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 marginalisation of these latent chemical species through Gaussian process priors. 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. 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.