1. Max-Planck-Institut für molekulare Genetik EBSV06 Martin Vingron Max-Planck-Institut für molekulare Genetik Reporting on work mainly by Tobias Müller, Antje Krause, Hannes Luz Family Specific Rates of Protein Evolution or, more general Markov models in protein evolution: Resolvent method, Systers, FSR

2. Max-Planck-Institut für molekulare Genetik EBSV06 Amino Acid Replacement

3. Max-Planck-Institut für molekulare Genetik EBSV06 Degree of Divergence

4. Max-Planck-Institut für molekulare Genetik EBSV06 Markov Assumption

5. 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 F L

6. Max-Planck-Institut für molekulare Genetik EBSV06 The Model Variables

7. Max-Planck-Institut für molekulare Genetik EBSV06 The Problem

8. Max-Planck-Institut für molekulare Genetik EBSV06 Dayhoffs Estimation Procedure

9. Max-Planck-Institut für molekulare Genetik EBSV06 Linear Approximation

10. Max-Planck-Institut für molekulare Genetik EBSV06 Shortcomings

11. Max-Planck-Institut für molekulare Genetik EBSV06 The Problem (revisited) Homologous Sequences Evolutionary Distance Input DataRates

12. Max-Planck-Institut für molekulare Genetik EBSV06 An alternative Representation The întergral is called Resolvent of the transition probabilities.

13. Max-Planck-Institut für molekulare Genetik EBSV06 Resolvent Estimation Procedure

14. Max-Planck-Institut für molekulare Genetik EBSV06 ML Estimation of alignment distance

15. Max-Planck-Institut für molekulare Genetik EBSV06 Resolvent function theoretical estimated theoretical estimated ij

16. Max-Planck-Institut für molekulare Genetik EBSV06 Amino Acid Score Matrix

17. Max-Planck-Institut für molekulare Genetik EBSV06 Here we are… VT160

18. Max-Planck-Institut für molekulare Genetik EBSV06 Proportion of true relations found The proof of the pudding…. … is in the eating! Number of false positive matches 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.