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

Theresa Niederberger - Gene Center Munich2 The archaeal exosome: Structure 3’-5’ exoribonuclease Highly conserved: –Eucaryotes, archaea: Exosome –Procaryotes: PNPase Side view Top view cap structure hexameric ring Hartung, Hopfner; Biochem Soc Trans Lorentzen, Conti; Nat Struct. Mol. Biol / Mol. Cell 2005

Theresa Niederberger - Gene Center Munich3 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 Munich4 RNA Decay by the archaeal exosome Problem: The full model has108 parameters! Solution: Polymerization can be neglected Association, cleavage, dissociation are related  Flexible k a i, global k c, fixed k d Only 28 parameters left 30-mer 29-mer 3-mer 28-mer (30 timepoints between 0 min and 25 min) Polymerization of RNA i Cleavage of RNA i Association of RNA i and the cleavage site Dissociation of RNA i from the cleavage site

Theresa Niederberger - Gene Center Munich5 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´) rejection step 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) Smoothness prior

Markov Chain Monte Carlo Theresa Niederberger - Gene Center Munich6 Andrieu, Jordan, Machine Learning 2003 „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

Parameter Identifiability Theresa Niederberger - Gene Center Munich7 Catalytic efficiency

Robustness w.r.t. initial parameters Theresa Niederberger - Gene Center Munich8 Traceplots for the processivity for RNA of length 4 (in the Rrp4 exosome) Initial development

Goodness of fit Theresa Niederberger - Gene Center Munich9 The model even acts as noise filter!

Results Theresa Niederberger - Gene Center Munich10 There is clear evidence for a difference in the processing of long and short RNAs between the two mutants Suprising, as no simultaneous interactions with cap structure and cleavage site can occur. Possible explanation: Rrp4 holds the hexamer ring stronger together than Csl4. Additional binding site in Rrp4 log(catalytic efficiency)

Results Theresa Niederberger - Gene Center Munich11 Short RNA is not fixed by the binding site any more

Theresa Niederberger - Gene Center Munich12 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.

Exosome variants Theresa Niederberger - Gene Center Munich13 Csl4 Exosome Wild type with Csl4 cap Rrp4 Exosome Wild type with Rrp44 cap Capless Exosome Wild type without cap Csl4 Exosome R65E Csl4 protein with R65E mutation in Rrp41 Csl4 Exosome Y70A Csl4 protein with Y70A mutation in Rrp42 Interface mutant Exosome that does not form a hexamer ring Crosslink mutant Exosome with hexamer ring fixed by a crosslinker

Mixing - Autocorrelation Theresa Niederberger - Gene Center Munich14

Catalytic efficiency Based on Michaelis-Menton:  Catalytic Efficiency: Theresa Niederberger - Gene Center Munich15

Smoothness prior Theresa Niederberger - Gene Center Munich16

Simulation - Results Theresa Niederberger - Gene Center Munich17 Relative squared error: