Designing RNA Structures From Theoretical Models to Real Molecules - - PowerPoint PPT Presentation

Designing RNA Structures

From Theoretical Models to Real Molecules Peter Schuster Institut für Theoretische Chemie und Molekulare Strukturbiologie der Universität Wien Microbiology Seminar Mount Sinai School of Medicine, 25.05.2004

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

1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules

1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules

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

nd 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

5'-e

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

70 60 50 40 30 20 10 GCGGAUUUAGCUCAGDDGGGAGAGCMCCAGACUGAAYAUCUGGAGMUCCUGUGTPCGAUCCACAGAAUUCGCACCA

Sequence Secondary structure Symbolic notation

• A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

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):

2 2 6 5 6 8 C ’

1

C ’

1

5 4 4 6 2 9 7 4 3 3 2 1 1

54.4 55.7

10.72 Å 2 2 6 5 6 8 C ’

1

C ’

1

5 4 4 4 2 9 7 6 3 3 1 1

56.2 57.4

10.44 Å

U = A C G

• Watson-Crick type base pairs

O O O H H H H H H N N N N O O H N N H O N N N N N N N

G=U U=G

Deviation from Watson-Crick geometry Deviation from Watson-Crick geometry

Wobble base pairs

RNA sequence

Empirical parameters Biophysical chemistry: thermodynamics and kinetics

RNA structure

• f minimal free

energy

Sequence, structure, and design

Inverse folding of RNA: Biotechnology, design of biomolecules with predefined structures and functions RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function

5’-end 3’-end

S1

(h)

S9

(h)

Free energy G0

• Minimum of free energy

Suboptimal states

S0

(h) S2

(h)

S3

(h)

S4

(h)

S7

(h)

S6

(h)

S5

(h)

S8

(h)

The minimum free energy and suboptimal structures on a discrete space of conformations

3'-end

"H-type pseudoknot"

5'-end 3'-end pseudoknot

"Kissing loops"

5'-end

··((((····· [[ ·))))····(((((·]] ·····))))) ··· Two classes of pseudoknots in RNA structures

5'-End 3'-End

70 60 50 40 30 20 10

5'-End 3'-End

70 60 50 40 30 20 10

End-on-end stacking of double helical regions yields the L-shape of tRNAphe

1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules

RNA sequence

Empirical parameters Biophysical chemistry: thermodynamics and kinetics

RNA structure

• f minimal free

energy

Sequence, structure, and design

Inverse folding of RNA: Biotechnology, design of biomolecules with predefined structures and functions RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function

UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG

Criterion of Minimum Free Energy

Sequence Space Shape Space

Computed numbers of minimum free energy structures over different nucleotide alphabets

• P. Schuster, Molecular insights into evolution of phenotypes. In: J. Crutchfield & P.Schuster,

Evolutionary Dynamics. Oxford University Press, New York 2003, pp.163-215.

Reference for postulation and in silico verification of neutral networks

Evolution in silico

• W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG

Criterion of Minimum Free Energy

Sequence Space Shape Space

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

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

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

fk f Sk = ( )

Sequence space Structure space Real numbers

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

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 = 0.444 ,

/

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

U

• I

I

j j

• cr

2 0.5 3 0.423 4 0.370

GC,AU GUC,AUG AUGC

Mean degree of neutrality and connectivity of neutral networks

A connected neutral network formed by a common structure

Giant Component

A multi-component neutral network formed by a rare structure

1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules

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

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

Compatible sequences Structure

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

Structure Incompatible sequence

5’-end 3’-end

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.

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

14 15 18 17 23 19 27 22 38 45 25 36 33 39 40 43 41

3.30 7.40

5 3 7 4 10 9 6

13 12

3.10

11 21 20 16 28 29 26 30 32 42 46 44 24 35 34 37 49 31 47 48

S0 S1

Kinetic folding

S0 S1 S2 S3 S4 S5 S6 S7 S8 S10 S9

Suboptimal structures

g

metastable stable suboptimal structures

An RNA molecule with two (meta)stable conformations

5.10

2 8

14 15 18 17 23 19 27 22 38 45 25 36 33 39 40 43 41

3.30 7.40

5 3 7 4 10 9 6

13 12

3.10

11 21 20 16 28 29 26 30 32 42 46 44 24 35 34 37 49 31 47 48

S0 S1

Kinetic folding

S0 S1 S2 S3 S4 S5 S6 S7 S8 S10 S9

Suboptimal structures

g

metastable stable suboptimal structures

5.90

An RNA molecule with two (meta)stable conformations

Kinetics of RNA refolding between a long living metastable conformation and the minmum free energy structure

1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules

Structure S Structure S

1

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

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

Sequence of mutants from the intersection to both reference ribozymes

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

Loop BC Loop AB SS A

C K C T G15- G24- G30- G36- G39- G9- G3-

5 5 5 5 5 5

Al T1D

SS C

G15- G30- C K

5 5 5

Al T1D C K

5 5 5

Al T1D

T1 V1 T2 K K K T T T

JN2C

T1 V1 T2 T1 V1 T2 5’ hairpin 3’-hairpin

JN2C small fragments

Loop BC Loop AB

• G39
• G24

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.

Loop2D Loop R Loop1D

C K C T G13- G23- G33- C44- G3-

5 5 5 5 5 5

Al T1D

5

T1 V1 T2 K K K T T T T1 3 h

J1LH sequencing gels

4 5 8 9 11

19 20 24 25 27 33 34

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 35 37

40

42 43 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 2.09 3.4 2.36 2.44 2.44 2.44 1.46 1.44 1.66

1.9

2.14

2.51 2.14 2.51

2.14 1.47

1.49

3.04 2.97 3.04 4.88 6.13 6.8 2.89

Free energy [kcal / mole]

J1LH barrier tree

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

hokXL nascent transcript

3' A A A A A A A A A A A A A A A A A A G G G G G G G G G G G G G G G C C CC C C C C C C C C C C C A A A A A G G G G G G C C C C C C C C C C U U U U U U U U UU U U U U U U U A A A A A G C C U U U U U U U U

• A A

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

SD SD I II

5' 5'

• A

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

ucb tac sokT

mok hok

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.

• G

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

• AGG

GG U U A AG G C C CC U U U 3'

ucb II

• A

A A G G G G G G G G G C C C C C C C U U U U U U 5'

I tac

U A A A G C U U U

metastable

C G G U A

pseudoknot

• A

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

• C

G

• G

G G G G C U U U UU U U 3' 5'

ucb I II tac

stable

Refolding of the 5‘-end of the hokXL mRNA

stable ucb

3’

• G

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

• C

G

• G

G G G G C U U U U U U U 5'

tac

G G C U G A

• A

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

predicted saddle point ucb I tac

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

• C

G U G U G U G U U G U G U G C

• A
• G

U A

• C
• .

. . . . . . A A

• G

G C

3' 5'

U U U U C-G G-C G C C

• A A

A A A G G G GG GG G G G G G G G G C C C C C C C C U U G G G G G C C U U U U U U U U U U U U U U U U U 5'

I II tac

A A

ucb

G C C C A A A A G U

3’

A G A G G G C U

metastable

Transition from the metastable to the stable comformation

G G G C C C C C A A A A U U U U U G G G G G G G G G G G C C C C C C C A A A A G AA A A U U U U U U U U U U U U U U U U U U U U UU U U U U U U U UA A A A A G G G G G GG G G GGG C C C CC C CC C CCC C G G G G G C C C C C C C A A A A A A A U U U G C C A A A A A U U U U U U U U

• G

C

• G

G G G G C U U U U U U

• hok

mRNA XL

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

• SD

3' 5'

I II

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

mok

ucb partial stem tac tac FL Tr

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

fbi sokT SD

hok

125 nts

• A

A A A A A A A A A A A A A A A A A A G G G G G G G G G G G G G C C C C C C C C C C C C C C C C C C C U U U U U U U U U U U U U U G G G G G G G G G G G C C C C C C C A A A A A A U U U U U U U U U U U U A A A G G C CC U U G G G G G G G G G G C C C C C C C C A A U U G G G G C C C C UUU G C C A A A A A U U U U U U U U G G C C A A A A A U U UU U

Truncated, refolded mRNA hok

I II

3' 5'

SD

A A A A A A A A G G G GG G G G CC C C C U U U

hok

A A A A A G G G G GG G G C C C C C U UU

ucb tac tac stem sokT SD

mok

125 nts

G AA G C

• G

G G G G C U U U U U U

RNA 9:1456-1463, 2003

Evidence for neutral networks and shape space covering

Evidence for neutral networks and intersection of apatamer functions

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 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

Coworkers

Universität 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, AT 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

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