Dynamic nested effects models Benedict Anchang Spang Group - - PowerPoint PPT Presentation

Dynamic nested effects models

Benedict Anchang Spang Group – University of Regensburg

ECCB Ghent, 26.09.2010

Dynam ic nested effects m odels

Pathways can be partially reconstructed from the nested structure of downstream effects in knock down experiments

Benedict Anchang Spang Group - University of Regensburg

Target genes (S2) Target genes (S1) if S1 is upstream of S2 (S1S2)

⊂

(Markowetz, Bloch, Spang Bioinformatics 2005) … add all other NEM papers

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Up-/downstream relations do not imply signal flow

Benedict Anchang Spang Group - University of Regensburg

S1 is upstream S2 S2 is upstream S3 S1 is upstream S3 This does not imply signal flows directly from S1 to S3

S1 S2 S3

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Transitive edges represent feed forward loops

Feed forward loops are a frequent network motif in signaling networks Feed forward loops cause time delays

Benedict Anchang Spang Group - University of Regensburg

S1 S2 S3

Network motifs: theory and experimental approaches (Uri Alon, Nature 2007)

Note that signaling through an AND gate is interrupted, if one of the incoming signals is interrupted. The AND becomes an OR.

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Time delays between signaling events can not be

• bserved directly. They need to be estimated

We can only observe perturbation propagation times from interventions to read outs but not for individual edges

Challenge

To estimate the perturbation propagation rates for all edges

Benedict Anchang Spang Group - University of Regensburg

Dynam ic nested effects m odels

S1 S2 S3 E3

3

2 1 1

Estimated time delays can serve as evidence for feed forward loops

Benedict Anchang Spang Group - University of Regensburg

Transitive edges exist They short cut signaling

2 1 1

S1 S2 S3 E3

3

1+2+1 ≠ 1+1

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We model signaling as a stochastic process with exponentially distributed time delays

Benedict Anchang Spang Group - University of Regensburg

exponential convolution

S1 S2 S3

∏

=

− − = →

2 1

)) ( 1 ( 1 ) 3 1 (

λ λ t

F S S P the first blocked signal wins AND-Gate ) exp( T

k k

λ λ −

[ ]

∑∏

= ≠

− −       − =

q b b b a b a a

t t F

1

) exp( 1 ) ( λ λ λ λ

λ

Dynamic Nested effects models(DNEMs)

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Stochasticity speeds up signaling

Benedict Anchang Spang Group - University of Regensburg

We model rates of signal propagation. The actual times spent for signal propagation remain random variables Assume the expected time spent in the shortcut is E[T1] and through Y it is E[T2], then the expected time for the perturbation effect to arrive in Z is E[min(T1,T2)] < min(E[T1],E[T2])

T1 T2

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To avoid singularities, we assume independent binary noise at the readouts

Benedict Anchang Spang Group - University of Regensburg

) 1 ))( ( 1 ( ) ( )) ( 1 ( ) 1 )( ( ) , | D (

D 1 D

α β α β λ

λ λ λ λ

− − + × − + − = Φ

∏ ∏

= =

t F t F t F t F P ) ( ) 3 1 ( t F S S P

λ

= →

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We use discrete Gibbs sampling to estimate the joint distribution of signal propagation rates

Benedict Anchang Spang Group - University of Regensburg

) ( ) ( ) ( ) , | ( ) | , ( D P P P D P D P Θ Θ = Θ λ λ λ

Interventions in S-genes S0 implicitly selects E-genes Observations in E-genes

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We use discrete Gibbs sampling for detecting the presence of a direct signal or transitive edge

Benedict Anchang Spang Group - University of Regensburg

Parameters

Rate constants including a very small value X  signal never arrives X indicates that a transitive edge does not exist: No shortcut

Priors

Uniform on with a total weight

• f 0.5 and 0.5 prior probability for X

which disfavours transitive edges

n

λ λ −

n

λ λ −

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DNEM detects all transitive edges and estimates time delays accurately in simulation

Benedict Anchang Spang Group - University of Regensburg

Estimated time delays

Light grey=high probability Dark grey=low probability

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Early stem cell differentiation in mice

Benedict Anchang Spang Group - University of Regensburg

Transition of stem cells from undifferentiated state to differentiated state Signaling genes Nanog,Oct4, Sox2, Esrrb,Tbx3,Tcl1 Microarray data 8 time points after RNAi knock down

Dissecting self-renewal in stem cells with RNA interference (Ivanova, Dobrin, Lu, Kotenko, Levorse, DeCoste, Schafer, Lun and Lemischka, Nature 2006)

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Nested structure estimated from last time point

Benedict Anchang Spang Group - University of Regensburg

Robust Back Bone Nanog Sox2 Oct4 Tcl1 Tbx3 ? Esrrb ?

Feed Forward Loops ?

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We observe good mixing and convergence for sampling rate parameters

Benedict Anchang Spang Group - University of Regensburg

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Posterior distribution of time delays on edges

Benedict Anchang Spang Group - University of Regensburg

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The temporal expression data holds evidence for many feed forward loops

Benedict Anchang Spang Group - University of Regensburg

Fast Medium Slow Feed forward loops (FFLs) dominating network motif in application FFL stabilizes the differentiated state of cells relative to the self –renewal state Nanog plays a key role in differentiation Possible role of the remaining Signaling genes is making cell differentiation a one way process A reversal would lead to a latent cancer risk

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Summary

Benedict Anchang Spang Group - University of Regensburg

DNEMs can be used to model dynamics

• f networks from times series

microarray data They infer feed forward loops from estimated time delays DNEMS capture the stochastic nature of signaling processes

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Acknowledgement

Benedict Anchang Spang Group - University of Regensburg

Rainer Spang (University of Regensburg) Mohammad J. Sadeh (University of Regensburg) Peter Oefner (University of Regensburg)

• Juby Jacob (Roche)

Achim Tresch (LMU)

• Marcel O. Vlad (Stanford) (Of late)
• Florian Markowetz

(Cambridge)

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Thank you for the attention !!

Benedict Anchang Spang Group - University of Regensburg