Sensitivity Analysis of Discrete Models and Application in Biological Networks

Understanding sensitivity is an important step to study system robustness and adaptability. In this work, we model and investigate intra-cellular networks via discrete modeling approach, which assigns a set of discrete values and a deterministic update rule to each model element. The models can be analyzed formally or simulated in a stochastic manner. We propose a comprehensive framework to study sensitivity in these models. In the framework, we define element influence (activity) and sensitivity with respect to the state distribution of the modeled system. Previous sensitivity analysis approaches all assume uniform state distribution, which is usually not true in biology. We perform both static and dynamic sensitivity analysis, the former assuming uniform state distribution, and the latter using a distribution estimated from stochastic simulation trajectories under a particular scenario. Additionally, we extended the element update functions to include weights according to these computed influences. Adding weights generates a weighted directed graph, and therefore, enables identifying key elements in the model and dominant signaling pathways that determine the behavior of the overall model. In the end, we apply our sensitivity analysis framework on pathway extraction in the intra-cellular networks that control T cells differentiation.