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Max-Planck-Institut für molekulare Genetik
EBSV06
Martin VingronMax-Planck-Institut für molekulare Genetik
Reporting on work mainly byTobias Müller, Antje Krause, Hannes Luz
Family Specific Rates of Protein Evolutionor, more general
Markov models in protein evolution: Resolvent method, Systers, FSR
Max-Planck-Institut für molekulare Genetik
EBSV06
Amino Acid Replacement
Max-Planck-Institut für molekulare Genetik
EBSV06
Degree of Divergence
Max-Planck-Institut für molekulare Genetik
EBSV06
Markov Assumption
Max-Planck-Institut für molekulare Genetik
EBSV06
Exponential function
p(t) = exp(qt)
P(t) = exp(Qt)
The same works with matrices:
Infinitesimal generator, Rate matrix
Transition probabilites
A
C
R
K
FL
Max-Planck-Institut für molekulare Genetik
EBSV06
The Model Variables
Max-Planck-Institut für molekulare Genetik
EBSV06
The Problem
Max-Planck-Institut für molekulare Genetik
EBSV06
Dayhoff‘s Estimation Procedure
Max-Planck-Institut für molekulare Genetik
EBSV06
Linear Approximation
Max-Planck-Institut für molekulare Genetik
EBSV06
Shortcomings
Max-Planck-Institut für molekulare Genetik
EBSV06
The Problem (revisited)
Homologous Sequences
Evolutionary Distance
Input Data Rates
Max-Planck-Institut für molekulare Genetik
EBSV06
An alternative Representation
The întergral is called Resolvent of the transition probabilities.
Max-Planck-Institut für molekulare Genetik
EBSV06
Resolvent Estimation Procedure
Max-Planck-Institut für molekulare Genetik
EBSV06
ML Estimation of alignment distance
Max-Planck-Institut für molekulare Genetik
EBSV06
Resolvent function
theoreticalestimated
theoreticalestimated
ij
Max-Planck-Institut für molekulare Genetik
EBSV06
Amino Acid Score Matrix
Max-Planck-Institut für molekulare Genetik
EBSV06
Here we are…
VT160VT160
Max-Planck-Institut für molekulare Genetik
EBSV06
Proportion of true relations found
The proof of the pudding….… is in the eating!
Nu
mb
er
of
fals
e p
osi
tive
m
atc
hes
Nu
mb
er
of
fals
e p
osi
tive
matc
hes
Proportion of true relations found
Many false positives, few true homologs
Few false positives,many true homologs
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, 21:3824-3831. [2] Gavin E. Crooks, and Steven E. Brenner 2005. An alternative model of amino acid replacement, 7,21, 975-980.
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