An appropriate bounded invariant region for a bistable reaction-diffusion model of the caspase-3/8 feedback loop

The apoptotic caspase-3/8 feedback loop describes the core of the extrinsic pro-apoptotic signaling pathway, an essential part of apoptosis. Latter is a prototype of the programmed cell death, which enables organisms to remove damaged or infected cells. The reaction network of the caspase-3/8 feedback loop in a single cell is modeled by a reaction-diffusion system, which shows a bistable behavior. In this work, we present an appropriate bounded invariant region for the bistable reaction-diffusion system in order to theoretically confirm that diffusion rapidly balances the concentrations of the different caspase types. This justifies the decomposition of the dynamics into a diffusion dominated part on a very short time scale and a pure reaction driven dynamics on a large time scale.