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

A dynamic model for RNA decay by the archaeal exosome:

Parameter identification by MCMC

Theresa Niederberger

Computational Biology - Gene Center Munich

26.03.2010 Theresa Niederberger - Gene Center Munich 2

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. 2009 Lorentzen, Conti; Nat Struct. Mol. Biol. 2005 / Mol. Cell 2005


The archaeal exosome: function

Lorentzen, Conti,EMBO reports‘07

Processive decay: RNA in the processing chamber is cleaved base-per-base


RNA Decay by the archaeal exosome

Problem:The full model has108 parameters!Solution:• Polymerization can be neglected• Association, cleavage, dissociation are related

Flexible kai , global kc , fixed kd

Only 28 parameters left

30-mer29-mer

3-mer

28-mer...

(30 timepoints between 0 min and 25 min)

Polymerization of RNAi

Cleavageof RNAi

Association of RNAi and the cleavage site

Dissociation of RNAi from the cleavage site


A brief reminder on MCMCA 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)

),´)(q)()|D(P

)´(q´)(´)|D(P(min´)(r 1

,D~D N

Smoothness prior

),k(k xjx

jx' 2LN

Markov Chain Monte Carlo

26.03.2010 Theresa Niederberger - Gene Center Munich 6Andrieu, 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


dc

cia

kk

kk

Catalytic efficiency

Robustness w.r.t. initial parameters


Traceplots for the processivity for RNA of length 4 (in the Rrp4 exosome)

Initial development

Goodness of fit


The model even acts as noise filter!

Results


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(

cata

lytic

eff

icie

ncy)

Results


Short RNA is not fixed by the binding site any more


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


Csl4 ExosomeWild type

with Csl4 cap

Rrp4 ExosomeWild type

with Rrp44 cap

Capless ExosomeWild type

without cap

Csl4 Exosome R65ECsl4 protein with R65E

mutation in Rrp41

Csl4 Exosome Y70ACsl4 protein with Y70A

mutation in Rrp42

Interface mutantExosome that does not

form a hexamer ring

Crosslink mutantExosome with hexamer

ring fixed by a crosslinker

Mixing - Autocorrelation


Catalytic efficiency

Based on Michaelis-Menton:

Catalytic Efficiency:


id

ic

ic

ia

im

ici

kk

kk

K

kv

ia

id

ici

m k

kkK

dc

cia

kk

kk

Smoothness prior


Simulation - Results


Relative squared error:

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

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