Noise-induced oscillatory shuttling of NF-{\kappa}B in a two compartment IKK-NF-{\kappa}B-I{\kappa}B-A20 signaling model

NF-{\kappa}B is a pleiotropic protein whose nucleo-cytoplasmic trafficking is tightly regulated by multiple negative feedback loops embedded in the NF-{\kappa}B signaling network and contributes to diverse gene expression profiles important in immune cell differentiation, cell apoptosis, and innate immunity. The intracellular signaling processes and their control mechanisms, however, are susceptible to both extrinsic and intrinsic noise. In this article, we present numerical evidence for a universal dynamic behavior of NF-{\kappa}B, namely oscillatory nucleo-cytoplasmic shuttling, due to the fundamentally stochastic nature of the NF-{\kappa}B signaling network. We simulated the effect of extrinsic noise with a deterministic ODE model, using a statistical ensemble approach, generating many copies of the signaling network with different kinetic rates sampled from a biologically feasible parameter space. We modeled the effect of intrinsic noise by simulating the same networks stochastically using the Gillespie algorithm. The results demonstrate that extrinsic noise diversifies the shuttling patterns of NF-{\kappa}B response, whereas intrinsic noise induces oscillatory behavior in many of the otherwise non-oscillatory patterns. We identify two key model parameters which significantly affect the NF-{\kappa}B dynamic response and deduce a two-dimensional phase-diagram of the NF-{\kappa}B response as a function of these parameters. We conclude that if single-cell experiments are performed, a rich variety of NF-{\kappa}B response will be observed, even if population-level experiments, which average response over large numbers of cells, do not evidence oscillatory behavior.