Sensitivity Analysis of Discrete Models and Application in Biological Networks

Understanding sensitivity is an important step to study system robustness against perturbations and adaptability to the environment. In this work, we model and investigate intra-cellular networks via discrete modeling approach, and we propose a framework to study sensitivity in these models. The discrete modeling approach assigns a set of discrete values and an update rule to each model element. The models can be analyzed formally or simulated in a deterministic or a stochastic manner. In our framework, we define element activity and sensitivity with respect to the state distribution of the modeled system. Previous sensitivity analysis approaches 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. Within our sensitivity analysis framework, we first compute element-to-element influences, then we extend the element update functions to include weights according to these computed influences. Adding weights to element interaction rules helps to identify key elements in the model and dominant signaling pathways that determine the behavior of the overall model. When studying cellular signaling networks, we are particularly interested in the response of elements to perturbations, as our goal is often to reach the desired model state via least number of interventions. We have applied our sensitivity analysis framework on pathway extraction and evaluation in the intra-cellular networks that controls T cell differentiation. Additionally, we propose four different ranking algorithms to extract the most important pathways from a given source element to a given target element. We then evaluate these four algorithms using cross validation of corresponding extraction results. Our results show that, in different application occasions, different pathway extraction and evaluation algorithms should be adopted to help find "globally valid" or "globally effective" pathways