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Statistical Alignment: Computational Properties, Homology Testing and Goodness-of-Fit

Statistical Alignment: Computational Properties, Homology Testing and Goodness-of-Fit. J. Hein, C. Wiuf, B. Knudsen, M.B. Moller and G. Wibling. Main Objective of the paper.

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Statistical Alignment: Computational Properties, Homology Testing and Goodness-of-Fit

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  1. Statistical Alignment: Computational Properties, Homology Testing and Goodness-of-Fit J. Hein, C. Wiuf, B. Knudsen, M.B. Moller and G. Wibling

  2. Main Objective of the paper • To show how to accelerate the statistical alignment algorithms several orders of magnitude using the model of insertion and deletions by Thorne, Kishino, and Felsenstein in 1991 (TKF91 model). • To propose a new homology test based on the model. • To describe a goodness-of-fit test that allows testing the proposed insertion-deletion process inherent to the model.

  3. Why isn’t statistical alignment popular? • Computationally VERY SLOW • Authors of the paper accelerated the statistical alignment algorithms several orders of magnitude compared with the TKF91 algorithm. • Lack of user-friendly software? • Usually written in Fortran or C, or the compiled program only works in UNIX environment, but most biologists don’t know much about it. • Authors of the paper have provided a web interface to the program

  4. parsimony and similarity alignments • Parsimony strategy: minimizing the distance • For example: • Similarity strategy: maximizing the similarity score • For example: BLAST

  5. TKF91 model of substitutions • continuous time Markov model on the state space of nucleotides or amino acids • Rate matrix Q is specified • Describes the intensity of different substitution events over an infinitesimal time period. • Probability that i has changed to j after time t is • The process is assumed to be time reversible:

  6. TKF91 model of the indel process • Can be view as a Markov model with all sequences as possible states • indel part of the model • links connecting the letters of the sequences • each has a mortal link on the right • left end has an immortal link • For example:  A  G  G  • If the type of the nucleotide is ignored, can be represented as    

  7. TKF91 model • mortal link can give birth to a new mortal link or die out • immortal link can also give birth but would not die • Therefore, the rates can be written as:  A  G  G  I0 S1 I1/D1 S2 I2/D2 S3 I3/D3 where I is the birth rate D is the death rate, D>I S is the substitution rate

  8. TKF91 model To calculate the probability of a particular alignment: s(1):  A  T  - s(2):  C  T  G  P(s(1), s(2), alignment) = (p1’’)(AP1 PAC)(T P2 PTT G)

  9. Calculating the probability of two sequences • Without conditioning on the alignment, it is necessary to sum over all alignments weighted with their probabilities according to the TKF91 process. • Confine likelihood calculations to a band close to the similarity based alignment allows an efficient numerical optimization algorithm for finding the maximum likelihood estimate • The recursions originally presented by Thorne, Kishino and Felsenstein can be simplified.

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