What we can Learn in Evolution from RNA Molecules Peter Schuster - - PowerPoint PPT Presentation

What we can Learn in Evolution from RNA Molecules

Peter Schuster

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

Lab Inauguration Meeting Köln, 03.12.2004

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

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

RNA

RNA as scaffold for supramolecular complexes

ribosome ? ? ? ? ? RNA as transmitter of genetic information

DNA

...AGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUC...

messenger-RNA protein transcription translation RNA as

• f genetic information

working copy

RNA is modified by epigenetic control RNA RNA editing Alternative splicing of messenger

Functions of RNA molecules

RNA is the catalytic subunit in supramolecular complexes

RNA as regulator of gene expression Gene silencing by small interfering RNAs Allosteric control of transcribed RNA

Riboswitches metabolites controlling transcription and translation through

The world as a precursor of the current + biology RNA DNA protein

RNA as catalyst Ribozyme RNA as adapter molecule

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

leu genetic code

RNA as carrier of genetic information

RNA viruses and retroviruses RNA evolution in vitro Evolutionary biotechnology RNA aptamers, artificial ribozymes, allosteric ribozymes

Examples of ‘natural selection’ with RNA molecules

An example of ‘artificial selection’ with RNA molecules or ‘breeding’ of biomolecules

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

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 3'-end 5’-end

70 60 50 40 30 20 10

Definition of RNA structure

Definition and physical relevance of RNA secondary structures

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

The Vienna RNA-Package: A library of routines for folding, inverse folding, sequence and structure alignment, cofolding, kinetic folding, …

RNA sequence RNA structure

• f minimal free

energy

RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Empirical parameters Biophysical chemistry: thermodynamics and kinetics

Sequence, structure, and design

Inverse folding of RNA: Biotechnology, design of biomolecules with predefined structures and functions

G G G G G G G G G G G G G G G G U U U U U U U U U U U A A A A A A A A A A A A U C C C C C C C C C C C C 5’-end 3’-end

S1

(h)

S9

(h)

F r e e e n e r g y G

• Minimum of free energy

Suboptimal conformations

S0

(h) S2

(h)

S3

(h)

S4

(h)

S7

(h)

S6

(h)

S5

(h)

S8

(h)

The minimum free energy structures on a discrete space of conformations

UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG

Criterion of Minimum Free Energy

Sequence Space Shape Space

Reference for postulation and in silico verification of neutral networks

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Structure space Real numbers Mapping from sequence space into structure space and into function

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Structure space Real numbers

Sk I. = ( ) ψ

Sequence space Structure space

Sk I. = ( ) ψ

Sequence space Structure space

The pre-image of the structure Sk in sequence space is the neutral network Gk

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

Hamming distance d (I ,I ) =

H 1 2

4 d (I ,I ) = 0

H 1 1

d (I ,I ) = d (I ,I )

H H 1 2 2 1

d (I ,I ) d (I ,I ) + d (I ,I )

H H H 1 3 1 2 2 3

• (i)

(ii) (iii)

The Hamming distance between genotypes induces a metric in sequence space

Neutral networks are sets of sequences forming the same object in a phenotype space. The neutral network Gk is, for example, the pre- image of the structure Sk in sequence space: Gk = -1(Sk) π{j | (Ij) = Sk} The set is converted into a graph by connecting all sequences of Hamming distance one. Neutral networks of small biomolecules can be computed by exhaustive folding of complete sequence spaces, i.e. all RNA sequences of a given chain length. This number, N=4n , 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.

AUCAAUCAG GUCAAUCAC GUCAAUCAU GUCAAUCAA G U C A A U C C G G U C A A U C G G GUCAAUCUG G U C A A U G A G G U C A A U U A G GUCAAUAAG GUCAACCAG G U C A A G C A G GUCAAACAG GUCACUCAG G U C A G U C A G GUCAUUCAG GUCCAUCAG GUCGAUCAG GUCUAUCAG GUGAAUCAG GUUAAUCAG GUAAAUCAG GCCAAUCAG GGCAAUCAG GACAAUCAG UUCAAUCAG CUCAAUCAG

GUCAAUCAG

One-error neighborhood

The surrounding of GUCAAUCAG in sequence space

Degree of neutrality of neutral networks and the connectivity threshold

n = 9 ; 3n = 27

Degree of neutrality of neutral networks and the connectivity threshold

λj = 27 = 0.444

/

12

“j”

Degree of neutrality of neutral networks and the connectivity threshold

λj = 27 = 0.444

/

12

λk =

(k)

j

| | Gk G S S

k k k

= ( ) | ( ) =

• 1

U

• I

I

j j

Degree of neutrality of neutral networks and the connectivity threshold

λj = 27 = 0.444

/

12

λk =

(k)

j

| | Gk λ λ

k cr . . . .

> λ λ

k cr . . . .

< network is connected Gk network is connected Gk not

λ κ

cr = 1 -

• 1 (

1)

/ κ- Connectivity threshold: G S S

k k k

= ( ) | ( ) =

• 1

U

• I

I

j j

Degree of neutrality of neutral networks and the connectivity threshold

λj = 27 = 0.444

/

12

λk =

(k)

j

| | Gk λ λ

k cr . . . .

> λ λ

k cr . . . .

< network is connected Gk network is connected Gk not

λ κ

cr = 1 -

• 1 (

1)

/ κ- Connectivity threshold: G S S

k k k

= ( ) | ( ) =

• 1

U

• I

I

j j

Alphabet size :

• cr

2 0.5 3 0.423 4 0.370 AUGC AUG , UGC AU,GC,DU

Degree of neutrality of neutral networks and the connectivity threshold

Giant Component

A multi-component neutral network formed by a rare structure

A connected neutral network formed by a common structure

Gk Neutral Network

Structure S

k

Gk C

• 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 its suboptimal structures.

Sh S1

(h)

S6

(h)

S7

(h)

S5

(h)

S2

(h)

S9

(h)

Free energy G

• Local minimum

Suboptimal conformations

Search for local minima in conformation space

5.10 5.90

2 8

3.30 7.40

5 3 7 4 10 9 6

S0 S1

Kinetic folding

S0 S1 S2 S3 S4 S5 S6 S7 S8 S10 S9

Suboptimal structures

g

Suboptimal structures

Suboptimal secondary structures of an RNA sequence

5.10 5.90

2 8

3.30 7.40

5 3 7 4 10 9 6

S0 S1

Kinetic folding

S0 S1 S2 S3 S4 S5 S6 S7 S8 S10 S9

Suboptimal structures

g

Metastable Stable Suboptimal structures structure

An RNA molecule with two (meta)stable conformations

Structure

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

Compatible sequence Structure

5’-end 3’-end

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

Compatible sequence Structure

5’-end 3’-end

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

Compatible sequence Structure

5’-end 3’-end

Single nucleotides: A U G C , , ,

Single bases pairs are varied independently

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

Compatible sequence Structure

5’-end 3’-end

Base pairs: AU , UA GC , CG GU , UG

Base pairs are varied in strict correlation

Structure S Structure S

1

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

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

5.10 5.90

2 8

3.30 7.40

5 3 7 4 10 9 6

S0 S1

Kinetic folding

S0 S1 S2 S3 S4 S5 S6 S7 S8 S10 S9

Suboptimal structures

lim t finite folding time

A typical energy landscape of a sequence with two (meta)stable comformations

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

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

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

Evolution in silico

• W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

Stock Solution Reaction Mixture

Replication rate constant: fk = / [ + dS

(k)]

dS

(k) = dH(Sk,S)

Selection constraint: Population size, N = # RNA molecules, is controlled by the flow Mutation rate: p = 0.001 / site replication N N t N ± ≈ ) ( The flowreactor as a device for studies of evolution in vitro and in silico

f0 f f1 f2 f3 f4 f6 f5 f7

Replication rate constant: fk = / [ + dS

(k)]

dS

(k) = dH(Sk,S)

Evaluation of RNA secondary structures yields replication rate constants

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 between structures in parentheses notation forms a metric in structure space

5'-End 3'-End

70 60 50 40 30 20 10

Randomly chosen initial structure Phenylalanyl-tRNA as target structure

space 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

In silico optimization in the flow reactor: Evolutionary 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

44

Average structure distance to target dS

• Evolutionary trajectory

1250 10

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

Final conformation of optimization

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 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

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

28 neutral point mutations during a long quasi-stationary epoch Transition inducing point mutations Neutral point mutations

Neutral genotype evolution during phenotypic stasis

AUGC GC Movies of optimization trajectories over the AUGC and the GC alphabet

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

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--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

Structure S Structure S

1

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

• J. H. A. Nagel, C. Flamm, I. L. Hofacker, K. Franke, M. H. de Smit, P. Schuster, and
• C. W. A. Pleij. Structural parameters affecting the kinetic competition of RNA hairpin

formation, in press 2004.

• J. H. A. Nagel, J. Møller-Jensen, C. Flamm, K. J. Öistämö, J. Besnard, I. L. Hofacker,
• A. P. Gultyaev, M. H. de Smit, P. Schuster, K. Gerdes and C. W. A. Pleij. The refolding

mechanism of the metastable structure in the 5’-end of the hok mRNA of plasmid R1, submitted 2004.

J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and C.W.A. Pleij. Structural parameters affecting the kinetic competition of RNA hairpin formation, in press 2004.

JN2C

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

5' 5' 3' 3'

CUGUUUUUGCA U AGCUUCUGUUG GCAGAAGC GCAGAAGC

• 19.5 kcal·mol
• 1
• 21.9 kcal·mol
• 1

A A A B B B C C C

3 3 3 15 15 15 36 36 36 24 24 24

JN1LH

1D 1D 1D 2D 2D 2D R R R

G GGGUGGAAC GUUC GAAC GUUCCUCCC CACGAG CACGAG CACGAG

• 28.6 kcal·mol
• 1

G/

• 31.8 kcal·mol
• 1

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

• 28.2 kcal·mol
• 1

G G G G G G GG CCC C C C C C U G G G G C C C C A A A A A A A A U U U U U G G C C A A

• 28.6 kcal·mol
• 1

3 3 3 13 13 13 23 23 23 33 33 33 44 44 44

5' 5' 3’ 3’

J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and C.W.A. Pleij. Structural parameters affecting the kinetic competition of RNA hairpin formation, in press 2004.

4 5 8 9 11

1 9 2 2 4 2 5 2 7 3 3 3 4

36

38 39 41 46 47

3

49

1

2 6 7 10

1 2 1 3 1 4 1 5 1 6 1 7 1 8 2 1 22 2 3 2 6 2 8 2 9 3 3 1 32 3 5 3 7

40

4 2 4 3 44 45 48 50

• 26.0
• 28.0
• 30.0
• 32.0
• 34.0
• 36.0
• 38.0
• 40.0
• 42.0
• 44.0
• 46.0
• 48.0
• 50.0

2.77 5.32 2 . 9 3.4 2.36 2 . 4 4 2.44 2.44 1.46 1.44 1.66

1.9

2.14

2.51 2.14 2.51

2 . 1 4 1 . 4 7

1.49

3.04 2.97 3.04 4.88 6.13 6 . 8 2.89

Free energy [kcal / mole]

J1LH barrier tree

1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design

„...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

• rganism and the nature of the conditions.

...“

Charles Darwin, Origin of species (1859)

Motoo Kimura’s Populationsgenetik der 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.

Mount Fuji

Example of a smooth landscape on Earth

Dolomites Bryce Canyon

Examples of rugged landscapes on Earth

Genotype Space Fitness

Start of Walk End of Walk

Evolutionary optimization in absence of neutral paths in sequence space

Genotype Space F i t n e s s

Start of Walk End of Walk Random Drift Periods Adaptive Periods

Evolutionary optimization including neutral paths in sequence space

Grand Canyon

Example of a landscape on Earth with ‘neutral’ ridges and plateaus

Conformational and mutational landscapes of biomolecules as well as fitness landscapes of evolutionary biology are rugged.

Genotype Space Fitness Start of Walk End of Walk

Adaptive or non-descending walks on rugged landscapes end commonly at one of the low lying local maxima.

Genotype Space Fitness Start of Walk End of Walk

Selective neutrality in the form of neutral networks plays an active role in evolutionary optimization and enables populations to reach high local maxima or even the global optimum.

Evolutionary design

• f aptamers

Evolutionary design

• f allosteric RNA

molecules Evolutionary design

• f ribozymes

Evolutionary design

• f deoxyribozymes

Evolutionary design

• f RNA and DNA

Examples of evolutionary design of RNA or DNA molecules

Evolutionary design

• f aptamers

Evolutionary design

• f allosteric RNA

molecules Evolutionary design

• f ribozymes

Evolutionary design

• f deoxyribozymes

Design of small interfering RNA molecules Design of riboswitches Primer design for PCR

in situ

Engineering of ribosomal protein synthesis

Design of RNA and DNA molecules

Examples of evolutionary and rational design of RNA and DNA molecules

Acknowledgement of support

Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Project No. EU-980189 Austrian Genome Research Program – GEN-AU Siemens AG, Austria Universität Wien and the Santa Fe Institute

Universität Wien

Coworkers

Walter Fontana, Harvard Medical School, MA Christian Reidys, Christian Forst, Los Alamos National Laboratory, NM Peter Stadler, Bärbel Stadler, Universität Leipzig, GE Jord Nagel, Kees Pleij, Universiteit Leiden, NL Ivo L.Hofacker, Christoph Flamm, Universität Wien, AT Andreas Wernitznig, Michael Kospach, Universität Wien, AT Ulrike Langhammer, Ulrike Mückstein, Stefanie Widder Jan Cupal, Kurt Grünberger, Andreas Svrček-Seiler, Stefan Wuchty Stefan Bernhart, Lukas Endler Ulrike Göbel, Institut für Molekulare Biotechnologie, Jena, GE Walter Grüner, Stefan Kopp, Jaqueline Weber, Thomas Wiehe

Universität Wien

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