Self-Organization and Evolution

Transcription

1

2 Self-Organization and Evolution Peter Schuster Institut für Theoretische hemie und Molekulare Strukturbiologie der Universität Wien Wissenschaftliche esellschaft: Dynamik Komplexität menschliche Systeme AKH Wien,

3 Equilibrium thermodynamics is based on two major statements: 1. The energy of the universe is a constant (first law). 2. The entropy of the universe never decreases (second law). arnot, Mayer, Joule, Helmholtz, lausius, D.Jou, J.asas-Vázquez,.Lebon, Extended Irreversible Thermodynamics, 1996

4 S max 2 ( ds) < 0 U,V,equil Entropy Approach towards equilibrium Spontaneous processes S > 0 Enlarged scale Fluctuations around equilibrium Time Entropy and fluctuations at equilibrium

5 Environment ds > 0 env Self-organization is spontaneous creation of order. Selforganization ds = ds i + ds e < 0 ds i > 0 ds e < 0 ds = ds + ds > 0 tot env Entropy is equivalent to disorder. Hence there is no spontaneous creation of order at equilibrium. Self-organization requires export of entropy to an environment which is almost always tantamount to an energy flux or transport of matter in an open system. Entropy production and self-organization in open systems

6 Four examples of self-organization and spontaneous creation of order Hydrodynamic pattern formation in the atmosphere of Jupiter Fractal pattern in the solution manifold of mathematical equations haotic dynamics in model equations for atmospheric flow Pattern formation in chemical reactions Examples of self-organization and pattern formation

7 View from south pole South pole Red spot Jupiter: Observation of the gigantic vortex Picture taken from James leick, haos. Penguin Books, New York, 1988

8 omputer simulation of the gigantic vortex on Jupiter View from south pole Particles turning counterclockwise Particles turning clockwise Jupiter: omputer simulation of the giant vortex Philip Marcus, Picture taken from James leick, haos. Penguin Books, New York, 1988

9 Mandelbrot set z z 2+ c with z = x + i y The Mandelbrot set as an example of fractal patterns in mathematics Picture taken from James leick, haos. Penguin Books, New York, 1988

10 Mandelbrot set z z 2+ c with z = x + i y The Mandelbrot set as an example of fractal patterns in mathematics: Enlargement no.1 Picture taken from James leick, haos. Penguin Books, New York, 1988

11 Mandelbrot set z z 2+ c with z = x + i y The Mandelbrot set as an example of fractal patterns in mathematics: Enlargement no.2 Picture taken from James leick, haos. Penguin Books, New York, 1988

12 Mandelbrot set z z 2+ c with z = x + i y The Mandelbrot set as an example of fractal patterns in mathematics: Enlargement no.3 Picture taken from James leick, haos. Penguin Books, New York, 1988

13 Lorenz attractor dx/dt = σ (y x) dy/dt = ρ x y xz dz/dt = β z + xy A trajectory of the Lorenz attractor in the chaotic regime

14 Stock Solution Reaction Mixture p T T ds env ds i d e S ds 0 ds 0 ds 0 Isolated system U = const., V = const., ds 0 losed system T = const., p = const., d = du-pdv- TdS 0 Open system ds = + ds 0 ds env ds = d S+ d S ds i i 0 e Entropy changes in different thermodynamic systems with chemical reactions

15 Stock Solution [a] = a 0 Reaction Mixture [a],[b] A A A A A AA A A A A A A A A A A A A B B B B B B B B B B B B Flow rate r = R -1 Reactions in the continuously stirred tank reactor (STR)

16 oncentration a [a 0 ] Flow rate r [t -1 ] A B Reversible first order reaction in the flow reactor

17 oncentration a [a 0 ] Flow rate r [t ] A + B 2 B Autocatalytic second order reaction in the flow reactor

18 oncentration a [a 0 ] Flow rate r [t ] = 0 = = = A + B A 2 B B Autocatalytic second order and uncatalyzed reaction in the flow reactor

19 oncentration a [a 0 ] Flow rate r [t ] A +2 B 3B Autocatalytic third order reaction in the flow reactor

20 oncentration a [a 0 ] Flow rate r [t -1 ] = 0 = = = = A +2 B A 3B B Autocatalytic third order and uncatalyzed reaction in the flow reactor

21 Autocatalytic third order reactions Direct, A + 2 X 3 X, or hidden in the reaction mechanism (Belousow-Zhabotinskii reaction). Multiple steady states Oscillations in homogeneous solution Deterministic chaos Turing patterns Spatiotemporal patterns (spirals) Deterministic chaos in space and time Pattern formation in autocatalytic third order reactions.nicolis, I.Prigogine. Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations. John Wiley, New York 1977

22 Formation of target waves and spirals in the Belousov-Zhabotinskii reaction Winding number: number of left-handed spirals minus number of right-handed spirals Target waves and spirals in the Belousov-Zhabotinskii reaction Pictures taken from Arthur T. Winfree, The geometry of biological time. Springer-Verlag, New York, 1980.

23 Autocatalytic second order reactions Direct, A + I 2 I, or hidden in the reaction mechanism hemical self-enhancement ombustion and chemistry of flames Selection of laser modes Selection of molecular or organismic species competing for common sources Autocatalytic second order reaction as basis for selection processes. The autocatalytic step is formally equivalent to replication or reproduction.

24 Stock Solution [A] = a 0 Reaction Mixture: A; I, k=1,2,... k k 1 A + I 2 I 1 1 d 1 k 2 A + I 2 I 2 2 d 2 k 3 A + I 2 I 3 3 d 3 k 4 A + I 2 I 4 4 d 4 k 5 A + I 2 I 5 5 d 5 Replication in the flow reactor P.Schuster & K.Sigmund, Dynamics of evolutionary optimization, Ber.Bunsenges.Phys.hem. 89: (1985)

25 oncentration of stock solution a 0 A + I + I 1 2 A + I 1 A k 1 A + I 2 I 1 1 d 1 k 2 A + I 2 I 2 2 d 2 k 3 A + I 2 I 3 3 d 3 k 4 A + I 2 I 4 4 d 4 k 5 A + I 2 I 5 5 d 5 k > k > k > k > k Flow rate r = R -1 Selection in the flow reactor: Reversible replication reactions

26 oncentration of stock solution a 0 A + I 1 A f 1 A + I 2 I 1 1 f 2 A + I 2 I 2 2 f 3 A + I 2 I 3 3 f 4 A + I 2 I 4 4 f 5 A + I 2 I 5 5 f > f > f > f > f Flow rate r = R -1 Selection in the flow reactor: Irreversible replication reactions

27 (A) + I 1 f 1 I 1 + I 1 dx / dt = f x - x j j j j Φ =( f j - Φ) xj (A) + I 2 f 2 I 2 + I 2 Φ =Σ i f i x i ; Σ x = 1 ; i,j i i =1,2,...,n [A] = a = constant f m = max { f; j=1,2,...,n} j (A) + I j f j Ij + Ij x (t) 1 for t m (A) + I m f m I m + I m s = (f m+1 -f m )/f m succession of temporarily fittest variants: m m+1... (A) + I n f n I n + I n Selection of the fittest or fastest replicating species I m

28 1 Fraction of advantageous variant s = 0.1 s = 0.02 s = Time [enerations] Selection of advantageous mutants in populations of N = individuals

29 Thermodynamics of isolated systems: state function Entropy is a non-decreasing Second law S S max Valid in the limit of infinite time, lim t. Evolution of Populations: Ronald Fisher s conjecture Mean fitness is a non-decreasing function f = k x k (t) f k / k x k (t) f max is need Optimization heuristics in the sense that it only almost always true and the process not reach the optimum in finite times.

30 A A U U U A U A A U U = possible different sequences ombinatorial diversity of sequences: N = 4 A U = adenylate = uridylate = cytidylate = guanylate ombinatorial diversity of heteropolymers illustrated by means of an RNA aptamer that binds to the antibiotic tobramycin

31 5' 3' Plus Strand Synthesis 5' 3' Plus Strand 3' Synthesis 5' 3' Plus Strand Minus Strand 3' 5' omplex Dissociation 5' 3' Plus Strand 5' Minus Strand + 3' omplementary replication as the simplest copying mechanism of RNA

32 5' 3' Plus Strand 5' 3' AAUAA AAUUAA Plus Strand Insertion 3' 5' 3' Minus Strand AAUAA AAUA Plus Strand 5' 3' Deletion Point Mutation Mutations represent the mechanism of variation in nucleic acids

33 Σ dx / dt = f x - x j i iq ji i j Φ I 1 + Ij Φ = Σ f x i i i ; Σ x = 1 ; i i Σ Q i ij = 1 f j Q 1j I 2 + Ij Q = (1-p) p ij n-d(i,j) d(i,j) p... Error rate per digit f j Q 2j d(i,j)... Hamming distance between I i and Ij (A) + I j f j Q jj Ij + Ij [A] = a = constant f j Q nj I n + Ij hemical kinetics of replication and mutation

34 oncentration Master sequence Mutant cloud Sequence space The molecular quasispecies in sequence space

35 oncentration Master sequence Mutant cloud Off-the-cloud mutations Sequence space The molecular quasispecies and mutations producing new variants

36 Ronald Fisher s conjecture of optimization of mean fitness in populations does not hold in general for replication-mutation systems: In general evolutionary dynamics the mean fitness of populations may also decrease monotonously or even go through a maximum or minimum. It does also not hold in general for recombination of many alleles and general multi-locus systems in population genetics. Optimization of fitness is, nevertheless, fulfilled in most cases, and can be understood as a useful heuristic.

37 Optimization of RNA molecules in silico W.Fontana, P.Schuster, A computer model of evolutionary optimization. Biophysical hemistry 26 (1987), W.Fontana, W.Schnabl, P.Schuster, Physical aspects of evolutionary optimization and adaptation. Phys.Rev.A 40 (1989), M.A.Huynen, W.Fontana, P.F.Stadler, Smoothness within ruggedness. The role of neutrality in adaptation. Proc.Natl.Acad.Sci.USA 93 (1996), W.Fontana, P.Schuster, ontinuity in evolution. On the nature of transitions. Science 280 (1998), W.Fontana, P.Schuster, Shaping space. The possible and the attainable in RNA genotypephenotype mapping. J.Theor.Biol. 194 (1998),

38 Three-dimensional structure of phenylalanyl-transfer-rna

39 Sequence 5'-End 3'-End AUUUAUADDAAMAAUAAYA UUAMUUUTPAUAAAAUUAA 3'-End 5'-End 70 Secondary Structure Symbolic Notation 5'-End 3'-End Definition and formation of the secondary structure of phenylalanyl-trna

40 enotype-phenotype Mapping I S = ( I ) S f = ƒ( S ) Evaluation of the Phenotype Mutation Q j f 2 I 2 f 1 I1 I n I 1 f n I 2 f 2 f 1 I n+1 f n+1 f Q f 3 I 3 Q f 3 I 3 f 4 I 4 I f I 4 I 5 f 4 f 5 f 5 I 5 Evolutionary dynamics including molecular phenotypes

41 riterion of Minimum Free Energy UUUAAAUUAUUAUUUUUA UAAAUUUUAAAUUAAUUUUUUUUAUU UUAAAAAUUUAAAUUUUUUUAU AUUUUAAUAUAUUAUUAUUUUAUAAUAUU UAUUUAAUAAAUUUUUAAUUAAUAUUA Sequence Space Shape Space

42 Stock Solution Reaction Mixture The flowreactor as a device for studies of evolution in vitro and in silico

43 50 S Average structure distance to target d Evolutionary trajectory Time (arbitrary units) In silico optimization in the flow reactor: Trajectory

44 36 Relay steps Number of relay step 38 Evolutionary trajectory Time Average structure distance to target d S Endconformation of optimization

45 36 Relay steps Number of relay step 38 Evolutionary trajectory Time Average structure distance to target d S Reconstruction of the last step 43 44

46 36 Relay steps Number of relay step Average structure distance to target d S 42 Evolutionary trajectory Reconstruction of last-but-one step ( 44) Time

47 36 Relay steps Number of relay step Average structure distance to target d S Evolutionary trajectory Reconstruction of step ( 43 44) Time

48 36 Relay steps Number of relay step Average structure distance to target d S Evolutionary trajectory Reconstruction of step ( ) Time

49 Average structure distance to target d S 10 Relay steps Number of relay step Evolutionary trajectory Time Evolutionary process Reconstruction Reconstruction of the relay series

50 50 Relay steps S Average structure distance to target d Evolutionary trajectory Time (arbitrary units) In silico optimization in the flow reactor: Trajectory and relay steps

51 50 Relay steps S Average structure distance to target d Uninterrupted presence Evolutionary trajectory Time (arbitrary units) In silico optimization in the flow reactor: Uninterrupted presence

52 50 Relay steps Main transitions Average structure distance to target d S Evolutionary trajectory Time (arbitrary units) In silico optimization in the flow reactor: Main transitions

53 Main transition leading to clover leaf Average structure distance to target d S 10 Relay steps Evolutionary trajectory Number of relay step Time Reconstruction of a main transitions ( 38)

54 Main transition leading to clover leaf Average structure distance to target d S 10 Relay steps Evolutionary trajectory Number of relay step Time Evolutionary process Reconstruction Final reconstruction 36 44

55 50 Relay steps Main transitions Average structure distance to target d S Uninterrupted presence Evolutionary trajectory Time (arbitrary units) In silico optimization in the flow reactor

56 Variation in genotype space during optimization of phenotypes

57 Statistics of evolutionary trajectories Population size N Number of replications < n > rep Number of transitions < n > tr Number of main transitions < n > dtr The number of main transitions or evolutionary innovations is constant.

58 Three important steps in the formation of the trna clover leaf from a randomly chosen initial structure corresponding to three main transitions.

59 ...Variations neither useful not injurious would not be affected by natural selection, and would be left either a fluctuating element, as perhaps we see in certain polymorphic species, or would ultimately become fixed, owing to the nature of the organism and the nature of the conditions.... harles Darwin, Origin of species (1859)

60 Adaptive Periods End of Walk Fitness Random Drift Periods Start of Walk enotype Space Evolution in genotype space sketched as a non-descending walk in a fitness landscape

61 Evolution of RNA molecules based on Qβ phage D.R.Mills, R,L,Peterson, S.Spiegelman, An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule. Proc.Natl.Acad.Sci.USA 58 (1967), S.Spiegelman, An approach to the experimental analysis of precellular evolution. Quart.Rev.Biophys. 4 (1971), K.Biebricher, Darwinian selection of self-replicating RNA molecules. Evolutionary Biology 16 (1983), 1-52.K.Biebricher, W.. ardiner, Molecular evolution of RNA in vitro. Biophysical hemistry 66 (1997), Strunk, T. Ederhof, Machines for automated evolution experiments in vitro based on the serial transfer concept. Biophysical hemistry 66 (1997),

62 RNA sample Time Stock solution: Q RNA-replicase, ATP, TP, TP and UTP, buffer The serial transfer technique applied to RNA evolution in vitro

63 Reproduction of the original figure of the serial transfer experiment with Q RNA β D.R.Mills, R,L,Peterson, S.Spiegelman, An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule. Proc.Natl.Acad.Sci.USA 58 (1967),

64 Decrease in mean fitness due to quasispecies formation The increase in RNA production rate during a serial transfer experiment

65 Bacterial Evolution S. F. Elena, V. S. ooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants. Science 272 (1996), D. Papadopoulos, D. Schneider, J. Meier-Eiss, W. Arber, R. E. Lenski, M. Blot. enomic evolution during a 10,000-generation experiment with bacteria. Proc.Natl.Acad.Sci.USA 96 (1999),

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

67 Distance to ancestor Distance within sample Time (enerations) Time (enerations) Variation of genotypes in a bacterial serial transfer experiment D. Papadopoulos, D. Schneider, J. Meier-Eiss, W. Arber, R. E. Lenski, M. Blot. enomic evolution during a 10,000-generation experiment with bacteria. Proc.Natl.Acad.Sci.USA 96 (1999),

68 Evolutionary design of RNA molecules D.B.Bartel, J.W.Szostak, In vitro selection of RNA molecules that bind specific ligands. Nature 346 (1990), Tuerk, L.old, SELEX - Systematic evolution of ligands by exponential enrichment: RNA ligands to bacteriophage T4 DNA polymerase. Science 249 (1990), D.P.Bartel, J.W.Szostak, Isolation of new ribozymes from a large pool of random sequences. Science 261 (1993), R.D.Jenison, S..ill, A.Pardi, B.Poliski, High-resolution molecular discrimination by RNA. Science 263 (1994),

69 Amplification Diversification Selection ycle enetic Diversity Selection Selection cycle used in applied molecular evolution to design molecules with predefined properties no Desired Properties??? yes

70 Retention of binders Elution of binders hromatographic column The SELEX technique for the evolutionary design of aptamers

71 A A A A A U U U U U U A A A A A U U U U U U Formation of secondary structure of the tobramycin binding RNA aptamer L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, hemistry & Biology 4:35-50 (1997)

72 The three-dimensional structure of the tobramycin aptamer complex L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, hemistry & Biology 4:35-50 (1997)

73 A ribozyme switch E.A.Schultes, D.B.Bartel, One sequence, two ribozymes: Implication for the emergence of new ribozyme folds. Science 289 (2000),

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

75 The sequence at the intersection: An RNA molecules which is 88 nucleotides long and can form both structures

76 Reference for the definition of the intersection and the proof of the intersection theorem

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

78 Sequence of mutants from the intersection to both reference ribozymes

79 Reference for postulation and in silico verification of neutral networks

80 oworkers Walter Fontana, Santa Fe Institute, NM hristian Reidys, hristian Forst, Los Alamos National Laboratory, NM Peter Stadler, Universität Wien, AT Ivo L.Hofacker hristoph Flamm Bärbel Stadler, Andreas Wernitznig, Universität Wien, AT Michael Kospach, Ulrike Mückstein, Stefanie Widder, Stefan Wuchty Jan upal, Kurt rünberger, Andreas Svrček-Seiler Ulrike öbel, Institut für Molekulare Biotechnologie, Jena, E Walter rüner, Stefan Kopp, Jaqueline Weber