Tracing the Sources of Complexity in Evolution. Peter Schuster

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2 Tracing the Sources of Complexity in Evolution Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Springer Complexity Lecture ICCS11 Wien,

3 Web-Page for further information:

4 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

5 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

6 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

7 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

8 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

9 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Optimization at different levels of complexity

10 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

11 Three necessary conditions for Darwinian evolution are: 1. Multiplication, 2. Variation, and 3. Selection. Charles Darwin, None of the three conditions involves specific properties of the evolving entity except for the capability of reproduction: Darwinian evolution is universal for reproducing objects no matter whether they are molecules or societies. Darwinian evolution, however, is not the only mechanism driving biological evolution.

12 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

13 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

14 system mechanism driving force external constraint result biomolecule cell cell / molecule organism evolutionary design genetics and metabolism host/parasite coevolution cell differentiation and development better performance better usage of resources mutual arms races improvment by task splitting population natural selection maximization of progeny ecosystem global competition and coevolution climate changes singular events adaptation to environments survival in new environments thermodynamic and kinetic stability biochemical kinetics of metabolism availability and survival of host cells regulation and control of cell proliferation resources limiting population size total carrying capacity global sustainability functional biomolecules prokaryotic cell viroids and viruses multicellular organism optimized variants speciation new classes and phyla Adaptation at different levels of complexity

15 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

16 Genotypes, phenotypes, and fitness

17 Genotypes, phenotypes, and fitness

18 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

19 Make things as simple as possible, but not simpler! Albert Einstein Albert Einstein s razor, precise refence is unknown.

20 The paradigm of structural biology

21 The paradigm of structural biology

22 The paradigm of structural biology

23 The paradigm of structural biology

24 The paradigm of structural biology

25 James D. Watson, 1928-, and Francis H.C. Crick, Nobel prize fifty years double helix The three-dimensional structure of a short double helical stack of B-DNA

26 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

27 The logics of DNA replication Taq = thermus aquaticus

28 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

29 Nucleobase and base pair mutations

30 Nucleobase and base pair mutations

31 Nucleobase and base pair mutations

32 A case study: A simple RNA molecule

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44 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

45 The inverse folding algorithm searches for sequences that form a given RNA secondary structure under the minimum free energy criterion.

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47 Inversion of genotype-phenotype mapping

48 Neutral networks in sequence space

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50 Realistic fitness landscapes 1.Ruggedness: nearby lying genotypes may unfold into very different phenotypes 2.Neutrality: many different genotypes give rise to phenotypes with identical selection behavior

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52 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

53 Three necessary conditions for Darwinian evolution are: 1. Multiplication, 2. Variation, and 3. Selection. Charles Darwin, All three conditions are fulfilled not only by cellular organisms but also by nucleic acid molecules DNA or RNA in suitable cell-free experimental assays: Darwinian evolution in the test tube

54 Evolution in the test tube: G.F. Joyce, Angew.Chem.Int.Ed. 46 (2007),

55 Christof K. Biebricher, Kinetics of RNA replication C.K. Biebricher, M. Eigen, W.C. Gardiner, Jr. Biochemistry 22: , 1983

56 RNA replication by Q-replicase C. Weissmann, The making of a phage. FEBS Letters 40 (1974), S10-S18

57 stable does not replicate! metastable replicates! C.K. Biebricher, R. Luce In vitro recombination and terminal recombination of RNA by Q replicase. The EMBO Journal 11:

58 Manfred Eigen n i i n i i i j i n i ji j x x f Φ n j Φ x x W x 1 1 1, 1,2, ; dt d Mutation and (correct) replication as parallel chemical reactions M. Eigen Naturwissenschaften 58:465, M. Eigen & P. Schuster Naturwissenschaften 64:541, 65:7 und 65:341

59 Mutation-selection equation: [I i ] = x i 0, f i > 0, Q ij 0 Solutions are obtained after integrating factor transformation by means of an eigenvalue problem f x f x n i x x Q f dt dx n j j j n i i i j n j ji j i ; ;, 1,2,, (0) (0) ;, 1,2, ; exp 0 exp n i i ki k n j k k n k jk k k n k ik i x h c n i t c t c t x n j i h H L n j i L n j i Q f W ij ij ij i, 1,2,, ; ;, 1,2,, ; ;, 1,2,, ; 1 1, 0,1, ; 1 n k L W L k

60 quasispecies driving virus populations through threshold The error threshold in replication and mutation

61 single peak landscape step linear landscape Model fitness landscapes I

62 Error threshold on the single peak landscape

63 Error threshold on the step linear landscape

64 linear and multiplicative hyperbolic Model fitness landscapes II

65 The linear fitness landscape shows no error threshold

66 single peak landscape realistic landscape Rugged fitness landscapes over individual binary sequences with n = 10

67 Error threshold: Individual sequences n = 10, = 2, s = 491 and d = 0, 0.5,

68 d = 0.5 d = 1.0 Case I: Strong quasispecies n = 10, f 0 = 1.1, f n = 1.0, s = 919

69 d = d = 1.0 Case III: multiple transitions n = 10, f 0 = 1.1, f n = 1.0, s = 637

70 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

71 Motoo Kimuras population genetics of neutral evolution. Evolutionary rate at the molecular level. Nature 217: , The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge, UK, 1983.

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

73 Pairs of neutral sequences in replication networks P. Schuster, J. Swetina Bull. Math. Biol. 50: ) ( ) ( lim p x p x p d H = 1 a p x a p x p p 1 ) ( lim ) ( lim d H = 2 Random fixation in the sense of Motoo Kimura d H 3 1 ) ( 0,lim ) ( lim or 0 ) ( 1,lim ) ( lim p x p x p x p x p p p p

74 A fitness landscape including neutrality

75 Neutral network: Individual sequences n = 10, = 1.1, d = 0.5

76 Neutral network: Individual sequences n = 10, = 1.1, d = 0.5

77 Consensus sequence of a quasispecies with strongly coupled sequences of Hamming distance d H (X i,,x j ) = 1 and 2.

78 0, 0 largest eigenvalue and eigenvector diagonalization of matrix W complicated but not complex W = G F mutation matrix fitness landscape ( complex ) complex sequence structure complex mutation selection Complexity in molecular evolution

79 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

80 Evolution in silico W. Fontana, P. Schuster, Science 280 (1998),

81 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

82 In silico optimization in the flow reactor: Evolutionary Trajectory

83 Randomly chosen initial structure RNA phe as target structure

84 Randomly chosen initial structure RNA phe as target structure

85 Randomly chosen initial structure RNA phe as target structure

86 Randomly chosen initial structure RNA phe as target structure

87 Evolutionary trajectory Spreading of the population on neutral networks Drift of the population center in sequence space

88 Richard Lenski, Bacterial evolution under controlled conditions: A twenty years experiment. Richard Lenski, University of Michigan, East Lansing

89 1 year Epochal evolution of bacteria in serial transfer experiments under constant conditions S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants. Science 272 (1996),

90 1 year Epochal evolution of bacteria in serial transfer experiments under constant conditions S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants. Science 272 (1996),

91 The twelve populations of Richard Lenski s long time evolution experiment Enhanced turbidity in population A-3

92 Innovation by mutation in long time evolution of Escherichia coli in constant environment Z.D. Blount, C.Z. Borland, R.E. Lenski Proc.Natl.Acad.Sci.USA 105:

93 Contingency of E. coli evolution experiments

94 1. Adaptation in biology 2. Cycles of evolution 3. Molecules from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives

95 (i) Fitness landscapes for the evolution of molecules are obtainable by standard techniques of physics and chemistry. (ii) Fitness landscapes for evolution of viroids and viruses under controlled conditions are accessible in principle. (iii) Systems biology can be carried out for especially small bacteria and an extension to bacteria of normal size is to be expected for the near future. (iv) The computational approach for selection on known fitness landscapes ODEs or stochastic processes is standard. (v) The efficient description of migration and splitting of populations in sequence space requires new mathematical techniques.

96 Consideration of multistep and nonlinear replication mechanisms as well as accounting for epigenetic phenomena is readily possible within the molecular approach.

97 Coworkers Walter Fontana, Harvard Medical School, MA Matin Nowak, Harvard University, MA Ivo L.Hofacker, Christoph Flamm, Andreas Svrček-Seiler, Universität Wien, AT Universität Wien Peter Stadler, Bärbel Stadler, Universität Leipzig, GE Sebastian Bonhoeffer, ETH Zürich, CH Christian Reidys, University of Southern Denmark, Odense, DK Christian Forst, University of Texas Southwestern Medical Center, TX Kurt Grünberger, Michael Kospach, Andreas Wernitznig, Stefanie Widder, Stefan Wuchty, Universität Wien, AT Jan Cupal, Ulrike Langhammer, Ulrike Mückstein, Jörg Swetina, Universität Wien, AT Ulrike Göbel, Walter Grüner, Stefan Kopp, Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE

98 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 Siemens AG, Austria Universität Wien and the Santa Fe Institute

99 Thank you for your attention!

100 Web-Page for further information:

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