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Basic String Alignment. Probability theory and statistics String alignment problem Basic string alignment algorithms. Author: Roel Wijgers email: rwijgers@cs.uu.nl. Probability Theory. Conditional chance: P(A|B) = P(A /\ B) / P(B) Independence of A and B: when P(A /\ B) = P(A)P(B).

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basic string alignment

Basic String Alignment

Probability theory and statistics

String alignment problem

Basic string alignment algorithms

Author: Roel Wijgers email: rwijgers@cs.uu.nl

probability theory
Probability Theory
  • Conditional chance:
  • P(A|B) = P(A /\ B) / P(B)
  • Independence of A and B:
  • when P(A /\ B) = P(A)P(B)

Author: Roel Wijgers email: rwijgers@cs.uu.nl

string alignment
String Alignment
  • No gaps allowed:
  • Gaps allowed in one of the strings:
  • Gaps allowed in both strings:

Author: Roel Wijgers email: rwijgers@cs.uu.nl

matching models
Matching models

The random model, i.e. each letter a occurs independently with some frequency qa

This means that the probability of two sequences x and y is defined as follows :

Author: Roel Wijgers email: rwijgers@cs.uu.nl

matching models 2
Matching models(2)

Independence between values xiand yjis not very usefull:

odds ratio:

Author: Roel Wijgers email: rwijgers@cs.uu.nl

matching models 3
Matching models(3)

We rather have an additional scoring system, i.e.:

This scoring system is called the log-odds ratio, and

associated with it is the log-likelihood ratio:

Author: Roel Wijgers email: rwijgers@cs.uu.nl

log likelihood table
Log likelihood table

Author: Roel Wijgers email: rwijgers@cs.uu.nl

gap penalties
Gap penalties

We expect to penalise gaps. You can use different functions for this, although the linear function is most common to use:

Author: Roel Wijgers email: rwijgers@cs.uu.nl

gap penalties 2
Gap penalties(2)

Where f(g) is a geometric distribution:

Author: Roel Wijgers email: rwijgers@cs.uu.nl

alignment algorithms
Alignment algorithms

Author: Roel Wijgers email: rwijgers@cs.uu.nl

global alignment needleman wunsch algorithm
Global alignment: Needleman-Wunsch algorithm

Find the optimal global alignment between 2 sequences, allowing gaps.

Author: Roel Wijgers email: rwijgers@cs.uu.nl

global alignment needleman wunsch algorithm 2
Global alignment: Needleman-Wunsch algorithm(2)

Author: Roel Wijgers email: rwijgers@cs.uu.nl

local alignment smith waterman algorithm
Local alignment: Smith-Waterman algorithm

Find the best alignment between subsequences of x and y.

Author: Roel Wijgers email: rwijgers@cs.uu.nl

local alignment smith waterman algorithm14
Local alignment: Smith-Waterman algorithm

Author: Roel Wijgers email: rwijgers@cs.uu.nl

repeated matches
Repeated Matches

Search for multiple local matches.

  • One of the sequences is fixed and

contains the domain or motif.

  • We have some threshold T to exclude short

local alignments.

Author: Roel Wijgers email: rwijgers@cs.uu.nl

repeated matches 2
Repeated Matches(2)

Author: Roel Wijgers email: rwijgers@cs.uu.nl

overlap matches
Overlap matches

We expect that one of the sequences contains the other, or they overlap.

Author: Roel Wijgers email: rwijgers@cs.uu.nl

overlap matches 2
Overlap matches(2)

Author: Roel Wijgers email: rwijgers@cs.uu.nl

questions

Questions

Author: Roel Wijgers email: rwijgers@cs.uu.nl