Selektive Neutralität und Effizienz der Evolution - TBIpks/Presentation/wien-nhm.pdf · Selektive...

Selektive Neutralität und Effizienz der EvolutionWas wir aus Evolutionsexperimenten lernen können

Peter SchusterInstitut für Theoretische Chemie und Molekulare

Strukturbiologie der Universität Wien

Seminar des Naturhistorischen Museums

Wien, 28.04.2004

Web-Page for further information:

http://www.tbi.univie.ac.at/~pks

200 400 600 800 1000

0.2

00

0.4

0.6

0.8

1

Zeit [Generationen]

Ant

eil a

n vo

rteilh

afte

r Var

iant

e

s = 0.1

s = 0.01

s = 0.02

s = (f - f ) / f2 1 1

Selektion vorteilhafter Varianten in einer Population von N = 10 000 Individuen

Massif Central

Mount FujiBeispiele glatter Landschaften

Dolomiten

Beispiele zerklüfteter Landschaften Bryce Canyon

Sequenzraum

Mitt

lere

Fitn

eß

Start der Optimierung

Ende

Optimierung auf einer Fitneßlandschaft ohne selektive Neutralität

Sequenzraum

Mitt

lere

Fitn

eß




Ende

Ende

Ende

Optimierung auf einer Fitneßlandschaft ohne selektive Neutralität

Sequenzraum

Mitt

lere

Fitn

eß


Ende

Zufallsdrift

Adaptive Perioden

Evolutionäre Optimierung auf einer Landschaft mit neutralen Zonen

Grand Canyon

Beispiel einer Landschaft mit neutralen Graten und Plateaus

Neutrale Grate und Plateaus

„...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. ...“

Charles Darwin, Origin of species (1859)

The molecular clock of evolution

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. Canbridge University Press. Cambridge, UK, 1983.

Molecular evolution through comparison of sequences from different organisms

Five kingdoms.L. Margulis, K.V. Schwartz, W.H.Freeman & Co., 1982

Evolution at the molecular level.R.K. Selander, A.G. Clark, T.S. Whittam, eds. Sinauer Associates, 1991.

Generation time 10 000 generations 106 generations 107 generations RNA molecules 10 sec

1 min 27.8 h = 1.16 d

6.94 d 115.7 d 1.90 a

3.17 a 19.01 a

Bacteria 20 min 10 h

138.9 d 11.40 a

38.03 a 1 140 a

380 a 11 408 a

Higher multicelluar organisms

10 d 20 a

274 a 20 000 a

27 380 a 2 × 107 a

273 800 a 2 × 108 a

Time scales of evolutionary change

Bacterial Evolution

S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants. Science 272 (1996), 1802-1804

D. Papadopoulos, D. Schneider, J. Meier-Eiss, W. Arber, R. E. Lenski, M. Blot. Genomic evolution during a 10,000-generation experiment with bacteria. Proc.Natl.Acad.Sci.USA 96 (1999), 3807-3812

24 h 24 h

Serial transfer of Escherichia colicultures in Petri dishes

1 day 6.67 generations 1 month 200 generations

ÎÎ

1 year 2400 generationsÎ

lawn of E.coli

nutrient agar

1 year

Epochal evolution of bacteria in serial transfer experiments under constant conditionsS. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants. Science 272 (1996), 1802-1804

2000 4000 6000 8000

Time

5

10

15

20

25H

amm

ing

dist

ance

to a

nces

tor

Generations

Variation of genotypes in a bacterial serial transfer experimentD. Papadopoulos, D. Schneider, J. Meier-Eiss, W. Arber, R. E. Lenski, M. Blot. Genomic evolution during a 10,000-generation experiment with bacteria. Proc.Natl.Acad.Sci.USA 96 (1999), 3807-3812

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), 217-224

S.Spiegelman, An approach to the experimental analysis of precellular evolution. Quart.Rev.Biophys. 4 (1971), 213-253

C.K.Biebricher, Darwinian selection of self-replicating RNA molecules. Evolutionary Biology 16 (1983), 1-52

C.K.Biebricher, W.C. Gardiner, Molecular evolution of RNA in vitro. Biophysical Chemistry 66 (1997), 179-192

G.Strunk, T. Ederhof, Machines for automated evolution experiments in vitro based on the serial transfer concept. Biophysical Chemistry 66 (1997), 193-202

RNA sample

Stock solution: Q RNA-replicase, ATP, CTP, GTP and UTP, bufferb

Time0 1 2 3 4 5 6 69 70

The serial transfer technique applied to RNA evolution in vitro

Reproduction of the original figure of theserial transfer experiment with Q RNAβ

D.R.Mills, R,L,Peterson, S.Spiegelman,

. Proc.Natl.Acad.Sci.USA (1967), 217-224

An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule58

Decrease in mean fitnessdue to quasispecies formation

The increase in RNA production rate during a serial transfer experiment

Evolutionary design of RNA molecules

D.B.Bartel, J.W.Szostak, In vitro selection of RNA molecules that bind specific ligands. Nature 346 (1990), 818-822

C.Tuerk, L.Gold, SELEX - Systematic evolution of ligands by exponential enrichment: RNA ligands to bacteriophage T4 DNA polymerase. Science 249 (1990), 505-510

D.P.Bartel, J.W.Szostak, Isolation of new ribozymes from a large pool of random sequences. Science 261 (1993), 1411-1418

R.D.Jenison, S.C.Gill, A.Pardi, B.Poliski, High-resolution molecular discrimination by RNA. Science 263 (1994), 1425-1429

Y. Wang, R.R.Rando, Specific binding of aminoglycoside antibiotics to RNA. Chemistry &Biology 2 (1995), 281-290

Jiang, A. K. Suri, R. Fiala, D. J. Patel, Saccharide-RNA recognition in an aminoglycoside antibiotic-RNA aptamer complex. Chemistry & Biology 4 (1997), 35-50

No new principle will declare itself from below a heap of facts.

Sir Peter Medawar, 1985

G

G

G

C

C

C

C

C

C

G

G

G

C

C

C

G

G

G

C

C

C

G

G

G

G

G

G

C

C

C

Plus Strand

Plus Strand

Plus Strand

Minus Strand

Minus Strand

Minus Strand

3'

3'

3'5'

5'

5'

5'

5'

5'3'

3'

3'

+

Replication of DNA is a higly complex copying mechanism involving more than ten different proteinmolecules. Complementarity is determined byWatson-Crick base pairs:

GÍC and A=T

James Watson and Francis Crick, 1953

dx / dt = x - x

x

i i i

j j

; Σ = 1 ; i,j

f

f

i

j

Φ

Φ

fi Φ = (

= Σ

x - i )

j jx =1,2,...,n

[I ] = x 0 ; i i Æ i =1,2,...,n ; Ii

I1

I2

I1

I2

I1

I2

I i

I n

I i

I nI n

+

+

+

+

+

+

(A) +

(A) +

(A) +

(A) +

(A) +

(A) +

fn

fi

f1

f2

I mI m I m++(A) +(A) +fm

fm fj= max { ; j=1,2,...,n}

xm(t) 1 for t Á Á¸

[A] = a = constant

Reproduction of organisms or replication of molecules as the basis of selection

G

G

G

C

C

C

G

C

C

G

C

C

C

G

C

C

C

G

C

G

G

G

G

C

Plus Strand

Plus Strand

Minus Strand

Plus Strand

3'

3'

3'

3'

5'

3'

5'

5'

5'

Point Mutation

Insertion

Deletion

GAA AA UCCCG

GAAUCC A CGA

GAA AAUCCCGUCCCG

GAAUCCA

The origins of changes in RNA sequences are replication errors called mutations.

Theory of molecular evolution

M.Eigen, Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58 (1971), 465-526

C.J. Thompson, J.L. McBride, On Eigen's theory of the self-organization of matter and the evolution of biological macromolecules. Math. Biosci. 21 (1974), 127-142

B.L. Jones, R.H. Enns, S.S. Rangnekar, On the theory of selection of coupled macromolecular systems. Bull.Math.Biol. 38 (1976), 15-28

M.Eigen, P.Schuster, The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle. Naturwissenschaften 58 (1977), 465-526

M.Eigen, P.Schuster, The hypercycle. A principle of natural self-organization. Part B: The abstract hypercycle. Naturwissenschaften 65 (1978), 7-41

M.Eigen, P.Schuster, The hypercycle. A principle of natural self-organization. Part C: The realistic hypercycle. Naturwissenschaften 65 (1978), 341-369

J. Swetina, P. Schuster, Self-replication with errors - A model for polynucleotide replication.Biophys.Chem. 16 (1982), 329-345

J.S. McCaskill, A localization threshold for macromolecular quasispecies from continuously distributed replication rates. J.Chem.Phys. 80 (1984), 5194-5202

M.Eigen, J.McCaskill, P.Schuster, The molecular quasispecies. Adv.Chem.Phys. 75 (1989), 149-263

C. Reidys, C.Forst, P.Schuster, Replication and mutation on neutral networks. Bull.Math.Biol. 63(2001), 57-94

Chemical kinetics of molecular evolution

M. Eigen, P. Schuster, `The Hypercycle´, Springer-Verlag, Berlin 1979

Ij

In

I2

Ii

I1 I j

I j

I j

I j

I j

I j +

+

+

+

+

(A) +

fj Qj1

fj Qj2

fj Qji

fj Qjj

fj Qjn

Q (1- ) ij-d(i,j) d(i,j) = lp p

p .......... Error rate per digit

d(i,j) .... Hamming distance between Ii and Ij

........... Chain length of the polynucleotidel

dx / dt = x - x

x

i j j i

j j

Σ

; Σ = 1 ;

f

f x

j

j j i

Φ

Φ = Σ

Qji

QijΣi = 1

[A] = a = constant

[Ii] = xi 0 ; Æ i =1,2,...,n ;

Chemical kinetics of replication and mutation as parallel reactions

spaceSequence

Con

cent

ratio

n

Master sequence

Mutant cloud

The molecular quasispecies in sequence space

OCH2

OHO

O

PO

O

O

N1

OCH2

OHO

PO

O

O

N2

OCH2

OHO

PO

O

O

N3

OCH2

OHO

PO

O

O

N4

N A U G Ck = , , ,

3' - end

5' - end

NaØ

NaØ

NaØ

NaØ

RNA

nd 3’-endGCGGAU AUUCGCUUA AGUUGGGA G CUGAAGA AGGUC UUCGAUC A ACCAGCUC GAGC CCAGA UCUGG CUGUG CACAG

3'-end

5’-end

70

60

50

4030

20

10

Definition of RNA structure

5'-e

Optimization of RNA molecules in silico

W.Fontana, P.Schuster, A computer model of evolutionary optimization. Biophysical Chemistry 26 (1987), 123-147

W.Fontana, W.Schnabl, P.Schuster, Physical aspects of evolutionary optimization and adaptation. Phys.Rev.A 40 (1989), 3301-3321

M.A.Huynen, W.Fontana, P.F.Stadler, Smoothness within ruggedness. The role of neutralityin adaptation. Proc.Natl.Acad.Sci.USA 93 (1996), 397-401

W.Fontana, P.Schuster, Continuity in evolution. On the nature of transitions. Science 280(1998), 1451-1455

W.Fontana, P.Schuster, Shaping space. The possible and the attainable in RNA genotype-phenotype mapping. J.Theor.Biol. 194 (1998), 491-515

B.M.R. Stadler, P.F. Stadler, G.P. Wagner, W. Fontana, The topology of the possible: Formal spaces underlying patterns of evolutionary change. J.Theor.Biol. 213 (2001), 241-274

Evolution in silico

W. Fontana, P. Schuster, Science 280 (1998), 1451-1455

Optimized element: RNA structure

Stock Solution Reaction Mixture

Replication rate constant:

fk = g / [a + DdS(k)]

DdS(k) = dH(Sk,St)

Selection constraint:

# RNA molecules is controlled by the flow

NNtN ±≈)(

The flowreactor as a device for studies of evolution in vitro and in silico

5'-End

3'-End

70

60

50

4030

20

10

Randomly chosen initial structure

Phenylalanyl-tRNA as target structure

spaceSequence

Con

cent

ratio

n

Master sequence

Mutant cloud

“Off-the-cloud” mutations

The molecular quasispeciesin sequence space

f0 ft

f1

f2

f3

f4

f6

f5f7

Replication rate constant:

fk = g / [a + DdS(k)]

DdS(k) = dH(Sk,St)

Evaluation of RNA secondary structures yields replication rate constants

In silico optimization in the flow reactor: Trajectory (biologists‘ view)

Time (arbitrary units)

Aver

age

dist

ance

from

initi

al s

truct

ure

50

-d

D

S

500 750 1000 12502500

50

40

30

20

10

0

Evolutionary trajectory

1008

1214

Time (arbitrary units)

Aver

age

stru

ctur

e di

stan

ce

to ta

rget

d S

D

5002500

20

10

Uninterrupted presence

Evolutionary trajectory

Num

ber of relay step

28 neutral point mutations during a long quasi-stationary epoch

Transition inducing point mutations Neutral point mutations

Neutral genotype evolution during phenotypic stasis

Variation in genotype space during optimization of phenotypes

Mean Hamming distance within the population and drift velocity of the population centerin sequence space.

Spread of population in sequence space during a quasistationary epoch: t = 150

AUGC GC

Movies of optimization trajectories over the AUGC and the GC alphabet

Alphabet Runtime Transitions Main transitions No. of runs

AUGC 385.6 22.5 12.6 1017 GUC 448.9 30.5 16.5 611 GC 2188.3 40.0 20.6 107

Statistics of trajectories and relay series (mean values of log-normal distributions)

Theory of sequence – structure mappings

P. Schuster, W.Fontana, P.F.Stadler, I.L.Hofacker, From sequences to shapes and back: A case study in RNA secondary structures. Proc.Roy.Soc.London B 255 (1994), 279-284

W.Grüner, R.Giegerich, D.Strothmann, C.Reidys, I.L.Hofacker, P.Schuster, Analysis of RNA sequence structure maps by exhaustive enumeration. I. Neutral networks. Mh.Chem. 127 (1996), 355-374

W.Grüner, R.Giegerich, D.Strothmann, C.Reidys, I.L.Hofacker, P.Schuster, Analysis of RNA sequence structure maps by exhaustive enumeration. II. Structure of neutral networks and shape space covering. Mh.Chem. 127 (1996), 375-389

C.M.Reidys, P.F.Stadler, P.Schuster, Generic properties of combinatory maps. Bull.Math.Biol. 59 (1997), 339-397

I.L.Hofacker, P. Schuster, P.F.Stadler, Combinatorics of RNA secondary structures. Discr.Appl.Math. 89 (1998), 177-207

C.M.Reidys, P.F.Stadler, Combinatory landscapes. SIAM Review 44 (2002), 3-54

Reference for postulation and in silico verification of neutral networks

A connected neutral network

Giant Component

A multi-component neutral network

RNA 9:1456-1463, 2003

Evidence for neutral networks and shape space covering

Evidence for neutral networks and intersection of apatamer functions

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

GkNeutral Network

Structure S k

Gk Cà k

Compatible Set Ck

The compatible set Ck of a structure Sk consists of all sequences which form Sk as its minimum free energy structure (the neutral network Gk) or one of itssuboptimal structures.

Structure S 0

Structure S 1

The intersection of two compatible sets is always non empty: C0 Ú C1 â Ù

A ribozyme switch

E.A.Schultes, D.B.Bartel, Science 289 (2000), 448-452

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

The sequence at the intersection:

An RNA molecules which is 88 nucleotides long and can form both structures

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

Wolfgang Wieser. Die Erfindung der Individualität oder die zwei Gesichter der Evolution. Spektrum Akademischer Verlag, Heidelberg 1998.

A.C.Wilson. The Molecular Basis of Evolution. Scientific American, Oct.1985, 164-173.

1968

2004Evolution (Cartoon Î 1980)

Acknowledgement of support

Fonds zur Förderung der wissenschaftlichen Forschung (FWF)

Projects No. 09942, 10578, 11065, 1309313887, and 14898

Jubiläumsfonds der Österreichischen Nationalbank

Project No. Nat-7813

European Commission: Project No. EU-980189

Siemens AG, Austria

The Santa Fe Institute and the Universität Wien

The software for producing RNA movies was developed by Robert Giegerich and coworkers at the Universität Bielefeld

Universität Wien

CoworkersUniversität Wien

Walter Fontana, Santa Fe Institute, NM

Christian Reidys, Christian Forst, Los Alamos National Laboratory, NM

Peter Stadler, Bärbel Stadler, Universität Leipzig, GE

Ivo L.Hofacker, Christoph Flamm, Universität Wien, AT

Andreas Wernitznig, Michael Kospach, Universität Wien, ATUlrike Langhammer, Ulrike Mückstein, Stefanie Widder

Jan Cupal, Kurt Grünberger, Andreas Svrček-Seiler, Stefan Wuchty

Ulrike Göbel, Institut für Molekulare Biotechnologie, Jena, GEWalter Grüner, Stefan Kopp, Jaqueline Weber

Web-Page for further information:

http://www.tbi.univie.ac.at/~pks

Selektive Neutralität und Effizienz der Evolution - TBIpks/Presentation/wien-nhm.pdf · Selektive...

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