Mathematical and computational modelling is often required in order to infer, given data, the behaviour over time of parameters in biological processes that are difficult to measure experimentally. The aim of this project is to investigate possible network motifs, or mechanisms, which result in the observed waves of gene expression in HeLa cells resulting from extracellular stimulation by EGF.Bayesian inference with a Gaussian Process prior is employed to model the behaviour over time of the transcription factor Elk-1. Once the profile over time is established, it is used to predict targets of Elk-1, some of which are novel and require verification in the lab. The targets identified by the predictive model are verified against experimentally obtained ChIP-chip data, with mixed results. The approach is also compared to some other predictive techniques, such as k-means clustering, with positive results.Future modifications are necessary to increase the predictive power of the current model, including: varying the choice of genes comprising the training data; investigating alternate Gaussian Process priors when generating the transcription factor's concentration profile; and utilizing a more fully Bayesian approach when developing the predictive model. Once gene targets have been identified for our transcription factors of interest, the model could be extended to cover a larger sub-network. At this point, transcription factors other than Elk-1 would have to be investigated, as many genetic targets are regulated by more than one transcription factor. Some of the regulatory mechanisms could involve species further up the signaling cascade. The goal envisioned is to gradually build up a quantitative description of the transcriptional response to extracellular signaling in the sub-network of interest.