1. Darwinian evolution in laboratory experiments 2. Modeling the evolution of molecules 3. From RNA sequences to structures and back 4. Evolution on neutral networks 5. Origins of complexity
5' - end N 1 O CH 2 O GCGGAU UUA GCUC AGUUGGGA GAGC CCAGA G CUGAAGA UCUGG AGGUC CUGUG UUCGAUC CACAG A AUUCGC ACCA 5'-end 3’-end N A U G C k = , , , OH O N 2 O P O CH 2 O Na � O O OH N 3 O P O CH 2 O Na � O Definition of RNA structure O OH N 4 O P O CH 2 O Na � O O OH 3' - end O P O Na � O
5'-End 3'-End Sequence GCGGAUUUAGCUCAGDDGGGAGAGCMCCAGACUGAAYAUCUGGAGMUCCUGUGTPCGAUCCACAGAAUUCGCACCA 3'-End 5'-End 70 60 Secondary structure 10 50 20 40 30 � Symbolic notation 5'-End 3'-End A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs
RNA sequence Biophysical chemistry: thermodynamics and kinetics RNA folding : Structural biology, spectroscopy of biomolecules, Empirical parameters understanding molecular function RNA structure of minimal free energy Sequence, structure, and design
5’-end 3’-end A C (h) C S 5 (h) S 3 U (h) G C S 4 A U A U (h) S 1 U G (h) S 2 (h) C G S 8 0 G (h) (h) S 9 S 7 G C � A U y g A r A e n e (h) A S 6 C C e U e A Suboptimal conformations r U G G F C C A G G U U U G G G A C C A U G A G G G C U G (h) S 0 Minimum of free energy The minimum free energy structures on a discrete space of conformations
hairpin loop hairpin hairpin loop loop stack free stack stack joint stack end bulge free end free end stack internal loop stack hairpin loop Elements of RNA hairpin loop multiloop secondary structures hairpin as used in free energy loop calculations s t a c k stack stack ∑ ∑ ∑ ∑ ∆ = + + + + 300 free free G g h n b n i n ( ) ( ) ( ) L end ij kl l b i end 0 , stacks of hairpin bulges internal base pairs loops loops
RNA sequence Iterative determination of a sequence for the Inverse folding of RNA : given secondary RNA folding : structure Biotechnology, Structural biology, design of biomolecules spectroscopy of Inverse Folding with predefined biomolecules, Algorithm structures and functions understanding molecular function RNA structure of minimal free energy Sequence, structure, and design
Inverse folding algorithm I 0 � I 1 � I 2 � I 3 � I 4 � ... � I k � I k+1 � ... � I t S 0 � S 1 � S 2 � S 3 � S 4 � ... � S k � S k+1 � ... � S t I k+1 = M k (I k ) and � d S (S k ,S k+1 ) = d S (S k+1 ,S t ) - d S (S k ,S t ) < 0 M ... base or base pair mutation operator d S (S i ,S j ) ... distance between the two structures S i and S j ‚Unsuccessful trial‘ ... termination after n steps
Intermediate compatible sequences Initial trial sequences Stop sequence of an unsuccessful trial Intermediate compatible sequences Target sequence Target structure S k Approach to the target structure S k in the inverse folding algorithm
Minimum free energy criterion 1st 2nd 3rd trial 4th 5th Inverse folding of RNA secondary structures The inverse folding algorithm searches for sequences that form a given RNA secondary structure under the minimum free energy criterion.
Mapping from sequence space into structure space
The pre-image of the structure S k in sequence space is the neutral network G k
One-error neighborhood GUUAAUCAG GUAAAUCAG GUGAAUCAG GCCAAUCAG GUCUAUCAG GGCAAUCAG GUCGAUCAG GACAAUCAG GUCCAUCAG CUCAAUCAG GUCAUUCAG UUCAAUCAG G A C U G A C U G GUCAAUCAG AUCAAUCAG GUCACUCAG GUCAAUCAC GUCAAACAG GUCAAUCAU G U C A A GUCAAUCAA G C A G GUCAACCAG G U GUCAAUAAG C A G A G U U GUCAAUCUG U C C G A C C U A G A C U A A C The surrounding of U A G U U G A G GUCAAUCAG in sequence space G A G
Degree of neutrality of neutral networks and the connectivity threshold
A multi-component neutral network formed by a rare structure: � < � cr
A connected neutral network formed by a common structure: � > � cr
1. Darwinian evolution in laboratory experiments 2. Modeling the evolution of molecules 3. From RNA sequences to structures and back 4. Evolution on neutral networks 5. Origins of complexity
Genotype = Genome Mutation GGCUAUCGUACGUUUACCCAAAAAGUCUACGUUGGACCCAGGCAUUGGAC.......G Fitness in reproduction: Unfolding of the genotype: Number of genotypes in RNA structure formation the next generation Phenotype Selection Evolution of phenotypes: RNA structures
Replication rate constant : f k = � / [ � + � d S (k) ] � d S (k) = d H (S k ,S � ) Selection constraint : Population size, N = # RNA molecules, is controlled by the flow ≈ ± N t N N ( ) Mutation rate : p = 0.001 / site � replication The flowreactor as a device for studies of evolution in vitro and in silico
Replication rate constant: f k = � / [ � + � d S (k) ] � d S (k) = d H (S k ,S � ) f 6 f 7 f 5 f 0 f 4 f � f 3 f 1 f 2 Evaluation of RNA secondary structures yields replication rate constants
Randomly chosen Phenylalanyl-tRNA as initial structure target structure
Formation of a quasispecies in sequence space
Migration of a quasispecies through sequence space
Genotype-Phenotype Mapping Evaluation of the = � ( ) S { I { S { Phenotype I { ƒ f = ( S ) { { f { Q { f 1 j f 1 Mutation I 1 f 2 f n+1 I 1 I n+1 I 2 f n f 2 I n I 2 f 3 I 3 Q Q I 3 f 3 I { I 4 f 4 f { I 5 I 4 I 5 f 4 f 5 f 5 Evolutionary dynamics including molecular phenotypes
AUGC alphabet GC alphabet connected neutral network disconnected Evolutionary optimization of RNA structure
00 09 31 44 Three important steps in the formation of the tRNA clover leaf from a randomly chosen initial structure corresponding to three main transitions .
In silico optimization in the flow reactor: Evolutionary Trajectory
28 neutral point mutations during a long quasi-stationary epoch Transition inducing point mutations Neutral point mutations leave the change the molecular structure molecular structure unchanged Neutral genotype evolution during phenotypic stasis
Evolutionary trajectory Spreading of the population on neutral networks Drift of the population center in sequence space
Spreading and evolution of a population on a neutral network: t = 150
Spreading and evolution of a population on a neutral network : t = 170
Spreading and evolution of a population on a neutral network : t = 200
Spreading and evolution of a population on a neutral network : t = 350
Spreading and evolution of a population on a neutral network : t = 500
Spreading and evolution of a population on a neutral network : t = 650
Spreading and evolution of a population on a neutral network : t = 820
Spreading and evolution of a population on a neutral network : t = 825
Spreading and evolution of a population on a neutral network : t = 830
Spreading and evolution of a population on a neutral network : t = 835
Spreading and evolution of a population on a neutral network : t = 840
Spreading and evolution of a population on a neutral network : t = 845
Spreading and evolution of a population on a neutral network : t = 850
Spreading and evolution of a population on a neutral network : t = 855
Mount Fuji Example of a smooth landscape on Earth
Dolomites Bryce Canyon Examples of rugged landscapes on Earth
End of Walk Fitness Start of Walk Genotype Space Evolutionary optimization in absence of neutral paths in sequence space
End of Walk Adaptive Periods s s e n t i F Random Drift Periods Start of Walk Genotype Space Evolutionary optimization including neutral paths in sequence space
Grand Canyon Example of a landscape on Earth with ‘neutral’ ridges and plateaus
1. Darwinian evolution in laboratory experiments 2. Modeling the evolution of molecules 3. From RNA sequences to structures and back 4. Evolution on neutral networks 5. Origins of complexity
Chemical kinetics of molecular evolution M. Eigen, P. Schuster, `The Hypercycle´, Springer-Verlag, Berlin 1979
Four phases of major transitions leading to radical innovations in evolution M.Eigen, P.Schuster: 1978 J.Maynard Smith, E. Szathmáry: 1995
A model genome with 12 genes 1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Regulatory gene Enzyme Structural gene Metabolite Sketch of a genetic and metabolic network
All higher forms of life share the almost same sets genes. Differences come about through different expression of genes and multiple usage of gene products. Are there molecules with multiple functions ? How do they look like? RNA switches as an example
Many suboptimal structures Metastable structures One sequence - one structure Partition function Conformational switches 3.30 3.40 3.10 49 48 47 2.80 46 Free Energy 45 44 42 43 41 40 38 39 37 36 35 34 33 32 31 29 30 28 27 2.60 26 25 24 23 22 21 20 3.10 19 18 17 16 S10 15 13 14 12 S8 3.40 2.90 S9 11 10 9 S7 5.10 3.00 S5 8 S6 7 6 5 S4 4 S3 3 7.40 S2 2 5.90 S1 S0 S0 S0 S1 Minimum free energy structure Suboptimal structures Kinetic structures RNA secondary structures derived from a single sequence
Structure S k G k Neutral Network � G k C k Compatible Set C k The compatible set C k of a structure S k consists of all sequences which form S k as its minimum free energy structure (the neutral network G k ) or one of its suboptimal structures.
Structure S 0 Structure S 1 The intersection of two compatible sets is always non empty: C 0 � C 1 � �
Reference for the definition of the intersection and the proof of the intersection theorem
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
Acknowledgement of support Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Universität Wien Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No. 98-0189, 12835 (NEST) Austrian Genome Research Program – GEN-AU: Bioinformatics Network (BIN) Österreichische Akademie der Wissenschaften Siemens AG, Austria Universität Wien and the Santa Fe Institute
Coworkers Peter Stadler , Bärbel M. Stadler , Universität Leipzig, GE Paul E. Phillipson , University of Colorado at Boulder, CO Universität Wien Heinz Engl, Philipp Kügler , James Lu , Stefan Müller , RICAM Linz, AT Jord Nagel , Kees Pleij , Universiteit Leiden, NL Walter Fontana , Harvard Medical School, MA Christian Reidys , Christian Forst , Los Alamos National Laboratory, NM Ulrike Göbel, Walter Grüner , Stefan Kopp , Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE Ivo L.Hofacker , Christoph Flamm , Andreas Svr č ek-Seiler , Universität Wien, AT Kurt Grünberger, Michael Kospach , Andreas Wernitznig , Stefanie Widder, Stefan Wuchty , Universität Wien, AT Jan Cupal , Stefan Bernhart , Lukas Endler, Ulrike Langhammer , Rainer Machne, Ulrike Mückstein , Hakim Tafer, Thomas Taylor, Universität Wien, AT
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