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

Pathways can be partially reconstructed from the nested structure of downstream effects in knock down experiments ⊂ Target genes (S2) Target genes (S1) if S1 is upstream of S2 (S1  S2) (Markowetz, Bloch, Spang Bioinformatics 2005) … add all other NEM papers Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Up-/downstream relations do not imply signal flow S1 S1 is upstream S2 S2 is upstream S3 S1 is upstream S3 S2 This does not imply signal flows directly from S1 to S3 S3 Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Transitive edges represent feed forward loops Feed forward loops are a S1 frequent network motif in signaling networks S2 Feed forward loops cause time delays 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. Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Time delays between signaling events can not be observed 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 Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Estimated time delays can serve as evidence for feed forward loops 1 1 2 2 1 1 S1 S2 S3 E3 S1 S2 S3 E3 3 3 1+2+1 ≠ 1+1 Transitive edges exist They short cut signaling Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

We model signaling as a stochastic process with exponentially distributed time delays S1 exponential λ − λ exp( ) T k k   λ q [ ] ∑∏ = − − λ convolution   ( ) a 1 exp( ) F t t λ λ − λ b   = ≠ 1 b a b a b S2 the first blocked signal wins AND-Gate 2 ∏ → = − − ( 1 3 ) 1 ( 1 ( )) P S S F λ t S3 λ = 1 Dynamic Nested effects models(DNEMs) Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Stochasticity speeds up signaling We model rates of signal propagation. The actual times spent for signal propagation remain random variables T 1 T 2 Assume the expected time spent in the shortcut is E[T 1 ] and through Y it is E[T 2 ], then the expected time for the perturbation effect to arrive in Z is E[min(T 1 ,T 2 )] < min(E[T 1 ],E[T 2 ]) Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

To avoid singularities, we assume independent binary noise at the readouts → = ( 1 3 ) ( ) P S S F t λ ∏ λ Φ = − β + − α ( D | , ) ( )( 1 ) ( 1 ( )) P F t F t λ λ = D 1 ∏ × β + − − α ( ) ( 1 ( ))( 1 ) F t F t λ λ = D 0 Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

We use discrete Gibbs sampling to estimate the joint distribution of signal propagation rates λ Θ λ Θ ( | , ) ( ) ( ) P D P P Θ λ = ( , | ) P D ( ) P D Interventions in S-genes S0 implicitly selects E-genes Observations in E-genes Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

We use discrete Gibbs sampling for detecting the presence of a direct signal or transitive edge Parameters λ − λ Rate constants 0 n including a very small value X  signal never arrives X indicates that a transitive edge does not exist: No shortcut Priors λ − λ Uniform on with a total weight 0 n of 0.5 and 0.5 prior probability for X which disfavours transitive edges Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

DNEM detects all transitive edges and estimates time delays accurately in simulation Light grey=high probability Dark grey=low probability Estimated time delays Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Early stem cell differentiation in mice 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 Dissecting self-renewal in stem cells with RNA interference knock down (Ivanova, Dobrin, Lu, Kotenko, Levorse, DeCoste, Schafer, Lun and Lemischka, Nature 2006) Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Nested structure estimated from last time point Robust Back Bone Nanog Tbx3 ? Feed Forward Loops ? Sox2 Esrrb ? Oct4 Tcl1 Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

We observe good mixing and convergence for sampling rate parameters Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Posterior distribution of time delays on edges Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

The temporal expression data holds evidence for many feed forward loops Feed forward loops (FFLs) dominating network motif in application Fast Medium Slow 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 Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Summary DNEMs can be used to model dynamics of networks from times series microarray data They infer feed forward loops from estimated time delays DNEMS capture the stochastic nature of signaling processes Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Acknowledgement 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) Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg

Thank you for the attention !! Dynam ic nested Benedict Anchang effects m odels Spang Group - University of Regensburg