Type I interferon (IFN) signaling pathways play an essential role in the defense against early viral infections; however, the diverse and intricate molecular mechanisms of virus-triggered type I IFN responses are still poorly understood. In this study, we analyzed and compared two classes of models i.e., deterministic ordinary differential equations (ODEs) and stochastic models to elucidate the dynamics and stochasticity of type I IFN signaling pathways. Bifurcation analysis based on an ODE model reveals that the system exhibits a bistable switch and a one-way switch at high or low levels when the strengths of the negative and positive feedbacks are tuned. Furthermore, we compared the stochastic simulation results under the Master and Langevin equations. Both of the stochastic equations generate the bistable switch phenomenon, and the distance between two stable states are smaller than normal under the simulation of the Langevin equation. The quantitative computations also show that a moderate ratio between positive and negative feedback strengths is required to ensure a reliable switch between the different IFN concentrations that regulate the immune response. Moreover, we propose a multi-state stochastic model based on the above deterministic model to describe the multi-cellular system coupled with the diffusion of IFNs. The perturbation and inhibition analysis showed that the positive feedback, as well as noises, has little effect on the stochastic expression of IFNs, but the negative feedback of ISG56 on the activation of IRF7 has a great influence on IFN stochastic expression. Together, these results reveal that positive feedback stabilizes IFN gene expression, and negative feedback may be the main contribution to the stochastic expression of the IFN gene in the virus-triggered type I IFN response. These findings will provide new insight into the molecular mechanisms of virus-triggered type I IFN signaling pathways.
- Bifurcation analysis
- Mathematical model
- Type I IFN signaling pathways