RNA Structures

Stability, Folding and the Role ofHydrogen Bonding and Protons

Peter SchusterInstitut für Theoretische Chemie und Molekulare

Strukturbiologie der Universität Wien

Schloß Ringberg, 05.03.2002

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

Na

Na

Na

Na

The chemical formula of RNA consisting of nucleobases, ribose rings, phosphate groups, and sodium counterions

Structural Constraints and Hydrogen Bonding in RNA

Single stranded RNA molecules form structures, which combine double-helical stacking (A-type) regions with loops and metal ion (Mg2 )coordinated centers.

The three-dimensional structure of a short double helical stack

Canonical Watson-Crick base pairs:

cytosine – guanineuracil – adenine

W.Saenger, Principles of Nucleic Acid Structure, Springer, Berlin 1984

O

O

OO

O

H

H

HH

H

H

H

HH

H

H

N

NNN

N

N

N

N

N

N

NO

O

HN

N

H

O

NN

N

NN

N

N

G=U

G C

U=G

Canonical Watson-Crick base-pair Wobble base-pairs

Wobble base pairs in RNA double-helical stacks

CG

``A´´U

2,6-diamino purine

2-keto, 6-amino purine

2,6-diketo purine

5-keto, 7-amino, 1,6,8-triaza indolicine

5- , 7- , 1,6,8-triaza indolicine

amino keto

2-amino,6-keto purine2-keto, 4-amino pyrimidine

2- , 4- pyrimidineamino keto

2,4-di pyrimidineketo

2,6-diamin pyrimidineo

2- , 6-keto pyrazineamino

2- , 6- pyrazineketo amino

Color code:

Donor—Acceptor

Acceptor—Donor

Hydrogen bonding patterns for Watson-Crick base pairs

S.A. Benner et al., Reading the palimpsest: Contemporary biochemical data and the RNA world. In: R.F.Gesteland and J.F.Atkins, eds. The RNA World, pp.27-70. CSHL Press, 1993

Classification of purine-pyrimidine base pairs

Classification of purine-purine base pairs

Classification of pyrimidine-pyrimidine base pairs

General classificationof base pairs

N.B.Leontis and E. Westhof, RNA 7:499-512 (2001)

Stacking of heterocyclic aromatic molecules without sugar-phosphate backbone

Example: N6,N9-dimethyl adenine, D. Pörschke and F. Eggers, Eur.J.Biochem. 26:490-498 (1972)

Stacking of RNA single strands

Example: poly-A, D.Pörschke. Elementary steps of base recognition and helix-coil transitions in nucleic acids. In: I.Pecht and R.Rigler, eds. Chemical Relaxation in Molecular Biology, pp.191-218. Springer-Verlag, Berlin 1977.

Three-dimensional structure ofphenylalanyl-transfer-RNA

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 of 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

4030

20

10

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

Secondary Structure

Symbolic Notation

Definition of the secondary structure of phenylalanyl-tRNA

5.10

2

2.90

8

1415

18

2.60

17

23

19

2722

38

45

25

3633

3940

3.10

43

3.40

41

3.30

7.40

5

3

7

3.00

4

109

3.40

6

1312

3.10

11

2120

16

2829

26

3032

424644

24

353437

49

2.80

31

4748

S0S1

Kinetic Structures

Free

Ene

rgy

S0 S0S1

S2

S3S4S5 S6

S7S8

S10S9

Minimum Free Energy Structure Suboptimal Structures

T = 0 K , t T > 0 K , t T > 0 K , t finite

5.90

Different notions of RNA structure

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 ofMinimum Free Energy

Sequence Space Shape Space

Sk I. = ( )ψ Gk k = ( )f S

Sequence space Shape space Non-negativenumbers

Mapping from sequence space into phenotype space and into free energies

.... GC UC ....CA

.... GC UC ....GU

.... GC UC ....GA .... GC UC ....CU

d =1H

d =1H

d =2H

Point mutations as moves in sequence space

λj = 27 ,/12 λk = (k)j

| |Gk

λ κcr = 1 - -1 ( 1)/ κ-

λ λk cr . . . .>

λ λk cr . . . .<

Network is connectedGk

Network is connectednotGk

Connectivity Threshold:

Alphabet Size : = 4AUGC

G S Sk k k= ( ) | ( ) = -1 I Ij j

cr

2 0.5

3 0.4226

4 0.3700

Mean degree of neutrality and connectivity of neutral networks

A connected neutral network

Giant Component

A multi-component neutral network

Kinetic Folding of RNA at Elementary Step Resolution

The RNA folding process is resolved to base pair closure, base pair cleavageand base pair shift. The kinetic folding behavior is determined by computation of a sufficiently large ensemble of individual folding trajectories and taking an average over them. The folding behavior is illustrated by barrier trees showing the path of lowest energy between two local minima of free energy.

C.Flamm, W.Fontana, I.L.Hofacker and P.Schuster. RNA, 6:325-338 (2000)

closure

shift

cleavage

Move set for elementary stepsin kinetic RNA folding

Folding dynamics of the sequence GGCCCCUUUGGGGGCCAGACCCCUAAAAAGGGUC

CUGGGAAAAAUCCCCAGACCGGGGGUUUCCCCGG

G

G

G

GG

G

G

G

G

G

G

G

G

G

G

G

G

G

C

C

C

C

C

C

CC

UU

UU

U

U

G

G

G

G

G

C

C

C

C

C

C

C

CC

C

C

C

CU

UU

AA

A

AA

A

A

A

A

A

U

3’-end

Min

imum

free

ene

rgy

conf

orm

atio

n S 0

Subo

ptim

al c

onfo

rmat

ion

S 1

C

G

One sequence is compatible with two structures

Sh

S1(h)

S6(h)

S7(h)

S5(h)

S2(h)

S9(h)

Free

ene

rgy

G

0

Local minimum

Suboptimal conformations

Search for local minima in conformation space

Free

ene

rgy

G

0

Free

ene

rgy

G

0

"Reaction coordinate"

Sk Sk

S SSaddle point T k

T k

"Barrier tree"

5.10

2

2.90

8

1415

18

2.60

17

23

19

2722

38

45

25

3633

3940

3.10

43

3.40

41

3.30

7.40

5

3

7

3.00

4

109

3.40

6

1312

3.10

11

2120

16

2829

26

3032

424644

24

353437

49

2.80

31

4748

S0S1

Barrier tree of a sequence with two conformations 5

.90

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

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 knowncatalytically activeRNA molecule

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

Coworkers

Walter Fontana, Santa Fe Institute, NM

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

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

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

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

RNA StructuresCoworkers