Paper Title
Fixed Points Analysis of a Protein Signaling Pathway, with Predefined Biological Conditions

Abstract
In this paper, we present the use of the Boolean model to study the dynamic evolution of a protein-protein interaction network, with the final purpose of analyzing its fixed points. We are particularly interested in exploring the dynamic evolution of the complex protein kinase mTORC1 signaling pathway as numerous studies show the great impact that this protein has on some metabolic processes and tumor diseases. Boolean modeling is performed only on the main proteins selected; meanwhile, two conditions are predefined since the beginning. The state of each input, corresponding to the initial condition of the system, is set to be constant over time, whereas the state of each output, corresponding to the final implications produced, is determined to be under the experiment. Consequently, only one of the fixed points generated ensures this to happen. In this final steady state, it is shown that the crucial nodes, i.e., proteins that can transmit the signal and are active in these signaling pathways, are mTORC1, PI3K, and Akt. Finally, we suggest that even though Boolean modeling may produce many attractors, not all can be considered as real possible, stable states for the biological system. Keywords - Boolean Model, Synchronous/Asynchronous Update, Nodes, Fixed Point, Network, Dynamical Evolution, Protein Kinase.