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Evolution of Biomolecular Structure 2006 and RNA Secondary - - PowerPoint PPT Presentation
Evolution of Biomolecular Structure 2006 and RNA Secondary - - PowerPoint PPT Presentation
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
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Web-Page for further information: http://www.tbi.univie.ac.at/~pks
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N = 4n NS < 3n 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
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RNA sequence RNA structure
- f minimal free
energy
RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Empirical parameters Biophysical chemistry: thermodynamics and kinetics
Sequence, structure, and design
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RNA sequence RNA structure
- f minimal free
energy
RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Inverse Folding Algorithm Iterative determination
- f a sequence for the
given secondary structure
Sequence, structure, and design
Inverse folding of RNA: Biotechnology, design of biomolecules with predefined structures and functions
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RNA secondary structures derived from a single sequence
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Peter Schuster, Prediction of RNA Secondary Structures: From Theory to Models and Real Molecules. Reports on Progress in Physics 69:1419-1477 (2006)
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Sequence space
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CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... G A G T A C A C
Hamming distance d (I ,I ) =
H 1 2
4 d (I ,I ) = 0
H 1 1
d (I ,I ) = d (I ,I )
H H 1 2 2 1
d (I ,I ) d (I ,I ) + d (I ,I )
H H H 1 3 1 2 2 3
- (i)
(ii) (iii)
The Hamming distance between sequences induces a metric in sequence space
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Every point in sequence space is equivalent
Sequence space of binary sequences with chain length n = 5
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Sequence space and structure space
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Hamming distance d (S ,S ) =
H 1 2
4 d (S ,S ) = 0
H 1 1
d (S ,S ) = d (S ,S )
H H 1 2 2 1
d (S ,S ) d (S ,S ) + d (S ,S )
H H H 1 3 1 2 2 3
- (i)
(ii) (iii)
The Hamming distance between structures in parentheses notation forms a metric in structure space
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Two measures of distance in shape space: Hamming distance between structures, dH(Si,Sj) and base pair distance, dP(Si,Sj)
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Structures are not equivalent in structure space
Sketch of structure space
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? ? ?
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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 .(..(((....)))..)... 0.10
M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, I.L. Hofacker, P.F. Stadler. 2004. J.Phys.A: Math.Gen. 37:4731-4741.
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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 .(..(((....)))..)... 0.10
M.T. Wolfinger, W.A. Svrcek-Seiler, C. Flamm, I.L. Hofacker, P.F. Stadler. 2004. J.Phys.A: Math.Gen. 37:4731-4741.
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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.
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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.
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Replication rate constant: fk = / [ + dS
(k)]
dS
(k) = dH(Sk,S)
Selection constraint: Population size, N = # RNA molecules, is controlled by the flow Mutation rate: p = 0.001 / site replication N N t N ± ≈ ) ( The flowreactor as a device for studies of evolution in vitro and in silico
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Phenylalanyl-tRNA as target structure Randomly chosen initial structure
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In silico optimization in the flow reactor: Evolutionary Trajectory
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Kinetic Folding
Compatible structures: Set of stuctures compatible with a given sequence stability restriction Conformation space Folding trajectory in conformation space: Time ordered series of structures Folding process: Average of trajectories on the ensemble level Criterium: minimizing free energy
Evolutionary optimization
Compatible sequences: Set of sequences compatible with a given structure mfe restriction Neutral network Genealogy on a neutral network: Time ordered series of sequences Optimization process: Average over genealogies on the population level Criterium: maximizing fitness
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Prediction of RNA kinetic folding
- f secondary structures based on
Arrhenius kinetics
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Prediction of RNA kinetic folding
- f secondary structures based on
Arrhenius kinetics
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Prediction of RNA kinetic folding
- f secondary structures based on
Arrhenius kinetics
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Prediction of RNA kinetic folding
- f secondary structures based on
Arrhenius kinetics
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Prediction of RNA kinetic folding
- f secondary structures based on
Arrhenius kinetics
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Design of RNA molecules with with predefined folding kinetics
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Construction of a combined landscape for folding and evolution
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Acknowledgement of support
Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 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
Universität Wien
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Coworkers
Peter Stadler, Bärbel M. Stadler, Universität Leipzig, GE Jord Nagel, Kees Pleij, Universiteit Leiden, NL 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
Universität Wien
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It has been great !!!! Thank you all !!!!
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Web-Page for further information: http://www.tbi.univie.ac.at/~pks
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