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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