Multistability and robustness of the MAPK pathway

In this paper, we propose a qualitative model of the MAPK signaling cascade and analyze its multi-stability properties. Building on our previous work, we employ Lyapunov and invariant sets theory to analyze the system. In particular we focus on the first stage of a class of MAPK cascades, known as the Mos subsystem, which is the target of a positive feedback loop. Under general assumptions, we show that the system is bistable when three equilibria are present, regardless of the specific feedback dynamics.