1. Sequences are related
Darwin: all organisms are related through descent with modification
Related molecules have similar functions in different organisms
Phylogenetic tree based on ribosomal RNA:
three domains of life

2. Sequences are related, II
Phylogenetic tree of globin-type proteins found in humans

3. Why compare sequences? Determination of evolutionary relationships
Prediction of protein function and structure (database searches).
Protein 1: binds oxygen
Sequence similarity
Protein 2: binds oxygen ?

4. Dotplots: visual sequence comparison
Place two sequences along axes of plot
Place dot at grid points where two sequences have identical residues
Diagonals correspond to conserved regions

5. Pairwise alignments 43.2% identity; Global alignment score: 374
alpha V-LSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHF-DLS-----HGSA
: :.: .:. : : :::: .. : :.::: :... .: :. .: : ::: :.
beta VHLTPEEKSAVTALWGKV--NVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNP
alpha QVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHL
.::.::::: :.....::.: ::.:: ::.::: ::.::.. :. .:: :.
beta KVKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHF
alpha PAEFTPAVHASLDKFLASVSTVLTSKYR
:::: :.:. .: .:.:...:. ::.
beta GKEFTPPVQAAYQKVVAGVANALAHKYH

6. Pairwise alignment
% identity in 3 aa overlap
SPA
:::
Percent identity is not a good measure of alignment quality

7. Pairwise alignments: alignment score
43.2% identity; Global alignment score: 374
alpha V-LSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHF-DLS-----HGSA
: :.: .:. : : :::: .. : :.::: :... .: :. .: : ::: :.
beta VHLTPEEKSAVTALWGKV--NVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNP
alpha QVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHL
.::.::::: :.....::.: ::.:: ::.::: ::.::.. :. .:: :.
beta KVKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHF
alpha PAEFTPAVHASLDKFLASVSTVLTSKYR
:::: :.:. .: .:.:...:. ::.
beta GKEFTPPVQAAYQKVVAGVANALAHKYH

8. Alignment scores: substitution matrices
A C G T
A C G T
A C G G C A
: : : :
A G G G T A
= 12
Standard DNA
identity matrix
Scoring example

9. Pairwise alignments: insertions/deletions
43.2% identity; Global alignment score: 374
alpha V-LSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHF-DLS-----HGSA
: :.: .:. : : :::: .. : :.::: :... .: :. .: : ::: :.
beta VHLTPEEKSAVTALWGKV--NVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNP
alpha QVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHL
.::.::::: :.....::.: ::.:: ::.::: ::.::.. :. .:: :.
beta KVKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHF
alpha PAEFTPAVHASLDKFLASVSTVLTSKYR
:::: :.:. .: .:.:...:. ::.
beta GKEFTPPVQAAYQKVVAGVANALAHKYH

10. Alignment scores: insertions/deletions
C A T A G G G T A T T G
C A T A A T T G
x (-0.1)=-10.3
Affine gap penalties:
Multiple insertions/deletions may be one evolutionary event =>
Separate penalties for gap opening and gap elongation

11. Pairwise alignments: conservative substitutions
43.2% identity; Global alignment score: 374
alpha V-LSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHF-DLS-----HGSA
: :.: .:. : : :::: .. : :.::: :... .: :. .: : ::: :.
beta VHLTPEEKSAVTALWGKV--NVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNP
alpha QVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHL
.::.::::: :.....::.: ::.:: ::.::: ::.::.. :. .:: :.
beta KVKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHF
alpha PAEFTPAVHASLDKFLASVSTVLTSKYR
:::: :.:. .: .:.:...:. ::.
beta GKEFTPPVQAAYQKVVAGVANALAHKYH

12. Serine (S) and Threonine (T) have similar physicochemical properties
Amino acid properties
Serine (S) and Threonine (T) have similar physicochemical properties
Aspartic acid (D) and Glutamic acid (E) have similar properties
=>
Substitution of S/T or E/D should result in scores that are only moderately lower than identities

13. Substitution scores: similar residues score higher
transition
transversion
Different transition and transversion costs:
A C G T A C G T
A C G G C A
: : : :
A G G G T A
= 15

14. Protein substitution matrices
BLOSUM50 matrix:
Positive scores on diagonal (identities)
Similar residues get higher scores
Dissimilar residues get smaller (negative) scores
A 5 R N D C Q E G H I L K M F P S T W Y V
A R N D C Q E G H I L K M F P S T W Y V

15. Estimation of the BLOSUM 50 matrix
For each alignment in the BLOCKS database the sequences are grouped into clusters with at least 50% identical residues (for BLOSUM 50)
All pairs of sequences are compared, and the observed pair frequencies are noted (e.g., A is paired with A in 40% of all cases, A with C in 1.2%, etc.)
Expected pair frequencies are computed from single amino acid frequencies.
For each amino acid pair the substitution scores are essentially computed as:
ID FIBRONECTIN_2; BLOCK
COG9_CANFA GNSAGEPCVFPFIFLGKQYSTCTREGRGDGHLWCATT
COG9_RABIT GNADGAPCHFPFTFEGRSYTACTTDGRSDGMAWCSTT
FA12_HUMAN LTVTGEPCHFPFQYHRQLYHKCTHKGRPGPQPWCATT
HGFA_HUMAN LTEDGRPCRFPFRYGGRMLHACTSEGSAHRKWCATTH
MANR_HUMAN GNANGATCAFPFKFENKWYADCTSAGRSDGWLWCGTT
MPRI_MOUSE ETDDGEPCVFPFIYKGKSYDECVLEGRAKLWCSKTAN
PB1_PIG AITSDDKCVFPFIYKGNLYFDCTLHDSTYYWCSVTTY
SFP1_BOVIN ELPEDEECVFPFVYRNRKHFDCTVHGSLFPWCSLDAD
SFP3_BOVIN AETKDNKCVFPFIYGNKKYFDCTLHGSLFLWCSLDAD
SFP4_BOVIN AVFEGPACAFPFTYKGKKYYMCTRKNSVLLWCSLDTE
SP1_HORSE AATDYAKCAFPFVYRGQTYDRCTTDGSLFRISWCSVT
COG2_CHICK GNSEGAPCVFPFIFLGNKYDSCTSAGRNDGKLWCAST
COG2_HUMAN GNSEGAPCVFPFTFLGNKYESCTSAGRSDGKMWCATT
COG2_MOUSE GNSEGAPCVFPFTFLGNKYESCTSAGRNDGKVWCATT
COG2_RABIT GNSEGAPCVFPFTFLGNKYESCTSAGRSDGKMWCATS
COG2_RAT GNSEGAPCVFPFTFLGNKYESCTSAGRNDGKVWCATT
COG9_BOVIN GNADGKPCVFPFTFQGRTYSACTSDGRSDGYRWCATT
COG9_HUMAN GNADGKPCQFPFIFQGQSYSACTTDGRSDGYRWCATT
COG9_MOUSE GNGEGKPCVFPFIFEGRSYSACTTKGRSDGYRWCATT
COG9_RAT GNGDGKPCVFPFIFEGHSYSACTTKGRSDGYRWCATT
FINC_BOVIN GNSNGALCHFPFLYNNHNYTDCTSEGRRDNMKWCGTT
FINC_HUMAN GNSNGALCHFPFLYNNHNYTDCTSEGRRDNMKWCGTT
FINC_RAT GNSNGALCHFPFLYSNRNYSDCTSEGRRDNMKWCGTT
MPRI_BOVIN ETEDGEPCVFPFVFNGKSYEECVVESRARLWCATTAN
MPRI_HUMAN ETDDGVPCVFPFIFNGKSYEECIIESRAKLWCSTTAD
PA2R_BOVIN GNAHGTPCMFPFQYNQQWHHECTREGREDNLLWCATT
PA2R_RABIT GNAHGTPCMFPFQYNHQWHHECTREGRQDDSLWCATT
Pair-freq(obs)
Pair-freq(expected)
log

16. Protein substitution matrices
PAM series
Estimated from reconstructed phylogenetic trees of closely related sequences which tends to favor single base substitutions
Matrices for longer evolutionary distances are calculated by extrapolation
BLOSUM series
Estimated from ungapped core alignments of protein families (the BLOCKS database)
Extrapolation is not used – matrices for large evolutionary distances are calculated directly from the alignments

17. Substitution matrices and evolutionary distance
Substitution matrices come as series of matrices calculated for different evolutionary distances
”Hard” matrices are designed for short distances
Hard matrices a designated by low numbers in the PAM series (20) and high numbers in the BLOSUM series (80)
Hard matrices correspond to short, highly conserved regions
”Soft” matrices are designed for longer distances
Soft matrices have high PAM values (250) and low BLOSUM values (45)
Soft matrices correspond to longer, less well conserved regions

18. Pairwise alignment Optimal alignment:
alignment having the highest possible score given a substitution matrix and a set of gap penalties

19. Pairwise alignment: the problem
The number of possible pairwise alignments increases explosively with the length of the sequences:
Two protein sequences of length 100 amino acids can be aligned in approximately 1060 different ways
Time needed to test all possibilities is same order of magnitude as the entire lifetime of the universe.

20. Pairwise alignment: the solution
”Dynamic programming”
(the Smith-Waterman algorithm)

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

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

23. Dynamic programming: computation of scores
T C G C A T C A
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. x
Fill in scores one row at a time, starting in upper left corner of matrix, ending in lower right corner.
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.
score(x,y-1) - gap-penalty
score(x-1,y-1) + substitution-score(x,y)
score(x-1,y) - gap-penalty
score(x,y) = max

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

25. Dynamic programming: example

26. Dynamic programming: example

27. Dynamic programming: example

28. Dynamic programming: example

29. Dynamic programming: example
T C G C A
: : : :
T C - C A
= 2

30. Global versus local alignments
Global alignment: align full length of both sequences.
Local alignment: find best partial alignment of two sequences
Global alignment
Seq 1
Local alignment
Seq 2

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-1) - gap-penalty
score(x-1,y-1) + substitution-score(x,y)
score(x-1,y) - gap-penalty
score(x,y) = max

32. Local alignment: example

33. 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.

34. Database searching Using pairwise alignments to search
databases for similar sequences

35. 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 alignments are 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).

36. 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

37. BLAST flavors BLASTN Nucleotide query sequence Nucleotide database
BLASTP
Protein query sequence
Protein database
BLASTX
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
Compares all reading frames of query with all reading frames of the database

38. 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

39. Database searching: detection limit

40. Significance testing: a gentle reminder
All tests of statistical significance involve a comparison between:
(1) an observed value
(2) the value that one would expect to find, on average, if only random variability was operating in the situation.
P-value: probability of obtaining observed value by chance
H0: coin is fair (50% heads)
H1: coin is unfair (>50% heads)
Test: 100 coin tosses, 59 heads
P(x>=59 heads) = 4.46%
Significantly different from random expectation (at the 5% level)

41. Alignment scores follow extreme value distributions
Alignment of unrelated/random sequences result in scores following an extreme value distribution
P(Sx) = 1-exp(-Kmne-x)
m, n: sequence lengths.
K, l: free parameters.
This can be shown analytically for ungapped alignments and has been found empirically to also hold for gapped alignments under commonly used conditions.

42. Database searching: significance of hits
Alignment algorithms will always produce alignments, regardless of whether it is meaningful or not
=> important to have way of selecting significant alignments from large set of database hits.
Solution: fit distribution of scores from database search to extreme value distribution; determine p-value of hit from this fitted distribution.
Example: scores fitted to extreme value distribution.
99.9% of this distribution is located below score=112
=> hit with score = 112 has a p-value of 0.1%

43. Database searching: Expectancy (E) values
In addition to p-values, database hits can be evaluated using expectancy values (E-values):
The E value is the number of hits, having score S or greater, that would be expected for random reasons in a search over the entire database

44. Database searching: Expectancy (E) values
E-values and p-values are related via the size of the database:
E(score >= S) = database-size x P(score >= S)
E.g., if a database contains protein sequences, then a p-value of 0.1% corresponds to an E-value of:
E = x 0.1% = 10
E-values are a good measure of significance since they take the database size into account (typically you will want E-values well below 1).

45. 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).