Computational Biology, Part 7 Similarity Functions and Sequence Comparison with Dot Matrices Robert F. Murphy Copyright  1996, All rights reserved.

Similarity Functions Used to facilitate comparison of two sequence elements Used to facilitate comparison of two sequence elements logical valued (true or false, 1 or 0) logical valued (true or false, 1 or 0)  test whether first argument matches (or could match) second argument numerical valued numerical valued  test degree to which first argument matches second

Logical valued similarity functions Let Search(I)=‘A’ and Sequence(J)=‘R’ Let Search(I)=‘A’ and Sequence(J)=‘R’ A Function to Test for Exact Match A Function to Test for Exact Match  MatchExact(Search(I),Sequence(J)) would return FALSE since A is not R A Function to Test for Possibility of a Match using IUB codes for Incompletely Specified Bases A Function to Test for Possibility of a Match using IUB codes for Incompletely Specified Bases  MatchWild(Search(I),Sequence(J)) would return TRUE since R can be either A or G

Numerical valued similarity functions return value could be probability (for DNA) return value could be probability (for DNA)  Let Search(I) = 'A' and Sequence(J) = 'R'  SimilarNuc (Search(I),Sequence(J)) could return 0.5  since chances are 1 out of 2 that a purine is adenine return value could be similarity (for protein) return value could be similarity (for protein)  Let Seq1(I) = 'K' (lysine) and Seq2(J) = 'R' (arginine)  SimilarProt(Seq1(I),Seq2(J)) could return 0.8  since lysine is similar to arginine usually use integer values for efficiency usually use integer values for efficiency

Scoring (similarity) matrices For each pair of characters in alphabet, value is proportional to degree of similarity (or other scoring criterion) between them For each pair of characters in alphabet, value is proportional to degree of similarity (or other scoring criterion) between them For proteins, most frequently used is Mutation Data Matrix from Dayhoff, 1978 (MDM 78 ) For proteins, most frequently used is Mutation Data Matrix from Dayhoff, 1978 (MDM 78 )

Dayhoff PAM250 similarity matrix (partial)

Origin of PAM 250 matrix Take aligned set of closely related proteins Take aligned set of closely related proteins For each position in the set, find the most common amino acid observed there For each position in the set, find the most common amino acid observed there Calculate the frequency with which each other amino acid is observed at that position Calculate the frequency with which each other amino acid is observed at that position Combine frequencies from all positions to give table showing frequencies for each amino acid changing to each other amino acid Combine frequencies from all positions to give table showing frequencies for each amino acid changing to each other amino acid Take logarithm and normalize for frequency of each amino acid Take logarithm and normalize for frequency of each amino acid

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.

Sequence comparison with dot matrices - References W.M. Fitch. An improved method of testing for evolutionary homology. J. Mol. Biol. 16:9-16 (1966) W.M. Fitch. An improved method of testing for evolutionary homology. J. Mol. Biol. 16:9-16 (1966) W.M. Fitch. Locating gaps in amino acid sequences to optimize the homology between two proteins. Biochem. Genet. 3: (1969) W.M. Fitch. Locating gaps in amino acid sequences to optimize the homology between two proteins. Biochem. Genet. 3: (1969)

Sequence comparison with dot matrices - References A.J. Gibbs & G.A. McIntyre. The diagram, a method for comparing sequences. Its use with amino acid and nucleotide sequences. Eur. J. Biochem. 16:1-11 (1970) A.J. Gibbs & G.A. McIntyre. The diagram, a method for comparing sequences. Its use with amino acid and nucleotide sequences. Eur. J. Biochem. 16:1-11 (1970) A.D. McLachlan. Test for comparing related amino acid sequences: cytochrome c and cytochrome c551. J. Mol. Biol. 61: (1971) A.D. McLachlan. Test for comparing related amino acid sequences: cytochrome c and cytochrome c551. J. Mol. Biol. 61: (1971)

Sequence comparison with dot matrices - References J. Pustell & F.C. Kafatos. A high speed, high capacity homology matrix: zooming through SV40 and polyoma. Nucleic Acids Res. 10: (1982) J. Pustell & F.C. Kafatos. A high speed, high capacity homology matrix: zooming through SV40 and polyoma. Nucleic Acids Res. 10: (1982) J. Pustell & F.C. Kafatos. A convenient and adaptable package of computer programs for DNA and protein sequence management, analysis and homology determination. Nucleic Acids Res. 12: (1984) J. Pustell & F.C. Kafatos. A convenient and adaptable package of computer programs for DNA and protein sequence management, analysis and homology determination. Nucleic Acids Res. 12: (1984)

Examples for protein sequences (Demonstration A5, Sequence 1 vs. 2) (Demonstration A5, Sequence 1 vs. 2) (Demonstration A5, Sequence 2 vs. 3) (Demonstration A5, 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 A5, 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 A5, 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 A6) (Demonstration A6)

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

Displaying matrices by Pustell method with MacVector Goal: Determine differences in arrangements of elements of pBluescript family of vectors Goal: Determine differences in arrangements of elements of pBluescript family of vectors Starting point: Use sequences of three of the members of the family: open the first three files in the Common Vectors: Bluescript folder. Starting point: Use sequences of three of the members of the family: open the first three files in the Common Vectors: Bluescript folder.

Dot matrices with MacVector From Analyze menu select Pustell DNA matrix. Dialog appears. From Analyze menu select Pustell DNA matrix. Dialog appears.

Dot matrices with MacVector Select SYNBL2KSM and SYNBL2SKM. Use defaults for all else. Select SYNBL2KSM and SYNBL2SKM. Use defaults for all else.

Dot matrices with MacVector 23 reagons of homology (“diagonals”) obtained. Request “Matrix map” only (don’t need “Aligned sequences”) 23 reagons of homology (“diagonals”) obtained. Request “Matrix map” only (don’t need “Aligned sequences”)

Dot matrices with MacVector Note inversion near nucleotide 700 (the direction of the polylinker is reversed between the two vectors) Note inversion near nucleotide 700 (the direction of the polylinker is reversed between the two vectors)

Dot matrices with MacVector To examine effect of threshold, decrease “min. % score” from 65 to 55 To examine effect of threshold, decrease “min. % score” from 65 to 55

Dot matrices with MacVector Now we get many (223) diagonals. Now we get many (223) diagonals.

Dot matrices with MacVector Note presence of many short regions of at least 55% homology. Note presence of many short regions of at least 55% homology.

Dot matrices with MacVector Now increase threshold to 90%. Now increase threshold to 90%.

Dot matrices with MacVector Now just 3 diagonals are found. Now just 3 diagonals are found.

Dot matrices with MacVector Note absence of short homologous regions (“noise”). Note absence of short homologous regions (“noise”).

Dot matrices with MacVector Now compare SYNBL2KSP to SYNBL2SKM. Now compare SYNBL2KSP to SYNBL2SKM.

Dot matrices with MacVector 22 diagonals found using default settings. 22 diagonals found using default settings.

Dot matrices with MacVector Note second large inversion at one end of sequences. Note second large inversion at one end of sequences.

More dot matrices with MacVector - DNA homology Goal: Duplicate Figure 6 of Chapter 3 of Sequence Analysis Primer Goal: Duplicate Figure 6 of Chapter 3 of Sequence Analysis Primer Get Accession numbers J02289 (Polyoma) and J02400 (SV40) from Entrez Get Accession numbers J02289 (Polyoma) and J02400 (SV40) from Entrez Do Pustell DNA Matrix analysis using parameters similar to those used in text (window size = 41, %identity = 51) Do Pustell DNA Matrix analysis using parameters similar to those used in text (window size = 41, %identity = 51)

More dot matrices with MacVector - DNA homology

More dot matrices with MacVector - protein homology Goal: Reproduce Figure 15 from Chapter 3 of Sequence Analysis Primer Goal: Reproduce Figure 15 from Chapter 3 of Sequence Analysis Primer Get Accession numbers P17678 (Chicken) and X17254 (human) erythroid transcription factors using Entrez Get Accession numbers P17678 (Chicken) and X17254 (human) erythroid transcription factors using Entrez Do Pustell Protein Matrix Analysis Do Pustell Protein Matrix Analysis

Reading for next class B & O, Chapter 7 just pp B & O, Chapter 7 just pp Additional optional reading: Sequence Analysis Primer, pp “Dynamic Programming Methods” (on web site as Reading 1) Additional optional reading: Sequence Analysis Primer, pp “Dynamic Programming Methods” (on web site as Reading 1) (03-510) Durbin et al, Sections (03-510) Durbin et al, Sections Everybody: Look over paper by Needleman and Wunsch on web site (Reading 2) Everybody: Look over paper by Needleman and Wunsch on web site (Reading 2)

Summary, Part 7 Similarity functions or similarity matrices describe (quantitatively) the degree of similarity between two sequence elements (bases or amino acids) Similarity functions or similarity matrices describe (quantitatively) the degree of similarity between two sequence elements (bases or amino acids) The Dayhoff MDM78 matrix is a similarity matrix commonly used to estimate the degree to which a change from one amino acid to another can be “tolerated” in a protein The Dayhoff MDM78 matrix is a similarity matrix commonly used to estimate the degree to which a change from one amino acid to another can be “tolerated” in a protein

Summary, Part 7 Dot matrices graphically present regions of identity or similarity between two sequences Dot matrices graphically present regions of identity or similarity between two sequences The use of windows and thresholds can reduce “noise” in dot matrices The use of windows and thresholds can reduce “noise” in dot matrices Inversions, duplications and palindromes have unique “signatures” in dot matrices Inversions, duplications and palindromes have unique “signatures” in dot matrices