A dynamic model for RNA decay by the archaeal exosome: Parameter identification by MCMC

1. A dynamic model for RNA decay by the archaeal exosome:Parameter identification by MCMC Theresa Niederberger Computational Biology - Gene Center Munich

2. The archaeal exosome: Structure • 3’-5’ exoribonuclease • Highly conserved: • Eucaryotes, archaea: Exosome • Procaryotes: PNPase cap structure Side view Top view hexameric ring Hartung, Hopfner; Biochem Soc Trans. 2009 Lorentzen, Conti; Nat Struct. Mol. Biol. 2005 / Mol. Cell 2005 Theresa Niederberger - Gene Center Munich

3. The archaeal exosome: function Lorentzen, Conti, EMBO reports‘07 Processive decay: RNA in the processing chamber is cleaved base-per-base Theresa Niederberger - Gene Center Munich

4. RNA Decay by the archaeal exosome Polymerization of RNAi 30-mer 29-mer Association of RNAi and the cleavage site 28-mer ... Dissociation of RNAi from the cleavage site Cleavage of RNAi • Problem: • The full model has108parameters! • Solution: • Polymerization can be neglected • Association, cleavage, dissociation are related • Flexible kai , global kc , fixed kd • Only 28 parameters left  3-mer (30 timepoints between 0 min and 25 min) Theresa Niederberger - Gene Center Munich

5. A brief reminder on MCMC A Markov Chain Monte Carlo Sampling method (Metropolis-Hastings algorithm): • Ingredients: • A likelihood function P(D| θ) (i.e., an error model) • A prior distribution on the parameters π(θ) • A proposal function (transition kernel) q(θ→θ´) Smoothness prior proposal step Construct a sequence of samples: S1. Generate a candidate sample θ´ from q(θ→θ´) S2. Calculate S3. Accept θ´ with probability r(θ→ θ´) (add θ´ to the sequence), otherwise stay at θ (add θ to the sequence another time) rejection step Theresa Niederberger - Gene Center Munich

6. Markov Chain Monte Carlo „Good“ Markov Chain, fast convergence: Sample is representative of the posterior distribution „Bad“ Markov Chains, slow convergence: Sample is not (yet) representative of the posterior distribution Theresa Niederberger - Gene Center Munich Andrieu, Jordan, Machine Learning 2003

7. Parameter Identifiability Catalytic efficiency Theresa Niederberger - Gene Center Munich

8. Robustness w.r.t. initial parameters Traceplots for the processivity for RNA of length 4 (in the Rrp4 exosome) Initial development Theresa Niederberger - Gene Center Munich

9. Goodness of fit The model even acts as noise filter! Theresa Niederberger - Gene Center Munich

10. Results There is clear evidence for a difference in the processing of long and short RNAs between the two mutants Additional binding site in Rrp4 log(catalytic efficiency) Suprising, as no simultaneous interactions with cap structure and cleavage site can occur. Possible explanation: Rrp4 holds the hexamer ring stronger together than Csl4. Theresa Niederberger - Gene Center Munich

11. Results Short RNA is not fixed by the binding site any more Theresa Niederberger - Gene Center Munich

12. Acknowledgments Gene Center Munich: Achim Tresch Karl-Peter Hopfner, Sophia Hartung The results of this work will appear as a featured article in Nucleic Acids Research. Theresa Niederberger - Gene Center Munich

13. Exosome variants Csl4 Exosome Wild type with Csl4 cap Rrp4 Exosome Wild type with Rrp44 cap Capless Exosome Wild type without cap Interface mutant Exosome that does not form a hexamer ring Crosslink mutant Exosome with hexamer ring fixed by a crosslinker Csl4 Exosome R65E Csl4 protein with R65E mutation in Rrp41 Csl4 Exosome Y70A Csl4 protein with Y70A mutation in Rrp42 Theresa Niederberger - Gene Center Munich

14. Mixing - Autocorrelation Theresa Niederberger - Gene Center Munich

15. Catalytic efficiency Based on Michaelis-Menton: • Catalytic Efficiency: Theresa Niederberger - Gene Center Munich

16. Smoothness prior Theresa Niederberger - Gene Center Munich

17. Simulation - Results Relative squared error: Theresa Niederberger - Gene Center Munich