Computational design of a circular RNA with prion-like behavior Stefan Badelt 1 , Christoph Flamm 1 and Ivo L. Hofacker 1 , 2 { stef,xtof,ivo } @tbi.univie.ac.at 1 Institute for Theoretical Chemistry , University of Vienna, W¨ ahringerstraße 17/3, A-1090 Vienna, Austria 2 Research Group Bioinformatics and Computational Biology , University of Vienna, W¨ ahringerstraße 29, A-1090 Vienna, Austria Oct 07, 2014 1
Prions and conformational self-replication Prions are proteins known to be the infectious agents for several neurological diseases (e.g. Altzheimer, Creuzfeld-Jakob, ...) The “ protein only hypothesis ” states that a single mis-folded infectious prion can convert the other correctly folded proteins to the infectious agent. PrP + N N C C PrP C PrP C + N N C C N N N N PrP C PrP Sc PrP C -PrP Sc PrP Sc -PrP Sc dimer PrP Sc oligomer heterodimer PrP Sc protofibril PrP Sc oligomer N PrP Sc N PrP Sc N PrP Sc Annu. Rev. Pathol. Mech. Dis. 2008.3:11-40. Downloaded from www.annualreviews.org by University of Vienna - Main Library and Archive Services on 07/31/14. For personal use only. Can we design a minimal RNA with prion-like behavior? 2
Prions and conformational self-replication Requirements for an RNA prion Energy Landscape maximize refolding barrier free energy [kcal/mol] S1 S2 E(B) normal infectious S2 S1 MFE 3
Prions and conformational self-replication Requirements for an RNA prion Energy Landscape maximize refolding barrier free energy [kcal/mol] S1 S2 E(B) normal infectious S2 S1 MFE S1 S2 S2 S2 minimize refolding barrier + + free energy [kcal/mol] HIV Dis type E(B) kissing loop komplex S1 S2 MFE S2 S2 S2 S2 S1 S2 3
Computational RNA folding Sequence ⇒ Structure UGCGACGUCCGACCUCGUUUACGCCAGUACCCCACUUCUCUUUG ✵ � ✁ ✂✄☎ ✆ ✝✄ free energy [kcal/mol] equilibrium Z partition function folding pa thways suboptimal structure prediction MFE minimum free energy structure prediction − E ( S ) − E ( S ) P ( S ) = e Z = � kT G = − kTln ( Z ) S ∈ Ω e kT Z 4
Computational RNA design Structure ⇒ Sequence (inverse of RNA folding problem) Simplest case: Find a sequence that forms a predefined structure ⇒ structure is the MFE of the designed sequence ⇒ maximize probability of the desired structure ⇒ sequence must be biologically reasonable (GC content) Even harder: Find a sequence that forms two predefined structures ⇒ sequence must be bi-stable (like a Prion) .(((.((.(((...))).)).))) (((...)))((...))((...)). 5
Computational Prion design • switch.pl with two conformations and HIV-Dis loop ....(((((((..((((...(((((...)))))...))))..))))))) (((((((.........)))))))....((((((.........)))))). NNNNNNNAACCGACGANNNNNNNNNNNNNNNNNAACGUCGGANNNNNNN • Generate lots of sequences (128 different results) • Select candidate with required prion features 6
Evaluation of prion-like behavior Z dup Z Z Z M ❝ ✞ ❝ ✟ ❙ ✞ ❙ ✟ Partition function of the Dimer: Z D = Z c 1 ∗ Z c 2 ∗ Z dup (1) Partition function of all Structures that are neither S 1 nor S 2: Z ! S 1 & ! S 2 = Z M − Z S 1 − Z S 2 Equilibrium Constant for Dimerization: [M]+[M] ⇔ [D] K = [ D ] [ M ] 2 = Z D Z 2 M 7
Evaluation of prion-like behavior ✶ e number of species ☛ ✏✌ Monom ❡ ✓ ✔ ✕ ✖ ✗ ✖ ✘ ✙ ✮ ☛ ✏✍ ❉ ✚✛ ❡ ✓ ✔ ✕ ✖ ✗ ✖ ✘ ✙ ✮ ☛ ✏ ✒ ☛ ✏✑ 0 ✶ ✠ ✡ ☛ ☞ ✶ ✠ ✡ ☛ ✌ ✶ ✠ ✡ ☛ ✼ ✶ ✠ ✡ ☛ ✍ ✶ ✠ ✡ ☛ ✎ ☛ ✏ ☛ ☛ ☛ ✶ ☛ ✏ ☛ ☛ ✶ ☛ ✏ ☛ ✶ ☛ ✏ ✶ ✶ concentra K [ D ] = [ M ] ∗ [ M ] 8
Evaluation of prion-like behavior ✥ M e number of species ★ ✯✪ Z Monom ✤ ✢ ✲ ✳ ✴ ✷ ✸ ✹ ✸ ✺ ✻✽ ★ ✯✬ ✾ ✿❀ ✲ ✳ ✴ ✷ ✸ ✹ ✸ ✺ ✻✽ ❁✸ ✳ ❂ ❃ ✸ ❂ ✳ ✲ ❄ Z ✤ ✣ ❁✸ ✳ ❂ ❃ ✸ ❂ ✳ ✲ ❅ ✲ s ★ ✯ ✱ ❖ ✸ ❆ ✲ ✳ ✴ ✸ ✳ ❂ ❃ ✸ ❂ ✳ Z dup ★ ✯ ✰ ❩ ✜ ✢ 0 Z ✥ ✦ ✧ ★ ✩ ✥ ✦ ✧ ★ ✪ ✥ ✦ ✧ ★ ✫ ✥ ✦ ✧ ★ ✬ ✥ ✦ ✧ ★ ✭ ★ ✯ ★ ★ ★ ✥ ★ ✯ ★ ★ ✥ ★ ✯ ★ ✥ ★ ✯ ✥ ✥ concentra ✜ ✣ � Z S 1+ c 1 � [ S 1] = Z S 1 + Z S 1+ c 2 · [ M ] + · [ D ] (2) Z M Z c 1 Z c 2 � Z S 2+ c 1 � [ S 2] = Z S 2 + Z S 2+ c 2 · [ M ] + · [ D ] Z M Z c 1 Z c 2 9
Evaluation of prion-like behavior S1 and S2 are separated by a high energy barrier: 5 S2 S1 0 -5 -10.70 kcal/mol 6.00 kcal/mol -12.70 kcal/mol free energy [kcal/mol] -10 0 20 40 60 80 length of refolding path [base-pair moves] 10
Evaluation of prion-like behavior S2 catalyzes reaction from S1 to S2: 5 S2 S1 0 -5 -10.70 kcal/mol 6.00 kcal/mol -12.70 kcal/mol free energy [kcal/mol] -10 0 20 40 60 80 -17.00 kcal/mol -16.10 kcal/mol -22.00 kcal/mol S2 + S2 + kiss -20 Energy Model 1 S1 + S2 Energy Model 2 -25 -33.60 kcal/mol -30 -23.40 kcal/mol -35 -31.80 kcal/mol -39.00 kcal/mol -29.70 kcal/mol 0 20 40 60 80 length of refolding path [base-pair moves] 10
Evaluation of prion-like behavior S2 catalyzes reaction from S1 to S2: 6.00 kcal/mol 5 S2 S2 => S1: 0 S1 16.70 kcal/mol -5 -10.70 kcal/mol -12.70 kcal/mol free energy [kcal/mol] -10 0 20 40 60 80 -17.00 kcal/mol -16.10 kcal/mol -22.00 kcal/mol S2 + S2 + kiss -20 Energy Model 1 S1 + S2 S1 => S2: Energy Model 2 -25 13.60 kcal/mol -33.60 kcal/mol -30 S1 => S2: -23.40 kcal/mol -35 -31.80 kcal/mol 9.80 kcal/mol -39.00 kcal/mol -29.70 kcal/mol 0 20 40 60 80 length of refolding path [base-pair moves] 10
Summary • RNAprions are a from of conformational self-replication • Computatinal RNA folding and design • HIV-Dis loops can be used to favor the infectious conformation for dimers • Different energy models for refolding pathways all show that S2 can act as a catalyst 11
thanks to This work: Ivo L. Hofacker Christoph Flamm General: Sabine M¨ uller Peter F. Stadler the TBI group Badelt et al. (2014) Design of a circular RNA with prion-like behavior Flamm et al. (2001) Design of multi-stable RNA Molecules Weixlbaumer et al. (2004) Determination of Thermodynamic Parameters for HIV-1 DIS Type Loop-Loop Kissing Complexes Lorenz et al. (2011) ViennaRNA Package 2.0 The research was funded by the Austrian Science Fund (FWF): W1207-B09, I670-B11 12
Computational RNA folding GCGGAUUUAGCUCAGUUGGGAGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUCGAUCCACAGAAUUCGCACCA Acceptor Stem T-Loop D-Loop A secondary structure is a list of base pairs ( i , j ), where: • A base may participate in at most one base pair. • Base pairs must not cross, i.e., no two pairs ( i , j ) and ( k , l ) may have i < k < j < l . • Only isosteric base-pairs GC, CG, AU, UA, GU, UG are allowed. • Hairpin loops have at least length 3 ( | j − i | > 3) 13
Computational RNA folding H H I I I � E ( S ) = E ( l ) M l ∈S loop H I p I I M Nearest Neighbor Energy Model: The free energy E of a secondary structure S is the sum of the energies of its loops l • Energies depend on loop type and size, with some sequence dependence. • Most relevant parameters are measured experimentally. 14
Computational RNA design switch.pl in a nutshell: • build a dependency graph • mutate an initial sequence guided by dependency graph • accept/reject mutations according to a cost function .(((.((.(((...))).)).))) (((...)))((...))((...)). Cost Function: ⇒ E ( x , S 1 ) + E ( x , S 2 ) − 2 G ( x ) + ξ ( E ( x , S 1 ) − ( E ( x , S 2 ) + ǫ )) 2 15
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