Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics

Motivation: Computational modelling of the dynamics of gene regu-latory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and exibility, but calibrating these models to data is often an extremely difcult statistical problem. Results: Here we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efcient variational appro-ximation which allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two bio-logical case studies, showing that the method allows a high degree of exibility and is capable of testable novel biological predictions