Dynamic deterministic effects propagation networks: learning signalling pathways from longitudinal protein array data

Abstract

Motivation: Network modelling in systems biology has become an important tool to study molecular interactions in cancer research, because understanding the interplay of proteins is necessary for developing novel drugs and therapies. De novo reconstruction of signalling pathways from data allows to unravel interactions between proteins and make qualitative statements on possible aberrations of the cellular regulatory program. We present a new method for reconstructing signalling networks from time course experiments after external perturbation and show an application of the method to data measuring abundance of phosphorylated proteins in a human breast cancer cell line, generated on reverse phase protein arrays.

Results: Signalling dynamics is modelled using active and passive states for each protein at each timepoint. A fixed signal propagation scheme generates a set of possible state transitions on a discrete timescale for a given network hypothesis, reducing the number of theoretically reachable states. A likelihood score is proposed, describing the probability of measurements given the states of the proteins over time. The optimal sequence of state transitions is found via a hidden Markov model and network structure search is performed using a genetic algorithm that optimizes the overall likelihood of a population of candidate networks. Our method shows increased performance compared with two different dynamical Bayesian network approaches. For our real data, we were able to find several known signalling cascades from the ERBB signalling pathway.

Availability: Dynamic deterministic effects propagation networks is implemented in the R programming language and available at http://www.dkfz.de/mga2/ddepn/.

Fig. 1.

Overview of the approach: given a network hypothesis (A), we generate a set of reachable system states by applying a fixed signal propagation scheme (B) which in effect reduces the number of possible system states. An optimal path through these reachable system states over time is identified by an HMM (C). Using the series of system states from the HMM, model parameters for two Gaussian distributions for each protein (one for active, one for passive) are estimated (D) and a total likelihood of our measurements given the network and model parameters is calculated (E). We use this likelihood score in a GA in order to optimize the overall score for an evolving population of candidate networks (F) and generate a final network from this population, after we found convergence in the GA.

Fig. 2.

Performance of state recovery for increasing number of nodes N (A) and number of stimuli nstim (B).

Fig. 3.

(A) ROC curves and AUCs for different settings of input (nstim) and combinatorial stimuli (cstim) and population sizes (p). SN and SP were calculated as average of each 25 network reconstructions with network size of N = 10. (B) Example SN and SP plot for th = 0.5 for all settings. For p = 500, SP was high at ∼0.83, while SN increased from ∼0.17 to ∼0.4. This shows, that DDEPN found edges with strong support from the data with low FP rates. The increase in SN for bigger population sizes shows, that broader sampling of the network search space yielded better inference results.

Fig. 4.

ROC curves and AUCs for DDEPN network reconstruction compared with G1DBN and ebdbNet. (A) For nstim = 1,cstim = 0, a slight improvement of AUCs was observed, and performances were limited for all approaches. (B) For nstim = 2,cstim = {0, 1}, a clear increase in AUC was found for DDEPN, showing the improved quality of the network reconstructions.

Fig. 5.

Network reconstructed from HCC1954 data. Interactions found in the literature are marked as thick lines. Dark nodes mark the input stimuli. The numbers at the edges show the proportion of networks in the final GA population, in which the respective edge was contained.