Designing RNA Structures From Theoretical Models to Real Molecules Peter Schuster Institut für Theoretische Chemie und Molekulare Strukturbiologie der Universität Wien Microbiology Seminar Mount Sinai School of Medicine, 25.05.2004
Web-Page for further information: http://www.tbi.univie.ac.at/~pks
1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules
1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules
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'-e nd 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
5'-End 3'-End Sequence GCGGAUUUAGCUCAGDDGGGAGAGCMCCAGACUGAAYAUCUGGAGMUCCUGUGTPCGAUCCACAGAAUUCGCACCA 3'-End 5'-End 70 60 Secondary structure 10 50 20 30 40 � Symbolic notation 5'-End 3'-End A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs
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 .“
4 6 5 4 7 6 6 8 5 � C G 3 1 1 9 4 2 C ’ 2 1 C ’ 3 1 2 2 55.7 � 54.4 � 10.72 Å 4 6 5 4 7 6 6 8 5 3 U = A 1 1 4 9 2 C ’ 2 1 C ’ 3 1 2 57.4 � 56.2 � 10.44 Å Watson-Crick type base pairs
O N H O G=U N N O H N N Deviation from H N Watson-Crick geometry H O N U=G N H O N O H N N Deviation from N H N Watson-Crick geometry H Wobble base pairs
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 (h) S 5 (h) S 3 (h) S 4 (h) S 1 Free energy G0 (h) S 2 � (h) S 8 (h) (h) S 9 S 7 (h) S 6 Suboptimal states (h) S 0 Minimum of free energy The minimum free energy and suboptimal structures on a discrete space of conformations
3'-end pseudoknot "H-type pseudoknot" "Kissing loops" 3'-end 5'-end 5'-end ··((((····· [[ ·))))····(((((·]] ·····))))) ··· Two classes of pseudoknots in RNA structures
3'-End 60 70 3'-End 5'-End 5'-End 50 70 20 60 10 10 50 20 30 40 30 40 End-on-end stacking of double helical regions yields the L-shape of tRNA phe
1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules
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
Criterion of Minimum Free Energy UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG Sequence Space Shape Space
Computed numbers of minimum free energy structures over different nucleotide alphabets P. Schuster, Molecular insights into evolution of phenotypes . In: J. Crutchfield & P.Schuster, Evolutionary Dynamics. Oxford University Press, New York 2003, pp.163-215.
Reference for postulation and in silico verification of neutral networks
Evolution in silico W. Fontana, P. Schuster, Science 280 (1998), 1451-1455
Criterion of Minimum Free Energy UUUAGCCAGCGCGAGUCGUGCGGACGGGGUUAUCUCUGUCGGGCUAGGGCGC GUGAGCGCGGGGCACAGUUUCUCAAGGAUGUAAGUUUUUGCCGUUUAUCUGG UUAGCGAGAGAGGAGGCUUCUAGACCCAGCUCUCUGGGUCGUUGCUGAUGCG CAUUGGUGCUAAUGAUAUUAGGGCUGUAUUCCUGUAUAGCGAUCAGUGUCCG GUAGGCCCUCUUGACAUAAGAUUUUUCCAAUGGUGGGAGAUGGCCAUUGCAG Sequence Space Shape Space
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
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
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. fk = ( f Sk ) Sequence space Real numbers Structure space The pre-image of the structure S k in sequence space is the neutral network G k
Step 00 Sketch of sequence space Random graph approach to neutral networks
Step 01 Sketch of sequence space Random graph approach to neutral networks
Step 02 Sketch of sequence space Random graph approach to neutral networks
Step 03 Sketch of sequence space Random graph approach to neutral networks
Step 04 Sketch of sequence space Random graph approach to neutral networks
Step 05 Sketch of sequence space Random graph approach to neutral networks
Step 10 Sketch of sequence space Random graph approach to neutral networks
Step 15 Sketch of sequence space Random graph approach to neutral networks
Step 25 Sketch of sequence space Random graph approach to neutral networks
Step 50 Sketch of sequence space Random graph approach to neutral networks
Step 75 Sketch of sequence space Random graph approach to neutral networks
Step 100 Sketch of sequence space Random graph approach to neutral networks
� � � U � -1 � � G = ( S ) | ( ) = I I S k k j j k � � (k) j / λ j = λ k = 12 27 = 0.444 , | G k | / κ - λ κ -1 ( 1) Connectivity threshold: cr = 1 - � � � AUGC Alphabet size : = 4 cr 2 0.5 GC,AU λ λ > network G k is connected cr . . . . k 3 0.423 GUC,AUG λ λ < network G k is not connected cr . . . . 4 0.370 k AUGC Mean degree of neutrality and connectivity of neutral networks
A connected neutral network formed by a common structure
Giant Component A multi-component neutral network formed by a rare structure
1. RNA structures 2. Neutrality in secondary structures 3. Compatibility and metastable structures 4. Some experiments with RNA molecules
Structure
3’-end C U G G G A A A A A U C C C C A G A C C G G G G G U U U C C C C G 5’-end G Structure Compatible sequence
3’-end C A A U G U A G G G C A A G C A A G C A U G C C C A U C C G C A G A A C G C C G G C G G C G G G C G U U C G U C C G C C U G C G 5’-end U U G Structure Compatible sequence
3’-end C A A U G A U G G G C A A G C A A G C A U C G C C A U C C C G A G Single nucleotides: A U G C , , , A A C G C C G G C G G C G G G C G U U G C U C C G C C U G C G 5’-end U U G Structure Compatible sequence Single bases pairs are varied independently
3’-end C A A U G A U G G G C A A G C A A G C A U C G C C A U C C AU , UA G C A G Base pairs: GC , CG A A C G C GU , UG C G G C G G C G G G C G U U G C U C C G C C U G C G 5’-end U U G Structure Compatible sequence Base pairs are varied in strict correlation
3’-end 3’-end C C A A A A U U G G U U A A G G G G G C G C A A A A G C G C A A A A G C G C A A U U C C G G C C C C A A U U C C C C G G C C A A G G A A A A C C G C G C C C G G G C G C G G G G C G U G G G G G C G C G U U U U C G C G U U C C C G C G C C C C U G U G C U G G 5’-end U 5’-end U U U G G Structure Compatible sequences
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