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RNA – Das Zaubermolekül
Peter SchusterInstitut für Theoretische Chemie und Molekulare
Strukturbiologie der Universität Wien
Dies Academicus
Leipzig, 02.12.2002
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++
Replication:DNA 2 DNA→Tr
ansc
riptio
n:
D
NA
RN
A→
Metabolism
Food
Waste
NucleotidesAmino Acids
Lipids Carbohydrates
Small Molecules
Translation: RNA Protein→
ProteinmRNA
Ribosom
A conventional simplified sketch of cellular metabolism
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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
NaØ
NaØ
NaØ
NaØ
RNA
nd 3’-endGCGGAU AUUCGCUUA AGUUGGGA G CUGAAGA AGGUC UUCGAUC A ACCAGCUC GAGC CCAGA UCUGG CUGUG CACAG
3'-end
5’-end
70
60
50
4030
20
10
Definition of RNA structure
5'-e
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Canonical or Watson-Crick base pairs:
cytosine – guanineGÍC
uracil – adenineA=U
W.Saenger, Principles of Nucleic Acid Structure, Springer, Berlin 1984
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The three-dimensional structure of a short double helical stack
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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 CÍ
U=G
Canonical Watson-Crick base-pair Wobble base-pairs
Wobble base pairs in RNA double-helical stacks
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RNA
RNA as scaffold for supramolecular complexes
ribosome
? ? ? ? ?
RNA as adapter molecule
GA
C...
CU
G ..
.
leu
genetic code
RNA as transmitter of genetic information
DNA
...AGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUC...
messenger-RNA
protein
transcription
translation
RNA as of genetic informationworking copy
RNA as carrier of genetic information
RNA
RNA
viruses and retroviruses
as information carrier inevolution and
evolutionary biotechnologyin vitro
RNA as catalyst
ribozyme
The RNA
DNA protein
world as a precursor of
the current + biology
RNA as regulator of gene expression
gene silencing by small interfering RNAs
RNA is modified by epigenetic control
RNA
RNA
editing
Alternative splicing of messenger
RNA is the catalytic subunit in supramolecular complexes
Functions of RNA molecules
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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
G.Bauer, H.Otten, J.S.McCaskill, Travelling waves of in vitro evolving RNA.Proc.Natl.Acad.Sci.USA 86 (1989), 7937-7941
C.K.Biebricher, W.C.Gardiner, Molecular evolution of RNA in vitro. Biophysical Chemistry 66 (1997), 179-192
G.Strunk, T.Ederhof, Machines for automated evolution experiments in vitro based on the serial transfer concept. Biophysical Chemistry 66 (1997), 193-202
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RNA sample
Stock solution: Q RNA-replicase, ATP, CTP, GTP and UTP, bufferb
Time0 1 2 3 4 5 6 69 70
The serial transfer technique applied to RNA evolution in vitro
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Reproduction of the original figure of theserial transfer experiment with Q RNAβ
D.R.Mills, R,L,Peterson, S.Spiegelman,
. Proc.Natl.Acad.Sci.USA (1967), 217-224
An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule58
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Decrease in mean fitnessdue to quasispecies formation
The increase in RNA production rate during a serial transfer experiment
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No new principle will declare itself from below a heap of facts.
Sir Peter Medawar, 1985
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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 thesimplest copying mechanism of RNAComplementarity is determined byWatson-Crick base pairs:
GÍC and A=U
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dx / dt = x - x
x
i i i
j j
; Σ = 1 ; i,j
f
f
i
j
Φ
Φ
fi Φ = (
= Σ
x - i )
j jx =1,2,...,n
[I ] = x 0 ; i i Æ i =1,2,...,n ; Ii
I1
I2
I1
I2
I1
I2
I i
I n
I i
I nI n
+
+
+
+
+
+
(A) +
(A) +
(A) +
(A) +
(A) +
(A) +
fn
fi
f1
f2
I mI m I m++(A) +(A) +fm
fm fj= max { ; j=1,2,...,n}
xm(t) 1 for t Á Á¸
[A] = a = constant
Reproduction of organisms or replication of molecules as the basis of selection
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s = ( f2-f1) / f1; f2 > f1 ; x1(0) = 1 - 1/N ; x2(0) = 1/N
200 400 600 800 1000
0.2
00
0.4
0.6
0.8
1
Time [Generations]
Frac
tion
of a
dvan
tage
ous v
aria
nt
s = 0.1
s = 0.01
s = 0.02
Selection of advantageous mutants in populations of N = 10 000 individuals
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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 AAUCCCGUCCCG
GAAUCCA
Mutations in nucleic acids represent the mechanism of variation of genotypes.
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Theory of molecular evolution
M.Eigen, Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58 (1971), 465-526
C.J.Thompson, J.L.McBride, On Eigen's theory of the self-organization of matter and the evolution of biological macromolecules. Math. Biosci. 21 (1974), 127-142
B.L.Jones, R.H.Enns, S.S.Rangnekar, On the theory of selection of coupled macromolecular systems.Bull.Math.Biol. 38 (1976), 15-28
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.Swetina, P.Schuster, Self-replication with errors - A model for polynucleotide replication.Biophys.Chem. 16 (1982), 329-345
J.S.McCaskill, A localization threshold for macromolecular quasispecies from continuously distributed replication rates. J.Chem.Phys. 80 (1984), 5194-5202
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
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Ij
In
I2
Ii
I1 I j
I j
I j
I j
I j
I j +
+
+
+
+
(A) +
fj Qj1
fj Qj2
fj Qji
fj Qjj
fj Qjn
Q (1- ) ij-d(i,j) d(i,j) = lp p
p .......... Error rate per digit
d(i,j) .... Hamming distance between Ii and Ij
........... Chain length of the polynucleotidel
dx / dt = x - x
x
i j j i
j j
Σ
; Σ = 1 ;
f
f x
j
j j i
Φ
Φ = Σ
Qji
QijΣi = 1
[A] = a = constant
[Ii] = xi 0 ; Æ i =1,2,...,n ;
Chemical kinetics of replication and mutation as parallel reactions
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Error rate p = 1-q0.00 0.05 0.10
Quasispecies Uniform distribution
Quasispecies as a function of the replication accuracy q
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spaceSequence
Con
cent
ratio
n
Master sequence
Mutant cloud
The molecular quasispecies in sequence space
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In the case of non-zero mutation rates (p>0 or q<1) the Darwinian principle of optimization of mean fitness can be understood only as an optimization heuristic. It is valid only on part of the concentration simplex. There are other well defined areas were the mean fitness decreases monotonously or were it may show non-monotonous behavior. The volume of the part of the simplex where mean fitness isnon-decreasing in the conventional sense decreases with inreasing mutation rate p.
In systems with recombination a similar restriction holds for Fisher‘s „universal selection equation“. Its global validity is restricted to the one-gene (single locus) model.
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Theory of genotype – phenotype mapping
P. Schuster, W.Fontana, P.F.Stadler, I.L.Hofacker, From sequences to shapes and back: A case study in RNA secondary structures. Proc.Roy.Soc.London B 255 (1994), 279-284
W.Grüner, R.Giegerich, D.Strothmann, C.Reidys, I.L.Hofacker, P.Schuster, Analysis of RNA sequence structure maps by exhaustive enumeration. I. Neutral networks. Mh.Chem. 127 (1996), 355-374
W.Grüner, R.Giegerich, D.Strothmann, C.Reidys, I.L.Hofacker, P.Schuster, Analysis of RNA sequence structure maps by exhaustive enumeration. II. Structure of neutral networks and shape space covering. Mh.Chem. 127 (1996), 375-389
C.M.Reidys, P.F.Stadler, P.Schuster, Generic properties of combinatory maps. Bull.Math.Biol. 59 (1997), 339-397
I.L.Hofacker, P. Schuster, P.F.Stadler, Combinatorics of RNA secondary structures. Discr.Appl.Math. 89 (1998), 177-207
C.M.Reidys, P.F.Stadler, Combinatory landscapes. SIAM Review 44 (2002), 3-54
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Genotype-phenotype relations are highly complex and only the mostsimple cases can be studied. One example is the folding of RNA sequences into RNA structures represented in course-grained form as secondary structures.
The RNA genotype-phenotype relation is understood as a mapping from the space of RNA sequences into a space of RNA structures.
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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 Tertiary structure
Symbolic notation
The RNA secondary structure is a listing of GC, AU, and GU base pairs. It is understood in contrast to the full 3D-or tertiary structure at the resolution of atomic coordinates. RNA secondary structures are biologically relevant. They are, for example, conserved in evolution.
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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)
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UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC
GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG
UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG
CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG
GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG
Minimum free energycriterion
Inverse folding
1st2nd3rd trial4th5th
The inverse folding algorithm searches for sequences that form a given RNA secondary structure under the minimum free energy criterion.
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UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC
GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG
UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG
CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG
GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG
Criterion ofMinimum Free Energy
Sequence Space Shape Space
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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 ) = 0H 1 1
d (S ,S ) = d (S ,S )H H1 2 2 1
d (S ,S ) d (S ,S ) + d (S ,S )H H H1 3 1 2 2 3¶
(i)
(ii)
(iii)
The Hamming distance induces a metric in sequence space
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The RNA model considers RNA sequences as genotypes and simplified RNA structures, called secondary structures, as phenotypes.
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 graphsin sequence space.
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Sk I. = ( )ψfk f Sk = ( )
Sequence space Phenotype space Non-negativenumbers
Mapping from sequence space into phenotype space and into fitness values
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Sk I. = ( )ψfk f Sk = ( )
Sequence space Phenotype space Non-negativenumbers
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Sk I. = ( )ψfk f Sk = ( )
Sequence space Phenotype space Non-negativenumbers
The pre-image of the structure Sk in sequence space is the neutral network Gk
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Neutral networks are sets of sequences forming the same structure. Gk is the pre-image of the structure Sk in sequence space:
Gk = y-1(Sk) π {yj | y(Ij) = Sk}
The set is converted into a graph by connecting all sequences of Hamming distance one.
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=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.
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Random graph approach to neutral networks
Sketch of sequence spaceStep 00
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Random graph approach to neutral networks
Sketch of sequence spaceStep 01
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Random graph approach to neutral networks
Sketch of sequence spaceStep 02
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Random graph approach to neutral networks
Sketch of sequence spaceStep 03
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Random graph approach to neutral networks
Sketch of sequence spaceStep 04
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Random graph approach to neutral networks
Sketch of sequence spaceStep 05
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Random graph approach to neutral networks
Sketch of sequence spaceStep 10
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Random graph approach to neutral networks
Sketch of sequence spaceStep 15
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Random graph approach to neutral networks
Sketch of sequence spaceStep 25
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Random graph approach to neutral networks
Sketch of sequence spaceStep 50
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Random graph approach to neutral networks
Sketch of sequence spaceStep 75
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Random graph approach to neutral networks
Sketch of sequence spaceStep 100
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λj = 27 ,/12 λk = ø l (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 : = 4k ñ kAUGC
G S Sk k k= ( ) | ( ) = y y-1 U { }I Ij j
k lcr
2 0.5
3 0.4226
4 0.3700
Mean degree of neutrality and connectivity of neutral networks
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Giant Component
A multi-component neutral network
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A connected neutral network
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CUGGGAAAAAUCCCCAGACCGGGGGUUUCCCCGG
CUGGGAAAAAUCCCCAGACCGGGGGUUUCCGCGG
G G
G G
G GG G
G G
G G
G G
C C
C G
C C
C C
U U
U UG G
G GG GG GG G
C CC C
C C
C C
C CC C
C C
U U
U U
A AA A
A A
A A
A A
U U
Com
patib
le
Inco
mpa
tible
5’-end 5’-end
3’-end 3’-end
Compatibility of sequences with structures
A sequence is compatible with its minimum free energy structure and all its suboptimal structures.
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G Ck à k Gk
Neutral network
Compatible set Ck
The compatible set Ck of a structure Sk consists of all sequences which form Sk as its minimum free energy structure (neutral network Gk) or one of itssuboptimal structures.
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CUGGGAAAAAUCCCCAGACCGGGGGUUUCCCCGG
G
G
G
G
GG
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
A sequence at the intersection of two neutral networks is compatible with both structures
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: á ì âC1 C2
: â ì áC1 C2
G1
G2
The intersection of two compatible sets is always non empty: C1 Ú C2 â Ù
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Reference for the definition of the intersection and the proof of the intersection theorem
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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 neutralityin 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
B.M.R.Stadler, P.F.Stadler, G.P.Wagner, W.Fontana, The topology of the possible: Formal spaces underlying patterns of evolutionary change. J.Theor.Biol. 213 (2001), 241-274
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5'-End
3'-End
70
60
50
4030
20
10
Randomly chosen initial structure
Phenylalanyl-tRNA as target structure
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Stock Solution Reaction Mixture
Fitness function:
fk = g / [a + DdS(k)]
DdS(k) = ds(Ik,It)
The flowreactor as a device for studies of evolution in vitro and in silico
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spaceSequence
Con
cent
ratio
n
Master sequence
Mutant cloud
“Off-the-cloud” mutations
The molecular quasispeciesin sequence space
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S{ = y( )I{
f S{ {ƒ= ( )
S{
f{
I{M
utat
ion
Genotype-Phenotype Mapping
Evaluation of the
Phenotype
Q{jI1
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
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In silico optimization in the flow reactor: Trajectory (biologists‘ view)
Time (arbitrary units)
Aver
age
dist
ance
from
initi
al s
truct
ure
50
-d
D
S
500 750 1000 12502500
50
40
30
20
10
0
Evolutionary trajectory
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In silico optimization in the flow reactor: Trajectory (physicists‘ view)
Time (arbitrary units)
Aver
age
stru
ctur
e di
stan
ce to
targ
et
d
DS
500 750 1000 12502500
50
40
30
20
10
0
Evolutionary trajectory
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In silico optimization in the flow reactor: Main transitions
Main transitionsRelay steps
Time (arbitrary units)
Aver
age
stru
ctur
e di
stan
ce to
targ
et
d
DS
500 750 1000 12502500
50
40
30
20
10
0
Evolutionary trajectory
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Shift Roll-Over
Flip Double Flipa a b
aa
b
α α
αα
β
β
Closing of Constrained Stacks
Multi-loop
Main or discontinuous transitions: Structural innovations, occurrarely on single point mutations
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In silico optimization in the flow reactor
Time (arbitrary units)
Aver
age
stru
ctur
e di
stan
ce to
targ
et
d
DS
500 750 1000 12502500
50
40
30
20
10
0
Relay steps Main transitions
Uninterrupted presence
Evolutionary trajectory
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Elongation of StacksShortening of Stacks
Opening of Constrained Stacks
Multi-loop
Minor or continuous transitions: Occur frequently on single point mutations
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Statistics of evolutionary trajectories
Population size
N
Number of replications
< n >rep
Number of transitions
< n >tr
Number of main transitions
< n >dtr
The number of main transitions or evolutionary innovations is constant.
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„...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)
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Genotype Space
Fitn
ess
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
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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
Y.Wang, R.R.Rando, Specific binding of aminoglycoside antibiotics to RNA. Chemistry & Biology 2 (1995), 281-290
L.Jiang, A.K.Suri, R.Fiala, D.J.Patel, Saccharide-RNA recognition in an aminoglycoside antibiotic-RNA aptamer complex. Chemistry & Biology 4 (1997), 35-50
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yes
Selection Cycle
no
GeneticDiversity
Desired Properties? ? ?
Selection
Amplification
Diversification
Selection cycle used inapplied molecular evolutionto design molecules withpredefined properties
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Retention of binders Elution of binders
Chr
omat
ogra
phic
col
umn
The SELEX technique for the evolutionary design of aptamers
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Secondary structures of aptamers binding theophyllin, caffeine, and related compounds
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additional methyl group
Dissociation constants and specificity of theophylline, caffeine, and related derivatives of uric acid for binding to a discriminating aptamer TCT8-4
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tobramycin
A
AA
AA C
C C CC
C
CC
G G G
G
G
G
G
G U U
U
U
U U5’-
3’-
AAAAA UUUUUU CCCCCCCCG GGGGGGG5’- -3’
RNA aptamer
Formation of secondary structure of the tobramycin binding RNA aptamer
L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Saccharide-RNA recognition in an aminoglycoside antibiotic-RNA aptamer complex. Chemistry & Biology 4:35-50 (1997)
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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)
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A ribozyme switch
E.A.Schultes, D.B.Bartel, One sequence, two ribozymes: Implication for the emergenceof new ribozyme folds. Science 289 (2000), 448-452
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Two ribozymes of chain lengths n = 88 nucleotides: An artificial ligase (A) and a natural cleavage ribozyme of hepatitis-d-virus (B)
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The sequence at the intersection:
An RNA molecules which is 88 nucleotides long and can form both structures
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Two neutral walks through sequence space with conservation of structure and catalytic activity
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Reference for postulation and in silico verification of neutral networks
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Coworkers
Peter Stadler, Universität Leipzig, GE
Walter Fontana, Santa Fe Institute, NM
Christian Reidys, Christian Forst, Los Alamos National Laboratory, NM
Ivo L.Hofacker, Christoph Flamm, Universität Wien, AT
Bärbel Stadler, Andreas Wernitznig, Universität Wien, ATMichael Kospach, Ulrike Langhammer, Ulrike Mückstein, Stefanie Widder
Jan Cupal, Kurt Grünberger, Andreas Svrček-Seiler, Stefan Wuchty
Ulrike Göbel, Institut für Molekulare Biotechnologie, Jena, GEWalter Grüner, Stefan Kopp, Jaqueline Weber