Martin Vingron

1

Family Specific Rates of Protein Evolution or,
more general Markov models in protein evolution
Resolvent method, Systers, FSR

• Martin Vingron
• Max-Planck-Institut für molekulare Genetik
• Reporting on work mainly by
• Tobias Müller, Antje Krause, Hannes Luz

2
Amino Acid Replacement
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Degree of Divergence
4
Markov Assumption
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Exponential function
F
L
A

• p(t) exp(qt)

K
C
R
The same works with matrices
P(t) exp(Qt)
Infinitesimal generator, Rate matrix
Transition probabilites
6
The Model Variables
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The Problem
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Dayhoffs Estimation Procedure
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Linear Approximation
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Shortcomings
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The Problem (revisited)
Homologous Sequences
Evolutionary Distance
Input Data
Rates
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An alternative Representation
The întergral is called Resolvent of the
transition probabilities.
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Resolvent Estimation Procedure
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ML Estimation of alignment distance
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Resolvent function
theoretical estimated
theoretical estimated
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Amino Acid Score Matrix
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Here we are
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The proof of the pudding. is in the eating!
Number of false positive matches
References 1 Gavin A. Price , Gavin E. Crooks
, Richard E. Green , and Steven E. Brenner 2005.
Statistical evaluation of pairwise
proteinsequence comparison with the Bayesian
bootstrap.Bioinformatics, 213824-3831. 2
Gavin E. Crooks, and Steven E. Brenner 2005. An
alternative model of amino acid replacement,
7,21, 975-980.