ENERGY LANDSCAPES AND FOLDING KINETICS OF PAIRWISE INTERACTING RNAS - - PowerPoint PPT Presentation

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Munich, Sept, 5 , 2016

ENERGY LANDSCAPES AND FOLDING KINETICS OF PAIRWISE INTERACTING RNAS

, Christoph Flamm , Ivo L. Hofacker Stefan Badelt1

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(1) DNA and Natural Algorithms Group, California Institute of Technology (2) Theoretical Biochemistry Group (tbi), University of Vienna

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OUTLINE

RNA modeling and RNA energy landscapes Coarse grained RNA folding kinetics Folding kinetics of RNA-RNA interactions Analysis of toehold-mediated interactions

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RNA STRUCTURE

GCGGAUUUAGCUCAGUUGGGAGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUCGAUCCACAGAAUUCGCACCA

1 10 20 30 40 50 60 70 G C G G A U U U A G C U C A G U U G G G A G A G C G C C A G A C U G A A G A U C U G G A G G U C C U G U G U U C G A U C C A C A G A A U U C G C A C C A 10 20 30 40 50 60 70 1

A secondary structure is a list of base pairs, where: A base may participate in at most one base pair Base pairs must not cross (no pseudoknots) Only isosteric base-pairs (GC, AU, GU) are allowed.

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THE NEAREST NEIGHBOR ENERGY MODEL

H: Hairpin loop I: Interior loop M: Multi loop E: Exterior loop H H M I I I I I

5' 3'

E I I

A C G G G C U G A C U U A A U U G U C G A G G A A A C C A U C U G C G C A U 10 20 30

5' 3'

E(s) = e(l) ∑

l∈s

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ENERGY LANDSCAPES

An energy landscape is defined by Conformation space Neighborhood relation [Move set] Energy function

s ∈ Ω M(s) E(s)

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ENERGY LANDSCAPES

free energy [kcal/mol]

Z = ∑s∈Ω e

−E(s) kT

G = −kT ln Z P(s) = e−E(s)/kT

Z

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ENERGY LANDSCAPES

Free energy

Christoph Flamm, Walter Fontana, Ivo L Hofacker, and Peter Schuster RNA folding at elementary step resolution. RNA, 6:325–338, 2000. Michael T. Wolfinger, Andreas Svrcek-Seiler, Christoph Flamm, Ivo L. Hofacker, and Peter F. Stadler. Efficient computation of RNA folding dynamics. Journal of Physics A: Mathematical and General, 37:4731–4741, 2004.

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... where is a constant to relate folding to wall-clock time KINETICS Calculate transition rates from energy barriers

Δ = E( ) − E( ) G‡ sj si = { kij k0 k0e− ΔG‡

RT

if Δ ≤ 0 G‡

• therwise

k0

• N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller. Equation of state

calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087–1092, 1953.

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free energy [kcal/mol]

α β

= P(i|α) kαβ ∑

i∈α ∑ j∈β

kij

THE CHEMICAL MASTER EQUATION

= ( (t) − (t) ) d (t) Pi dt ∑

i≠j

Pj kji Pi kij

... together with the rates of gradient basin transitions ...

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• 10.0
• 8.0
• 6.0
• 4.0
• 2.0

... can be solved for 60-80 nucleotides sequence length

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RNA-RNA INTERACTIONS are concentration dependent...

= = [AB] [A][B] KAB Z ′

AB

ZAZB

G A U A C C G U A G G A U A C G A U A C C G U A G C G U A G G A U A C C G U A G G A U A C C G U A G G A U A C C G U A G G A U A C C G U A G G A U A C C G U A G

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RNA-RNA INTERACTIONS are concentration dependent...

= = [AB] [A][B] KAB Z ′

AB

ZAZB

G A U A C C G U A G G A U A C G A U A C C G U A G C G U A G G A U A C C G U A G G A U A C C G U A G G A U A C C G U A G G A U A C C G U A G G A U A C C G U A G

LAB

LB

LA

L'AB

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DESIGN SEQUENCE PAIRS

C C G G U U U G U C U U U C G G U A A A C C G A 10 20

switch-RNA

C U C G G A A G G U A A A U C C 10

trigger-RNA

switch-RNA trigger-RNA

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DESIGN SEQUENCE PAIRS

10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

• ccupa ncy [m ol/l]

1m M switch-RNA 1m M trigge r-RNA

switch monomers trigger monomers switch/trigger dimers

C C G G U U U G U C U U U C G G U A A A C C G A 10 20

switch-RNA

C U C G G A A G G U A A A U C C 10

trigger-RNA

switch-RNA trigger-RNA

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DESIGN SEQUENCE PAIRS

10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

• ccupa ncy [m ol/l]

1m M switch-RNA 1m M trigge r-RNA

switch monomers trigger monomers switch/trigger dimers

2x random coil metastable state intramolecular equilibrium

C C G G U U U G U C U U U C G G U A A A C C G A 10 20

switch-RNA

C U C G G A A G G U A A A U C C 10

trigger-RNA

switch-RNA trigger-RNA

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RNA-RNA INTERACTIONS

toehold interactions

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G G G U G U G U A C C

refolding using a toehold Cliffhanger design

U A A A A C C C U U U U U C G G U U G A A C C G A A A A A C C C C U G G G G C

refolding without a toehold Conan design

A C G U A U A U U U U C C C C A A A A A C C C G U G G A U U U U G G A A A C C C G G G U G C

refolding with or without a toehold Hulk design

A C U G G G G G G G G G U U U A A A A A A U U G C C C C A C C U U A A U U U U U A A C C C

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10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0 0.2 0.4 0.6 0.8 1.0

• ccupa ncy [m ol/l]

1e 9 Cliffha nge r de sign: 1nM switch-RNA 1m M trigge r-RNA

C G G G U G G G U U G U G U A C A C G A A A C A C G G C C U A C U A C A U A A U U C A C U U C

C G G G U G G G U U G U G U A C A C G A A A C A C G G C C U A

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10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0 0.2 0.4 0.6 0.8 1.0

• ccupa ncy [m ol/l]

1e 9 Cona n de sign: 1nM switch-RNA 1m M trigge r-RNA

C G C A C C U U G U G G G U U U G G G A C A C C U G C G A G A

C G C A C C U U G U G G G U U U G G G A C A C C U G C G A G A A U U U C A A A U U C A C A A C

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10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0 0.2 0.4 0.6 0.8 1.0

• ccupa ncy [m ol/l]

1e 9 Hulk de sign: 1nM switch-RNA 1m M trigge r-RNA

C U G A G G U G G G G U A G G A U A A G A U U G C C C C A C A

C U G A G G U G G G G U A G G A U A A G A U U G C C C C A C A C C U U A U U C U A C C U U A A

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10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0 0.2 0.4 0.6 0.8 1.0

• ccupa ncy [m ol/l]

1e 9 Cliffha nge r de sign: 1nM switch-RNA 1m M trigge r-RNA

10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0 0.2 0.4 0.6 0.8 1.0

• ccupa ncy [m ol/l]

1e 9 Cona n de sign: 1nM switch-RNA 1m M trigge r-RNA

10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6

tim e [se conds]

0.0 0.2 0.4 0.6 0.8 1.0

• ccupa ncy [m ol/l]

1e 9 Hulk de sign: 1nM switch-RNA 1m M trigge r-RNA

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

• 18.0
• 16.0
• 14.0
• 12.0
• 10.0
• 8.0

0.7 1.4 3.1 3.1 0.8 0.8 0.8 0.8 2.6 2.6 3.5 2.2 0.8 2.4 3.5 1.2 0.8 0.6 0.8 0.8 1.0 1.3 0.7 1.0 1.3 0.799999 1.2 1.2 0.8 0.9 0.8 0.8 1.2 1.2 2.6 0.8 1.4 1.7 0.8 0.8 0.7 1.2 1.1 0.7 0.8 0.6 0.8 1.5 1.0 3.0 3.5 3.1 0.8 1.9 1.3 1.3 0.8 0.7 1.0 1.3 0.8 1.6 1.5 4.2 0.8 1.9 2.0 1.9 1.4 1.2 1.0 0.599999 2.0 2.3 2.6 1.5 1.3 2.6 2.3 2.9 2.0 2.6 0.7 1.3 2.42.8 1.2 1.2 0.8 2.3 1.3 1.1 2.3 1.2 2.6 2.6 3.0 2.8 2.3 4.4 4.2 3.9 2.8 3.5 0.7 0.7 3.7 3.9

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THANKS TO

Coworkers: Ivo L. Hofacker, Christoph Flamm ViennaRNA package: Ronny Lorenz

Stefan Badelt, PhD Thesis, University of Vienna, (2016) "Control of RNA function by conformational design." This research was funded in parts by the FWF International Programme I670, the DK RNA program FG748004 and the FWF project "SFB F43 RNA regulation of the transcriptome".

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THE TBI

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RNA-RNA INTERACTIONS

LA LB LAB L'AB

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RNA-RNA INTERACTIONS

LA LB LAB L'AB

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