What we can Learn in Evolution from RNA Molecules Peter Schuster Institut für Theoretische Chemie The Santa Fe Institute und Molekulare Strukturbiologie and Santa Fe, New Mexico USA Universität Wien, Austria Lab Inauguration Meeting Köln, 03.12.2004
Web-Page for further information: http://www.tbi.univie.ac.at/~pks
1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design
1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design
RNA as transmitter of genetic information RNA as adapter molecule RNA is the catalytic subunit in RNA as scaffold for supramolecular supramolecular complexes complexes DNA RNA as catalyst transcription ...AGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUC... messenger- RNA . . translation . C G A leu U G C protein genetic code . . . working copy RNA as of genetic information Ribozyme ribosome ? ? ? ? ? RNA RNA is modified by epigenetic control RNA RNA editing The world as a precursor of DNA protein the current + biology RNA Alternative splicing of messenger RNA as regulator of gene expression Allosteric control of transcribed RNA RNA as carrier of genetic information RNA viruses and retroviruses RNA evolution in vitro Evolutionary biotechnology RNA aptamers, artificial ribozymes, allosteric ribozymes Riboswitches controlling Gene silencing by transcription and translation small interfering RNAs Functions of RNA molecules metabolites through
Examples of ‘natural selection’ with RNA molecules
An example of ‘artificial selection’ with RNA molecules or ‘breeding’ of biomolecules
1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design
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 � 3'-end O O OH Definition of RNA structure 5’-end N 4 O P O CH 2 O Na � 70 O O OH 60 3' - end O P O 10 Na � O 50 20 30 40
Definition and physical relevance of RNA secondary structures RNA secondary structures are listings of Watson-Crick and GU wobble base pairs, which are free of knots and pseudokots . D.Thirumalai, N.Lee, S.A.Woodson, and D.K.Klimov. Annu.Rev.Phys.Chem . 52 :751-762 (2001): „ Secondary structures are folding intermediates in the formation of full three-dimensional structures .“
The Vienna RNA-Package : A library of routines for folding, inverse folding, sequence and structure alignment, cofolding, kinetic folding, …
RNA sequence Biophysical chemistry: thermodynamics and kinetics Inverse folding of RNA : RNA folding : Biotechnology, Structural biology, design of biomolecules spectroscopy of with predefined biomolecules, structures and functions 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
Criterion of Minimum Free Energy UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG Sequence Space Shape Space
Reference for postulation and in silico verification of neutral networks
1. RNA and properties and function 2. RNA structures 3. Neutral networks and intersections 4. RNA evolution in silico 5. Intersection molecules and RNA switches 6. Neutrality in evolution and design
ψ = ( ) Sk I. = ( ) fk f Sk Sequence space Real numbers Structure space Mapping from sequence space into structure space and into function
ψ = ( ) Sk I. = ( ) fk f Sk Sequence space Real numbers Structure space
ψ = ( ) Sk I. Sequence space Structure space
ψ = ( ) Sk I. Sequence space Structure space The pre-image of the structure S k in sequence space is the neutral network G k
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 (i) d (I ,I ) = 0 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 genotypes induces a metric in sequence space
Neutral networks are sets of sequences forming the same object in a phenotype space. The neutral network G k is, for example, the pre- image of the structure S k in sequence space: G k = � -1 (S k ) π { � j | � (I j ) = S k } The set is converted into a graph by connecting all sequences of Hamming distance one. Neutral networks of small biomolecules can be computed by exhaustive folding of complete sequence spaces, i.e. all RNA sequences of a given chain length. This number, N=4 n , 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.
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
n = 9 ; 3n = 27 Degree of neutrality of neutral networks and the connectivity threshold
Degree of neutrality of neutral networks and the connectivity threshold
“j” λ j = / 12 27 = 0.444 Degree of neutrality of neutral networks and the connectivity threshold
U � � -1 � � G S S = ( ) | ( ) = I I k k k j j � � (k) j λ k = G k | | λ j = / 12 27 = 0.444 Degree of neutrality of neutral networks and the connectivity threshold
U � � -1 � � G S S = ( ) | ( ) = I I k k k j j � � (k) j λ k = G k | | λ j = / 12 27 = 0.444 λ λ G k network is connected > cr . . . . k λ λ G k not < network is connected cr . . . . k / κ - λ κ -1 ( 1) Connectivity threshold: cr = 1 - Degree of neutrality of neutral networks and the connectivity threshold
U � � -1 � � G S S = ( ) | ( ) = I I k k k j j � � (k) j λ k = G k | | � Alphabet size : � � cr 2 0.5 AU,GC,DU λ j = / 12 27 = 0.444 3 0.423 AUG , UGC 4 0.370 AUGC λ λ G k network is connected > cr . . . . k λ λ G k not < network is connected cr . . . . k / κ - λ κ -1 ( 1) Connectivity threshold: cr = 1 - Degree of neutrality of neutral networks and the connectivity threshold
Giant Component A multi-component neutral network formed by a rare structure
A connected neutral network formed by a common structure
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.
(h) S 5 (h) S 1 (h) S 2 (h) (h) 0 S 9 S 7 Free energy G � (h) S 6 Suboptimal conformations Search for local minima in conformation space S h Local minimum
g 3.30 49 48 47 46 45 44 42 43 41 40 38 39 36 37 34 35 33 32 31 29 30 28 27 25 26 24 23 22 21 20 0 19 1 . 3 18 S 10 17 16 15 13 14 12 S 8 S 9 10 11 5.10 S 7 9 S 5 S 6 8 7 6 5 S 4 4 S 3 3 7.40 S 2 5.90 2 S 1 S 0 S1 S0 Suboptimal structures Kinetic folding Suboptimal structures Suboptimal secondary structures of an RNA sequence
g 3.30 49 48 47 46 45 44 42 43 41 40 38 39 36 37 34 35 33 32 31 29 30 28 27 25 26 24 23 22 21 20 0 19 1 . 3 18 S 10 17 16 15 13 14 12 S 8 S 9 10 11 5.10 S 7 9 S 5 S 6 8 7 6 5 S 4 4 S 3 3 7.40 S 2 5.90 2 S 1 S 0 S1 S0 Suboptimal structures Metastable Stable Kinetic folding Suboptimal structures structure An RNA molecule with two ( meta ) stable conformations
Structure
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