Efficient Learning of Signaling Networks from Perturbation Time Series via Dynamic Nested Effect Models Paurush Praveen * 1 , Aachim Tresch 2 , Holger Froehlich 1 Bonn-Aachen International Center for IT, Dahlmannstr. 2, 53113 Bonn; 2. Gene Center Munich, Feodor-Lynen-Str. 25, 81377 Munich Teaser A novel and computationally efficient approach for reconstructing signaling cascades from measured temporal downstream effects of targeted interventions via an extension of Nested Effects Model (NEM’s) 4. Conclusions  A novel approach to efficiently infer signaling cascades from high dimensional perturbation time series data.  Extending NEM’s as introduced by Markowetz et al. to dynamic level  Overcoming the time consuming Gibbs sampling [4] with fast and efficient greedy hill climber or Metropolis Hastings algorithm. The method can be useful for generating hypothesis from high dimensional perturbation effect data for a dynamic system. References: [1] Markowetz, F., Bloch, J., and Spang, R. (2005). Non-transcriptional pathway features reconstructed from secondary effects of RNA interference. Bioinformatics (Oxford, England), 21(21):402632. [2] Fröhlich, H., Tresch, A., and Beissbarth, T. (2009). Nested Eects Models for Learning Signaling Networks from Perturbation Data. Biometrical Journal, 2(51):304323 . [3] Ghahramani, Z. (1997). Learning Dynamic Bayesian Networks. Lecture Notes In Computer Science, 1387:168197 [4] Anchang, B., Sadeh, M. J., Jacob, J., Tresch, A., Vlad, M. O., Oefner, P. J., and Spang,R. (2009). Modeling the temporal interplay of molecular signaling and gene expression by using dynamic nested eects models. Proceedings of the National Academy of Sciences of the United States of America, 106(16):644752. [5] Ivanova, N., Dobrin, R., Lu, R., Kotenko, I., Levorse, J., DeCoste, C., Schafer, X., Lun, Y., and Lemischka, I. R. (2006). Dissecting self-renewal in stem cells with RNA interference. Nature, 442(7102):533–538 [6] H. Fröhlich, P. Praveen, A. Tresch (2011), Fast and Efficient Dynamic Nested Effects Models, Bioinformatics, 27, 238-244. Further Information: Paurush Praveen :praveen@bit.uni-bonn.de Aachim Tresch: tresch@lmb.uni-muenchen.de Holger Froehlich : frohlich@bit.uni-bonn.de URL: http://www.abi.bit.uni-bonn.de • Paurush Praveen is supported by state of NRW via B-IT Research School grant. 1. Introduction In the current form, NEM can model only static system. Modeling temporal data needs extension of the existing NEM approach. In order to achieve this it is required to modify the existing likelihood formula and a feasible learning approach. The current work aims to reach these goals Figure 4: Inferred networks for murine stem cell development [5] . 95% confidence intervals (%) shown at each edge in (a) which was generated by hill climbing method. Time lag weighed edges are shown in network (b) which was generated by MCMC based learning. 3. Results 2. Approach Unrolling Unrolling of the signal flow over time occurs in the wiring of S-genes. This yields a weighted adjacency matrix ψ ij . The zeroes in the matrix indicate the absence of influence between nodes and the non-zeroes indicate time steps after which there is an influence of node i on node j. Unlike the classical Dynamic Bayesian Network [3] an edge can skip certain number of time steps, not connecting consecutive time layers (Figure 2). Figure 1: Working principle of Nested Effects Model Network Learning Network learning here aims to find optimal weighted adjacency matrix ψ consisting of discrete values (0,1,….,T). This is achieved by greedy hill climbing approach [6] or via Markov Chain Monte Carlo method. Reverse engineering of biological networks is the key to understand the living systems. This can be achieved by perturbing a gene of interest and studying the affected genes. NEM’s [1,2] are a class of graphical models that allow inferring networks from high dimensional, indirect downstream perturbation effects (Figure 1). The knowledge from such relations in the living cells can be crucial for drug target identification and biomarker analysis in various diseases. Figure 2: Unrolling of the signal flow in the network along time (t = time index). a) Network topology and parametrization of the dynamic NEM. b) Predicted effects (Grayed box) resulting from single and multiple perturbations. Likelihood The likelihood formula for static NEMs is modified to incorporate a time dependent activation state s(t) for each S-gene : (1) On unrolling of the signal flow over time we have (2) (2) In the absence of more precise information we define : (3) (4) Prior The prior by Froehlich et al. (2007) is used to punish high edge weights and to additionally include prior knowledge into the network scoring (4). (4) Here, υ is the scaling parameter selected by BIC or DIC criterion depending on learning approach, which can be greedy hill climbing or MCMC based. a b Nanog Oct4 Sox2 Esrrb Tbx3 Tcl1 Network For Murine Stem Cell Development Fast Signalling Intermediate Signalling Slow Signalling Figure 3: Results for the sensitivity and specificity of the dynoNEM Model for various parameters as compared to the simpleDNEM approach (simpleDNEM approach refers to the use of static NEM to learn network structure for time series data). Starting from left, the parameters are (a) length of time series, (b) number of E-genes. The plots show an improvement in the performance of the method compared to the simpleDNEM method. The plot (c) depicts the convergence of the MCMC method for structure learning. a b 0 1000 2000 3000 4000 5000 6000 -8000 -6000 -4000 -2000 0 Iteration (x100) result$all.likelihoods Network likelihood plot showing MCMC convergence Log Bayes Factor = 19.569 c F1000 Posters. 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