Analyzing robustness of NF-kappaB signaling transduction networks via bifurcation analysis

Robustness is a widely observed and important property of biological systems. The nuclear factor-kB (NF-kB) signaling pathway is an important cellular signaling pathway that is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Oscillation is a common phenomenon in complex biological systems and it plays key roles in many cellular processes. Upon stimulation of TNFa, damped oscillations of NF-kB activity have been observed both experimentally and computationally in previous works. Bifurcation analysis has proven to be a powerful tool to identify the presence of complex behavior of dynamic systems. Based on a mathematical model of the TNFa mediated IkB-NF-kB signaling transduction pathway and also a simplified IkBα-NF-kB computational model with IkBβ and IkBε knock out, bifurcation analysis is performed to investigate the mechanism of biological robustness of the NF-kB signaling transduction pathway. In particular, we focused on the periodic solutions emerged via Hopf bifurcations and identified the parameter regions in which a stable periodic solution exists. Numerical study results confirm that IkBa is the key inhibitor of the NF-kB network and the cellular system has retained robustness even when some components are knocked out.