Designing RNA Structures

Transcription

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2 Designing RN Structures From Theoretical Models to Real Molecules Peter Schuster Institut für Theoretische hemie und Molekulare Strukturbiologie der niversität Wien Microbiology Seminar Mount Sinai School of Medicine,

3 WebPage for further information:

4 1. RN structures 2. Neutrality in secondary structures 3. ompatibility and metastable structures 4. Some experiments with RN molecules

5 1. RN structures 2. Neutrality in secondary structures 3. ompatibility and metastable structures 4. Some experiments with RN molecules

6 O 5' end H 2 O N 1 5'end 3 end O OH N k =,,, O P O H 2 O N 2 Na O O OH O P O H 2 O N 3 3'end Na O 5 end Definition of RN structure O O P OH O H 2 O N 4 70 Na O O OH O Na P O O 3' end

7 Sequence 5'End DDMYMTP 3'End 3'End 5'End 70 Secondary structure Symbolic notation 5'End 3'End symbolic notation of RN secondary structure that is equivalent to the conventional graphs

8 Definition and physical relevance of RN secondary structures RN secondary structures are listings of Watsonrick and wobble base pairs, which are free of knots and pseudokots. D.Thirumalai, N.Lee, S..Woodson, and D.K.Klimov. nnu.rev.phys.hem. 52: (2001): Secondary structures are folding intermediates in the formation of full threedimensional structures.

9 Å 54.4 = Å 56.2 Watsonrick type base pairs

10 O N N O N H H N O N = N H H Deviation from Watsonrick geometry O N N H O N = O H N H N N N Deviation from Watsonrick geometry H Wobble base pairs

11 RN sequence RN folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Biophysical chemistry: thermodynamics and kinetics Empirical parameters Inverse folding of RN: Biotechnology, design of biomolecules with predefined structures and functions RN structure of minimal free energy Sequence, structure, and design

12 5 end 3 end S 5 (h) S 4 (h) S 3 (h) Free energy 0 S 6 (h) S 7 (h) S 8 (h) S 2 (h) S 9 (h) S 1 (h) Suboptimal states (h) S 0 Minimum of free energy The minimum free energy and suboptimal structures on a discrete space of conformations

13 3'end pseudoknot "Htype pseudoknot" "Kissing loops" 5'end 3'end 5'end (((( [[ )))) ((((( ]] ))))) Two classes of pseudoknots in RN structures

14 3'End 5'End 'End 50 5'End Endonend stacking of double helical regions yields the Lshape of trn phe

15 1. RN structures 2. Neutrality in secondary structures 3. ompatibility and metastable structures 4. Some experiments with RN molecules

16 RN sequence RN folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Biophysical chemistry: thermodynamics and kinetics Empirical parameters Inverse folding of RN: Biotechnology, design of biomolecules with predefined structures and functions RN structure of minimal free energy Sequence, structure, and design

17 riterion of Minimum Free Energy Sequence Space Shape Space

18 omputed numbers of minimum free energy structures over different nucleotide alphabets P. Schuster, Molecular insights into evolution of phenotypes. In: J. rutchfield & P.Schuster, Evolutionary Dynamics. Oxford niversity Press, New York 2003, pp

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20 Reference for postulation and in silico verification of neutral networks

21 Evolution in silico W. Fontana, P. Schuster, Science 280 (1998),

22 riterion of Minimum Free Energy Sequence Space Shape Space

23 TTTTTTTTTTTTTTT... TTTTTTTTTTTTTT... Hamming distance d (I,I ) = H (i) (ii) (iii) d (I,I) = 0 H 1 1 d (I,I) = d (I,I) H 1 2 H 2 1 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

24 Hamming distance d (S,S ) = H (i) (ii) (iii) d (S,S) = 0 H 1 1 d (S,S ) = d (S,S ) H 1 2 H 2 1 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

25 S k = ψ( I. ) f k = fs ( k ) Sequence space Structure space Real numbers Mapping from sequence space into structure space and into function

26 S k = ψ( I. ) f k = fs ( k ) Sequence space Structure space Real numbers

27 S k = ψ( I. ) f k = fs ( k ) Sequence space Structure space Real numbers The preimage of the structure S k in sequence space is the neutral network k

28 Step 00 Sketch of sequence space Random graph approach to neutral networks

29 Step 01 Sketch of sequence space Random graph approach to neutral networks

30 Step 02 Sketch of sequence space Random graph approach to neutral networks

31 Step 03 Sketch of sequence space Random graph approach to neutral networks

32 Step 04 Sketch of sequence space Random graph approach to neutral networks

33 Step 05 Sketch of sequence space Random graph approach to neutral networks

34 Step 10 Sketch of sequence space Random graph approach to neutral networks

35 Step 15 Sketch of sequence space Random graph approach to neutral networks

36 Step 25 Sketch of sequence space Random graph approach to neutral networks

37 Step 50 Sketch of sequence space Random graph approach to neutral networks

38 Step 75 Sketch of sequence space Random graph approach to neutral networks

39 Step 100 Sketch of sequence space Random graph approach to neutral networks

40 1 k k j j k = ( S) I ( I) = S λ j = 12 / 27 = 0.444, λ k = (k) j k onnectivity threshold: / κ λcr = 1 κ 1 ( 1) λ λ lphabet size : = 4 > λ k cr.... < λ k cr.... network k is connected network k is not connected cr ,, Mean degree of neutrality and connectivity of neutral networks

41 connected neutral network formed by a common structure

42 iant omponent multicomponent neutral network formed by a rare structure

43 1. RN structures 2. Neutrality in secondary structures 3. ompatibility and metastable structures 4. Some experiments with RN molecules

44 Structure

45 3 end 5 end Structure ompatible sequence

46 ompatible sequence Structure 5 end 3 end

47 ompatible sequence Structure 5 end 3 end Single nucleotides:,,, Single bases pairs are varied independently

48 ompatible sequence Structure 5 end 3 end Base pairs:,,, Base pairs are varied in strict correlation

49 ompatible sequences Structure 5 end 5 end 3 end 3 end

50 Structure Incompatible sequence 5 end 3 end

51 Structure S k Neutral Network k k k ompatible Set k The compatible set k of a structure S k consists of all sequences which form S k as its minimum free energy structure (the neutral network k ) or one of its suboptimal structures.

52 Structure S 0 Structure S 1 The intersection of two compatible sets is always non empty: 0 1

53 Reference for the definition of the intersection and the proof of the intersection theorem

54 3.30 S 10 S S 9 8 S S 7 5 S 6 S 4 S 3 S S 1 S 0 S 1 S 0 suboptimal structures Suboptimal structures metastable Kinetic folding stable n RN molecule with two (meta)stable conformations

55 3.30 S 10 S S 9 8 S S 7 5 S 6 S 4 S 3 S S 1 S 0 S 1 S 0 suboptimal structures Suboptimal structures metastable Kinetic folding stable n RN molecule with two (meta)stable conformations

56 Kinetics of RN refolding between a long living metastable conformation and the minmum free energy structure

57 1. RN structures 2. Neutrality in secondary structures 3. ompatibility and metastable structures 4. Some experiments with RN molecules

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60 Structure S 0 Structure S 1 The intersection of two compatible sets is always non empty: 0 1

61 ribozyme switch E..Schultes, D.B.Bartel, Science 289 (2000),

62 Two ribozymes of chain lengths n = 88 nucleotides: n artificial ligase () and a natural cleavage ribozyme of hepatitis virus (B)

63 The sequence at the intersection: n RN molecules which is 88 nucleotides long and can form both structures

64 Two neutral walks through sequence space with conservation of structure and catalytic activity

65 Sequence of mutants from the intersection to both reference ribozymes

66 J.H.. Nagel,. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and.w.. Pleij. Structural parameters affecting the kinetic competition of RN hairpin formation, in press J.H.. Nagel, J. MøllerJensen,. Flamm, K.J. Öistämö, J. Besnard, I.L. Hofacker,.P. ultyaev, M.H. de Smit, P. Schuster, K. erdes and.w.. Pleij. The refolding mechanism of the metastable structure in the 5 end of the hok mrn of plasmid R1, submitted 2004.

67 B ' 5' 3' 3' B B kcal mol kcal mol 1 J.H.. Nagel,. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and.w.. Pleij. JN2 Structural parameters affecting the kinetic competition of RN hairpin formation, in press 2004.

68 K T1D l 5 T1 V1 T2 K T K T K T T SS 30 K T1D l 5 5 hairpin 3 hairpin T1 V1 T2 T1 V1 T2 5 5 K T1D l Loop B 15 Loop B Loop B 15 Loop B SS JN2 JN2 small fragments

69 1D R 2D J.H.. Nagel,. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and.w.. Pleij. 1D 2D / 3 44 R 23 5' kcal mol kcal mol 1 JN1LH R 23 / 13 1D 2D ' kcal mol kcal mol 1 Structural parameters affecting the kinetic competition of RN hairpin formation, in press 2004.

70 K T1D l 5 T1 V1 T2 K T K T K T T T1 3 h 5 Loop2D Loop R Loop1D J1LH sequencing gels

71 Free energy [kcal / mole] J1LH barrier tree

72 hokxl nascent transcript 3' SD SD I II 5' 5' ucb tac sokt mok hok J.H.. Nagel, J. MøllerJensen,. Flamm, K.J. Öistämö, J. Besnard, I.L. Hofacker,.P. ultyaev, M.H. de Smit, P. Schuster, K. erdes and.w.. Pleij. The refolding mechanism of the metastable structure in the 5 end of the hok mrn of plasmid R1, submitted 2004.

73 3' ucb II 5' I tac metastable pseudoknot 3' 5' ucb I II tac stable Refolding of the 5 end of the hokxl mrn

74 tac I II 3 ucb 5' metastable tac I 5' ucb 3'.. predicted saddle point..... stable tac 5' 3 ucb Transition from the metastable to the stable comformation

75 hok mrn XL SD 3' 5' I II mok ucb partial stem tac tac FL Tr fbi sokt SD hok 125 nts Truncated, refolded mrn hok I II 3' 5' SD hok ucb tac tac stem sokt SD mok 125 nts

76 RN 9: , 2003 Evidence for neutral networks and shape space covering

77 Evidence for neutral networks and intersection of apatamer functions

78 cknowledgement of support Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No , 10578, 11065, , and niversität Wien Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat7813 European ommission: Project No. E Siemens, ustria The Santa Fe Institute and the niversität Wien The software for producing RN movies was developed by Robert iegerich and coworkers at the niversität Bielefeld

79 oworkers Walter Fontana, Santa Fe Institute, NM niversität Wien hristian Reidys, hristian Forst, Los lamos National Laboratory, NM Peter Stadler, Bärbel Stadler, niversität Leipzig, E Ivo L.Hofacker, hristoph Flamm, niversität Wien, T ndreas Wernitznig, Michael Kospach, niversität Wien, T lrike Langhammer, lrike Mückstein, Stefanie Widder Jan upal, Kurt rünberger, ndreas SvrčekSeiler, Stefan Wuchty lrike öbel, Institut für Molekulare Biotechnologie, Jena, E Walter rüner, Stefan Kopp, Jaqueline Weber

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