The study of biological systems is drawing the attention of many scientists giving a description of their behavior based on mathematical modeling and numerical approaches. Most of the time, this pathway is followed either when experimental data for a given network is missing or a prediction of the system evolution is made. In both cases, the states of each element of the network as well as the interactions between them are important for modeling the biological system. Here we use a discrete model such as Boolean modeling for making a prediction of the evolution of mTOR signaling pathway based on different initial states of the system and different ways of interactions between elements. We focus on synchronous update of the nodes' states in order to find and analyze the fixed points of the system. It is shown that the system reaches different stable states represented in each case by a fixed point, or it enters in a cycle limit, depending on the initial state of the system and on the way of the interactions between elements, as well. In all cases we see that mTORC1, in which we are mainly focused, becomes inactive. Although this study is limited, we aim to generalize this case of study to other similar cases which can lead us to other in-depth analysis.

Keywords : Boolean Model, Synchronous Update, Nodes, Network, Dynamical Evolution.