A systematic survey of the response of a model NF- [Formula: see text] signalling pathway to [Formula: see text] stimulation

White's lab established that strong, continuous stimulation with tumour necrosis factor- [Formula: see text] ([Formula: see text]) can induce sustained oscillations in the subcellular localisation of the transcription factor nuclear factor [Formula: see text] (NF- [Formula: see text]). But the intensity of the [Formula: see text] signal varies substantially, from picomolar in the blood plasma of healthy organisms to nanomolar in diseased states. We report on a systematic survey using computational bifurcation theory to explore the relationship between the intensity of [Formula: see text] stimulation and the existence of sustained NF- [Formula: see text] oscillations. Using a deterministic model developed by Ashall et al. in 2009, we find that the system's responses to [Formula: see text] are characterised by a supercritical Hopf bifurcation point: above a critical intensity of [Formula: see text] the system exhibits sustained oscillations in NF-kB localisation. For [Formula: see text] below this critical value, damped oscillations are observed. This picture depends, however, on the values of the model's other parameters. When the values of certain reaction rates are altered the response of the signalling pathway to [Formula: see text] stimulation changes: in addition to the sustained oscillations induced by high-dose stimulation, a second oscillatory regime appears at much lower doses. Finally, we define scores to quantify the sensitivity of the dynamics of the system to variation in its parameters and use these scores to establish that the qualitative dynamics are most sensitive to the details of NF- [Formula: see text] mediated gene transcription.