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1-month Practical Course Genome Analysis Lecture 3: Residue exchange matrices

C. E. N. T. E. R. F. O. R. I. N. T. E. G. R. A. T. I. V. E. B. I. O. I. N. F. O. R. M. A. T. I. C. S. V. U. 1-month Practical Course Genome Analysis Lecture 3: Residue exchange matrices Centre for Integrative Bioinformatics VU (IBIVU)

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1-month Practical Course Genome Analysis Lecture 3: Residue exchange matrices

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  1. C E N T E R F O R I N T E G R A T I V E B I O I N F O R M A T I C S V U 1-month Practical Course Genome Analysis Lecture 3: Residue exchange matrices Centre for Integrative Bioinformatics VU (IBIVU) Vrije Universiteit Amsterdam The Netherlands ibi.vu.nl heringa@cs.vu.nl

  2. Amino acid exchange matrices 2020 How do we get one? And how do we get associated gap penalties? First systematic method to derive a.a. exchange matrices by Margaret Dayhoff et al. (1968) – Atlas of Protein Structure

  3. A 2 R -2 6 N 0 0 2 D 0 -1 2 4 C -2 -4 -4 -5 12 Q 0 1 1 2 -5 4 E 0 -1 1 3 -5 2 4 G 1 -3 0 1 -3 -1 0 5 H -1 2 2 1 -3 3 1 -2 6 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3 W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4 B 0 -1 2 3 -4 1 2 0 1 -2 -3 1 -2 -5 -1 0 0 -5 -3 -2 2 Z 0 0 1 3 -5 3 3 -1 2 -2 -3 0 -2 -5 0 0 -1 -6 -4 -2 2 3 A R N D C Q E G H I L K M F P S T W Y V B Z PAM250 matrix amino acid exchange matrix (log odds) Positive exchange values denote mutations that are more likely than randomly expected, while negative numbers correspond to avoided mutations compared to the randomly expected situation

  4. Amino acid exchange matrices Amino acids are not equal: 1. Some are easily substituted because they have similar: • physico-chemical properties • chemical structure 2. Some mutations between amino acids occur more often due tosimilar codons The two above observations give us ways to define substitutionmatrices

  5. The 20 common amino acids

  6. A 2 R -2 6 N 0 0 2 D 0 -1 2 4 C -2 -4 -4 -5 12 Q 0 1 1 2 -5 4 E 0 -1 1 3 -5 2 4 G 1 -3 0 1 -3 -1 0 5 H -1 2 2 1 -3 3 1 -2 6 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3 W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4 B 0 -1 2 3 -4 1 2 0 1 -2 -3 1 -2 -5 -1 0 0 -5 -3 -2 2 Z 0 0 1 3 -5 3 3 -1 2 -2 -3 0 -2 -5 0 0 -1 -6 -4 -2 2 3 A R N D C Q E G H I L K M F P S T W Y V B Z Substitution matrices

  7. A 2 R -2 6 N 0 0 2 D 0 -1 2 4 C -2 -4 -4 -5 12 Q 0 1 1 2 -5 4 E 0 -1 1 3 -5 2 4 G 1 -3 0 1 -3 -1 0 5 H -1 2 2 1 -3 3 1 -2 6 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3 W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4 B 0 -1 2 3 -4 1 2 0 1 -2 -3 1 -2 -5 -1 0 0 -5 -3 -2 2 Z 0 0 1 3 -5 3 3 -1 2 -2 -3 0 -2 -5 0 0 -1 -6 -4 -2 2 3 A R N D C Q E G H I L K M F P S T W Y V B Z PAM250 matrix WR exchange is too large (due to paucity of data)

  8. PAM model The scores derived through the PAM model are an accurate description of the information content (or the relative entropy) of an alignment (Altschul, 1991). PAM-1 corresponds to about 1 million years of evolution PAM-120 has the largest information content of the PAM matrix series (Altschul, 1991) PAM-250 is the traditionally most popular matrix

  9. Summary Dayhoff’s PAM-matrices • Derived from global alignments of closely related sequences. • Matrices for greater evolutionary distances are extrapolated from those for lesser ones. • The number with the matrix (PAM40, PAM100) refers to the evolutionary distance; greater numbers are greater distances. • Several later groups have attempted to extend Dayhoff's methodology or re-apply her analysis using later databases with more examples. • Extensions of Dayhoff’s methodology: > Jones, Thornton and coworkers used the same methodology as Dayhoff but with modern databases (CABIOS 8:275).> Gonnett and coworkers (Science 256:1443) used a slightly different (but theoretically equivalent) methodology. > Henikoff & Henikoff (Proteins 17:49) compared these two newer versions of the PAM matrices with Dayhoff's originals.

  10. The BLOSUM matrices(BLOcks SUbstitution Matrix) • The BLOSUM series of matrices were created by Steve Henikoff and colleagues (PNAS 89:10915). • Derived from local, un-gapped alignments of distantly related sequences. • All matrices are directly calculated; no extrapolations are used. • Again: the observed frequency of each pair is compared to the expected frequency (which is essentially the product of the frequencies of each residue in the dataset). Then: Log-odds matrix.

  11. The Blocks Database • The Blocks Database contains multiple alignments of conserved regions in protein families. • Blocks are multiply aligned un-gapped segments corresponding to the most highly conserved regions of proteins. • The blocks for the BLOCKS database are made automatically by looking for the most highly conserved regions in groups of proteins represented in the PROSITE database. These blocks are then calibrated against the SWISS-PROT database to obtain a measure of the random distribution of matches. It is these calibrated blocks that make up the BLOCKS database. • The database can be searched by e-mail and World Wide Web (WWW) servers (http://blocks.fhcrc.org/help) to classify protein and nucleotide sequences.

  12. The Blocks Database Gapless alignment blocks

  13. The BLOSUM series • BLOSUM30, 35, 40, 45, 50, 55, 60, 62, 65, 70, 75, 80, 85, 90. • The number after the matrix (BLOSUM62) refers to the minimum percent identity of the blocks (in the BLOCKS database) used to construct the matrix (all blocks have >=62% sequence identity); • No extrapolations are made in going to higher evolutionary distances • High number - closely related sequences Low number - distant sequences • BLOSUM62 is the most popular: best for general alignment.

  14. BLOSUM62 Matrix, log-odds representation

  15. The log-odds matrix for BLOSUM62

  16. Based on an explicit evolutionary model Derived from small, closely related proteins with ~15% divergence Higher PAM numbers to detect more remote sequence similarities Errors in PAM 1 are scaled 250X in PAM 250 Based on empirical frequencies Uses much larger, more diverse set of protein sequences (30-90% ID) Lower BLOSUM numbers to detect more remote sequence similarities Errors in BLOSUM arise from errors in alignment PAM versus BLOSUM

  17. Comparing exchange matrices • To compare amino acid exchange matrices, the "Entropy" value can be used. This is a relative entropy value (H) which describes the amount of information available per aligned residue pair.

  18. Blosum Entropy PAM Entropy 30 0.1424 10 3.43 35 0.2111 50 2 40 0.2851 80 1.44 45 0.3795 100 1.18 50 0.4808 120 0.979 55 0.5637 180 0.591 60 0.6603 200 0.507 62 0.6979 250 0.354 65 0.7576 300 0.254 70 0.8391 350 0.186 75 0.9077 400 0.139 80 0.9868 450 0.105 85 1.0805 500 0.0803 90 1.1806 100 1.4516 Comparing exchange matrices To compare amino acid exchange matrices, the "Entropy" value can be used. This is a relative entropy value which describes the amount of information available per aligned residue pair. As two protein sequences diverge over time, information about the evolutionary process at work is lost (e.g. back mutations). Therefore, matrices with larger entropy values are more sensitive to less divergent sequences, while matrices with smaller entropy values are more sensitive to distantly related sequences.

  19. Specialized matrices • Claverie (J.Mol.Biol 234:1140) developed a set of substitution matrices designed explicitly for finding possible frameshifts in protein sequences.These matrices are designed solely for use in protein-protein comparisons; they should not be used with programs which blindly translate DNA (e.g. BLASTX, TBLASTN).

  20. Specialized matrices • Rather than starting from alignments generated by sequence comparison, Rissler et al (1988) and later Overington et al (1992) only considered proteins for which an experimentally determined three dimensional structure was available. • They then aligned similar proteins on the basis of their structure rather than sequence and used the resulting sequence alignments as their database from which to gather substitution statistics. In principle, the Rissler or Overington matrices should give more reliable results than either PAM or BLOSUM. However, the comparatively small number of available protein structures (particularly in the Rissler et al study) limited the reliability of their statistics. • Overington et al (1992) developed further matrices that consider the local environment of the amino acids.

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