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Evolution of Biomolecular Structure 2006 and RNA Secondary Structures in the Years to Come Peter Schuster Institut fr Theoretische Chemie, Universitt Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Evolution of


  1. Evolution of Biomolecular Structure 2006 and RNA Secondary Structures in the Years to Come Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Evolution of Biomolecular Structure 2006 UZA II, Universität Wien, 25.– 27.05.2006

  2. Web-Page for further information: http://www.tbi.univie.ac.at/~pks

  3. N = 4 n N S < 3 n Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _ � { AU , CG , GC , GU , UA , UG } A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

  4. RNA sequence Biophysical chemistry: thermodynamics and kinetics RNA folding : Structural biology, spectroscopy of biomolecules, Empirical parameters understanding molecular function RNA structure of minimal free energy Sequence, structure, and design

  5. RNA sequence Iterative determination of a sequence for the Inverse folding of RNA : given secondary RNA folding : structure Biotechnology, Structural biology, design of biomolecules spectroscopy of Inverse Folding with predefined biomolecules, Algorithm structures and functions understanding molecular function RNA structure of minimal free energy Sequence, structure, and design

  6. RNA secondary structures derived from a single sequence

  7. Peter Schuster, Prediction of RNA Secondary Structures: From Theory to Models and Real Molecules. Reports on Progress in Physics 69 :1419-1477 (2006)

  8. Sequence space

  9. CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... G A G T CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... A C A C Hamming distance d (I ,I ) = 4 H 1 2 (i) d (I ,I ) = 0 H 1 1 (ii) d (I ,I ) = d (I ,I ) H 1 2 H 2 1 � (iii) d (I ,I ) d (I ,I ) + d (I ,I ) H 1 3 H 1 2 H 2 3 The Hamming distance between sequences induces a metric in sequence space

  10. Every point in sequence space is equivalent Sequence space of binary sequences with chain length n = 5

  11. Sequence space and structure space

  12. Hamming distance d (S ,S ) = 4 H 1 2 (i) d (S ,S ) = 0 H 1 1 (ii) d (S ,S ) = d (S ,S ) H 1 2 H 2 1 � (iii) d (S ,S ) d (S ,S ) + d (S ,S ) H 1 3 H 1 2 H 2 3 The Hamming distance between structures in parentheses notation forms a metric in structure space

  13. Two measures of distance in shape space: Hamming distance between structures, d H (S i ,S j ) and base pair distance, d P (S i ,S j )

  14. Structures are not equivalent in structure space Sketch of structure space

  15. ? ? ?

  16. CUGCGGCUUUGGCUCUAGCC ....((((........)))) -4.30 (((.(((....))).))).. -3.50 (((..((....))..))).. -3.10 ..........(((....))) -2.80 ..(((((....)))...)). -2.20 ....(((..........))) -2.20 ((..(((....)))..)).. -2.00 ..((.((....))....)). -1.60 ....(((....)))...... -1.60 .....(((........))). -1.50 .((.(((....))).))... -1.40 ....((((..(...).)))) -1.40 .((..((....))..))... -1.00 (((.(((....)).)))).. -0.90 (((.((......)).))).. -0.90 ....((((..(....))))) -0.80 .....((....))....... -0.80 ..(.(((....))))..... -0.60 ....(((....)).)..... -0.60 (((..(......)..))).. -0.50 ..(((((....)).)..)). -0.50 ..(.(((....))).).... -0.40 ..((.......))....... -0.30 ..........((......)) -0.30 ...........((....)). -0.30 (((.(((....)))).)).. -0.20 ....(((.(.......)))) -0.20 ....(((..((....))))) -0.20 ..(..((....))..).... 0.00 .................... 0.00 M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, .(..(((....)))..)... 0.10 I.L. Hofacker, P.F. Stadler. 2004. J.Phys.A: Math.Gen. 37 :4731-4741.

  17. CUGCGGCUUUGGCUCUAGCC ....((((........)))) -4.30 (((.(((....))).))).. -3.50 (((..((....))..))).. -3.10 ..........(((....))) -2.80 ..(((((....)))...)). -2.20 ....(((..........))) -2.20 ((..(((....)))..)).. -2.00 ..((.((....))....)). -1.60 ....(((....)))...... -1.60 .....(((........))). -1.50 .((.(((....))).))... -1.40 ....((((..(...).)))) -1.40 .((..((....))..))... -1.00 (((.(((....)).)))).. -0.90 (((.((......)).))).. -0.90 ....((((..(....))))) -0.80 .....((....))....... -0.80 ..(.(((....))))..... -0.60 ....(((....)).)..... -0.60 (((..(......)..))).. -0.50 ..(((((....)).)..)). -0.50 ..(.(((....))).).... -0.40 ..((.......))....... -0.30 ..........((......)) -0.30 ...........((....)). -0.30 (((.(((....)))).)).. -0.20 ....(((.(.......)))) -0.20 ....(((..((....))))) -0.20 ..(..((....))..).... 0.00 .................... 0.00 M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, .(..(((....)))..)... 0.10 I.L. Hofacker, P.F. Stadler. 2004. J.Phys.A: Math.Gen. 37 :4731-4741.

  18. Arrhenius kinetics M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, I.L. Hofacker, P.F. Stadler. 2004. J.Phys.A: Math.Gen. 37 :4731-4741.

  19. Arrhenius kinetic Exact solution of the master equation M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, I.L. Hofacker, P.F. Stadler. 2004. J.Phys.A: Math.Gen. 37 :4731-4741.

  20. Replication rate constant : f k = � / [ � + � d S (k) ] � d S (k) = d H (S k ,S � ) Selection constraint : Population size, N = # RNA molecules, is controlled by the flow ≈ ± ( ) N t N N Mutation rate : p = 0.001 / site � replication The flowreactor as a device for studies of evolution in vitro and in silico

  21. Randomly chosen Phenylalanyl-tRNA as initial structure target structure

  22. In silico optimization in the flow reactor: Evolutionary Trajectory

  23. Kinetic Folding Evolutionary optimization Compatible structures : Compatible sequences : Set of stuctures compatible with Set of sequences compatible with a given sequence a given structure stability restriction mfe restriction Conformation space Neutral network Folding trajectory in conformation space : Genealogy on a neutral network : Time ordered series of structures Time ordered series of sequences Folding process : Optimization process : Average of trajectories on the Average over genealogies on the ensemble level population level Criterium : minimizing free energy Criterium : maximizing fitness

  24. Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

  25. Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

  26. Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

  27. Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

  28. Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

  29. Design of RNA molecules with with predefined folding kinetics

  30. Construction of a combined landscape for folding and evolution

  31. Acknowledgement of support Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Universität Wien Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No. 98-0189, 12835 (NEST) Austrian Genome Research Program – GEN-AU: Bioinformatics Network (BIN) Österreichische Akademie der Wissenschaften Siemens AG, Austria Universität Wien and the Santa Fe Institute

  32. Coworkers Peter Stadler , Bärbel M. Stadler , Universität Leipzig, GE Jord Nagel , Kees Pleij , Universiteit Leiden, NL Universität Wien Walter Fontana , Harvard Medical School, MA Christian Reidys , Christian Forst , Los Alamos National Laboratory, NM Ulrike Göbel, Walter Grüner , Stefan Kopp , Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE Ivo L.Hofacker , Christoph Flamm , Andreas Svr č ek-Seiler , Universität Wien, AT Kurt Grünberger, Michael Kospach, Andreas Wernitznig , Stefanie Widder, Michael Wolfinger, Stefan Wuchty , Universität Wien, AT Jan Cupal , Stefan Bernhart , Lukas Endler, Ulrike Langhammer , Rainer Machne, Ulrike Mückstein , Hakim Tafer, Thomas Taylor, Universität Wien, AT

  33. It has been great !!!! Thank you all !!!!

  34. Web-Page for further information: http://www.tbi.univie.ac.at/~pks

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