1. Biological Sequence Analysis Chapter 3

2. Protein Families Organism 1 Organism 2 Enzym e 1 Enzym e 2 Closely relatedSame Function MSEKKQPVDLGLLEEDDEFEEFPAEDWAGLDEDEDAHVWEDNWDDDNVEDDFSNQLRAELEKHGYKMETS ::::::.::::::::::::::::::::.:::::::::::::::::::::::::::::::::::::::::: MSEKKQTVDLGLLEEDDEFEEFPAEDWTGLDEDEDAHVWEDNWDDDNVEDDFSNQLRAELEKHGYKMETS Related Sequences Protein Family

3. Alignments ACDEFGHIKLM N ACEDFGHIPLM N 75%ID ACDEFGHIKLM N ACACFGKIKLM N 75%ID

4. Substitutions Glutamic acid Aspartic acidD E

5. Substitutions TThreonine SSerine

6. Substitutions AlanineA WTryptophane

7. Deriving Substitution Scores BLOSUM, Henikoff & Henikoff, 1992 Protein Family Block ABlock B

8. BLOSUM Matrices Henikoff & Henikoff, 1992...A......S......A... A8 AA1 AS 7 AA 6 AA 5 AA 4 AA 3 AA 2 AA 0 AA 1 AA 1 AS 2 SA 0 AS 1 AS 369 45 s w ws(s-1)/2 = 1x10x9/2 = f

9. BLOSUM Matrices Henikoff & Henikoff, 1992 AAACADAE 0.8000......... ARASATAVAWAYCCCD 00.2000000 VYWWWYYY 0000......... q Raw Frequencies

10. BLOSUM Matrices Henikoff & Henikoff, 1992 The probability of occurrence of the i’th amino acid in an i, j pair is: 45 pairs = 90 participants in pairs A’s in pairs: 36x2 + 9x1 = 81 AAAS S’s in pairs: 0x2 + 9x1 = 9 Probability p A for encountering an A: 81/90 = 0.9 Probability p S for encountering an S: 9/90 = 0.1

11. BLOSUM Matrices Henikoff & Henikoff, 1992 Expected probability, e, of occurrence of pairs: e AA = p A p A = 0.9x0.9 = 0.81 e AS = p A p S + p S p A = 0.9x0.1 + 0.1x0.9 = 2x(0.9x0.1) = 0.18 e SS = p S p S = 0.1x0.1 = 0.01

12. BLOSUM Matrices Henikoff & Henikoff, 1992 Odds and logodds: Odd ratio: logodd, s: means that the observed frequencies are as expected means that the observed frequencies are lower than expected means that the observed frequencies are higher than expected In the final BLOSUM matrices values are presented in half-bits, i.e., logodds are multiplied with 2 and rounded to nearest integer.

13. BLOSUM Matrices Henikoff & Henikoff, 1992 Segment clustering Sequences with more than X% ID are represented as one average sequence (cluster) Sequences are added to the cluster if it has more than X% ID to any of the sequences already in the cluster If the clustering level is more than 50% ID, the final Matrix is a BLOSUM50, more than 62% leads to the BLOSUM62 matrix, etc.

14. BLOSUM Matrices Henikoff & Henikoff, 1992 A R N D C Q E G H I L K M F P S T W Y V B Z X * A 4 -1 -2 -2 0 -1 -1 0 -2 -1 -1 -1 -1 -2 -1 1 0 -3 -2 0 -2 -1 0 -4 R -1 5 0 -2 -3 1 0 -2 0 -3 -2 2 -1 -3 -2 -1 -1 -3 -2 -3 -1 0 -1 -4 N -2 0 6 1 -3 0 0 0 1 -3 -3 0 -2 -3 -2 1 0 -4 -2 -3 3 0 -1 -4 D -2 -2 1 6 -3 0 2 -1 -1 -3 -4 -1 -3 -3 -1 0 -1 -4 -3 -3 4 1 -1 -4 C 0 -3 -3 -3 9 -3 -4 -3 -3 -1 -1 -3 -1 -2 -3 -1 -1 -2 -2 -1 -3 -3 -2 -4 Q -1 1 0 0 -3 5 2 -2 0 -3 -2 1 0 -3 -1 0 -1 -2 -1 -2 0 3 -1 -4 E -1 0 0 2 -4 2 5 -2 0 -3 -3 1 -2 -3 -1 0 -1 -3 -2 -2 1 4 -1 -4 G 0 -2 0 -1 -3 -2 -2 6 -2 -4 -4 -2 -3 -3 -2 0 -2 -2 -3 -3 -1 -2 -1 -4 H -2 0 1 -1 -3 0 0 -2 8 -3 -3 -1 -2 -1 -2 -1 -2 -2 2 -3 0 0 -1 -4 I -1 -3 -3 -3 -1 -3 -3 -4 -3 4 2 -3 1 0 -3 -2 -1 -3 -1 3 -3 -3 -1 -4 L -1 -2 -3 -4 -1 -2 -3 -4 -3 2 4 -2 2 0 -3 -2 -1 -2 -1 1 -4 -3 -1 -4 K -1 2 0 -1 -3 1 1 -2 -1 -3 -2 5 -1 -3 -1 0 -1 -3 -2 -2 0 1 -1 -4 M -1 -1 -2 -3 -1 0 -2 -3 -2 1 2 -1 5 0 -2 -1 -1 -1 -1 1 -3 -1 -1 -4 F -2 -3 -3 -3 -2 -3 -3 -3 -1 0 0 -3 0 6 -4 -2 -2 1 3 -1 -3 -3 -1 -4 P -1 -2 -2 -1 -3 -1 -1 -2 -2 -3 -3 -1 -2 -4 7 -1 -1 -4 -3 -2 -2 -1 -2 -4 S 1 -1 1 0 -1 0 0 0 -1 -2 -2 0 -1 -2 -1 4 1 -3 -2 -2 0 0 0 -4 T 0 -1 0 -1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -2 -1 1 5 -2 -2 0 -1 -1 0 -4 W -3 -3 -4 -4 -2 -2 -3 -2 -2 -3 -2 -3 -1 1 -4 -3 -2 11 2 -3 -4 -3 -2 -4 Y -2 -2 -2 -3 -2 -1 -2 -3 2 -1 -1 -2 -1 3 -3 -2 -2 2 7 -1 -3 -2 -1 -4 V 0 -3 -3 -3 -1 -2 -2 -3 -3 3 1 -2 1 -1 -2 -2 0 -3 -1 4 -3 -2 -1 -4 B -2 -1 3 4 -3 0 1 -1 0 -3 -4 0 -3 -3 -2 0 -1 -4 -3 -3 4 1 -1 -4 Z -1 0 0 1 -3 3 4 -2 0 -3 -3 1 -1 -3 -1 0 -1 -3 -2 -2 1 4 -1 -4 X 0 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 0 0 -2 -1 -1 -1 -1 -1 -4 * -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 1 ACDEFGHIKLMN ACEDFGHIPLMN ACDEFGHIKLM N ACACFGKIKLM N 4+9-2-4+6+6-1+4+5+4+5+6 = 424+9+2+2+6+6+8+4-1+4+5+6 = 55

15. A 10 20 30 40 50 60 70 humanD -----MSEKKQPVDLGLLEEDDEFEEFPAEDWAGLDEDEDAHVWEDNWDDDNVEDDFSNQLRAELEKHGYKMETS..:. : :.:. :......:. :::::::::::::::..::::.:::: Anophe MSDKENKDKPKLDLGLLEEDDEFEEFPAEDWAGNKEDEEELSVWEDNWDDDNVEDDFNQQLRAQLEKHK------ 10 20 30 40 50 60 B 10 20 30 40 50 60 70 humanD ----MSEKKQPVDLGLLEEDDEFEEFPAEDWAGLDEDEDAHVWEDNWDDDNVEDDFSNQLRAELEKHGYKMETS....:...:::::::::::::::::::::..:::..........::....:..::.......... Anophe MSDKENKDKPKLDLGLLEEDDEFEEFPAEDWAGNKEDEEELSVWEDNWDDDNVEDDFNQQLRAQLEKHK----- 10 20 30 40 50 60 Figure 3.3: (A) The human proteasomal subunit aligned to the mosquito homolog using the BLOSUM50 matrix. (B) The human proteasomal subunit aligned to the mosquito homolog using identity scores. Gaps 10 20 30 40 50 60 70 humanD ----MSEKKQPVDLGLLEEDDEFEEFPAEDWAGLDEDEDAH-VWEDNWDDDNVEDDFSNQLRAELEKHGYKMETS....:...:::::::::::::::::::::..:::... :::::::::::::::..::::.:::: Anophe MSDKENKDKPKLDLGLLEEDDEFEEFPAEDWAGNKEDEEELSVWEDNWDDDNVEDDFNQQLRAQLEKHK------ 10 20 30 40 50 60

16. Gap Penalties A gap is a kind like a mismatch but... Often the gap score (gap penalty) has an even lower value than the lowest mismatch score Having only one type of gap penalties is called a linear gap cost Biologically gaps are often inserted/deleted as a one or more event In most alignment algorithms is two gap penalties. One for making the first gap Another (higher score) for making an additional gap Affine gap penalty

17. Dynamic Programming The rest of the slides are stolen from Anders Gorm PetersenAnders Gorm Petersen

18. Alignment depicted as path in matrix T C G C A T C A T C G C A T C A TCGCA TC-CA TCGCA T-CCA

19. Position labeled “x”: TC aligned with TC --TC-TCTC TC--T-CTC Alignment depicted as path in matrix T C G C A T C A x Meaning of point in matrix: all residues up to this point have been aligned (but there are many different possible paths).

20. Dynamic programming: computation of scores T C G C A T C A x Any given point in matrix can only be reached from three possible positions (you cannot “align backwards”). => Best scoring alignment ending in any given point in the matrix can be found by choosing the highest scoring of the three possibilities.

21. Dynamic programming: computation of scores T C G C A T C A x Any given point in matrix can only be reached from three possible positions (you cannot “align backwards”). => Best scoring alignment ending in any given point in the matrix can be found by choosing the highest scoring of the three possibilities. score(x,y) = max score(x,y-1) - gap-penalty

22. Dynamic programming: computation of scores T C G C A T C A x Any given point in matrix can only be reached from three possible positions (you cannot “align backwards”). => Best scoring alignment ending in any given point in the matrix can be found by choosing the highest scoring of the three possibilities. score(x,y) = max score(x,y-1) - gap-penalty score(x-1,y-1) + substitution-score(x,y)

23. Dynamic programming: computation of scores T C G C A T C A x Any given point in matrix can only be reached from three possible positions (you cannot “align backwards”). => Best scoring alignment ending in any given point in the matrix can be found by choosing the highest scoring of the three possibilities. score(x,y) = max score(x,y-1) - gap-penalty score(x-1,y-1) + substitution-score(x,y) score(x-1,y) - gap-penalty

24. Dynamic programming: computation of scores T C G C A T C A x Any given point in matrix can only be reached from three possible positions (you cannot “align backwards”). => Best scoring alignment ending in any given point in the matrix can be found by choosing the highest scoring of the three possibilities. Each new score is found by choosing the maximum of three possibilities. For each square in matrix: keep track of where best score came from. Fill in scores one row at a time, starting in upper left corner of matrix, ending in lower right corner. score(x,y) = max score(x,y-1) - gap-penalty score(x-1,y-1) + substitution-score(x,y) score(x-1,y) - gap-penalty

25. Dynamic programming: example A C G T A 1 -1 -1 -1 C -1 1 -1 -1 G -1 -1 1 -1 T -1 -1 -1 1 Gaps: -2

26. Dynamic programming: example

29. T C G C A : : T C - C A 1+1-2+1+1 = 2

30. Global versus local alignments Global alignment: align full length of both sequences. (The “Needleman-Wunsch” algorithm). Local alignment: find best partial alignment of two sequences (the “Smith-Waterman” algorithm). Global alignment Seq 1 Seq 2 Local alignment

31. Local alignment overview The recursive formula is changed by adding a fourth possibility: zero. This means local alignment scores are never negative. Trace-back is started at the highest value rather than in lower right corner Trace-back is stopped as soon as a zero is encountered score(x,y) = max score(x,y-1) - gap-penalty score(x-1,y-1) + substitution-score(x,y) score(x-1,y) - gap-penalty 0

32. Local alignment: example

33. Substitution matrices and sequence similarity Substitution matrices come as series of matrices calculated for different degrees of sequence similarity (different evolutionary distances). ”Hard” matrices are designed for similar sequences –Hard matrices a designated by high numbers in the BLOSUM series (e.g., BLOSUM80) –Hard matrices yield short, highly conserved alignments ”Soft” matrices are designed for less similar sequences –Soft matrices have low BLOSUM values (45) –Soft matrices yield longer, less well conserved alignments

34. Alignments: things to keep in mind “Optimal alignment” means “having the highest possible score, given substitution matrix and set of gap penalties”. This is NOT necessarily the biologically most meaningful alignment. Specifically, the underlying assumptions are often wrong: substitutions are not equally frequent at all positions, affine gap penalties do not model insertion/deletion well, etc. Pairwise alignment programs always produce an alignment - even when it does not make sense to align sequences.

35. Database searching Using pairwise alignments to search databases for similar sequences Database Query sequence

36. Database searching Most common use of pairwise sequence alignments is to search databases for related sequences. For instance: find probable function of newly isolated protein by identifying similar proteins with known function. Most often, local alignment ( “Smith-Waterman”) is used for database searching: you are interested in finding out if ANY domain in your protein looks like something that is known. Often, full Smith-Waterman is too time-consuming for searching large databases, so heuristic methods are used (fasta, BLAST).

37. Database searching: heuristic search algorithms FASTA (Pearson 1995) Uses heuristics to avoid calculating the full dynamic programming matrix Speed up searches by an order of magnitude compared to full Smith-Waterman The statistical side of FASTA is still stronger than BLAST BLAST (Altschul 1990, 1997) Uses rapid word lookup methods to completely skip most of the database entries Extremely fast One order of magnitude faster than FASTA Two orders of magnitude faster than Smith-Waterman Almost as sensitive as FASTA

38. BLAST flavors BLASTN Nucleotide query sequence Nucleotide database BLASTP Protein query sequence Protein database BLASTX Nucleotide query sequence Protein database Compares all six reading frames with the database TBLASTN Protein query sequence Nucleotide database ”On the fly” six frame translation of database TBLASTX Nucleotide query sequence Nucleotide database Compares all reading frames of query with all reading frames of the database

39. Searching on the web: BLAST at NCBI Very fast computer dedicated to running BLAST searches Many databases that are always up to date Nice simple web interface But you still need knowledge about BLAST to use it properly

40. When is a database hit significant? Problem : –Even unrelated sequences can be aligned (yielding a low score) –How do we know if a database hit is meaningful? –When is an alignment score sufficiently high? Solution : –Determine the range of alignment scores you would expect to get for random reasons (i.e., when aligning unrelated sequences). –Compare actual scores to the distribution of random scores. –Is the real score much higher than you’d expect by chance?

41. Random alignment scores follow extreme value distributions The exact shape and location of the distribution depends on the exact nature of the database and the query sequence Searching a database of unrelated sequences result in scores following an extreme value distribution

42. Significance of a hit: one possible solution (1)Align query sequence to all sequences in database, note scores (2)Fit actual scores to a mixture of two sub-distributions: (a) an extreme value distribution and (b) a normal distribution (3)Use fitted extreme-value distribution to predict how many random hits to expect for any given score (the “E-value”)

43. Significance of a hit: example Search against a database of 10,000 sequences. An extreme-value distribution (blue) is fitted to the distribution of all scores. It is found that 99.9% of the blue distribution has a score below 112. This means that when searching a database of 10,000 sequences you’d expect to get 0.1% * 10,000 = 10 hits with a score of 112 or better for random reasons 10 is the E-value of a hit with score 112. You want E-values well below 1!

44. Database searching: E-values in BLAST BLAST uses precomputed extreme value distributions to calculate E-values from alignment scores For this reason BLAST only allows certain combinations of substitution matrices and gap penalties This also means that the fit is based on a different data set than the one you are working on A word of caution: BLAST tends to overestimate the significance of its matches E-values from BLAST are fine for identifying sure hits One should be careful using BLAST’s E-values to judge if a marginal hit can be trusted (e.g., you may want to use E-values of 10 -4 to 10 -5 ).

45. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Refresher: pairwise alignments Most used substitution matrices are themselves derived empirically from simple multiple alignmentsMost used substitution matrices are themselves derived empirically from simple multiple alignments Multiple alignment A/A 2.15% A/C 0.03% A/D 0.07%... Calculate substitution frequencies Score(A/C) = log Freq(A/C),observed Freq(A/C),expected Convert to scores

46. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Multiple alignment

47. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Multiple alignments: what use are they? Starting point for studies of molecular evolutionStarting point for studies of molecular evolution

48. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Multiple alignments: what use are they? Characterization of protein families:Characterization of protein families: –Identification of conserved (functionally important) sequence regions –Prediction of structural features (disulfide bonds, amphipathic alpha- helices, surface loops, etc.)

49. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Scoring a multiple alignment: the “sum of pairs” score...A......S......T... One column from alignment AA: 4, AS: 1, AT:0 AS: 1, AT: 0 ST: 1 Score: 4+1+0+1+0+1 = 7  In theory, it is possible to define an alignment score for multiple alignments (there are many alternative scoring systems)

50. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Multiple alignment: dynamic programming is only feasible for very small data sets In theory, optimal multiple alignment can be found by dynamic programming using a matrix with more dimensions (one dimension per sequence)In theory, optimal multiple alignment can be found by dynamic programming using a matrix with more dimensions (one dimension per sequence) BUT even with dynamic programming finding the optimal alignment very quickly becomes impossible due to the astronomical number of computationsBUT even with dynamic programming finding the optimal alignment very quickly becomes impossible due to the astronomical number of computations Full dynamic programming only possible for up to about 4-5 protein sequences of average lengthFull dynamic programming only possible for up to about 4-5 protein sequences of average length Even with heuristics, not feasible for more than 7-8 protein sequencesEven with heuristics, not feasible for more than 7-8 protein sequences Never used in practiceNever used in practice Dynamic programming matrix for 3 sequences For 3 sequences, optimal path must come from one of 7 previous points

51. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Multiple alignment: an approximate solution Progressive alignment (ClustalX and other programs):Progressive alignment (ClustalX and other programs): 3. Perform all pairwise alignments; keep track of sequence similarities between all pairs of sequences (construct “distance matrix”) 5. Align the most similar pair of sequences 7. Progressively add sequences to the (constantly growing) multiple alignment in order of decreasing similarity.

52. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Progressive alignment: details 1)Perform all pairwise alignments, note pairwise distances (construct “distance matrix”) 2) Construct pseudo-phylogenetic tree from pairwise distances S1 S2 S3 S4 6 pairwise alignments S1 S2 S3 S4 S1 S2 3 S3 1 3 S4 3 2 3 S1 S3S4S2 S1 S2 S3 S4 S1 S2 3 S3 1 3 S4 3 2 3 “Guide tree”

53. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Progressive alignment: details 3)Use tree as guide for multiple alignment: a)Align most similar pair of sequences using dynamic programming b)Align next most similar pair c)Align alignments using dynamic programming - preserve gaps S1 S3S4S2 S1 S3 S2 S4 S1 S3 S2 S4 New gap to optimize alignment of (S2,S4) with (S1,S3)

54. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Aligning profiles S1 S3 S2 S4 + S1 S3 S2 S4 New gap to optimize alignment of (S2,S4) with (S1,S3) Aligning alignments: each alignment treated as a single sequence (a profile) Full dynamic programming on two profiles

55. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Scoring profile alignments...A......S......T... + One column from alignment AS: 1, AT:0 SS: 4, ST:1 Score: 1+0+4+1 = 1.5 4 Compare each residue in one profile to all residues in second profile. Score is average of all comparisons.

56. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Additional ClustalX heuristics Sequence weighting:Sequence weighting: –scores from similar groups of sequences are down-weighted Variable substitution matrices:Variable substitution matrices: –during alignment ClustalX uses different substitution matrices depending on how similar the sequences/profiles are Variable gap penalties:Variable gap penalties:  gap penalties depend on substitution matrix  gap penalties depend on similarity of sequences  reduced gap penalties at existing gaps  increased gap penalties CLOSE to existing gaps  reduced gap penalties in hydrophilic stretches (presumed surface loop)  residue-specific gap penalties  and more...

57. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Other multiple alignment programs ClustalW / ClustalX pileup multalign multal saga hmmt DIALIGN SBpima MLpima T-Coffee...

58. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Other multiple alignment programs ClustalW / ClustalX pileup multalign multal saga hmmt DIALIGN SBpima MLpima T-Coffee...

59. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Global methods (e.g., ClustalX) get into trouble when data is not globally related!!!

60. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Global methods (e.g., ClustalX) get into trouble when data is not globally related!!! Clustalx

61. CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Global methods (e.g., ClustalX) get into trouble when data is not globally related!!! Clustalx Possible solutions: (1)Cut out conserved regions of interest and THEN align them (2)Use method that deals with local similarity (e.g. DIALIGN)