Evolution of RNA Molecules From Neutral Networks of Structures to - PowerPoint PPT Presentation

Evolution of RNA Molecules From Neutral Networks of Structures to Complex Interaction Patterns Peter Schuster Institut für Theoretische Chemie der Universität Wien, Austria and the Santa Fe Institute, NM Collectives formation and specialization in biological and social systems Santa Fe, 20.– 22.04.2005

Web-Page for further information: http://www.tbi.univie.ac.at/~pks

1. Folding and inverse folding of RNA 2. Neutral networks 3. Darwinian evolution of RNA 4. Learning by the Darwinian mechanism 5. Folding kinetics and metastable structures 6. Intersections and conformational switches

1. Folding and inverse folding of RNA 2. Neutral networks 3. Darwinian evolution of RNA 4. Learning by the Darwinian mechanism 5. Folding kinetics and metastable structures 6. Intersections and conformational switches

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 One sequence – one structure problem

5’-end 3’-end A C (h) C S 5 (h) S 3 U (h) G C S 4 U A 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 A r e n (h) e A S 6 C C e U e A Suboptimal conformations r U G G C F 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

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

1. Folding and inverse folding of RNA 2. Neutral networks 3. Darwinian evolution of RNA 4. Learning by the Darwinian mechanism 5. Folding kinetics and metastable structures 6. Intersections and conformational switches

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.

Mutant class 0 0 1 1 2 4 8 16 Binary sequences are encoded by their decimal equivalents: 2 3 5 6 9 10 12 17 18 20 24 = 0 and = 1, for example, C G ≡ "0" 00000 = CCCCC , 3 7 11 13 14 19 21 22 25 26 28 ≡ "14" 01110 = , C GGG C ≡ 4 "29" 11101 = , etc. GGG G C 15 23 27 29 30 5 31 Hypercube of dimension n = 5 Decimal coding of binary sequences Sequence space of binary sequences of chain lenght n = 5

CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... G A G T CGTCGTTACAATTTA GTTATGTGCGAATTC CAAATT AAAA ACAAGAG..... A C A C Hamming distance d (I ,I ) = 4 H 1 2 d (I ,I ) = 0 (i) H 1 1 (ii) d (I ,I ) = d (I ,I ) H 1 2 H 2 1 � (iii) d (I ,I ) d (I ,I ) + d (I ,I ) H 1 3 H 1 2 H 2 3 The Hamming distance between sequences induces a metric in sequence space

Mapping from sequence space into structure space and into function

Hamming distance d (S ,S ) = 4 H 1 2 d (S ,S ) = 0 (i) 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

The pre-image of the structure S k in sequence space is the neutral network G k

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures 3. Shape space covering of common structures 4. Neutral networks of common structures are connected

1. Folding and inverse folding of RNA 2. Neutral networks 3. Darwinian evolution of RNA 4. Learning by the Darwinian mechanism 5. Folding kinetics and metastable structures 6. Intersections and conformational switches

5' 3' Plus Strand Template Synthese 5' 3' Plus Strand 3' Template Synthese 5' 3' Plus Strand Minus Strand 5' 3' Komplexdissoziation 3' 5' Plus Strand Copying of single-strand RNA-molecules: + 5' 3' Plus-Minus-Replication Minus Strand

Variation of the RNA sequence through copying errors

I 1 I j + Σ Φ dx / dt = f Q ji x - x f j Q j1 i j j j i I j I 2 + Σ i Φ = Σ ; Σ = 1 ; f x x Q ij = 1 j j i j j � i =1,2,...,n ; f j Q j2 [Ii] = xi 0 ; I j I i + [A] = a = constant f j Q ji l -d(i,j) d(i,j) I j (A) + Q = (1- ) p p I j I j + ij f j Q jj p .......... Error rate per digit l ........... Chain length of the f j Q jn polynucleotide I j I n d(i,j) .... Hamming distance + between Ii and Ij Chemical kinetics of replication and mutation as parallel reactions

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

3'-End 5'-End 70 60 10 50 20 30 40 Randomly chosen Phenylalanyl-tRNA as initial structure target structure

Master sequence Mutant cloud n o i t a r t n e c n o C Sequence e c a p s The molecular quasispecies in sequence space

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: Evolutionary trajectory

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

1. Folding and inverse folding of RNA 2. Neutral networks 3. Darwinian evolution of RNA 4. Learning by the Darwinian mechanism 5. Folding kinetics and metastable structures 6. Intersections and conformational switches

Element in example 1: The RNA molecule

Master sequence Mutant cloud n o i t a r t n e c n o C Sequence e c a p s The molecular quasispecies in sequence space

Evolutionary trajectory Spreading of the population through diffusion on a neutral network Drift 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 in example 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