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CSE182-L5: Position specific scoring matrices

Regular Expression MatchingProtein Domains

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Protein Sequence Analysis

• What can you do if BLAST does not return a hit?– Sometimes, homology (evolutionary similarity) exists at

very low levels of sequence similarity.

• A: Accept hits at higher P-value. – This increases the probability that the sequence similarity

is a chance event.– How can we get around this paradox?– Reformulated Q: suppose two sequences B,C have the

same level of sequence similarity to sequence A. If A& B are related in function, can we assume that A& C are? If not, how can we distinguish?

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Silly Quiz

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Silly Quiz

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Protein sequence motifs

• Premise: • The sequence of a protein sequence gives clues

about its structure and function.• Not all residues are equally important in

determining function.• How can we identify these key residues?

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Prosite

• In some cases the sequence of an unknown protein is too distantly related to any protein of known structure to detect its resemblance by overall sequence alignment. However, relationships can be revealed by the occurrence in its sequence of a particular cluster of residue types, which is variously known as a pattern, motif, signature or fingerprint. These motifs arise because specific region(s) of a protein which may be important, for example, for their binding properties or for their enzymatic activity are conserved in both structure and sequence. These structural requirements impose very tight constraints on the evolution of this small but important portion(s) of a protein sequence. The use of protein sequence patterns or profiles to determine the function of proteins is becoming very rapidly one of the essential tools of sequence analysis. Many authors ( 3,4) have recognized this reality. Based on these observations, we decided in 1988, to actively pursue the development of a database of regular expression-like patterns, which would be used to search against sequences of unknown function.

Kay Hofmann ,Philipp Bucher, Laurent Falquet and Amos Bairoch

The PROSITE database, its status in 1999

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Basic idea• It is a heuristic approach. Start with the following:

– A collection of sequences with the same function.– Region/residues known to be significant for maintaining

structure and function. • Develop a pattern of conserved residues around

the residues of interest• Iterate for appropriate sensitivity and specificity

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Zinc Finger domain

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Proteins containing zf domains

How can we find a motif corresponding to a zf domain

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From alignment to regular expressions

* ALRDFATHDDF SMTAEATHDSI ECDQAATHEAS

ATH-[DE]

• Search Swissprot with the resulting pattern• Refine pattern to eliminate false positives• Iterate

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The sequence analysis perspective

• Zinc Finger motif

– C-x(2,4)-C-x(3)-[LIVMFYWC]-x(8)-H-x(3,5)-H – 2 conserved C, and 2 conserved H

• How can we search a database using these motifs?– The motif is described using a regular expression. What is

a regular expression?– How can we search for a match to a regular expression?

Not allowed to use Perl :-)• The ‘regular expression’ motif is weak. How can we make it

stronger

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Regular Expression MatchingProtein structure basics

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Zinc Finger domain

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The sequence analysis perspective

• Zinc Finger motif

– C-x(2,4)-C-x(3)-[LIVMFYWC]-x(8)-H-x(3,5)-H – 2 conserved C, and 2 conserved H

• How can we search a database using these motifs?– The motif is described using a regular expression. What is

a regular expression?

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Regular Expressions

• Concise representation of a set of strings over alphabet .

• Described by a string over• R is a r.e. if and only if

€

Σ,⋅,∗,+{ }

€

R = {ε} Base caseR = {σ },σ ∈ ΣR = R1 + R2 Union of stringsR = R1 ⋅R2 ConcatenationR = R

1

* 0 or more repetitions

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Regular Expression

• Q: Let ={A,C,E}– Is (A+C)*EEC* a regular expression?– *(A+C)?– AC*..E?

• Q: When is a string s in a regular expression?– R =(A+C)*EEC*– Is CEEC in R?– AEC?– ACEE?

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Regular Expression & Automata

Every R.E can be expressed by an automaton (a directed graph) with the following properties:– The automaton has a start and end node– Each edge is labeled with a symbol from , or

Suppose R is described by automaton AS R if and only if there is a path from start to end in A, labeled with s.

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Examples: Regular Expression & Automata

• (A+C)*EEC*

CA

C

start endE E

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Constructing automata from R.E

• R = {}• R = {}, • R = R1 + R2

• R = R1 · R2

• R = R1*

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Regular Expression Matching

• Given a database D, and a regular expression R, is a substring of D in R?

• Is there a string D[l..c] that is accepted by the automaton of R?

• Simpler Q: Is D[1..c] accepted by the automaton of R?

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Alg. For matching R.E.

• If D[1..c] is accepted by the automaton RA

– There is a path labeled D[1]…D[c] that goes from START to END in RA

D[1] D[2] D[c]

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Alg. For matching R.E.

• If D[1..c] is accepted by the automaton RA

– There is a path labeled D[1]…D[c] that goes from START to END in RA

– There is a path labeled D[1]..D[c-1] from START to node u, and a path labeled D[c] from u to the END

D[1] .. D[c-1]

D[c]

u

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D.P. to match regular expression

• Define:– A[u,] = Automaton

node reached from u after reading

– Eps(u): set of all nodes reachable from node u using epsilon transitions.

– N[c] = subset of nodes reachable from START node after reading D[1..c]

– Q: when is v N[c]

uu vv

uu Eps(u)Eps(u)

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• Q: when is v N[c]?• A: If for some u N[c-1], w = A[u,D[c]],

• v {w}+ Eps(w)

D.P. to match regular expression

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Algorithm

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The final step

• We have answered the question:– Is D[1..c] accepted by R?– Yes, if END N[c]

• We need to answer – Is D[l..c] (for some l, and some c) accepted

by R

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D[l..c]∈ R ⇔ D[1..c]∈ Σ∗R

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Profiles versus regular expressions

• Regular expressions are intolerant to an occasional mis-match.

• The Union operation (I+V+L) does not quantify the relative importance of I,V,L. It could be that V occurs in 80% of the family members.

• Profiles capture some of these ideas.

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Profiles

• Start with an alignment of strings of length m, over an alphabet A,

• Build an |A| X m matrix F=(fki)

• Each entry fki represents the frequency of symbol k in position i

0.71

0.14

0.14

0.28

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Scoring Profiles

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S(i, j) = fki

k

∑ M rk,s j[ ]

k

i

s

fki

Scoring Matrix

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Psi-BLAST idea

• Multiple alignments are important for capturing remote homology.

• Profile based scores are a natural way to handle this.

• Q: What if the query is a single sequence.• A: Iterate:

– Find homologs using Blast on query– Discard very similar homologs– Align, make a profile, search with profile.

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Psi-BLAST speed

• Two time consuming steps.1. Multiple alignment of homologs2. Searching with Profiles.

1. Does the keyword search idea work?

• Multiple alignment:– Use ungapped multiple

alignments only

• Pigeonhole principle again: – If profile of length m must score

>= T– Then, a sub-profile of length l must

score >= lT/m– Generate all l-mers that score at

least lT|/M– Search using an automaton

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Databases of Motifs

• Functionally related proteins have sequence motifs.• The sequence motifs can be represented in many ways,

and different biological databases capture these representations– Collection of sequences (SMART)– Multiple alignments (BLOCKS)– Profiles (Pfam (HMMs)/Impala))– Regular Expressions (Prosite)

• Different representations must be queried in different ways

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Databases of protein domains

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Pfamhttp://pfam.wustl.edu/

Also at SangerAlso at Sanger

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PROSITE

http://us.expasy.org/prosite/

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BLOCKS

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