1. CSE182-L5: Scoring matrices Dictionary Matching
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2. Scoring DNA
DNA has structure.
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3. DNA scoring matrices
So far, we considered a simple match/mismatch criterion.
The nucleotides can be grouped into Purines (A,G) and Pyrimidines.
Nucleotide substitutions within a group (transitions) are more likely than those across a group (transversions)
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4. Scoring proteins
Scoring protein sequence alignments is a much more complex task than scoring DNA
Not all substitutions are equal
Problem was first worked on by Pauling and collaborators
In the 1970s, Margaret Dayhoff created the first similarity matrices.
“One size does not fit all”
Homologous proteins which are evolutionarily close should be scored differently than proteins that are evolutionarily distant
Different proteins might evolve at different rates and we need to normalize for that
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5. PAM 1 distance
Two sequences are 1 PAM apart if they differ in 1 % of the residues.
1% mismatch
PAM1(a,b) = Pr[residue b substitutes residue a, when the sequences are 1 PAM apart]
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6. PAM1 matrix Align many proteins that are very similar
Is this a problem?
PAM1 distance is the probability of a substitution when 1% of the residues have changed
Estimate the frequency Pb|a of residue a being substituted by residue b.
S(a,b) = log10(Pab/PaPb) = log10(Pb|a/Pb)
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7. PAM 1
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8. PAM distance
Two sequences are 1 PAM apart when they differ in 1% of the residues.
When are 2 sequences 2 PAMs apart?
1 PAM
2 PAM
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9. Higher PAMs PAM2(a,b) = ∑c PAM1(a,c). PAM1 (c,b)
PAM2 = PAM1 * PAM1 (Matrix multiplication)
PAM250
= PAM1*PAM249
= PAM1250
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10. PAM250 based scoring matrix
S250(a,b) = log10(Pab/PaPb) = log10(PAM250(b|a)/Pb)
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11. Scoring using PAM matrices
Suppose we know that two sequences are 250 PAMs apart.
S(a,b) = log10(Pab/PaPb)= log10(Pb|a/Pb) = log10(PAM250(a,b)/Pb)
How does it help?
S250(A,V) >> S1(A,V)
Scoring of hum vs. Dros should be using a higher PAM matrix than scoring hum vs. mus.
An alignment with a smaller % identity could still have a higher score and be more significant
hum
mus
dros
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12. BLOSUM series of Matrices
Henikoff & Henikoff: Sequence substitutions in evolutionarily distant proteins do not seem to follow the PAM distributions
A more direct method based on hand-curated multiple alignments of distantly related proteins from the BLOCKS database.
BLOSUM60 Merge all proteins that have greater than 60%. Then, compute the substitution probability.
In practice BLOSUM62 seems to work very well.
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13. PAM vs. BLOSUM What is the correspondence? PAM1 Blosum1 PAM2 Blosum2
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14. The last step in Blast We have discussed Alignments
Db filtering using keywords
E-values and P-values
Scoring matrices
The last step: Database filtering requires us to scan a large sequence fast for matching keywords
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15. Dictionary Matching, R.E. matching, and position specific scoring
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16. Keyword search
Recall: In BLAST, we get a collection of keywords from the query sequence, and identify all db locations with an exact match to the keyword.
Question: Given a collection of strings (keywords), find all occrrences in a database string where they keyword might match.
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17. Dictionary Matching 1:POTATO 2:POTASSIUM 3:TASTE
P O T A S T P O T A T O
database
dictionary
Q: Given k words (si has length li), and a database of size n, find all matches to these words in the database string.
How fast can this be done?
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18. Dict. Matching & string matching
How fast can you do it, if you only had one word of length m?
Trivial algorithm O(nm) time
Pre-processing O(m), Search O(n) time.
Dictionary matching
Trivial algorithm (l1+l2+l3…)n
Using a keyword tree, lpn (lp is the length of the longest pattern)
Aho-Corasick: O(n) after preprocessing O(l1+l2..)
We will consider the most general case
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19. Direct Algorithm P O P O P O T A S T P O T A T O P O T A T O
Observations:
When we mismatch, we (should) know something about where the next match will be.
When there is a mismatch, we (should) know something about other patterns in the dictionary as well.
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20. The Trie Automaton P O T A U I S M E 1 r S 2 3 1:POTATO 2:POTASSIUM
Construct an automaton A from the dictionary
A[v,x] describes the transition from node v to a node w upon reading x.
A[u,’T’] = v, and A[u,’S’] = w
Special root node r
Some nodes are terminal, and labeled with the index of the dictionary word.
1:POTATO
2:POTASSIUM
3:TASTE u v P O T A U I S M E 1 r S 2 w 3
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21. An O(lpn) algorithm for keyword matching
Start with the first position in the db, and the root node.
If successful transition
Increment current pointer
Move to a new node
If terminal node “success”
Else
Retract ‘current’ pointer
Increment ‘start’ pointer
Move to root & repeat
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22. Illustration: c l P O T A S T P O T A T O v P O T A U I S M E 1 S Fa05
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23. Idea for improving the time
Suppose we have partially matched pattern i (indicated by l, and c), but fail subsequently. If some other pattern j is to match
Then prefix(pattern j) = suffix [ first c-l characters of pattern(i)) c l
P O T A S T P O T A T O
P O T A S S I U M
Pattern i
T A S T E
1:POTATO
2:POTASSIUM
3:TASTE
Pattern j
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24. Improving speed of dictionary matching
Every node v corresponds to a string sv that is a prefix of some pattern.
Define F[v] to be the node u such that su is the longest suffix of sv
If we fail to match at v, we should jump to F[v], and commence matching from there
Let lp[v] = |su| 2 3 4 5 1 P O T A U I S M E S 11 6 7 9 10 8
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25. An O(n) alg. For keyword matching
Start with the first position in the db, and the root node.
If successful transition
Increment current pointer
Move to a new node
If terminal node “success”
Else (if at root)
Increment ‘current’ pointer
Mv ‘start’ pointer
Move to root
Else
Move ‘start’ pointer forward
Move to failure node
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26. Illustration P O T A S T P O T A T O l c 1 P O T A T O v T S S I U M AE
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27. Time analysis l c P O T A S T P O T A T O
In each step, either c is incremented, or l is incremented
Neither pointer is ever decremented (lp[v] < c-l).
l and c do not exceed n
Total time <= 2n l c
P O T A S T P O T A T O
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28. Blast: Putting it all together
Input: Query of length m, database of size n
Select word-size, scoring matrix, gap penalties, E-value cutoff
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29. Blast Steps Generate an automaton of all query keywords.
Scan database using a “Dictionary Matching” algorithm (O(n) time). Identify all hits.
Extend each hit using a variant of “local alignment” algorithm. Use the scoring matrix and gap penalties.
For each alignment with score S, compute the bit-score, E-value, and the P-value. Sort according to increasing E-value until the cut-off is reached.
Output results.
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30. 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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31. Silly Quiz
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32. Silly Quiz
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33. 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.
Suppose we knew the key residues of a family. If our query matches in those residues, it is a member. Otherwise, it is not.
How can we identify these key residues?
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34. Prosite The PROSITE database, its status in 1999 Fa05 CSE 182
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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35. 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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36. EX: Zinc Finger domain
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37. Proteins containing zf domains
How can we find a motif corresponding to a zf domain
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38. 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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39. 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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40. 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
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41. 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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42. 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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43. Examples: Regular Expression & Automata
(A+C)*EEC* A C E E
start
end C
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44. Constructing automata from R.E
R = {}
R = {},   
R = R1 + R2
R = R1 · R2
R = R1*      
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45. 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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46. 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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47. 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 u
D[1] .. D[c-1]
D[c]
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48. D.P. to match regular expression v
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]  u
Eps(u)
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49. 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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50. Algorithm
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51. 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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52. 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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53. 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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54. Scoring Profiles
Scoring Matrix i k
fki s
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55. 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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56. Psi-BLAST speed Two time consuming steps.
Multiple alignment of homologs
Searching with Profiles.
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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57. 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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58. Databases of protein domains
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59. Pfam
Also at Sanger
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60. PROSITE
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61. Fa05
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62. BLOCKS
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63. Fa05
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