Modeling Evolution of Molecules New Variations of an Old Theme - PowerPoint PPT Presentation

N = 4 n N S < 3 n Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _ � { AU , CG , GC , GU , UA , UG } A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

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

GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G G A U C U G A C CC C A GG G G C U UGGA A U C UACG U G U C A G U AAG UC U A U C C C AA One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

G GGCUAUCGUACGUUUACCC AAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G G A U C U G A C CC C A GG G U G U G C A U A C G U A A A A G G C U A C U A C G U U C G U A C A G A C A G C G G C G U A G U G U A C G U C A A U C U A C G G C A C G U G G A C A G G C U G U U A G C U UGGA A U C UACG U G U C A G U AAG UC U A U C C C AA One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

U C A G U G C G G U A C C G A U G U G U U U A A C C C G G A C C G C A AA G C A U G C G U U U A C G G GGCUAUCGUACGUUUACCC AAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G G A U C U G A C G CC C A GG G C U UGGA A U C UACG U G U C A G U AAG UC U A U C C C AA One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

U C A A G G C U U C G U C C C C A G G G A G G G G U A C C G G A C UGG U U G U U G A U U U U A A C C UACG U G C C G U G A C A C C G G C A U AAG UC AA G C U A A U U C G C G U C U C AA U A C G U G GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGG CCCAGGCAUUGGACG GGCUAUCGUACGUUUACCC AAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G G A U C U G A C G CC C A GG G C U UGGA A U C UACG U G U C A G U AAG UC U A U C C C AA One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

U C A A G G C U U C G U C C C C A G G G A G G G G U A C C G G A C UGG U U G U U G A U U U U A A C C UACG U G C C G U G A C A C C G G C A U AAG UC AA G C U A A U U C G C G U C U C AA U A C G U G GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGG CCCAGGCAUUGGACG GGCUAUCGUACGUUUACCC AAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G G A U C U G A C C G CC C A GG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCA UGGACG G C U UGGA A U C UACG U G U C A A G C C U U AAG UC C C C AG G G A G U G A U G C G C C C AA C UGG A U A U C UACG U G U C A G U AAG UC U A U C C C AA One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

U C A A G G C U U C G U C C C C A G G G A G G G G U A C C G G A C UGG U U G U U G A U U U U A A C C UACG U G C C G U G A C A C C G G C A U AAG UC AA G C U A A U U C G C G U C U C AA U A C G U G GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGG CCCAGGCAUUGGACG GGCUAUCGUACGUUUACCC AAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G G A U C U G A C C G G CC C A GG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCA UGGACG GGCUAUCGUACGU UACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G C U UGGA A U A C G C G UACG U G G U C A U A G G C C A U C G U U AAG UC C C C AG G G A G U C G A U G G C U G G A C C C AA A C UGG A U C A U U ACC C C G UACG U G G U U G C A A G U U C U AAG UC G G U A C U U C A G C C AA U U A U C C C G C A A A A One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

GGCUAUCGUA U GUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUU A GACG GGCUAUCGUACGUUUAC U CAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACG C UUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGC C AUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGU G UACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUA A CGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCC U GGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCA C UGGACG G G A U GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGG U CCCAGGCAUUGGACG C U GGCUA G CGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG G A GGCUAUCGUACGUUUACCC G AAAGUCUACGUUGGACCCAGGCAUUGGACG C G CC C A GG GGCUAUCGUACGUUUACCCAAAAG C CUACGUUGGACCCAGGCAUUGGACG G C U UGGA A U C UACG U G U C A G U AAG UC U A U C C C AA One error neighborhood – Surrounding of an RNA molecule in sequence and shape space

Number Mean Value Variance Std.Dev. Total Hamming Distance: 150000 11.647973 23.140715 4.810480 Nonzero Hamming Distance: 99875 16.949991 30.757651 5.545958 Degree of Neutrality: 50125 0.334167 0.006961 0.083434 Number of Structures: 1000 52.31 85.30 9.24 1 (((((.((((..(((......)))..)))).))).))............. 50125 0.334167 2 ..(((.((((..(((......)))..)))).)))................ 2856 0.019040 3 ((((((((((..(((......)))..)))))))).))............. 2799 0.018660 4 (((((.((((..((((....))))..)))).))).))............. 2417 0.016113 5 (((((.((((.((((......)))).)))).))).))............. 2265 0.015100 6 (((((.(((((.(((......))).))))).))).))............. 2233 0.014887 7 (((((..(((..(((......)))..)))..))).))............. 1442 0.009613 8 (((((.((((..((........))..)))).))).))............. 1081 0.007207 9 ((((..((((..(((......)))..))))..)).))............. 1025 0.006833 10 (((((.((((..(((......)))..)))).))))).............. 1003 0.006687 11 .((((.((((..(((......)))..)))).))))............... 963 0.006420 12 (((((.(((...(((......)))...))).))).))............. 860 0.005733 13 (((((.((((..(((......)))..)))).)).)))............. 800 0.005333 14 (((((.((((...((......))...)))).))).))............. 548 0.003653 15 (((((.((((................)))).))).))............. 362 0.002413 16 ((.((.((((..(((......)))..)))).))..))............. 337 0.002247 G G A U 17 (.(((.((((..(((......)))..)))).))).).............. 241 0.001607 C U 18 (((((.(((((((((......))))))))).))).))............. 231 0.001540 G A 19 ((((..((((..(((......)))..))))...))))............. 225 0.001500 C G CC C A GG 20 ((....((((..(((......)))..)))).....))............. 202 0.001347 G C U UGGA A U C UACG U G U C A G U AAG UC U A U C Shadow – Surrounding of an RNA structure in shape space – AUGC alphabet C C AA

1. Replication and mutation 2. Quasispecies and error thresholds 3. Fitness landscapes and randomization 4. Lethal mutations 5. Ruggedness of natural landscapes 6. Simulation of stochastic phenomena

Structure of Phenylalanyl-tRNA as andomly chosen target structure initial sequence

Evolution in silico W. Fontana, P. Schuster, Science 280 (1998), 1451-1455

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Replication rate constant (Fitness) : f k = � / [ � + � d S (k) ] � d S (k) = d H (S k ,S � ) Selection pressure : The population size, N = # RNA moleucles, is determined by the flux: ≈ ± N t N N ( ) Mutation rate : p = 0.001 / Nucleotide � Replication The flow reactor as a device for studying the evolution of molecules in vitro and in silico .

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