[PPT] - RNA Bioinformatics Beyond the One Sequence-One Structure Paradigm PowerPoint Presentation

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RNA Bioinformatics Beyond the One Sequence-One Structure Paradigm Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

2008 Molecular Informatics and Bioinformatics Collegium Budapest, 27.– 29.03.2008

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

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1. Computation of RNA equilibrium structures 2. Inverse folding and neutral networks 3. Evolutionary optimization of structure 4. Suboptimal conformations and kinetic folding

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1. Computation of RNA equilibrium structures

2. Inverse folding and neutral networks 3. Evolutionary optimization of structure 4. Suboptimal conformations and kinetic folding

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O CH2 OH O O P O O O

N1

O CH2 OH O P O O O

N2

O CH2 OH O P O O O

N3

O CH2 OH O P O O O

N4

N A U G C

k =

, , ,

3' - end 5' - end Na Na Na Na

5'-end 3’-end

GCGGAU AUUCGC UUA AGUUGGGA G CUGAAGA AGGUC UUCGAUC A ACCA GCUC GAGC CCAGA UCUGG CUGUG CACAG

Definition of RNA structure

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N = 4n NS < 3n Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _ {AU,CG,GC,GU,UA,UG} A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

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Conventional definition of RNA secondary structures

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H-type pseudoknot

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j n n j j n n

S S S S

− − = − +

⋅ + =

∑

1 1 1 1

Counting the numbers of structures of chain length n n+1

M.S. Waterman, T.F. Smith (1978) Math.Bioscience 42:257-266

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Restrictions on physically acceptable mfe-structures: 3 and 2

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Size restriction of elements: (i) hairpin loop (ii) stack

σ λ ≥ ≥

stack loop

n n

⎣ ⎦

∑ ∑

+ − − = + − + − − + = + − + − + +

Ξ = Φ ⋅ Φ + = Ξ Φ + Ξ =

2 / ) 1 ( 1 1 2 1 2 2 2 1 1 1 1 1 λ σ σ λ m k k m m m k k m k m m m m m

S S S Sn # structures of a sequence with chain length n

Recursion formula for the number of physically acceptable stable structures

I.L.Hofacker, P.Schuster, P.F. Stadler. 1998. Discr.Appl.Math. 89:177-207

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RNA sequence: GUAUCGAAAUACGUAGCGUAUGGGGAUGCUGGACGGUCCCAUCGGUACUCCA

Empirical parameters Biophysical chemistry: thermodynamics and kinetics RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function

Sequence, structure, and design

RNA structure

f minimal free

energy

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S1

(h)

S9

(h)

F r e e e n e r g y G

Minimum of free energy

Suboptimal conformations

S0

(h) S2

(h)

S3

(h)

S4

(h)

S7

(h)

S6

(h)

S5

(h)

S8

(h)

The minimum free energy structures on a discrete space of conformations

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Elements of RNA secondary structures as used in free energy calculations

L

∑ ∑ ∑ ∑

+ + + + = ∆

loops internal bulges loops hairpin pairs base

f

stacks , 300

) ( ) ( ) (

i b l kl ij

n i n b n h g G

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Maximum matching

An example of a dynamic programming computation of the maximum number of base pairs Back tracking yields the structure(s).

i i+1 i+2 k Xi,k-1 j-1 j Xk+1,j j+1 [ k+1,j ] [i,k-1]

( ) { }

1 , , 1 1 , 1 , 1 ,

) 1 ( max , max

+ + − − ≤ ≤ +

+ + =

j k j k k i j k i j i j i

X X X X ρ

j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 i G G C G C G C C C G G C G C C 1 G * * 1 1 1 1 2 3 3 3 4 4 5 6 6 2 G * * 1 1 2 2 2 3 3 4 4 5 6 3 C * * 1 1 1 2 3 3 3 4 5 5 4 G * * 1 1 2 2 2 3 4 5 5 5 C * * 1 1 2 2 3 4 4 4 6 G * * 1 1 1 2 3 3 3 4 7 C * * 1 2 2 2 2 3 8 C * * 1 1 1 2 2 2 9 C * * 1 1 2 2 2 10 G * * 1 1 1 2 11 G * * 1 1 12 C * * 1 13 G * * 1 14 C * * 15 C *

Minimum free energy computations are based on empirical energies

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1. Computation of RNA equilibrium structures

2. Inverse folding and neutral networks

3. Evolutionary optimization of structure 4. Suboptimal conformations and kinetic folding

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RNA sequence: GUAUCGAAAUACGUAGCGUAUGGGGAUGCUGGACGGUCCCAUCGGUACUCCA

RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Inverse Folding Algorithm Iterative determination

f a sequence for the

given secondary structure

RNA structure

f minimal free

energy

Inverse folding of RNA: Biotechnology, design of biomolecules with predefined structures and functions

Sequence, structure, and design

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Compatibility of sequences and structures

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Compatibility of sequences and structures

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Inverse folding algorithm I0 I1 I2 I3 I4 ... Ik Ik+1 ... It S0 S1 S2 S3 S4 ... Sk Sk+1 ... St Ik+1 = Mk(Ik) and dS(Sk,Sk+1) = dS(Sk+1,St) - dS(Sk,St) < 0 M ... base or base pair mutation operator dS (Si,Sj) ... distance between the two structures Si and Sj ‚Unsuccessful trial‘ ... termination after n steps

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Approach to the target structure Sk in the inverse folding algorithm

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The inverse folding algorithm searches for sequences that form a given RNA secondary structure under the minimum free energy criterion.

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A mapping and its inversion

Gk =

( ) | ( ) =

1

U

S

I S

k j j k

I

( ) = I S

j k Space of genotypes: = { I

S I I I I I S S S S S

1 2 3 4 N 1 2 3 4 M

, , , , ... , } ; Hamming metric Space of phenotypes: , , , , ... , } ; metric (not required) N M = {

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1. Computation of RNA equilibrium structures 2. Inverse folding and neutral networks

3. Evolutionary optimization of structure

4. Suboptimal conformations and kinetic folding

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Phenylalanyl-tRNA as target structure Structure of andomly chosen initial sequence

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