Data-driven learning of the topology of molecular networks, e.g. via Dynamic Bayesian Networks (DBNs) has a long tradition in Bioinformatic. The vast majority of methods take gene expression as a proxy for protein expression in that context, which is principally problematic. 

We and others have established Nested Effects Models to overcome some of these issues by distinguishing between a latent (i.e. unobservable) signaling network structure and observable transcriptional downstream effects of targeted interventions. 

The goal of this project is to develop a more principled and flexible approach for learning the topology of a dynamical system that is only observable through transcriptional responses of possibly combinatorial and arbitrary complex perturbation experiments. More specifically, we focus on the situation that the latent dynamical system (i.e. signaling network) can be described as a network of binary state variables. We show, how candidate networks can be scored efficiently in this case and how topology learning can be achieved via adaptive Markov Chain Monte Carlo (MCMC). As an application, we plan to extend our method to incorporate multi-omics data.