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For class: Reading : finish ch. 9 I added a recent paper by Miranda to the suffix array section

Inexact matching

Take a baby-step into inexact matching

m-mismatch k-word problem
• Input: P query string, T text string
• Output: All (i,j) where d(P(i:i+k),T(j,j+k)) <= m

Slight variation

S-scoring k-word problem
• Input: P query string, T test string, scoring matrix
• Output: All (i,j) where score(P(i:i+k),T(j,j+k)) >= S

Pigeon Hole principle

Good matches usually contain exact matches

m-mismatch problem
• length s=floor(k/(m+1)) exact match must exist
• locate all s-words of P in T via exact matching
• extend left/right to find a k-word
  • O(k^2) to do this right
  • many methods don't bother to do this right

S-scoring problem
• every S scoring k-word match contains some s-word with score T
• form T-scoring neighborhood of s-words of P
• local all neighborhood words in T via exact matching
• extend left/right to find an k-word to a local MSP

Ungapped extension

Gapped extension

BLAST

Basic Local Alignment Search Tool

successor to FASTA and FASTP

• sacrifices sensitivity: doesn't explore all possible alignments
• seed size: 9-11 bps or 3-6 AAs
• originally: returned maximally scoring pairs, now returns alignments

big claim to fame: use of Altschul-Karlin-Dembo statistics to quantify

• judging the significance of a match
• setting (vaguely) justified thresholds

biggest claim to fame: very fast (PatternHunter might be better today)

• uses AC-style FSM to find seed matchs
• uses another exact matching technique to generate word neighborhoods

MSP statistics

An approximation to local alignment statistics

• Bernoulli sequence, p_i letter probabilities of length N and M
• per-letter scoring matrix s(x,y)

MSP result from Altschul-Karlin

E[Number of disinct MSP's with score >= S] = K N M exp{-zS}

z is a normalizing factor: SUM_{xy} p_x p_y exp{-z s(x,y)} = 1

Chen-Stein result

Number of MSPs distributed Poisson with avg E[S]

The many faces of BLAST

• BLASTn: nucleotide to nucleotide database
• BLASTp: protein to protein db
• BLASTx: translated nucleotide to protein db
• tBLASTn: protein to translated nucleotide db
• tBLASTx: translated nucleotide to translated nucleotide db

Gapped seeds - the wave of the future

Forget about extensions and gaps: just find seeds to `hit' every MSP

Example: MSP of length 20 with greater than 70% identity

Fundamental problem: seeds too short=noise, seeds too long=lack of signal

look for all 4-mers --> look for 1111

look for a gapped seed --> look for 11011

The problem of detecting an MSP of length X with p percent id is one of `hitting' binary strings with other binary strings

Consecutively spaced seeds don't hit as many MSP