Evolution of Biomolecular Structure 2006 and RNA Secondary Structures in the Years to Come. Peter Schuster

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2 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,

3 Web-Page for further information:

4 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

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

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

7 RNA secondary structures derived from a single sequence

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

9 Sequence space

10 CGTCGTTACAATTTAGGTTATGTGCGAATTCACAAATTGAAAATACAAGAG... CGTCGTTACAATTTAAGTTATGTGCGAATTCCCAAATTAAAAACACAAGAG... Hamming distance d (I,I ) = H (i) (ii) (iii) d (I,I) = 0 H 1 1 d (I,I) = d (I,I) H 1 2 H 2 1 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

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

12 Sequence space and structure space

13 Hamming distance d (S,S ) = H (i) (ii) (iii) d (S,S) = 0 H 1 1 d (S,S ) = d (S,S ) H 1 2 H 2 1 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

14 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 )

15 Structures are not equivalent in structure space Sketch of structure space

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23 CUGCGGCUUUGGCUCUAGCC...((((...)))) (((.(((...))).))) (((..((...))..))) (((...))) (((((...)))...)) (((...))) ((..(((...)))..)) ((.((...))...)) (((...))) (((...))) ((.(((...))).)) ((((..(...).)))) ((..((...))..)) (((.(((...)).)))) (((.((...)).))) ((((..(...))))) ((...)) (.(((...)))) (((...)).) (((..(...)..))) (((((...)).)..)) (.(((...))).) ((...)) ((...)) ((...)) (((.(((...)))).)) (((.(...)))) (((..((...))))) (..((...))..) (..(((...)))..) M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, I.L. Hofacker, P.F. Stadler J.Phys.A: Math.Gen. 37:

24 CUGCGGCUUUGGCUCUAGCC...((((...)))) (((.(((...))).))) (((..((...))..))) (((...))) (((((...)))...)) (((...))) ((..(((...)))..)) ((.((...))...)) (((...))) (((...))) ((.(((...))).)) ((((..(...).)))) ((..((...))..)) (((.(((...)).)))) (((.((...)).))) ((((..(...))))) ((...)) (.(((...)))) (((...)).) (((..(...)..))) (((((...)).)..)) (.(((...))).) ((...)) ((...)) ((...)) (((.(((...)))).)) (((.(...)))) (((..((...))))) (..((...))..) (..(((...)))..) M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, I.L. Hofacker, P.F. Stadler J.Phys.A: Math.Gen. 37:

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

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

27 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 = / site replication The flowreactor as a device for studies of evolution in vitro and in silico

28 Randomly chosen initial structure Phenylalanyl-tRNA as target structure

29 In silico optimization in the flow reactor: Evolutionary Trajectory

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

31 Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

32 Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

33 Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

34 Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

35 Prediction of RNA kinetic folding of secondary structures based on Arrhenius kinetics

36 Design of RNA molecules with with predefined folding kinetics

37 Construction of a combined landscape for folding and evolution

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

39 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 Svrček-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

40 It has been great!!!! Thank you all!!!!

41 Web-Page for further information:

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