Gaussian process modelling of latent chemical species: applications to inferring transcription factor activities

Motivation: Inference of latent chemical species in biochemical interaction networks is a key problem in estimation of the structure and parameters of the genetic, metabolic and protein interaction networks that underpin all biological processes. We present a framework for Bayesian marginalization of these latent chemical species through Gaussian process priors. Results: We demonstrate our general approach on three different biological examples of single input motifs, including both activation and repression of transcription. We focus in particular on the problem of inferring transcription factor activity when the concentration of active protein cannot easily be measured. We show how the uncertainty in the inferred transcription factor activity can be integrated out in order to derive a likelihood function that can be used for the estimation of regulatory model parameters. An advantage of our approach is that we avoid the use of a coarse-grained discretization of continuous time functions, which would lead to a large number of additional parameters to be estimated. We develop exact (for linear regulation) and approximate (for non-linear regulation) inference schemes, which are much more efficient than competing sampling-based schemes and therefore provide us with a practical toolkit for model-based inference.