a dynamic model for rna decay by the archaeal exosome: parameter identification by mcmc
DESCRIPTION
A dynamic model for RNA decay by the archaeal exosome: Parameter identification by MCMC. Theresa Niederberger Computational Biology - Gene Center Munich. The archaeal exosome: Structure. 3’-5’ exoribonuclease Highly conserved: Eucaryotes, archaea: Exosome Procaryotes: PNPase. cap structure. - PowerPoint PPT PresentationTRANSCRIPT
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
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The archaeal exosome: function
Lorentzen, Conti,EMBO reports‘07
Processive decay: RNA in the processing chamber is cleaved base-per-base
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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
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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
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dc
cia
kk
kk
Catalytic efficiency
Robustness w.r.t. initial parameters
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Traceplots for the processivity for RNA of length 4 (in the Rrp4 exosome)
Initial development
Goodness of fit
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The model even acts as noise filter!
Results
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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
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Short RNA is not fixed by the binding site any more
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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
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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
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Catalytic efficiency
Based on Michaelis-Menton:
Catalytic Efficiency:
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id
ic
ic
ia
im
ici
kk
kk
K
kv
ia
id
ici
m k
kkK
dc
cia
kk
kk
Smoothness prior
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Simulation - Results
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Relative squared error: