Hybrid modeling of p53 and Akt associated gene regulatory network

p53 is known as a genome guardian gene as it bears a putative function in the DNA damage associated gene regulatory networks (GRNs). These GRNs integrate many upstream signals to up-regulate p53 and in turn p53 either up-regulates or down-regulates many downstream signals. In this paper, we model a GRN comprising of the entities p53, Mdm2c, Mdm2n, and Akt using the qualitative and hybrid modeling frameworks. The qualitative model predicts a stable state and cycles representing the over expression and homeostasis of the entities, respectively. The model also predicts the bifurcation states, which cause divergence from the normal cyclic behaviours towards the stable state. We also compute the conditions in the form of delay constraints for the existence of cycles using hybrid model checking.