Statistics Inference of BLAST

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Statistics Inference of BLAST

• ??? Ai-Ling Hour
• ???? ?????
• 02-29052464
• 022446_at_mail.fju.edu.tw

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Contents

• Algorithms
• Parameters
• Score
• p-value
• E-value

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References

• http//www.ncbi.nlm.nih.gov/BLAST/tutorial/Altschu
  l-1.html

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http//www.bioinfbook.org/
http//www.sdsc.edu/babu/UCSD/week02/dbSearch_tut
.html
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BLAST procedure
Query seq.
Database
E-value threshold
Output Homolog Subject HSPs
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Preliminary

• BLAST programs
• Input / Output
• Gap penalty
• Score matrix
• Filter
• HSP
• Score
• E-Value

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Algorithm

• The original algorithm does not allow gaps but
  allows multiple hits to the same database
  sequence.
• BLAST programs were designed for fast database
  searching, with minimal sacrifice of sensitivity
  to distantly related sequences.
• BLAST programs search databases in a special,
  compressed format.
• BLAST looks first for short subsequences which it
  then tries to extend.

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How BLAST works

• Make a list of high scoring words (gtT)
• Compare wordlist against database
• If two hits within a given window, gapped
  extension of second hit in both directions

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BLAST Search Algorithm
http//www.ncbi.nlm.nih.gov/Education/BLASTinfo/BL
AST_algorithm.html
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better
large w
lower T
slower
Sensitivity
Search speed
faster
worse
small w
higher T
http//www.bioinfbook.org/
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Program Advanced Options
-G Cost to open gap Integer default 5 for
nucleotides 11 proteins -E Cost to extend gap
Integer default 2 nucleotides 1 proteins -q
Penalty for nucleotide mismatch Integer
default -3 -r reward for nucleotide match
Integer default 1 -e expect value Real
default 10 -W wordsize Integer default
11 nucleotides 3 proteins
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Filtering

• Low-complexity
• SEG amino acid sequences
• DUST nucleic acid sequences.
• Human repeats, ...
• lookup table
• Lower Case

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SEG output
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Score of Alignment

• How strong an alignment can be expected from
  chance alone
• To analyze how high a score is likely to arise by
  chance, a model of random sequences is needed.
• The expected score for aligning a random pair of
  amino acid is required to be negative
• An extreme value distribution

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The probability density function of the extreme
value distribution (characteristic value u0 and
decay constant l1)
0.40
0.35
0.30
0.25
normal distribution
extreme value distribution
probability
0.20
0.15
0.10
0.05
0
0
1
2
3
4
5
-1
-2
-3
-4
-5
x
http//www.bioinfbook.org/
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Extreme Value Distribution

• The most one can say reliably is that if 100
  random alignments have score inferior to the
  alignment of interest, the P-value in question is
  likely less than 0.01.
• Multiple tests An alignment with P-value 0.0001
  in the context of a single trial may be assigned
  a P-value of only 0.1 if it was selected as the
  best among 1000 independent trials.

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Entropy
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Entropy

• A random DNA, p0.25 for each
• H-4(0.25)(-2)2 bits
• p(A/T)0.9, p(C/G)0.1
• H-2(0.45)(-1.15)(0.05) (-4.32)1.47 bits

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lod Score

• Pairs of amino acids or nucleotides
• log2 odd ratio
• Random model qij pi pj
• Sij log (qij /pipj)
• Pairing randomly Sij 0

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Score

• The scores of any substitution matrix with
  negative expected score can be written uniquely
  in the form
• Sijln(qij/pipj)/?
• where the qij, called target frequencies, are
  positive numbers that sum to 1, the pi are
  background frequencies for the various residues,
  and lambda is a positive constant.

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Bit Score

• Raw scores have little meaning without detailed
  knowledge of the scoring system used, or more
  simply its statistical parameters K and lambda.
• Unless the scoring system is understood, citing a
  raw score alone is like citing a distance without
  specifying feet, meters, or light years.
• S(?S-ln K) / ln2

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Parameters

• The parameters K and ? can be thought of simply
  as natural scales for the search space size and
  the scoring system respectively.

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E-value

• Bit score S', which has a standard set of units.
• The E-value corresponding to a given bit score is
  simply
• Emn2-S

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E-value

• The number of hits one can "expect" to see just
  by chance when searching a database of a
  particular size
• The E value describes the random background noise
  that exists for matches between sequences.
• The expected number of HSPs with score at least S
  is given by the formula
• EKmne-?S

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p-value

• The number of random HSPs with score gt S is
  described by a Poisson distribution
• This means that the probability of finding
  exactly x HSPs with score gtS is given by
  e-E(Ex/x!), E is the E-value of S
• Specifically the chance of finding zero HSPs with
  score gtS is e-E, so the probability of finding
  at least one such HSP is 1- e-E

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E values and p values
Very small E values are very similar to p values.
E values of about 1 to 10 are far easier to
interpret than corresponding p values. E p 10
0.99995460 5 0.99326205 2 0.86466472 1 0.63212
056 0.1 0.09516258 (about 0.1) 0.05 0.04877058
(about 0.05) 0.001 0.00099950 (about
0.001) 0.0001 0.0001000
Table 4.4 page 107
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query length 142196 database 6,672,153
sequences 23,415,242,475 total letters E lt
1E-100
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query length 142196 database 6,672,153
sequences 23,415,242,475 total letters E lt
1E-100
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query length 352 database 6,672,153
sequences 23,415,242,475 total letters E lt
1E-50
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query length 352 database 6,672,153
sequences 23,415,242,475 total letters E lt
1E-50
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Thank you