In the last decades, the explosion of data from quantitative techniques has revolutionised our
understanding of biological processes. In this scenario, advanced statistical methods and algorithms
are becoming fundamental to decipher the dynamics of biochemical mechanisms such
those involved in the regulation of gene expression. Here we develop mechanistic models and
approximate inference techniques to reverse engineer the dynamics of gene regulation, from
mRNA and/or protein time series data.
We start from an existent variational framework for statistical inference in transcriptional
networks. The framework is based on a continuous-time description of the mRNA dynamics
in terms of stochastic differential equations, which are governed by latent switching variables
representing the on/off activity of regulating transcription factors. The main contributions of
this work are the following.
We speeded-up the variational inference algorithm by developing a method to compute
a posterior approximate distribution over the latent variables using a constrained optimisation
algorithm. In addition to computational benefits, this method enabled the extension to statistical
inference in networks with a combinatorial model of regulation.
A limitation of this framework is the fact that inference is possible only in transcriptional
networks with a single-layer architecture (where a single or couples of transcription factors regulate
directly an arbitrary number of target genes). The second main contribution in this work
is the extension of the inference framework to hierarchical structures, such as feed-forward
loop.
In the last contribution we define a general structure for transcription-translation networks.
This work is important since it provides a general statistical framework to model complex
dynamics in gene regulatory networks. The framework is modular and scalable to realistically
large systems with general architecture, thus representing a valuable alternative to traditional
differential equation models.
All models are embedded in a Bayesian framework; inference is performed using a variational
approach and compared to exact inference where possible. We apply the models to the
study of different biological systems, from the metabolism in E. coli to the circadian clock in
the picoalga O. tauri
