Abstract Background The octapeptide Angiotensin II is a key hormone that acts via its receptor AT1R in the brainstem to modulate the blood pressure control circuits and thus plays a central role in the cardiac and respiratory homeostasis. This modulation occurs via activation of a complex network of signaling proteins and transcription factors, leading to changes in levels of key genes and proteins. AT1R initiated activity in the nucleus tractus solitarius (NTS), which regulates blood pressure, has been the subject of extensive molecular analysis. But the adaptive network interactions in the NTS response to AT1R, plausibly related to the development of hypertension, are not understood. Results We developed and analyzed a mathematical model of AT1R-activated signaling kinases and a downstream gene regulatory network, with structural basis in our transcriptomic data analysis and literature. To our knowledge, our report presents the first computational model of this key regulatory network. Our simulations and analysis reveal a dynamic balance among distinct dimers of the AP-1 family of transcription factors. We investigated the robustness of this behavior to simultaneous perturbations in the network parameters using a novel multivariate approach that integrates global sensitivity analysis with decision-tree methods. Our analysis implicates a subset of Fos and Jun dependent mechanisms, with dynamic sensitivities shifting from Fos-regulating kinase (FRK)-mediated processes to those downstream of c-Jun N-terminal kinase (JNK). Decision-tree analysis indicated that while there may be a large combinatorial functional space feasible for neuronal states and parameters, the network behavior is constrained to a small set of AP-1 response profiles. Many of the paths through the combinatorial parameter space lead to a dynamic balance of AP-1 dimer forms, yielding a robust AP-1 response counteracting the biological variability. Conclusions Based on the simulation and analysis results, we demonstrate that a dynamic balance among distinct dimers of the AP-1 family of transcription factors underlies the robust activation of neuronal gene expression in the NTS response to AT1R activation. Such a differential sensitivity to limited set of mechanisms is likely to underlie the stable homeostatic physiological response.