BarMap & SundialsWrapper advanced RNA folding kinetics Stefan Badelt Institute for Theoretical Chemistry Theoretical Biochemistry Group stef@tbi.univie.ac.at February 17, 2015 1
Outline – BarMap.pm & SundialsWrapper.pm Two libraries . . . • BarMap.pm – interface to RNA folding kinetics on static landscapes – kinetics on time-varying energy landscapes • SundialsWrapper.pm – solving arbitrary CRNs using the Sundials CVODE C -library BarMap.pm barriers RNAsubopt treekin SEQUENCE 0.8 0.6 0.4 0.2 0 1 100 10000 1e+06 1e+08 Time/a.u. Sundials CVODE 0.8 0.6 0.4 SundialsWrapper.pm 0.2 0 1 100 10000 1e+08 1e+06 Time/a.u. 2
Outline – BarMap.pm & SundialsWrapper.pm Two libraries . . . • BarMap.pm – interface to RNA folding kinetics on static landscapes – kinetics on time-varying energy landscapes • SundialsWrapper.pm – solving arbitrary CRNs using the Sundials CVODE C -library . . . and many tools: • BarMapSimulator.pl – simulations on time-varying energy landscapes • interkin.pl – kinetics of (multiple) pairwise interacting RNAs • transkin.pl – co-transcriptional folding of long RNA molecules • . . . 2
BarMap library • BarMapSimulator.pl – kinetics on time-varying energy landscapes RNAsubopt barriers SEQUENCE treekin 1 0,8 occupancy 0,6 BarMap.pm 0,4 SEQUENCE 0,2 0 5000 10000 15000 20000 25000 time Ivo L. Hofacker, Christoph Flamm, Christian Heine, Michael T. Wolfinger, Gerik Scheuermann, and Peter F. Stadler, BarMap: RNA folding on dynamic energy landscapes , RNA, (2010) 3
BarMap and co-transcriptional folding 1 0,8 0,6 0,4 0,2 0 500 1000 1500 2000 2500 4
BarMap and co-transcriptional folding BarMap Simulation co-transcriptional folding 1 0,8 Population Density 0,6 0,4 0,2 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 Time [seconds] 4
BarMap including ligand interactions BarMap Simulation (no Theophylline) 1 X A, B Structure A Structure B Structure X 0.8 Population Density 0.6 0.4 0.2 -4.0 2.901 2.901 0 -6.0 2.0 0.01 0.1 1 10 100 1000 10000 Time [seconds] 1.4 -8.0 2.6 BarMap Simulation 2.2 1.4 3.4 2.5 2.5 8.86 9.16 2.0 (+ Theophylline) -10.0 1 3.2 3.3 8.36 2.8 2.2 2.0 1.4 -12.0 Structure A 2.6 Structure B 9.16 6.56 Structure X -14.0 3.6 2.8 2.8 3.96 0.8 3.9 3.9 2.8 2.8 3.3 3.3 -16.0 x 2.2 2.2 3.4 3.4 2.2 1.4 Population Density -18.0 3.4 2.5 2.5 0.6 1.6 1.6 3.5 3.2 3.5 -20.0 3.7 6.6 3.7 0.4 -22.0 6.1 6.1 -24.0 x 0.2 -26.0 2.1 2.2 2.1 2.2 -28.0 0 0.01 0.1 1 10 100 1000 10000 Time [seconds] Stefan Badelt, Stefan Hammer, Christoph Flamm, and Ivo L. Hofacker, Thermodynamic and kinetic folding of riboswitches , Methods in Enzymology, Elsevier, in press. Manja Wachsmuth, Sven Findeiß, Nadine Weissheimer, Peter F. Stadler and Mario M¨ orl, De novo design of a synthetic riboswitch that regultes termination transcription , NAR, (2012) 5
SundialsWrapper libary • SundialsWrapper.pm – solving arbitrary CRNs using the Sundials CVODE C -library ❇ ✞ � ✗ ✞ ✖ ✳ ✖ ♠ RNAsubopt barriers treekin SEQUENCE 0.8 0.6 0.4 0.2 0 1 100 10000 1e+06 1e+08 Time/a.u. Sundials CVODE t �✁✁✂ ✄☎✆ ❈ ✌✍✎ ✏ ✆ 0.8 ✥ ✝ ✞✟ t ✥ ✟ ✡✠ ✑ ✁� ☛ ☞ lar 0.6 ✥ ✄☎t � ✞ ✥ ♠ ✠✡ ✁ ✥ ✞ � ✒ ✄t � ✞ � ❛ ❈ ✓ ✔ ✟ ✁ tics ☛ ☞ lar 0.4 ✥ ✡✠☛ ✞✡ ✂ ✄☎ ✥ ✄☎t � ✞✥♠ ✠✡ ✁ Sundi ✞✡✟ ✕ rapper ☛ ☞ lar ✳ ✖ ♠ ✄☎t ✁� ✁ 0.2 ✥ ✥♠ ✠✡ 0 1 100 10000 1e+06 1e+08 Time/a.u. 6
SundialsWrapper libary • SundialsWrapper.pm – solving arbitrary CRNs using the Sundials CVODE C -library ✼ ✧ ✙ ✽ ✧ ✻ ✺ ✻ ✩ RNAsubopt barriers treekin SEQUENCE 0.8 0.6 0.4 0.2 0 1 100 10000 1e+06 1e+08 Time/a.u. Sundials CVODE ✘ ✙✚✚✛ ✜✢✣ ✮ ✯✰✱ ✲ ✣ 0.8 ✤ ✦ ✧★ ✘ ✤ ★ ✫✪ ✴ ✚✙ ✬ ✭ lar 0.6 ✤ ✜✢✘ ✙ ✧ ✤ ✩ ✪✫ ✚ ✤ ✧ ✙ ✵ ✜✘ ✙ ✧ ✙ ✶ ✮ ✷ ✸ ★ ✚ tics ✬ ✭ lar 0.4 ✤ ✫✪✬ ✧✫ ✛ ✜✢ ✤ ✜✢✘ ✙ ✧✤✩ ✪✫ ✚ Sundi ✧✫★ ✹ rapper ✬ ✭ lar ✺ ✻ ✩ ✜✢✘ ✚✙ ✚ 0.2 ✤ ✤✩ ✪✫ 0 1 100 10000 1e+06 1e+08 Time/a.u. 6
interkin.pl kinetics of interacting molecules • compute intra-molecular rates for each monomer • compute intra-molecular rates for all interacting dimers • compute transition rates between monomers and dimers A+B <=> AB barr barriers -- A,B,AB barriers -- AB 7
RNAfolding of interacting molecules A+B <=> AB 0,001 population density [mol/L] 0,0008 A C G A UG CC C G U A A U 0,0006 G C G C C G U A G A U A U U 0,0004 0,0002 0 1 1e+05 1e+10 arbitrary time units 8
RNAfolding of interacting molecules A+A <=> AA, B+B <=> BB, A+B <=> AB 0,001 population density [mol/L] 0,0008 A C G A UG CC C G U A A U 0,0006 G C G C C G U A G A U A U U 0,0004 G C A U G G U C A U C A U G G U A C U A 0,0002 C U G G U A C G 0 1 1e+05 1e+10 arbitrary time units 8
transkin.pl co-transcriptional folding of large RNAs S = () for each RNAsequence of the growing chain 1 s = MFE-structure of current sequence, unless s ∈ S { S = S + s compute refolding rates to all currently populated structures } 2 simulate CRN using SundialsWrapper 9
transkin.pl co-transcriptional folding of large RNAs cotranscriptional folding (843nt) 1 G A C U C U G U U U A U U A G G U C GA U U A A A G U A U G G G U A C A A G C G U U A A U A A C G C C G U U CA A A G G U A G C C U G A G U A C C A U G A A G C A G C U G G C U A G C C C G GG C UG C C U G A A C U G C C G G G U U A A G A GG G C C G C G C G A U C U C A G A A U U G G C C G A U C C C G G 0,8 U G U A G G C C C C G C G G C C U A U A C U A G U A C U G U A G U U G A C U G G C C C C G G C A G A U U AU G A U G C A U G U C G A G G C C C A U A U A C C G G G C G U A C G U U G G U C U A G G C C U U G C A U A C G C U A A G C G C C G G C A A U U G A C U G U C A 0,6 U G U G G G C U A U U G G A C U U G C G C G C G occupancy U U A G G G U C U C U G G U U A U A C G C G C G A A U U G G C C A U C G C G C U A U C G A C G G G G A A U A U G U A C C G G G C C G U A A U G U C G A A U U C C G G A G C U A C U G C A U G C A G U A C A G C G C U GC 0,4 G U C A G C C G U C A G U A A U A G C U C G U G A G U U A C C A U A A C G C U G G C C G A A U U A G C U U U A G C U A G A G C U G U A U C C G G G C G C G G C C A U G C C A G U C G G U A U G C C A U C G A U U G C U A U G U A C C G U G G CG G C U G G A U C A G U C 0,2 U A U G A C U G C G G C U C A G G G A C C G U C A G C G C G G C U G U C G U A U U A G C U U G A U A U U C G A G G A C A UC A A U U A U A U G A C A G U U U U U A A U U A A U U A A G U G C C G G U C U G U C U A A U U C G G C C A U U A A A G U G A A U U G A C A A A U U C G C A G U C U U U C A C U G C U U G A A U A A U U U A C G A U G U A U A C A G U A G C A G U A A C C U A G A U A A U U G G U A C G U A U C A A C U G G U A U U U G A G A U U A 0 G A C U A A U U A U U U U AA U G C A U G U U U A G G A U A A A C U A U U A A U C G G A A A AU A A A A U G G U A G C U A A G C A U G A G 0,01 0,1 1 10 U C C U A G A A time [s] 9
thanks to Design Projects: This work –XOR riboswitches Ivo L. Hofacker Peter F. Stadler Christoph Flamm Mario M¨ orl Regula Arreger Gesine Domin –RNAprions Sabine M¨ uller Sonja Petkovic –co-transc. folding of 3’ UTRs Andrea Tanzer Michael T. Wolfinger Michael Jantsch Konstantin Licht ... and the whole TBI group Mansoureh Tajaddod The research was funded by the Austrian Science Fund (FWF): W1207-B09, I670-B11 10
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