Mechanisms of molecular cooperation

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2 Mechanisms of molecular cooperation Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Homo Sociobiologicus Evolution of human cooperation Universitätszentrum Althanstraße I,

3 Web-Page for further information:

4 Chemical kinetics of molecular evolution

5 1. Cyclic reaction networks catalysts 2. Cyclic catalytic networks autocatalysts 3. Cyclic autocatalytic networks hypercycles 4. Neutrality a source for coexistent competitors

6 1. Cyclic reaction networks catalysts 2. Cyclic catalytic networks autocatalysts 3. Cyclic autocatalytic networks hypercycles 4. Neutrality a source for coexistent competitors

8 The Bethe - vonweizsäcker catalytic cycle ist responsible in part for the energy production in massive stars.

9 The tricarboxylic acid or citric acid cycle is fuelling the metabolic reactions of the cell.

10 Thecitricacid or Krebs cycle (enlarged) The reaction network of cellular metabolism published by Boehringer-Mannheim.

11 A B C D E F G H I J K L 1 Biochemical Pathways The reaction network of cellular metabolism published by Boehringer-Mannheim.

12 1. Cyclic reaction networks catalysts 2. Cyclic catalytic networks autocatalysts 3. Cyclic autocatalytic networks hypercycles 4. Neutrality a source for coexistent competitors

14 Complementary ( ) replication of RNA as an example of an autocatalytic cycle.

15 A synthetic oligopeptide ligase becomes a replicator for E = P K. Severin, D.H. Lee, A.J. Kennan, M.R. Ghadiri, Nature 389, , 1997 D.H. Lee, J.R. Granja, J.A. MartinezK. Severin, M.R. Ghadiri, Nature 382, , 1996

16 Cross-catalysis of peptide replicators D.H. Lee, K. Severin, Y. Yokobayashi, M.R. Ghadiri, Nature 390, , 1997

17 A chiroselective peptide replicator A. Saghatelian, Y. Yokobayashi, K. Soltani, M.R. Ghadiri, Nature 409, , 2001

18 Cross-catalysis of two RNA enzymes leads to self-sustained replication Tracey A. Lincoln, Gerald F. Joyce, Science 323, , 2009

19 Exponential growth levels off when the reservoir is exhausted (l.h.s.). RNA production in serial transfer experiments (r.h.s.) Tracey A. Lincoln, Gerald F. Joyce, Science 323, , 2009

20 RNA evolution of recombinant replicators Tracey A. Lincoln, Gerald F. Joyce, Science 323, , 2009

21 1. Cyclic reaction networks catalysts 2. Cyclic catalytic networks autocatalysts 3. Cyclic autocatalytic networks hypercycles 4. Neutrality a source for coexistent competitors

23 Hypercycles with one and two members are common in nature.

25 Hypercycle dynamics for n=3

26 Hypercycle dynamics for n=4

27 Hypercycle dynamics for n=6

28 1. Cyclic reaction networks catalysts 2. Cyclic catalytic networks autocatalysts 3. Cyclic autocatalytic networks hypercycles 4. Neutrality a source for coexistent competitors

29 Chemical kinetics of replication and mutation as parallel reactions

30 A fitness landscape including neutrality

31 Motoo Kimura Is the Kimura scenario correct for frequent mutations?

33 0.5 ) ( ) ( lim = = p x p x p d H = 1 a p x a p x p p = = 1 ) ( lim ) ( lim d H = 2 d H 3 1 ) ( 0,lim ) ( lim or 0 ) ( 1,lim ) ( lim = = = = p x p x p x p x p p p p Random fixation in the sense of Motoo Kimura Pairs of genotypes in neutral replication networks

34 Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

35 Consensus sequence of a quasispecies of two strongly coupled sequences of Hamming distance d H (X i,,x j ) = 1.

36 Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

37 Consensus sequence of a quasispecies of two strongly coupled sequences of Hamming distance d H (X i,,x j ) = 2.

38 N = 7 Neutral networks with increasing : = 0.10, s = 229

39 N = 24 Neutral networks with increasing : = 0.15, s = 229

40 N = 70 Neutral networks with increasing : = 0.20, s = 229

42 1D R 2D GGGUGGAACCACGAGGUUCCACGAGGAACCACGAGGUUCCUCCC 3 13 G An RNA switch J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and C.W.A. Pleij. 1D 2D CG CG A A A A C G C G C G C G A U A U A U A U G C G C G C G C U A/G A U 3 G C G C 44 GG R 23 CC 5' kcal mol kcal mol -1 JN1LH R 23 CG G/ A A C G C G U A U A G C G C A A 13 1D G C 2D C G 33 A A C G C G A U A U G G C C U U 3G C G C G C 44 5' kcal mol kcal mol -1 Structural parameters affecting the kinetic competition of RNA hairpin formation. Nucleic Acids Res. 34: , 2006.

43 A ribozyme switch E.A.Schultes, D.B.Bartel, Science 289 (2000),

44 Two ribozymes of chain lengths n = 88 nucleotides: An artificial ligase (A) and a natural cleavage ribozyme of hepatitis- -virus (B)

45 Thesequenceat theintersection: An RNA molecules which is 88 nucleotides long and can form both structures

46 Two neutral walks through sequence space with conservation of structure and catalytic activity

48 Web-Page for further information:

RNA Bioinformatics Beyond the One Sequence-One Structure Paradigm. Peter Schuster

RNA Bioinformatics Beyond the One Sequence-One Structure Paradigm Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA 2008 Molecular