Download - Self-Organization and Evolution - TBIpks/Presentation/wien-akh.pdf · Replication in the flow reactor P.Schuster & K.Sigmund, Dynamics of evolutionary optimization, Ber.Bunsenges.Phys.Chem.

Self-Organization and Evolution

Peter SchusterInstitut für Theoretische Chemie und Molekulare Strukturbiologie

der Universität Wien

Wissenschaftliche Gesellschaft: Dynamik – Komplexität –menschliche Systeme

AKH Wien, 12.06.2002

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).

Carnot, Mayer, Joule, Helmholtz, Clausius, ……

D.Jou, J.Casas-Vázquez, G.Lebon, Extended Irreversible Thermodynamics, 1996

Time

Fluctuations aroundequilibrium

Approach towards equilibrium

Spontaneous processes S > 0D

Smax

Entro

py Enla

rged

scal

e

( ) < 0U,V,equild S2

Entropy and fluctuations at equilibrium

Self-organization is spontaneous creation of order.

Entropy is equivalent to disorder. Hence there is no spontaneouscreation 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.

dSi > 0

dS = + < 0dSi dSe

Selforganization

dSe < 0

Environment

dS = + dS > 0tot envdS

dS > 0env

Entropy production and self-organization in open systems

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

•Chaotic dynamics in model equations for atmospheric flow

•Pattern formation in chemical reactions

Examples of self-organization and pattern formation

Red spotSouth pole

View from south pole

Jupiter: Observation of the gigantic vortexPicture taken from James Gleick, Chaos. Penguin Books, New York, 1988

Computer simulation of the gigantic vortex on Jupiter

Particles turningcounterclockwise

Particles turningclockwise

View from south pole

Jupiter: Computer simulation of the giant vortexPhilip Marcus, 1980. Picture taken from James Gleick, Chaos. Penguin Books, New York, 1988

z z + c2 Áwith z = x + i y

Mandelbrot set

The Mandelbrot set as an example of fractal patterns in mathematicsPicture taken from James Gleick, Chaos. Penguin Books, New York, 1988


Mandelbrot set

The Mandelbrot set as an example of fractal patterns in mathematics: Enlargement no.1Picture taken from James Gleick, Chaos. Penguin Books, New York, 1988


Mandelbrot set

The Mandelbrot set as an example of fractal patterns in mathematics: Enlargement no.2Picture taken from James Gleick, Chaos. Penguin Books, New York, 1988


Mandelbrot set

The Mandelbrot set as an exampleof fractal patterns in mathematics: Enlargement no.3Picture taken from James Gleick, Chaos. Penguin Books, New York, 1988

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

Isolated system

dS

U = const., V = const.,

0 Æ

dS 0Æ dS 0Æ dS 0Æ

Closed system

dG dU pdV TdS T = const., p = const.,

= - - 0¶

Open system

dS

dS d S d S

d S i e

i

dS = + 0

= +

0

Æ

Æ

dSenv

p

TT

Stock Solution Reaction Mixture

d Si

deSdSenv

Entropy changes in different thermodynamic systems with chemical reactions

Stock Solution [a] = a0 Reaction Mixture [a],[b]

A

A

A

A

AAA

A A

A

A

A

AA

A

A

A

A

A

B

BB

B

B

B

B

B

B

B

BB

Flow rate r = 1tR-

Reactions in the continuously stirred tank reactor (CSTR)

2.0 4.0 6.0 8.0 10.0

Flow rate r [t ] -1

1.0

0.8

0.6

1.2C

once

ntra

tion

a

[a

] 0

A B

Reversible first order reaction in the flow reactor

0.25 0.50 1.000.75 1.25

Flow rate r [t ] -1

1.0

0.8

0.6

1.2C

once

ntra

tion

a

[a

] 0

A + B 2 B

Autocatalytic second order reaction in the flow reactor

0.25 0.50 1.000.75 1.25

Flow rate r [t ] -1

1.0

0.8

0.6

1.2C

once

ntra

tion

a

[a

] 0

A

A + B

B

2 B

a = 0a = 0.001a = 0.1

a ¸ =

Autocatalytic second order and uncatalyzed reaction in the flow reactor

0.100.080.060.040.02 0.12 0.14 0.16 0.18

Flow rate r [t ] -1

1.0

0.8

0.6

1.2C

once

ntra

tion

a

[a

] 0

A +2 B 3B

Autocatalytic third order reaction in the flow reactor

0.100.080.060.040.02 0.12 0.14 0.16 0.18

Flow rate r [t ] -1

1.0

0.8

0.6

1.2C

once

ntra

tion

a

[a

] 0

A +2 B

A

3B

B

a = 0a = 0.001a = 0.0025a = 0.007

a ¸ =

Autocatalytic third order and uncatalyzed reaction in the flow reactor

Autocatalytic third order reactions

A + 2 X 3 XÁDirect, , or hiddenin 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

G.Nicolis, I.Prigogine. Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations. John Wiley, New York 1977

Formation of target waves and spirals in the Belousov-Zhabotinskii reaction

Winding number:

minusnumber of left-handed spirals

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.

Autocatalytic second order reactions

A + I 2 IÁDirect, , or hidden inthe reaction mechanism

Chemical self-enhancement

Selection of laser modes

Selection of molecular ororganismic species competingfor common sources

Combustion and chemistry of flames

Autocatalytic second order reaction as basis for selection processes.

The autocatalytic step is formally equivalent to replication or reproduction.

Stock Solution [A] = a0 Reaction Mixture: A; I , k=1,2,...k

A + I 2 I1 1

A + I 2 I2 2

A + I 2 I3 3

A + I 2 I4 4

A + I 2 I5 5

k1

k2

k3

k4

k5

d1

d2

d3

d4

d5

Replication in the flow reactorP.Schuster & K.Sigmund, Dynamics of evolutionary optimization, Ber.Bunsenges.Phys.Chem.89: 668-682 (1985)

Flow rate r = tR-1

Con

cent

ratio

n of

stoc

k so

lutio

n a

0

A + I1

A +

I+

I1

2

A

A + I 2 I2 2

A + I 2 I3 3

A + I 2 I4 4

A + I 2 I5 5

A + I 2 I1 1

k > k > k > k > k1 2 3 4 5

k1

k2

k3

k4

k5

d5

d4

d3

d2

d1

Selection in the flow reactor: Reversible replication reactions

Flow rate r = tR-1

Con

cent

ratio

n of

stoc

k so

lutio

n a

0

A + I1

A

A + I 2 I2 2

A + I 2 I3 3

A + I 2 I4 4

A + I 2 I5 5

A + I 2 I1 1

f > f > f > f > f1 2 3 4 5

f1

f2

f3

f4

f5

Selection in the flow reactor: Irreversible replication reactions

s = (fm+1-fm)/fm

succession of temporarilyfittest variants:

m Á m+1Á ...

dx / dt = x - x

x

j j j

i i

; Σ = 1 ; i,j

f

f

j

i

Φ

Φ

= (

= Σi ix

fj Φ - x) j

=1,2,...,n

[A] = a = constant

IjIj

I1

I2

I1

I2

I1

I2

Ij

In

Ij

InI n

+

+

+

+

+

+

(A) +

(A) +

(A) +

(A) +

(A) +

(A) +

fn

fj

f1

f2

ImI m Im++(A) +(A) +fm

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

x (t) 1 for t m Á Á ¸

Selection of the „fittest“ or fastest replicating species Im

200 400 600 800 1000

0.2

00

0.4

0.6

0.8

1

Time [Generations]

Frac

tion

of a

dvan

tage

ous v

aria

nt

s = 0.1

s = 0.01

s = 0.02

Selection of advantageous mutants in populations of N = 10 000 individuals

Thermodynamics of isolated systems: Entropy is a non-decreasingstate function

Second law S → Smax

Valid in the limit of infinite time, lim tÁ ¸.

Evolution of Populations: Mean fitness is a non-decreasing function

Ronald Fisher‘s conjecture f = Sk xk(t) fk / Sk xk(t) Á fmax

Optimization heuristics in the sense that it is only almost always true and the process need

not reach the optimum in finite times.

AAAAA UUUUUU CCCCCCCCG GGGGGGG

A

U

C

G

= adenylate= uridylate= cytidylate= guanylateCombinatorial diversity of sequences: N = 4{

4 = 1.801 10 possible different sequences27 16Ç

5’- -3’

Combinatorial diversity of heteropolymers illustrated by means of an RNA aptamer that binds to the antibiotic tobramycin

G

G

G

G

C

C

C G

C

C

G

C

C

G

C

C

G

C

C

G

C

C

C

C

G

G

G

G

G

C

G

C

Plus Strand

Plus Strand

Minus Strand

Plus Strand

Plus Strand

Minus Strand

3'

3'

3'

3'

3'

5'

5'

5'

3'

3'

5'

5'

5'+

Complex Dissociation

Synthesis

Synthesis

Complementary replication asthe simplest copying mechanism of RNA

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

Mutations represent the mechanism of variation in nucleic acids

Ij

In

I2

I1 Ij

Ij

Ij

Ij

Ij +

+

+

+

(A) +

fj Q1j

fj Q2j

fj Qjj

fj Qnj

Q (1-p) pijn-d(i,j) d(i,j) =

p .......... Error rate per digitd(i,j) .... Hamming distance between I and Ii j

dx / dt = x - x

x

j i i j

i i

Σ

; Σ = 1 ;

f

f x

i

i i i

Φ

Φ = Σ

Qji

QijΣi = 1

[A] = a = constant

Chemical kinetics of replication and mutation

spaceSequence

Con

cent

ratio

n

Master sequence

Mutant cloud

The molecular quasispecies in sequence space

spaceSequence

Con

cent

ratio

n

Master sequence

Mutant cloud

“Off-the-cloud” mutations

The molecular quasispecies and mutations producing new variants

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.

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 neutrality in 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

Three-dimensional structure ofphenylalanyl-transfer-RNA

5'-End

5'-End

5'-End

3'-End

3'-End

3'-End

70

60

50

4030

20

10

GCGGAU AUUCGCUUA AGDDGGGA M CUGAAYA AGMUC TPCGAUC A ACCAGCUC GAGC CCAGA UCUGG CUGUG CACAGSequence

Secondary Structure

Symbolic Notation

Definition and formation of the secondary structure of phenylalanyl-tRNA

S{ = y( )I{

f S{ {ƒ= ( )

S{

f{

I{M

utat

ion

Genotype-Phenotype Mapping

Evaluation of the

Phenotype

Q{ jI1

I2

I3

I4 I5

In

Q

f1

f2

f3

f4 f5

fn

I1

I2

I3

I4

I5

I{

In+1

f1

f2

f3

f4

f5

f{

fn+1

Q

Evolutionary dynamics including molecular phenotypes

UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC

GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG

UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG

CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG

GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG

Criterion ofMinimum Free Energy

Sequence Space Shape Space

Stock Solution Reaction Mixture

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

In silico optimization in the flow reactor: Trajectory

Time (arbitrary units)

Aver

age

stru

ctur

e di

stan

ce to

targ

et

d

DS

500 750 1000 12502500

50

40

30

20

10

0

Evolutionary trajectory

44Av

erag

e st

ruct

ure

dist

ance

to ta

rget

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

Endconformation of optimization

4443Av

erag

e st

ruct

ure

dist

ance

to ta

rget

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

Reconstruction of the last step 43 Á 44

444342Av

erag

e st

ruct

ure

dist

ance

to ta

rget

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

Reconstruction of last-but-one step 42 Á 43 (Á 44)

44434241Av

erag

e st

ruct

ure

dist

ance

to ta

rget

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

Reconstruction of step 41 Á 42 (Á 43 Á 44)

4443424140Av

erag

e st

ruct

ure

dist

ance

to ta

rget

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

Reconstruction of step 40 Á 41 (Á 42 Á 43 Á 44)

444342414039

Evolutionary process

Reconstruction

Aver

age

stru

ctur

e di

stan

ce to

targ

et

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

Reconstruction of the relay series

In silico optimization in the flow reactor: Trajectory and relay steps


Aver

age

stru

ctur

e di

stan

ce to

targ

et

d

DS

500 750 1000 12502500

50

40

30

20

10

0


Relay steps

In silico optimization in the flow reactor: Uninterrupted presence


Aver

age

stru

ctur

e di

stan

ce to

targ

et

d

DS

500 750 1000 12502500

50

40

30

20

10

0


Uninterrupted presence

Relay steps

In silico optimization in the flow reactor: Main transitions

Main transitionsRelay steps


Aver

age

stru

ctur

e di

stan

ce to

targ

et

d

DS

500 750 1000 12502500

50

40

30

20

10

0


Aver

age

stru

ctur

e di

stan

ce to

targ

et

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

383736

Main transition leading to clover leaf

Reconstruction of a main transitions 36 Á 37 (Á 38)

444342414039

Evolutionary process

Reconstruction

Aver

age

stru

ctur

e di

stan

ce to

targ

et

d S

D


1250

10

0

44

42

40

38

36Relay steps N

umber of relay step

Time

383736

Main transition leading to clover leaf

Final reconstruction 36 Á 44

In silico optimization in the flow reactor


Aver

age

stru

ctur

e di

stan

ce to

targ

et

d

DS

500 750 1000 12502500

50

40

30

20

10

0

Relay steps Main transitions

Uninterrupted presence


Variation in genotype space during optimization of phenotypes

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.

00 09 31 44

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

„...Variations neither useful not injurious wouldnot 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)

Genotype Space

Fitn

ess

Start of Walk

End of Walk

Random Drift Periods

Adaptive Periods

Evolution in genotype space sketched as a non-descending walk in a fitness landscape

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

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

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 20004000 40006000 60008000 800010000 10000

Time (Generations) Time (Generations)

5

10

15

20

25

Dist

anc

e to

anc

est

or

Dist

anc

e w

ithin

sa

mp

le

2

4

6

8

10

12

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

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

yes

Selection Cycle

no

GeneticDiversity

Desired Properties? ? ?

Selection

Amplification

Diversification

Selection cycle used inapplied molecular evolutionto design molecules withpredefined properties

Retention of binders Elution of binders

Chr

omat

ogra

phic

col

umn

The SELEX technique for the evolutionary design of aptamers

A

AA

AA C

C C CC

C

CC

G G G

G

G

G

G

G U U

U

U

U U5’-

3’-

AAAAA UUUUUU CCCCCCCCG GGGGGGG5’- -3’

Formation of secondary structure of the tobramycin binding RNA aptamer

L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Chemistry & Biology 4:35-50 (1997)

The three-dimensional structure of the tobramycin aptamer complex

L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Chemistry & Biology 4:35-50 (1997)

A ribozyme switch

E.A.Schultes, D.B.Bartel, One sequence, two ribozymes: Implication for the emergence of new ribozyme folds. 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

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

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

Sequence of mutants from the intersection to both reference ribozymes

Reference for postulation and in silico verification of neutral networks

Coworkers

Walter Fontana, Santa Fe Institute, NM

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

Peter Stadler, Universität Wien, ATIvo L.Hofacker

Christoph Flamm

Bärbel Stadler, Andreas Wernitznig, Universität Wien, ATMichael Kospach, Ulrike Mückstein, Stefanie Widder, Stefan Wuchty

Jan Cupal, Kurt Grünberger, Andreas Svrček-Seiler

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