Statistical Significance for Local Sequence Alignments Multiple Sequence Alignments Profilebased seq

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Statistical Significance forLocal Sequence
AlignmentsMultiple Sequence AlignmentsProfile-ba
sed sequence search

• A. Brüngger, Labhead BioinformaticsNovartis
  Pharma AG
• adrian.bruengger_at_pharma.novartis.com

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Local Alignments, Multiple Sequence Alignments,
Profile-based Searches

• Statistical Significance of Local Sequence
  Alignments
• Fast identification of identical k-mers
  Implementation detail
• Facts about the statistical significance of local
  alignments
• Statistical significance of local alignments in
  BLAST
• Multiple Sequence Alignments
• Dynamic Programming
• Iterative Approach for multiple sequence
  alignments CLUSTALW
• Construction of phylogenetic trees
• Profile-based sequence searches
• Patterns, motifs, profiles as domain footprints
• Databases of patterns and profiles PROSITE
• Example Sensitivity/selectivity of a pattern for
  ubiquitin conjugating enzymes

Outline follows David W. Mount, "Bioionformatics
- Sequence and Genome Analysis Cold Spring
Harbour Laboratory Press, 2001. Online
http//www.bioinformaticsonline.org
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Local Sequence Alignments Fast identification of
k-mers
query
MAAAPLLGAQGAPLEPVYPGDNATPEQMAQYAADLRRYIN
MLTRPRYGKRHKEDTLAFSE

ADAYYVALLLQPLQGTWGAPLEPMYPGDYATPEQMAQYETQLRRYINTLT
RPRYGKRAEEENTGGLP
database

• Fast identification of k-mers
• Indexing of all possible k-mers in database
• Index of a k-mer is easily computed
• A 0, C 1, D 2 Y 19
• Index of "ADAYY"

0 AAAAA - 1 AAAAC - 2 AAAAD
- ... 16399 ADAYY 1 ...
ALLLQ 7 ... ... VALLL 6
... 205-1 YYYYY -
A D A Y Y 0 2
0 19 19 204 203 202 201 200
0 16000 0 380 19 16399
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Statistical Significance of Local Sequence
Alignments

• Probability that q (lenm) is contained in t
  (lenn)
• a. There are (n-m) 'words' of length m in t
• b. In total, there are 4m sequences of length m
• c. p (n-m) / 4m

This is wrong. Why?

• The (n-m) words in t are not independent!
• Therefore
• probability p in general hard to compute (no
  analytical solution known so far!)
• simplest case! complication scoring, gapped
  alignment
• approximation formulas used in BLAST/FASTA
• probability of a certain score of a local
  alignment between t and q
• follows an extreme value distribution (not normal
  distribution)
• extreme value distribution changes with residual
  composition of sequences
• FASTA plots distribution of occurred scores vs.
  expected scores
• BLAST assigns an E-value to each hit
• expected number of hits with score of hit
• considers residual composition of query and
  database
• the same local alignment has different E-Values
  if it occurs for different DBs!

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Sample BLAST output
visualization of hits
summary of hits, containing E-Values
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Multiple Sequence Alignment

• Dynamic Programming for multiple sequence
  alignments
• Dynamic Programming can theoretically be used for
  aligning kgt2 sequences
• instead of 2-dimensional scoring matrix, a
  k-dimensional scoring matrix is used
• instead of 2-dimensional dynamic programming
  scheme, a k-dimensional one is used
• However, in practical terms, not feasible
• k-dimensional scoring matrix uses exponential
  space
• example 5 sequences, 100 residues each, dyn.pr.
  scheme 1005 cells, at least 10GB
• (Mathematically) optimal solution for aligning
  multiple sequences not feasible!
• Approximations used
• Idea of progressive methods
• align two sequences
• compute "consensus" sequence
• align consensus with third sequence
• repeat steps 2/3

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Multiple Sequence Alignments CLUSTALW (1)

• Basic steps
• step 1 Perform pairwise sequence alignments of
  all possible pairs
• step 2 Use scores to produce a phylogenetic
  tree
• step 3 align the sequences sequentially, guided
  by the tree
• the most closely related sequences are aligned
  first
• other sequences or groups of sequences are added
• Example Phylogenetic tree for 4 sequences

A B C D A 100 90 85 90 B 100 95
80 C 100 97 D
100 Percentage Identities inpairwise alignment
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Multiple Sequence Alignments CLUSTALW (2)

• Computation of Phylogenetic tree

A B C D A 100 95 80 90 B 100 95
85 C 100 97 D
100 Percentage Identities inpairwise alignment
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Multiple Sequence Alignments CLUSTALW (3)

• CLUSTALW
• seven globins

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Patterns/Motifs as domain footprints

• Available implementations

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Multiple sequence alignment of human ubiquitin
conjugating enzymes

• UBE2D2 FPTDYPFKPPKVAFTTRIYHPNINSN-GSICLDILR-----
  --------SQWSPALTISK
• UBE2D3 FPTDYPFKPPKVAFTTRIYHPNINSN-GSICLDILR-----
  --------SQWSPALTISK
• BAA91697 FPTDYPFKPPKVAFTTKIYHPNINSN-GSICLDILR-----
  --------SQWSPALTVSK
• UBE2D1 FPTDYPFKPPKIAFTTKIYHPNINSN-GSICLDILR-----
  --------SQWSPALTVSK
• UBE2E1 FTPEYPFKPPKVTFRTRIYHCNINSQ-GVICLDILK-----
  --------DNWSPALTISK
• UBCH9 FSSDYPFKPPKVTFRTRIYHCNINSQ-GVICLDILK-----
  --------DNWSPALTISK
• UBE2N LPEEYPMAAPKVRFMTKIYHPNVDKL-GRICLDILK-----
  --------DKWSPALQIRT
• AAF67016 IPERYPFEPPQIRFLTPIYHPNIDSA-GRICLDVLKLP---
  ------PKGAWRPSLNIAT
• UBCH10 FPSGYPYNAPTVKFLTPCYHPNVDTQ-GNICLDILK-----
  --------EKWSALYDVRT
• CDC34 FPIDYPYSPPAFRFLTKMWHPNIYET-GDVCISILHPPVDD
  PQSGELPSERWNPTQNVRT
• BAA91156 FPIDYPYSPPTFRFLTKMWHPNIYEN-GDVCISILHPPVDD
  PQSGELPSERWNPTQNVRT
• UBE2G1 FPKDYPLRPPKMKFITEIWHPNVDKN-GDVCISILHEPGED
  KYGYEKPEERWLPIHTVET
• UBE2B FSEEYPNKPPTVRFLSKMFHPNVYAD-GSICLDILQN----
  ---------RWSPTYDVSS
• UBE2I FKDDYPSSPPKCKFEPPLFHPNVYPS-GTVCLSILEED---
  --------KDWRPAITIKQ
• E2EPF5 LGKDFPASPPKGYFLTKIFHPNVGAN-GEICVNVLKR----
  ---------DWTAELGIRH
• UBE2L1 FPAEYPFKPPKITFKTKIYHPNIDEK-GQVCLPVISA----
  --------ENWKPATKTDQ
• UBE2L6 FPPEYPFKPPMIKFTTKIYHPNVDEN-GQICLPIISS----
  --------ENWKPCTKTCQ
• UBE2H LPDKYPFKSPSIGFMNKIFHPNIDEASGTVCLDVIN-----
  --------QTWTALYDLTN
• UBC12 VGQGYPHDPPKVKCETMVYHPNIDLE-GNVCLNILR-----
  --------EDWKPVLTINS

Pattern FYW-H-PC-N-IV-x(3,4)-G-x-IV-C-
LIV-x-IV PROSITE FYWLSP-H-PC-NH-LIV-x(
3,4)-G-x-LIV-C-LIV-x-LIV
Pattern that can be used to scan databases for
its occurrence or Sequence can be searched
against databse of patterns
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Patterns as footprints of functional protein
domains PROSITE

• Example Ubiquitin conjugating enzyme pattern
  entry

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Scanning a sequence vs. profile/pattern database
InterProScan (EBI)

• Example EphB2 (ephrin B2 receptor, receptor
  tyrosine kinase)

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Conclusions

• Statistical significance of local alignments
• no analytical formula for probability of a
  certain local alignment score
• local alignment scores follow extreme value
  distribution (not normal)
• BLAST reports expectation value, dependent on
  residual composition and size of sequences
• Multiple alignments
• dynamic programming not feasible ? approximation
  used
• progressive methods (align two seqs, consensus,
  align third)
• CLUSTALW all pairwise alignments ? guide tree
• Patterns, Motifs, Profiles
• characteristics of domains
• pattern/profile databases PROSITE
• search with pattern vs. sequence databases
• search with sequence vs. pattern database
  INTERPROSCAN
• Hidden Markov Models (HMM) Generalized profiles