CSE182-L5:
Position specific scoring matrices
Regular Expression Matching
Protein 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 Matching
Protein 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

R  {}
R  { },  
R  R1  R2
R  R1  R2
R  R*1
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
Base case
 Union of strings
Concatenation
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 A
S  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*
A
C
E
start
E
C
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end
Constructing automata from R.E
•
•
•
•
•
R = {}
R = {},   
R = R1 + R 2
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]
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
D[2]
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D[c]
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]
u
D[c]
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D.P. to match regular expression
u
• 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]
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u 

v
Eps(u)
D.P. to match regular expression
• Q: when is v  N[c]?
• A: If for some u  N[c-1], w = A[u,D[c]],
• v  {w}+ Eps(w)
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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

D[l..c]  R  D[1..c]   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
0.28
0.14
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Scoring Profiles
S(i, j)   f ki M rk ,s j 
k
Scoring Matrix
i

k
s
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fki
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 homologs
2. Searching with Profiles.
1. Does the keyword search idea work?
•
•
Multiple alignment:
–
Use ungapped multiple
alignments only
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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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Pfam
http://pfam.wustl.edu/
Also at Sanger
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PROSITE
http://us.expasy.org/prosite/
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BLOCKS
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