Kinetic Folding of RNA and the Design of Molecules with Predefined - PowerPoint PPT Presentation

Kinetic Folding of RNA and the Design of Molecules with Predefined Secondary Structures Peter Schuster Institut für Theoretische Chemie und Molekulare Strukturbiologie der Universität Wien Gunnar and Gunnel Källén Memorial Lecture Lund University, 10.– 11.05.2004

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

RNA as adapter molecule RNA is the catalytic subunit in RNA as scaffold for supramolecular RNA as transmitter of genetic information supramolecular complexes complexes DNA transcription ... CUG ... ...AGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUC... leu GAC messenger- RNA genetic code translation protein ribosome RNA as working copy of genetic information ? ? ? ? ? RNA as catalyst RNA RNA is modified by epigenetic control RNA editing Alternative splicing of messenger RNA ribozyme RNA as regulator of gene expression RNA as carrier of genetic information The RNA world as a precursor of RNA viruses and retroviruses the current DNA + protein biology RNA as information carrier in evolution in vitro and evolutionary biotechnology Functions of RNA molecules gene silencing by small interfering RNAs

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

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 .“

Stacking of free nucleobases or other planar heterocyclic compounds (N6,N9-dimethyl-adenine) The stacking interaction as driving force of structure Stacking of nucleic acid single strands (poly-A) formation in nucleic acids

James D. Watson and Francis H.C. Crick Nobel prize 1962 1953 – 2003 fifty years double helix Stacking of base pairs in nucleic acid double helices (B-DNA)

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 Sequence, structure, and function

5’-end 3’-end A C C (h) S 5 (h) U S 3 G C (h) A S 4 U A U (h) U G S 1 (h) S 2 C G (h) S 8 � 0 G C (h) Free energy G (h) S 9 S 7 A U A A A C C (h) U S 6 A U G G C Suboptimal conformations 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

How to compute RNA secondary structures Efficient algorithms based on dynamic programming are available for computation of minimum free energy and many suboptimal secondary structures for given sequences. M.Zuker and P.Stiegler. Nucleic Acids Res . 9 :133-148 (1981) M.Zuker, Science 244 : 48-52 (1989) Equilibrium partition function and base pairing probabilities in Boltzmann ensembles of suboptimal structures. J.S.McCaskill. Biopolymers 29 :1105-1190 (1990) The Vienna RNA Package provides in addition: inverse folding (computing sequences for given secondary structures), computation of melting profiles from partition functions, all suboptimal structures within a given energy interval, barrier tress of suboptimal structures, kinetic folding of RNA sequences, RNA-hybridization and RNA/DNA-hybridization through cofolding of sequences, alignment, etc.. I.L.Hofacker, W. Fontana, P.F.Stadler, L.S.Bonhoeffer, M.Tacker, and P. Schuster. Mh.Chem . 125 :167-188 (1994) S.Wuchty, W.Fontana, I.L.Hofacker, and P.Schuster. Biopolymers 49 :145-165 (1999) C.Flamm, W.Fontana, I.L.Hofacker, and P.Schuster. RNA 6 :325-338 (1999) Vienna RNA Package : http://www.tbi.univie.ac.at

hairpin loop hairpin hairpin loop loop stack free stack stack joint end stack bulge free end free end stack internal loop stack hairpin loop hairpin loop multiloop hairpin loop stack stack stack Elements of RNA secondary structures free free as used in free energy calculations end end

5’-end 3’-end A C C U G C A U A U U G C G G C A U A A A C C U A U G G free energy of stacking < 0 C C A G G U U U G G G A C C A U G A G G G C U G ∑ ∑ ∑ ∑ ∆ = + + + + 300 G g h ( n ) b ( n ) i ( n ) L 0 ij , kl l b i stacks of hairpin bulges internal base pairs loops loops Folding of RNA sequences into secondary structures of minimal free energy, � G 0 300

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

Minimal hairpin loop size: n lp � 3 Minimal stack length: n st � 2 Recursion formula for the number of acceptable RNA secondary structures

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.

� � � � T = 0 K , t T > 0 K , t T > 0 K , t finite 3.30 3.40 3.10 49 48 47 46 45 2.80 44 42 43 41 40 38 39 y 37 36 35 34 33 32 g 31 30 29 r 28 27 e 25 2.60 26 24 23 22 n 21 E 20 19 3.10 18 S 10 17 16 15 13 e 14 S 8 12 e 3.40 2.90 S 9 11 r 10 9 S 7 F 5.10 S 5 3.00 S 6 8 7 6 5 S 4 4 S 3 3 7.40 S 2 2 5.90 S 1 S 0 S 0 S1 S0 Minimum Free Energy Structure Suboptimal Structures Kinetic Structures Different notions of RNA structure including suboptimal conformations and folding kinetics

Suboptimal RNA Secondary Structures Michael Zuker. On finding all suboptimal foldings of an RNA molecule . Science 244 (1989), 48-52 Stefan Wuchty, Walter Fontana, Ivo L. Hofacker, Peter Schuster. Complete suboptimal folding of RNA and the stability of secondary structures. Biopolymers 49 (1999), 145-165

3' Total number of structures including all suboptimal conformations, stable 5' and unstable (with � G 0 >0): #conformations = 1 416 661 Minimum free energy structure AAAGGGCACAGGGUGAUUUCAAUAAUUUUA Sequence Example of a small RNA molecule: n=30

Density of stares of suboptimal structures of the RNA molecule with the sequence: AAAGGGCACAGGGUGAUUUCAAUAAUUUUA

Partition Function of RNA Secondary Structures John S. McCaskill . The equilibrium function and base pair binding probabilities for RNA secondary structure . Biopolymers 29 (1990), 1105-1119 Ivo L. Hofacker, Walter Fontana, Peter F. Stadler, L. Sebastian Bonhoeffer, Manfred Tacker, Peter Schuster. Fast folding and comparison of RNA secondary structures. Monatshefte für Chemie 125 (1994), 167-188

3' 5' Example of a small RNA molecule with two low-lying suboptimal conformations which contribute substantially to the partition function UUGGAGUACACAACCUGUACACUCUUUC Example of a small RNA molecule: n=28

U U G G A G U A C A C A A C C U G U A C A C U C U U U C C U U C U U U C U C A C A U G U C C A A C A C A U G A G G U U U U G G A G U A C A C A A C C U G U A C A C U C U U U C U C C U G G A U U A second suboptimal configuration C G A U ∆ E = 0.55 kcal / mole 0 →2 U A G C U A C C A C A C U U first suboptimal configuration U C ∆ E = 0.50 kcal / mole U → G G A G 0 1 C C U U A A U U G A U A C A C C A C C 3' U U U C U U U G G A G U C 5' C A minimum free energy A configuration U A G C � G = - 5.39 kcal / mole 0 U A C C A A C U U G G A G U A C A C A A C C U G U A C A C U C U U U C „Dot plot“ of the minimum free energy structure ( lower triangle ) and the partition function ( upper triangle ) of a small RNA molecule (n=28) with low energy suboptimal configurations

GCGGAU UUA GCUC AGUUGGGA GAGC G CCAGA CUGAAGA UCUGG AGGUC CUGUG UUCGAUC CACAG A AUUCGC ACCA GCGGAU UUA GCUC AGDDGGGA GAGC M CCAGA CUGAAYA UCUGG AGMUC CUGUG TPCGAUC CACAG A AUUCGC ACCA Phenylalanyl-tRNA as an example for the computation of the partition function

G first suboptimal configuration ∆ 0 E = 0.43 kcal / mole → 1 3’ 5’ tRNA phe without modified bases