Understanding Dynamic Patterns of NF-$\kappa $B Signaling: Derivation and Analysis of a Minimal Model through Sensitivity Analysis

Understanding the pleiotropism of NF-$\kappa $B signal transduction is a challenge of clear medical importance and systems biology. Current mathematical modeling frameworks for NF-$\kappa $B signal transduction, though limited to a small signaling module located in a downstream of IKK, heavily rely on the parameterizations and the numerical studies of ODE models and doubtless lack intuitive explanations about underlying mechanisms of the dynamic patterns of the NF-$\kappa $B signaling. Here we present a systematic way to derive a minimal model from an up-to-dated and detailed NF-$\kappa $B signaling network by means of sensitivity analysis. Using analysis of the minimal model, we predict a dose-response curve shape, existence of Hopf-bifurcation, and underlying mechanisms of all possible dynamic patterns of NF-$\kappa $B signaling. Simulating the detailed ODE model for NF-$\kappa $B signaling network with large sets of the parameter values that are sampled from the biologically feasible parameter space, we present an ensemble of all possible dynamic patterns of NF-$\kappa $B signaling and verify the predictions from the minimal model.