Structural properties of the MAPK pathway topologies in PC12 cells
In this paper we propose and analyze parameter-free models for the mitogen-activated protein kinase (MAPK) pathway in PC12 rat neural cells. Experiments show that the dynamic behavior of this pathway depends on the input growth factor. The response to epidermal growth factor (EGF) is a short peak followed by a relaxation, while the response to nerve growth factor (NGF) is sustained. In the latter case, the system can be driven to a new state, which persists after the stimulus has vanished. Ultimately, these dynamic behaviors correspond to different cell fates: EFG stimulation induces proliferation, while NGF stimulation induces differentiation. The biochemical mechanisms responsible for the different input-dependent dynamic response are still unclear. One hypothesis is that each input generates a specific interaction topology among the kinases. Starting from experimental results that support this hypothesis, we derive and analyze qualitative models for the two network topologies. Our approach is based on invariant set theory and non-smooth Lyapunov functions. We demonstrate analytically that the network behaviors and stability properties are structurally dependent on the topology, and do not depend on specific parameter values of the underlying biochemical interactions.