How innovation occurs in evolution of molecules Peter Schuster - - PowerPoint PPT Presentation

How innovation occurs in evolution of molecules

Peter Schuster Institut für Theoretische Chemie und Molekulare Strukturbiologie der Universität Wien Evolutionary innovation Praha, 30.05.2002

Darwinian principle is based on three functions:

• Reproduction efficiency expressed by fitness of phenotypes.
• Variation of genotypes through imperfect copying and recombination.
• Selection of phenotypes based on differences in fitness.

Two additional features are required:

• Large reservoirs of genotypes and sufficiently rich repertoires of phenotypes.
• Mapping of genotypes into phenotypes with suitable properties.

The genotypes or genomes of individuals are DNA or RNA sequences. They are changing from generation to generation through mutation and

• recombination. Species are reproductively related ensembles of

individuals. Genotypes unfold into phenotypes, being molecular structures, viruses or

• rganisms, which are the targets of the evolutionary selection process.

The most common mutations are point mutations, which consist of single nucleotide exchanges. The Hamming distance of two sequences is the minimal number of single nucleotide exchanges that mutually converts the two sequence into each other.

A A A A A U U U U U U C C C C C C C C G G G G G G G G A U C G

= adenylate = uridylate = cytidylate = guanylate

5’-

• 3’

Genotype: The sequence of an RNA molecule consisting of monomers chosen from four classes, A, U, G, and C.

Phenotype: Three-dimensional structure of phenylalanyl transfer-RNA

Hydrogen bonds

Hydrogen bonding between nucleotide bases is the principle of template action of RNA and DNA.

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 as the 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 AA UCCCGUCCCG GAAUCCA

Mutations represent the mechanism of variation in nucleic acids.

A A A A A U U U U U U C C C C C C C C G G G G G G G G A U C G

= adenylate = uridylate = cytidylate = guanylate

Combinatorial diversity of sequences: N = 4{ 4 = 1.801 10 possible different sequences

27 16

• 5’-
• 3’

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

Sk I. = ( ) ψ fk f Sk = ( )

Sequence space Phenotype space Non-negative numbers

Mapping from sequence space into phenotype space and into fitness values

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

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

• Time

1 2 3 4 5 6 69 70 The serial transfer technique applied to RNA evolution in vitro

The increase in RNA production rate during a serial transfer experiment

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-

• 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

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

Sir Peter Medawar, 1985

dx / dt = x - x x

j i i j i i

Σ

; Σ = 1 k k x

i i i i

Φ Φ = Σ

[A] = a = constant

Ij Ij I1 I2 I1 I2 I1 I2 Ij In Ij In In

+ + + + + +

(A) + (A) + (A) + (A) + (A) + (A) + kj kn kj k1 k2 Im Im Im

+

(A) + (A) + km

k = max {k ; j=1,2,...,n} x (t) 1 for t

m j m

• s = (km+1-km)/km

Selection of the „fittest“ or fastest replicating species

200 400 600 800 1000 0.2 0.4 0.6 0.8 1 Time [Generations] Fraction of advantageous variant s = 0.1 s = 0.01 s = 0.02

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

Theory of molecular evolution

M.Eigen, Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58 (1971), 465-526 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.S.McCaskill, A localization threshold for macromolecular quasi-species from continuously distributed replication rates. J.Chem.Phys. 80 (1984), 5194-5205 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

Ij Ij In I2 I1 Ij Ij Ij Ij

+ + + +

M + k Q

j 2j

k Q

j 1j

k Q

j nj

Σi

ij

Q = 1 Q = (1-p) p ; p ...... error rate per digit d(i,j) ...... Hamming distance between I and I

ij i j j i i ji i j i i i i i

n-d(i,j) d(i,j)

dx / dt = k Q x - x k x x Σ Φ Φ = Σ ; Σ = 1

Chemical kinetics of replication and mutation as parallel reactions

space Sequence C

• n

c e n t r a t i

• n

Master sequence Mutant cloud

The molecular quasispecies in sequence space

The RNA model considers RNA sequences as genotypes and simplified RNA structures, called secondary structures, as phenotypes. Variation is restricted to point mutations. The mapping from genotypes into phenotypes is many-to-one. Hence, it is redundant and not invertible. Genotypes, i.e. RNA sequences, which are mapped onto the same phenotype, i.e. the same RNA secondary structure, form neutral networks. Neutral networks are represented by graphs in sequence space.

RNA secondary structures and their properties

RNA secondary structures are listings of Watson-Crick and GU wobble base pairs, which are free of knots and pseudokots. Secondary structures are folding intermediates in the formation

• f full three-dimensional structures.

D.Thirumalai, N.Lee, S.A.Woodson, and D.K.Klimov. Annu.Rev.Phys.Chem. 52:751-762 (2001)

5'-End 5'-End 5'-End 3'-End 3'-End 3'-End

70 60 50 40 30 20 10 GCGGAU AUUCGC UUA AGDDGGGA M CUGAAYA AGMUC TPCGAUC A ACCA GCUC GAGC CCAGA UCUGG CUGUG CACAG

Sequence Secondary Structure Symbolic Notation

Definition and formation of the secondary structure of phenylalanyl-tRNA

RNA minimum free energy structures

Efficient algorithms based on dynamical programming are available for computation of secondary structures for given

• sequences. Inverse folding algorithms compute sequences

for given secondary structures.

M.Zuker and P.Stiegler. Nucleic Acids Res. 9:133-148 (1981) Vienna RNA Package: http:www.tbi.univie.ac.at (includes inverse folding, suboptimal structures, kinetic folding, etc.) I.L.Hofacker, W. Fontana, P.F.Stadler, L.S.Bonhoeffer, M.Tacker, and P. Schuster. Mh.Chem. 125:167-188 (1994)

UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG

Criterion of Minimum Free Energy

Sequence Space Shape Space

.... GC UC .... CA .... GC UC .... GU .... GC UC .... GA .... GC UC .... CU

d =1

H

d =1

H

d =2

H

Point mutations as moves in sequence space

CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... G A G T A C A C

Hamming distance d (S ,S ) =

H 1 2

4 d (S ,S ) = 0

H 1 1

d (S ,S ) = d (S ,S )

H H 1 2 2 1

d (S ,S ) d (S ,S ) + d (S ,S )

H H H 1 3 1 2 2 3

• (i)

(ii) (iii)

The Hamming distance induces a metric in sequence space

4 2 1 8 16 10 19 9 14 6 13 5 11 3 7 12 21 17 22 18 25 20 26 24 28 27 23 15 29 30 31

Binary sequences are encoded by their decimal equivalents: = 0 and = 1, for example, "0" 00000 = "14" 01110 = , "29" 11101 = , etc. ≡ ≡ ≡ , C CCCCC C C C G GGG GGG G

Mutant class

1 2

3 4

5

Sequence space of binary sequences of chain lenght n=5

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Phenotype space Non-negative numbers Mapping from sequence space into phenotype space and into fitness values

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Phenotype space Non-negative numbers

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Phenotype space Non-negative numbers

Neutral networks of small RNA molecules can be computed by exhaustive folding of complete sequence spaces, i.e. all RNA sequences of a given chain length. This number, N=4l , becomes very large with increasing length, and is prohibitive for numerical computations. Neutral networks can be modelled by random graphs in sequence

• space. In this approach, nodes are inserted randomly into sequence

space until the size of the pre-image, i.e. the number of neutral sequences, matches the neutral network to be studied.

Random graph approach to neutral networks Sketch of sequence space Step 00

Random graph approach to neutral networks Sketch of sequence space Step 01

Random graph approach to neutral networks Sketch of sequence space Step 02

Random graph approach to neutral networks Sketch of sequence space Step 03

Random graph approach to neutral networks Sketch of sequence space Step 04

Random graph approach to neutral networks Sketch of sequence space Step 05

Random graph approach to neutral networks Sketch of sequence space Step 10

Random graph approach to neutral networks Sketch of sequence space Step 15

Random graph approach to neutral networks Sketch of sequence space Step 25

Random graph approach to neutral networks Sketch of sequence space Step 50

Random graph approach to neutral networks Sketch of sequence space Step 75

Random graph approach to neutral networks Sketch of sequence space Step 100

λj = 27 ,

/

12 λk = (k)

j

| | Gk

λ κ

cr = 1 - -1 (

1)

/ κ- λ λ

k cr . . . .

> λ λ

k cr . . . .

< network is connected Gk network is connected not Gk Connectivity threshold: Alphabet size : = 4

• AUGC

G S S

k k k

= ( ) | ( ) =

• 1

Υ

• I

I

j j

• cr

2 0.5 3 0.4226 4 0.3700 Mean degree of neutrality and connectivity of neutral networks

Giant Component

A multi-component neutral network

A connected neutral network

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

s p a c e Sequence Concentration

Master sequence Mutant cloud “Off-the-cloud” mutations

The molecular quasispecies in sequence space

S{ = ( ) I{ f S

{ {

ƒ = ( )

S{ f{ I{

Mutation Genotype-Phenotype Mapping Evaluation of the Phenotype

Q{j

I1 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

Stock Solution Reaction Mixture

Fitness function for

• ptimization in the

flow reactor: fk = / [+ dS

(k)]

• dS

(k) = ds(Ik,I

) 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) A v e r a g e s t r u c t u r e d i s t a n c e t

• t

a r g e t d

• S

500 750 1000 1250 250 50 40 30 20 10

Evolutionary trajectory

Mean Hamming distance Position in sequence space Mean distance to target

Variation of the population in genotype space during optimization of phenotypes

t = 1.200 t = 1.360 t = 1.600 t = 4.000 t = 6.400 t = 6.640 t = 6.696 t = 6.840 time t in 106 replications

Spreading of a population during neutral evolution on a fitness plateau

44

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

00

Initial structure and final conformation of the optimization process

44 43

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

Reconstruction of the last step 43 44

44 43 42

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

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

44 43 42 41

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

Reconstruction of step 41 42 ( 43 44)

44 43 42 41 40

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

Reconstruction of step 40 41 ( 42 43 44)

44 43 42 41 40 39 Evolutionary process Reconstruction

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

Reconstruction of the relay series

Transition inducing point mutations Neutral point mutations

Change in RNA sequences during the final five relay steps 39 44

In silico optimization in the flow reactor: Trajectory and relay steps Time (arbitrary units) A v e r a g e s t r u c t u r e d i s t a n c e t

• t

a r g e t d

• S

500 750 1000 1250 250 50 40 30 20 10

Evolutionary trajectory

Relay steps

In silico optimization in the flow reactor: Uninterrupted presence Time (arbitrary units) A v e r a g e s t r u c t u r e d i s t a n c e t

• t

a r g e t d

• S

500 750 1000 1250 250 50 40 30 20 10

Evolutionary trajectory Uninterrupted presence

Relay steps

10 08 12 14 Time (arbitrary units) Average structure distance to target dS

• 500

250 20 10

Uninterrupted presence Evolutionary trajectory Number of relay step

09

Transition inducing point mutations Neutral point mutations

Neutral genotype evolution during phenotypic stasis

„...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)

Genotype Space F i t n e s s

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

18 19 20 21 26 28 29 31

Time (arbitrary units)

750 1000 1250

Average structure distance to target dS

• 30

20 10

Uninterrupted presence Evolutionary trajectory 35 30 25 20 Number of relay step

A random sequence of minor or continuous transitions in the relay series

18 19 20 21 26 28 29 31

A random sequence of minor or continuous transitions in the relay series

Elongation of Stacks Shortening of Stacks Opening of Constrained Stacks

Multi- loop

Minor or continuous transitions: Occur frequently on single point mutations

10 10

1

10

2

10

3

10

4

10

5

Rank

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

Frequency of occurrence

5'-End 3'-End

70 60 50 40 30 20 10

10 2 5

Common neighbors Minor transitions

Probability of occurrence of different structures in the mutational neighborhood of tRNAphe

In silico optimization in the flow reactor: Uninterrupted presence Time (arbitrary units) A v e r a g e s t r u c t u r e d i s t a n c e t

• t

a r g e t d

• S

500 750 1000 1250 250 50 40 30 20 10

Evolutionary trajectory Uninterrupted presence

Relay steps

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

38 37 36 Major transition leading to clover leaf

Reconstruction of a major transitions 36 37 ( 38)

44 43 42 41 40 39 Evolutionary process Reconstruction

Average structure distance to target dS

• Evolutionary trajectory

1250 10

44 42 40 38 36 Relay steps Number of relay step Time

38 37 36 Major transition leading to clover leaf

Final reconstruction 36 44

Shift Roll-Over Flip Double Flip

a a b a a b α α α α β β

Closing of Constrained Stacks

Multi- loop

Major or discontinuous transitions: Structural innovations, occur rarely on single point mutations

10 10

1

10

2

10

3

10

4

10

5

Rank

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

Frequency of occurrence

5'-End 3'-End

70 60 50 40 30 20 10

10 2 5

Rare neighbors Major transitions

Probability of occurrence of different structures in the mutational neighborhood of tRNAphe

In silico optimization in the flow reactor: Major transitions Relay steps Major transitions Time (arbitrary units) A v e r a g e s t r u c t u r e d i s t a n c e t

• t

a r g e t d

• S

500 750 1000 1250 250 50 40 30 20 10

Evolutionary trajectory

In silico optimization in the flow reactor Time (arbitrary units) A v e r a g e s t r u c t u r e d i s t a n c e t

• t

a r g e t d

• S

500 750 1000 1250 250 50 40 30 20 10

Relay steps Major transitions

Uninterrupted presence Evolutionary trajectory

S1

(j)

Sk

(j)

S2

(j)

S3

(j)

Sm

(j)

k k k k k

P P P P P

• P
• Transition probabilities determining the presence of phenotype Sk

(j) in the population

N N-1 1 2 3 4 5 6 7 8 9 10

x

µ ν µ ν λ µ ν λ µ ν λ µ ν λ µ ν λ µ ν λ µ ν λ µ ν λ µ ν ν ν λ µ λ

λ λ ν (x) = x + ( -x)

N

(x) = x µ µ

T1,0 T0,1

Time t P a r t i c l e n u m b e r ( t )

X

2 4 6 8 10 12

Calculation of transition probabilities by means of a birth-and-death process with immigration

S1

(j)

Sk

(j)

S2

(j)

S3

(j)

Sm

(j)

k k k k k

P P P P P

• P
• N

=

sat (j)

p . . < > l

• (j)

1

00 09 31 44

Three important steps in the formation of the tRNA clover leaf from a randomly chosen initial structure

Stable tRNA clover leaf structures built from binary, GC-only, sequences exist. The corresponding sequences are readily found through inverse folding. Optimization by mutation and selection in the flow reactor has so far always been unsuccessful.

5'-End 3'-End

70 60 50 40 30 20 10

The neutral network of the tRNA clover leaf in GC sequence space is not connected, whereas to the corresponding neutral network in AUGC sequence space is very close to the critical connectivity threshold,

cr . Here, both inverse folding

and optimization in the flow reactor are successful.

The success of optimization depends on the connectivity of neutral networks.

Main results of computer simulations of molecular evolution

• Individual trajectories are not reproducible. The sequences of the target structures
• btained and the relay series were different. Nevertheless, solutions of comparable or

the same quality are almost always achieved.

• Transitions between molecular phenotypes represented by RNA structures can be

classified with respect to the induced structural changes. Minor transitions of high probability of occurrence are opposed by major transitions of low probability.

• Major transitions represent the relevant structural innovations in the course of

molecular evolution.

• The number of minor transitions decreases with increasing population size.
• The number of major transitions or structural innovations is approximately

constant for given start and stop structures.

• Not all structures are accessible through evolution in the flow reactor.

Coworkers

Walter Fontana, Santa Fe Institute, NM Christian Reidys, Christian Forst, Los Alamos National Laboratory, NM Peter F. Stadler, Universität Wien, AT Ivo L. Hofacker Christoph Flamm Bärbel Stadler, Andreas Wernitznig, Universität Wien, AT Michael Kospach, Ulrike Langhammer, Ulrike Mückstein, Stefanie Widder, Jan Cupal, Kurt Grünberger, Andreas Svrček-Seiler, Stefan Wuchty Ulrike Göbel, Institut für Molekulare Biotechnologie, Jena, GE Walter Grüner, Stefan Kopp, Jaqueline Weber

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

Genetic Diversity

Desired Properties ? ? ? Selection Amplification Diversification

Selection cycle used in applied molecular evolution to design molecules with predefined properties

Retention of binders Elution of binders C h r

• m

a t

• g

r a p h i c c

• l

u m n

The SELEX technique for the evolutionary design of aptamers

A A A A A C C C C C C C C G G G G G G G G U U U U U U

5’- 3’-

A A A A A U U U U U U C C C C C C C C G G G G G G G G

5’-

• 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)

U U U U U G G G G G G G G G G G G G G G G G A A A A A A A A A A C C C C C C C C C C C C C C C

Cleavage site

The "hammerhead" ribozyme

OH OH OH ppp 5' 5' 3' 3'

The smallest known catalytically active RNA molecule