The Annals of Applied Statistics

Reconstructing evolving signalling networks by hidden Markov nested effects models

Xin Wang, Ke Yuan, Christoph Hellmayr, Wei Liu, and Florian Markowetz

Full-text: Open access


Inferring time-varying networks is important to understand the development and evolution of interactions over time. However, the vast majority of currently used models assume direct measurements of node states, which are often difficult to obtain, especially in fields like cell biology, where perturbation experiments often only provide indirect information of network structure. Here we propose hidden Markov nested effects models (HM-NEMs) to model the evolving network by a Markov chain on a state space of signalling networks, which are derived from nested effects models (NEMs) of indirect perturbation data. To infer the hidden network evolution and unknown parameter, a Gibbs sampler is developed, in which sampling network structure is facilitated by a novel structural Metropolis–Hastings algorithm. We demonstrate the potential of HM-NEMs by simulations on synthetic time-series perturbation data. We also show the applicability of HM-NEMs in two real biological case studies, in one capturing dynamic crosstalk during the progression of neutrophil polarisation, and in the other inferring an evolving network underlying early differentiation of mouse embryonic stem cells.

Article information

Ann. Appl. Stat. Volume 8, Number 1 (2014), 448-480.

First available in Project Euclid: 8 April 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Dynamic signalling networks gene perturbation hidden Markov nested effects models MCMC


Wang, Xin; Yuan, Ke; Hellmayr, Christoph; Liu, Wei; Markowetz, Florian. Reconstructing evolving signalling networks by hidden Markov nested effects models. Ann. Appl. Stat. 8 (2014), no. 1, 448--480. doi:10.1214/13-AOAS696.

Export citation


  • Ahmed, A. and Xing, E. P. (2009). Recovering time-varying networks of dependencies in social and biological studies. Proc. Natl. Acad. Sci. USA 106 11878–11883.
  • 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 effects models. Proc. Natl. Acad. Sci. USA 106 6447–6452.
  • Boutros, M. and Ahringer, J. (2008). The art and design of genetic screens: RNA interference. Nat. Rev. Genet. 9 554–566.
  • Boyer, L. A., Lee, T. I., Cole, M. F., Johnstone, S. E., Levine, S. S., Zucker, J. P., Guenther, M. G., Kumar, R. M., Murray, H. L., Jenner, R. G. et al. (2005). Core transcriptional regulatory circuitry in human embryonic stem cells. Cell 122 947–956.
  • Castro, M. A., Wang, X., Fletcher, M. N., Meyer, K. B. and Markowetz, F. (2012). RedeR: R/Bioconductor package for representing modular structures, nested networks and multiple levels of hierarchical associations. Genome Biol. 13 R29.
  • Failmezger, H., Praveen, P., Tresch, A. and Fröhlich, H. (2013). Learning gene network structure from time laps cell imaging in RNAi Knock downs. Bioinformatics 29 1534–1540.
  • Friedman, N. and Koller, D. (2003). Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning 50 95–125.
  • Fröhlich, H., Praveen, P. and Tresch, A. (2011). Fast and efficient dynamic nested effects models. Bioinformatics 27 238–244.
  • Fröhlich, H., Fellmann, M., Sueltmann, H., Poustka, A. and Beissbarth, T. (2007). Large scale statistical inference of signaling pathways from RNAi and microarray data. BMC Bioinformatics 8 386.
  • Fröhlich, H., Fellmann, M., Sültmann, H., Poustka, A. and Beissbarth, T. (2008). Estimating large-scale signaling networks through nested effect models with intervention effects from microarray data. Bioinformatics 24 2650–2656.
  • Gelman, A., Roberts, G. O. and Gilks, W. R. (1996). Efficient Metropolis jumping rules. Bayesian Stat. 5 599–607.
  • Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457–472.
  • Geyer, C. (2011). Introduction to Markov chain Monte Carlo. In Handbook of Markov Chain Monte Carlo (S. Brooks, A. Gelman, G. Jones and X. L. Meng, eds.). CRC Press, Boca Raton, FL.
  • Girolami, M. and Calderhead, B. (2011). Riemann manifold Langevin and Hamiltonian Monte Carlo methods. J. R. Stat. Soc. Ser. B Stat. Methodol. 73 123–214.
  • Grzegorczyk, M. and Husmeier, D. (2008). Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move. Machine Learning 71 265–305.
  • Grzegorczyk, M. and Husmeier, D. (2009). Nonstationary continuous dynamic Bayesian networks. Advances in Neural Information Processing Systems (NIPS) 22 682–690.
  • Guo, F., Hanneke, S., Fu, W. and Xing, E. P. (2007). Recovering temporally rewiring networks: A model-based approach. In Proceedings of the 24th International Conference on Machine Learning 321–328. ACM, Corvallis, OR.
  • Hanneke, S. and Xing, E. P. (2006). Discrete temporal models of social networks. In Proceedings of the 2006 Conference on Statistical Network Analysis 115–125. Springer, Berlin.
  • House, C. D., Vaske, C. J., Schwartz, A. M., Obias, V., Frank, B., Luu, T., Sarvazyan, N., Irby, R., Strausberg, R. L., Hales, T. G., Stuart, J. M. and Lee, N. H. (2010). Voltage-gated Na$+$ channel SCN5A is a key regulator of a gene transcriptional network that controls colon cancer invasion. Cancer Res. 70 6957–6967.
  • Husmeier, D., Dondelinger, F. and Lebre, S. (2010). Inter-time segment information sharing for nonhomogeneous dynamic Bayesian networks. Adv. Neural Inf. Process. Syst. 23 901–909.
  • Ivanova, N., Dobrin, R., Lu, R. et al. (2006). Dissecting self-renewal in stem cells with RNA interference. Nature 442 533–538.
  • Kalmar, T., Lim, C., Hayward, P., Muñoz-Descalzo, S., Nichols, J., Garcia-Ojalvo, J. and Arias, A. M. (2009). Regulated fluctuations in Nanog expression mediate cell fate decisions in embryonic stem cells. PLoS Biology 7 e1000149.
  • Ku, C.-J., Wang, Y., Weiner, O. D., Altschuler, S. J. and Wu, L. F. (2012). Network crosstalk dynamically changes during neutrophil polarization. Cell 149 1073–1083.
  • Lèbre, S. (2007). Stochastic process analysis for Genomics and Dynamic Bayesian Networks inference. Ph.D. thesis, Univ. d’Évry Val-d’Essonne, France.
  • Loh, Y.-H., Wu, Q., Chew, J.-L., Vega, V. B., Zhang, W., Chen, X., Bourque, G., George, J., Leong, B., Liu, J. et al. (2006). The Oct4 and Nanog transcription network regulates pluripotency in mouse embryonic stem cells. Nat. Genet. 38 431–440.
  • Madigan, D., York, J. and Allard, D. (1995). Bayesian graphical models for discrete data. International Statistical Review/Revue Internationale de Statistique 63 215–232.
  • Markowetz, F. (2006). Probabilistic models for gene silencing data. Ph.D. thesis, Free Univ. Berlin, Germany.
  • Markowetz, F. (2010). How to understand the cell by breaking it: Network analysis of gene perturbation screens. PLoS Comput. Biol. 6 e1000655.
  • Markowetz, F., Bloch, J. and Spang, R. (2005). Nontranscriptional pathway features reconstructed from secondary effects of RNA interference. Bioinformatics 21 4026–4032.
  • Markowetz, F., Kostka, D., Troyanskaya, O. G. and Spang, R. (2007). Nested effects models for high-dimensional phenotyping screens. Bioinformatics 23 i305–i312.
  • Masui, S., Nakatake, Y., Toyooka, Y. et al. (2007). Pluripotency governed by Sox2 via regulation of Oct3/4 expression in mouse embryonic stem cells. Nat. Cell Biol. 9 625–635.
  • Matoba, R., Niwa, H., Masui, S., Ohtsuka, S., Carter, M. G., Sharov, A. A. and Ko, M. S. (2006). Dissecting Oct3/4-regulated gene networks in embryonic stem cells by expression profiling. PLoS One 1 e26.
  • Murphy, K. P. (2002). Dynamic Bayesian networks: Representation, inference and learning. Ph.D. thesis, Univ. California.
  • Navarro, P., Festuccia, N., Colby, D., Gagliardi, A., Mullin, N. P., Zhang, W., Karwacki-Neisius, V., Osorno, R., Kelly, D., Robertson, M. et al. (2012). OCT4/SOX2-independent Nanog autorepression modulates heterogeneous Nanog gene expression in mouse ES cells. The EMBO Journal 31 4547–4562.
  • Neumann, B., Walter, T., Jean-Karim, H. et al. (2010). Phenotypic profiling of the human genome by time-lapse microscopy reveals cell division genes. Nature 464 721–727.
  • Niederberger, T., Etzold, S., Lidschreiber, M., Maier, K. C., Martin, D. E., Fröhlich, H., Cramer, P. and Tresch, A. (2012). MC EMiNEM maps the interaction landscape of the Mediator. PLoS Comput. Biol. 8 e1002568.
  • Niwa, H., Ogawa, K., Shimosato, D. and Adachi, K. (2009). A parallel circuit of LIF signalling pathways maintains pluripotency of mouse ES cells. Nature 460 118–122.
  • Robinson, J. W. and Hartemink, A. J. (2009). Nonstationary dynamic Bayesian networks. Adv. Neural Inf. Process. Syst. 21 1369–1376.
  • Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D. and Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychon. Bull. Rev. 16 225–237.
  • Sadeh, M. J., Moffa, G. and Spang, R. (2013). Considering unknown unknowns-reconstruction of nonconfoundable causal relations in biological networks. In Research in Computational Molecular Biology 234–248. Springer, Berlin.
  • Small, J. V., Geiger, B., Kaverina, I. and Bershadsky, A. (2002). How do microtubules guide migrating cells? Nat. Rev. Mol. Cell Biol. 3 957–964.
  • Song, l., Kolar, M. and Xing, E. P. (2009). Time-varying dynamic Bayesian networks. Adv. Neural Inf. Process. Syst. 22 1732–1740.
  • Tresch, A. and Markowetz, F. (2008). Structure learning in nested effects models. Stat. Appl. Genet. Mol. Biol. 7 Art. 9, 28.
  • van den Berg, D. L., Zhang, W., Yates, A., Engelen, E., Takacs, K., Bezstarosti, K., Demmers, J., Chambers, I. and Poot, R. A. (2008). Estrogen-related receptor beta interacts with Oct4 to positively regulate Nanog gene expression. Mol. Cell. Biol. 28 5986–5995.
  • Vaske, C. J., House, C., Luu, T., Frank, B., Yeang, C.-H., Lee, N. H. and Stuart, J. M. (2009). A factor graph nested effects model to identify networks from genetic perturbations. PLoS Comput. Biol. 5 e1000274, 16.