CSE182-L4:%20Scoring%20matrices,%20Dictionary%20Matching

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CSE182-L4 Scoring matrices, Dictionary Matching
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• Use the list for all course related queries,
  discussions,

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Silly Quiz

• Name a famous Bioinformatics Researcher

• Name a famous Bioinformatics Researcher who is a
  woman

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Scoring DNA

• DNA has structure.

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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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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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PAM 1 distance

• Two sequences are 1 PAM apart if they differ in 1
  of the residues.

1 mismatch

• PAM1(a,b) Prresidue b substitutes residue a,
  when the sequences are 1 PAM apart

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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 Pba of residue a being
  substituted by residue b.
• S(a,b) log10(Pab/PaPb) log10(Pba/Pb)

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PAM 1
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PAM distance

• Two sequences are 1 PAM apart when they differ in
  1 of the residues.
• When are 2 sequences 2 PAMs apart?

2 PAM
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Higher PAMs

• PAM2(a,b) ?c PAM1(a,c). PAM1 (c,b)
• PAM2 PAM1 PAM1 (Matrix multiplication)
• PAM250
• PAM1PAM249
• PAM1250

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Note This is not the score matrix What happens
as you keep increasing the power?
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Scoring using PAM matrices

• Suppose we know that two sequences are 250 PAMs
  apart.
• S(a,b) log10(Pab/PaPb) log10(Pba/Pb)
  log10(PAM250(a,b)/Pb)

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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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PAM vs. BLOSUM

• What is the correspondence?
• PAM1 Blosum1
• PAM2 Blosum2
• Blosum62
• PAM250 Blosum100

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Dictionary Matching, R.E. matching, and position
specific scoring
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Dictionary Matching
1POTATO 2POTASSIUM 3TASTE
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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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 (l1l2l3)n
• Using a keyword tree, lpn (lp is the length of
  the longest pattern)
• Aho-Corasick O(n) after preprocessing O(l1l2..)
• We will consider the most general case

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Direct Algorithm
P O P O P O T A S T P O T A T O
P O T A T O
P O T A T O
P O T A T O
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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The Trie Automaton

• Construct an automaton A from the dictionary
• Av,x describes the transition from node v to a
  node w upon reading x.
• Au,T v, and Au,S w
• Special root node r
• Some nodes are terminal, and labeled with the
  index of the dictionary word.

1POTATO 2POTASSIUM 3TASTE
v
u
1
r
S
2
w
3
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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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Illustration
P O T A S T P O T A T O
v
1
S
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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
1POTATO 2POTASSIUM 3TASTE
Pattern j
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Improving speed of dictionary matching

• Every node v corresponds to a string sv that is a
  prefix of some pattern.
• Define Fv 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 Fv,
  and commence matching from there
• Let lpv su

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1
S
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9
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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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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
U
I
S
M
A
S
E
T
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Time analysis

• In each step, either c is incremented, or l is
  incremented
• Neither pointer is ever decremented (lpv lt
  c-l).
• l and c do not exceed n
• Total time lt 2n

l
c
P O T A S T P O T A T O
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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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Blast Steps

1. Generate an automaton of all query keywords.
2. Scan database using a Dictionary Matching
   algorithm (O(n) time). Identify all hits.
3. Extend each hit using a variant of local
   alignment algorithm. Use the scoring matrix and
   gap penalties.
4. 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.
5. Output results.

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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?