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What we can learn from simple models of evolution Peter Schuster Institut fr Theoretische Chemie, Universitt Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Seminar Lecture Haifa, 03.03.2013 Web-Page for further

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What we can learn from simple models of evolution

Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

Seminar Lecture Haifa, 03.03.2013

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Web-Page for further information: http://www.tbi.univie.ac.at/~pks

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1. Gradualism and punctualism

  • 2. Contingency in evolution experiments
  • 3. Neutrality and its consequences
  • 4. In silico-evolution of RNA structures
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  • 1. Gradualism and punctualism
  • 2. Contingency in evolution experiments
  • 3. Neutrality and its consequences
  • 4. In silico-evolution of RNA structures
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Charles Darwin, 1809 - 1882

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The five concepts ofDarwin‘s theory of evolution from the „Origin of Species“, 23.11.1859 Ernst Mayr. 1991. One long argument. Harvard University Press.

  • 1. evolution – the fact as such
  • 2. common descent – all organisms have a common

ancestor

  • 3. multiplication of species – the formation of new

species from existing ones

  • 4. gradualism – all changes happen in (very) small steps
  • 5. natural selection – adaptation to the environment as

a result of the fact that only few individuals can master the competition for limited resources

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Stephen J. Gould, 1941 - 2002 Niles Eldredge, 1943 -

The concept of punctuated equilibrium

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Gradualism versus punctualism in butterfly species formation

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Elisabeth Vrba, 1943 -

A speciation model based on punctuated equilibrium

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1. Gradualism and punctualism

  • 2. Contingency in evolution experiments
  • 3. Neutrality and its consequences
  • 4. In silico-evolution of RNA structures
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Bacterial evolution under controlled conditions: A twenty years experiment. Richard Lenski, University of Michigan, East Lansing

Richard Lenski, 1956 -

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Bacterial evolution under controlled conditions: A twenty years experiment.

Richard Lenski, University of Michigan, East Lansing

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The twelve populations of Richard Lenski‘s long time evolution experiment

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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), 1802-1804 1 year

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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), 1802-1804 1 year

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

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Innovation by mutation in long time evolution of Escherichia coli in constant environment Z.D. Blount, C.Z. Borland, R.E. Lenski. 2008. Proc.Natl.Acad.Sci.USA 105:7899-7906

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Innovation by mutation in long time evolution of Escherichia coli in constant environment

Z.D. Blount, C.Z. Borland, R.E.

  • Lenski. 2008.

Proc.Natl.Acad.Sci.USA 105:7899-7906

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Contingency of E. coli evolution experiments

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1. Gradualism and punctualism

  • 2. Contingency in long-time evolution
  • 3. Neutrality and its consequences
  • 4. In silico-evolution of RNA structures
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What is neutrality ?

Selective neutrality = = several genotypes having the same fitness. Structural neutrality = = several genotypes forming molecules with the same structure.

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Charles Darwin. The Origin of Species. Sixth edition. John Murray. London: 1872

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Motoo Kimura‘s population genetics of neutral evolution. Evolutionary rate at the molecular level. Nature 217: 624-626, 1955. The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge, UK, 1983.

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Fixation of mutants in neutral evolution (Motoo Kimura, 1955)

The average time of replacement of a dominant genotype in a population is the reciprocal mutation rate, 1/, and therefore independent of population size.

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Motoo Kimura. The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge, UK, 1983.

The molecular clock of evolution

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Manfred Eigen 1927 -

∑ ∑ ∑

= = =

= = ⋅ = = − =

n i i i n i i i ji ji j i n i ji j

x f Φ x f Q W n j Φ x x W x

1 1 1

, 1 , , , 2 , 1 ; dt d 

Mutation and (correct) replication as parallel chemical reactions

  • M. Eigen. 1971. Naturwissenschaften 58:465,
  • M. Eigen & P. Schuster.1977. Naturwissenschaften 64:541, 65:7 und 65:341
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The continuously stirred tank reactor (CSTR) as a tool for studies on in vitro evolution and computer simulation.

Stock solution: activated monomers, ATP, CTP, GTP, UTP; a replicase, an enzyme that performs complementary replication; buffer solution

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quasispecies

The error threshold in replication and mutation

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A model fitness landscape that was accessible to computation in the nineteen eighties

single peak landscape

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Stationary population or quasispecies as a function

  • f the mutation or error

rate p

Error rate p = 1-q

0.00 0.05 0.10

Quasispecies Uniform distribution

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Realistic fitness landscapes 1.Ruggedness: nearby lying genotypes may develop into very different phenotypes 2.Neutrality: many different genotypes give rise to phenotypes with identical selection behavior 3.Combinatorial explosion: the number of possible genomes is prohibitive for systematic searches

and hence, any successful and applicable theory of molecular evolution must be able to predict evolutionary dynamics from a small or at least in practice measurable number of fitness values.

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O CH2 OH O O P O O O

N1

O CH2 OH O P O O O

N2

O CH2 OH O P O O O

N3

O CH2 OH O P O O O

N4

N A U G C

k =

, , ,

3' - end 5' - end Na Na Na Na

5'-end 3’-end

GCGGAU AUUCGC UUA AGUUGGGA G CUGAAGA AGGUC UUCGAUC A ACCA GCUC GAGC CCAGA UCUGG CUGUG CACAG

Definition of RNA structure

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A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _  {AU,CG,GC,GU,UA,UG} N = 4n NS < 3n

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many genotypes  one phenotype

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AGCUUAACUUAGUCGCU 1 A-G 1 A-U 1 A-C

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Motoo Kimura

Is the Kimura scenario correct for frequent mutations?

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Pairs of neutral sequences in replication networks

  • P. Schuster, J. Swetina. 1988. Bull. Math. Biol. 50:635-650

5 . ) ( ) ( lim

2 1

= =

→

p x p x

p

dH = 1

a p x a p x

p p

− = =

→ →

1 ) ( lim ) ( lim

2 1

dH = 2

Random fixation in the sense of Motoo Kimura

dH  3

1 ) ( lim , ) ( lim

  • r

) ( lim , 1 ) ( lim

2 1 2 1

= = = =

→ → → →

p x p x p x p x

p p p p

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A fitness landscape including neutrality

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

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

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Consensus sequences of a quasispecies of two strongly coupled sequences of Hamming distance dH(Xi,,Xj) = 1 and 2.

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Neutral networks with increasing :  = 0.10, s = 229

Adjacency matrix

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1. Gradualism and punctualism

  • 2. Contingency in evolution expeiments
  • 3. Neutrality and its consequences
  • 4. In silico-evolution of RNA structures
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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

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Computer simulation of RNA optimization

Walter Fontana and Peter Schuster, Biophysical Chemistry 26:123-147, 1987 Walter Fontana, Wolfgang Schnabl, and Peter Schuster, Phys.Rev.A 40:3301-3321, 1989

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Walter Fontana, Wolfgang Schnabl, and Peter Schuster, Phys.Rev.A 40:3301-3321, 1989

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Evolution in silico

  • W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

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Phenylalanyl-tRNA as target structure Structure of randomly chosen initial sequence

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The flow reactor as a device for studying the evolution of molecules in vitro and in silico. Replication rate constant (Fitness): fk =  / [ + dS

(k)]

dS

(k) = dH(Sk,S)

Selection pressure: The population size, N = # RNA moleucles, is determined by the flux: Mutation rate: p = 0.001 / Nucleotide  Replication

N N t N ± ≈ ) (

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Spreading of the population

  • n neutral networks

Drift of the population center in sequence space Evolutionary trajectory

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First adaptive phase in RNA structure optimization

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First adaptive phase in RNA structure optimization: RNA structures

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First adaptive phase in RNA structure optimization: RNA sequences

Transition inducing point mutations change the molecular structure Neutral point mutations leave the molecular structure unchanged

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First adaptive and quasistationary phase in RNA structure optimization

7 8 9 10

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Neutral genotype evolution during phenotypic stasis

Neutral point mutations leave the molecular structure unchanged Transition inducing point mutations change the molecular structure 28 neutral point mutations during a long quasi-stationary epoch

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Spreading and evolution of a population on a neutral network: t = 150

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Spreading and evolution of a population on a neutral network: t = 150

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Spreading and evolution of a population on a neutral network : t = 170

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Spreading and evolution of a population on a neutral network : t = 200

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Spreading and evolution of a population on a neutral network : t = 350

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Spreading and evolution of a population on a neutral network : t = 500

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Spreading and evolution of a population on a neutral network : t = 650

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Spreading and evolution of a population on a neutral network : t = 820

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Spreading and evolution of a population on a neutral network : t = 825

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Spreading and evolution of a population on a neutral network : t = 830

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Spreading and evolution of a population on a neutral network : t = 835

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Spreading and evolution of a population on a neutral network : t = 840

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Spreading and evolution of a population on a neutral network : t = 845

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Spreading and evolution of a population on a neutral network : t = 850

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Spreading and evolution of a population on a neutral network : t = 855

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A sketch of optimization on neutral networks

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Neutrality explains both punctuation and contingency

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Coworkers

Peter Stadler, Bärbel M. Stadler, Universität Leipzig, GE Paul E. Phillipson, University of Colorado at Boulder, CO Heinz Engl, Philipp Kügler, James Lu, Stefan Müller, RICAM Linz, AT Jord Nagel, Kees Pleij, Universiteit Leiden, NL Walter Fontana, Harvard Medical School, MA Martin Nowak, Harvard University, MA Christian Reidys, Nankai University, Tien Tsin, China Christian Forst, Los Alamos National Laboratory, NM Thomas Wiehe, 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, Stefan Wuchty, Jan Cupal, Stefan Bernhart, Lukas Endler, Ulrike Langhammer, Rainer Machne, Ulrike Mückstein, Erich Bornberg-Bauer, Universität Wien, AT

Universität Wien

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Universität Wien

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

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Thank you for your attention!

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Web-Page for further information: http://www.tbi.univie.ac.at/~pks

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