved patterns in otherwise different pairs of sequences

Global vs. Local Alignment Global GlobalLGPSSKQTGKGS-SRIWDN | | ||| | | LN-ITKSAGKGAIMRLGDA Local Local GKG ||| ||| GKG

Global vs. Local Alignment Global GlobalLGPSSKQTGKGS-SRIWDN | | ||| | | LN-ITKSAGKGAIMRLGDA Local Local TGKG ||| ||| AGKG

Why do sequence alignments? To find whether two (or more) genes or proteins are evolutionarily related to each other To find whether two (or more) genes or proteins are evolutionarily related to each other To find structurally or functionally similar regions within proteins To find structurally or functionally similar regions within proteins

Origin of similar genes Similar genes arise by gene duplication Similar genes arise by gene duplication Copy of a gene inserted next to the original Copy of a gene inserted next to the original Two copies mutate independently Two copies mutate independently Each can take on separate functions Each can take on separate functions All or part can be transferred from one part of genome to another All or part can be transferred from one part of genome to another

Methods for Pairwise Alignment Dot matrix analysis Dot matrix analysis Dynamic Programming Dynamic Programming Word or k-tuple methods (FASTA and BLAST) Word or k-tuple methods (FASTA and BLAST)

Sequence comparison with dot matrices Goal: Graphically display regions of similarity between two sequences (e.g., domains in common between two proteins of suspected similar function) Goal: Graphically display regions of similarity between two sequences (e.g., domains in common between two proteins of suspected similar function)

Sequence comparison with dot matrices Basic Method: For two sequences of lengths M and N, lay out an M by N grid (matrix) with one sequence across the top and one sequence down the left side. For each position in the grid, compare the sequence elements at the top (column) and to the left (row). If and only if they are the same, place a dot at that position. Basic Method: For two sequences of lengths M and N, lay out an M by N grid (matrix) with one sequence across the top and one sequence down the left side. For each position in the grid, compare the sequence elements at the top (column) and to the left (row). If and only if they are the same, place a dot at that position.

Examples for protein sequences (Demonstration A6, Sequence 1 vs. 2) (Demonstration A6, Sequence 1 vs. 2) (Demonstration A6, Sequence 2 vs. 3) (Demonstration A6, Sequence 2 vs. 3)

Interpretation of dot matrices Regions of similarity appear as diagonal runs of dots Regions of similarity appear as diagonal runs of dots Reverse diagonals (perpendicular to diagonal) indicate inversions Reverse diagonals (perpendicular to diagonal) indicate inversions Reverse diagonals crossing diagonals (Xs) indicate palindromes Reverse diagonals crossing diagonals (Xs) indicate palindromes  (Demonstration A6, Sequence 4 vs. 4)

Interpretation of dot matrices Can link or "join" separate diagonals to form alignment with "gaps" Can link or "join" separate diagonals to form alignment with "gaps"  Each a.a. or base can only be used once  Can't trace vertically or horizontally  Can't double back  A gap is introduced by each vertical or horizontal skip

Uses for dot matrices Can use dot matrices to align two proteins or two nucleic acid sequences Can use dot matrices to align two proteins or two nucleic acid sequences Can use to find amino acid repeats within a protein by comparing a protein sequence to itself Can use to find amino acid repeats within a protein by comparing a protein sequence to itself  Repeats appear as a set of diagonal runs stacked vertically and/or horizontally  (Demonstration A6, Sequence 5 vs. 6)

Uses for dot matrices Can use to find self base-pairing of an RNA (e.g., tRNA) by comparing a sequence to itself complemented and reversed Can use to find self base-pairing of an RNA (e.g., tRNA) by comparing a sequence to itself complemented and reversed Excellent approach for finding sequence transpositions Excellent approach for finding sequence transpositions

Filtering to remove “noise” A problem with dot matrices for long sequences is that they can be very noisy due to lots of insignificant matches (i.e., one A) A problem with dot matrices for long sequences is that they can be very noisy due to lots of insignificant matches (i.e., one A) Solution use a window and a threshold Solution use a window and a threshold  compare character by character within a window (have to choose window size)  require certain fraction of matches within window in order to display it with a “dot”

Example spreadsheet with window (Demonstration A7) (Demonstration A7)

How do we choose a window size? Window size changes with goal of analysis Window size changes with goal of analysis  size of average exon  size of average protein structural element  size of gene promoter  size of enzyme active site

How do we choose a threshold value? Threshold based on statistics Threshold based on statistics  using shuffled actual sequence  find average (m) and s.d. (  ) of match scores of shuffled sequence  convert original (unshuffled) scores (x) to Z scores Z = (x - m)/ Z = (x - m)/   use threshold Z of of 3 to 6  using analysis of other sets of sequences  provides “objective” standard of significance

Dot matrix analysis with DNA Strider (Mount, Fig 3.4) Get phage cI and phage P22 c2 repressor sequences from Genbank (X00166 and V01153 respectively) Get phage cI and phage P22 c2 repressor sequences from Genbank (X00166 and V01153 respectively) Use DNA Strider 1.4 (contact TA to get a copy) Use DNA Strider 1.4 (contact TA to get a copy) Use window size of 11 and stringency of 7 Use window size of 11 and stringency of 7

Dot matrix (Mount Fig 3.4) Note set of diagonals in lower right that do not line up due to insertion near 475 on cI Note set of diagonals in lower right that do not line up due to insertion near 475 on cI

Dot matrix analysis with DNA Strider (Mount, Fig 3.6) Get human LDL receptor protein sequence from Genbank (P01130) Get human LDL receptor protein sequence from Genbank (P01130) Use weighting “Identity” Use weighting “Identity” Use window size of 1 and stringency of 1 Use window size of 1 and stringency of 1 Use window size of 23 and stringency of 7 Use window size of 23 and stringency of 7

Dot matrix (Mount Fig 3.6) W=1 S=1 W=1 S=1 Note set of stacked diagonals in upper left Note set of stacked diagonals in upper left

Dot matrix (Mount Fig 3.6) W=23 S=7 W=23 S=7 Note set of stacked diagonals in upper left Note set of stacked diagonals in upper left

Reading for next class Mount, Chapter 3 through page 93 Mount, Chapter 3 through page 93 Look over paper by Needleman and Wunsch on web site Look over paper by Needleman and Wunsch on web site (03-510/710) Durbin et al, pp (03-510/710) Durbin et al, pp 17-32