1. Autocatalytic chemical reactions in the flow reactor 2. Replication, mutation, selection and Shannon information 3. Evolution in silico and optimization of RNA structures 4. Random walks and ‚ensemble learning‘ 5. Sequence-structure maps, neutral networks, and intersections
Evolution in silico W. Fontana, P. Schuster, Science 280 (1998), 1451-1455
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
5’-end 3’-end A C C U G C U A A U U G C G G C A U A A A C C U A U G G C C A G G U U U G G G A C C A U G A G RNAStudio.lnk G G C GGCGCGCCCGGCGCC U G GUAUCGAAAUACGUAGCGUAUGGGGAUGCUGGACGGUCCCAUCGGUACUCCA UGGUUACGCGUUGGGGUAACGAAGAUUCCGAGAGGAGUUUAGUGACUAGAGG Folding of RNA sequences into secondary structures of minimal free energy, � G 0 300
Hamming distance d (S ,S ) = 4 H 1 2 (i) d (S ,S ) = 0 H 1 1 (ii) d (S ,S ) = d (S ,S ) H 1 2 H 2 1 � (iii) d (S ,S ) d (S ,S ) + d (S ,S ) H 1 3 H 1 2 H 2 3 The Hamming distance between structures in parentheses notation forms a metric in structure space
Replication rate constant: f k = � / [ � + � d S (k) ] � (k) = d H (S k ,S � d S ) f 6 f 7 f 5 f 0 f � f 4 f 3 f 1 f 2 Evaluation of RNA secondary structures yields replication rate constants
Stock Solution Reaction Mixture Replication rate constant: f k = � / [ � + � d S (k) ] � (k) = d H (S k ,S � d S ) Selection constraint: # RNA molecules is controlled by the flow ≈ ± N ( t ) N N Constant mutation rate: p = 0.001 per site and replication The flowreactor as a device for studies of evolution in vitro and in silico
3'-End 5'-End 70 60 10 50 20 40 30 Randomly chosen Phenylalanyl-tRNA as initial structure target structure
Master sequence Mutant cloud “Off-the-cloud” Concentration mutations Sequence e c a p s The molecular quasispecies in 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 n+1 f 2 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 4 I { f 4 f { I 5 I 4 I 5 f 4 f 5 f 5 Evolutionary dynamics including molecular phenotypes
50 S d � 40 t e g r a t o t e 30 c n a t s i d e r u 20 t c u r t s e g a r 10 e v A Evolutionary trajectory 0 0 250 500 750 1000 1250 Time (arbitrary units) In silico optimization in the flow reactor: trajectory
Average structure distance to target dS 36 � Relay steps Number of relay step 10 38 40 42 44 Evolutionary trajectory 0 1250 Time 44 Final structure of the optimization process
Average structure distance to target dS 36 � Relay steps Number of relay step 10 38 40 42 44 Evolutionary trajectory 0 1250 Time 43 44 Reconstruction of the last step 43 � 44
Average structure distance to target dS 36 � Relay steps Number of relay step 10 38 40 42 44 Evolutionary trajectory 0 1250 Time 42 43 44 Reconstruction of last-but-one step 42 � 43 ( � 44)
Average structure distance to target dS 36 � Relay steps Number of relay step 10 38 40 42 44 Evolutionary trajectory 0 1250 Time 41 42 43 44 Reconstruction of step 41 � 42 ( � 43 � 44)
Average structure distance to target dS 36 � Relay steps Number of relay step 10 38 40 42 44 Evolutionary trajectory 0 1250 Time 40 41 42 43 44 Reconstruction of step 40 � 41 ( � 42 � 43 � 44)
Average structure distance to target dS 36 � Relay steps Number of relay step 10 38 40 42 44 Evolutionary trajectory 0 1250 Time Evolutionary process 39 40 41 42 43 44 Reconstruction Reconstruction of the relay series
Transition inducing point mutations Neutral point mutations Change in RNA sequences during the final five relay steps 39 � 44
50 Relay steps S d � 40 t e g r a t o t e 30 c n a t s i d e r u 20 t c u r t s e g a r 10 e v A Evolutionary trajectory 0 0 250 500 750 1000 1250 Time (arbitrary units) In silico optimization in the flow reactor: Trajectory and relay steps
Average structure distance Uninterrupted presence Number of relay step 08 to target dS 10 � 12 28 neutral point mutations during 20 14 a long quasi-stationary epoch Evolutionary trajectory 10 0 250 500 Time (arbitrary units) Transition inducing point mutations Neutral point mutations Neutral genotype evolution during phenotypic stasis
50 Relay steps Main transitions Average structure distance to target d � S 40 30 20 10 Evolutionary trajectory 0 0 250 500 750 1000 1250 Time (arbitrary units) In silico optimization in the flow reactor: Main transitions
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 .
AUGC GC Movies of optimization trajectories over the AUGC and the GC alphabet
0.2 0.15 y c n e 0.1 u q e r F 0.05 0 0 1000 2000 3000 4000 5000 Runtime of trajectories Statistics of the lengths of trajectories from initial structure to target ( AUGC -sequences)
Alphabet Runtime Transitions Main transitions No. of runs AUGC 385.6 22.5 12.6 1017 GUC 448.9 30.5 16.5 611 GC 2188.3 40.0 20.6 107 Statistics of trajectories and relay series (mean values of log-normal distributions)
Massif Central Examples of smooth landscapes on Earth Mount Fuji
Dolomites Examples of rugged landscapes on Earth Bryce Canyon
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
Neutral ridges and plateus
1. Autocatalytic chemical reactions in the flow reactor 2. Replication, mutation, selection and Shannon information 3. Evolution in silico and optimization of RNA structures 4. Random walks and ‚ensemble learning‘ 5. Sequence-structure maps, neutral networks, and intersections
Average structure distance Uninterrupted presence Number of relay step 08 to target dS 10 � 12 28 neutral point mutations during 20 14 a long quasi-stationary epoch Evolutionary trajectory 10 0 250 500 Time (arbitrary units) Transition inducing point mutations Neutral point mutations Neutral genotype evolution during phenotypic stasis
Variation in genotype space during optimization of phenotypes Mean Hamming distance within the population and drift velocity of the population center in sequence space.
Spread of population in sequence space during a quasistationary epoch: t = 150
Spread of population in sequence space during a quasistationary epoch: t = 170
Spread of population in sequence space during a quasistationary epoch: t = 200
Spread of population in sequence space during a quasistationary epoch: t = 350
Spread of population in sequence space during a quasistationary epoch: t = 500
Spread of population in sequence space during a quasistationary epoch: t = 650
Spread of population in sequence space during a quasistationary epoch: t = 820
Spread of population in sequence space during a quasistationary epoch: t = 825
Spread of population in sequence space during a quasistationary epoch: t = 830
Spread of population in sequence space during a quasistationary epoch: t = 835
Spread of population in sequence space during a quasistationary epoch: t = 840
Spread of population in sequence space during a quasistationary epoch: t = 845
Spread of population in sequence space during a quasistationary epoch: t = 850
Spread of population in sequence space during a quasistationary epoch: t = 855
Element of class 2: The ant worker
Ant colony Random foraging Food source Foraging behavior of ant colonies
Ant colony Food source detected Food source Foraging behavior of ant colonies
Ant colony Pheromone trail laid down Food source Foraging behavior of ant colonies
Ant colony Pheromone controlled trail Food source Foraging behavior of ant colonies
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