  Understanding deaths and life-death boundaries of cells is a fundamental
challenge in biological sciences. In this study, we present a theoretical
framework for investigating cell death. We conceptualize cell death as a
controllability problem within dynamical systems, and compute the life-death
boundary through the development of ``stoichiometric rays''. This method
utilizes enzyme activity as control parameters, exploiting the inherent
property of enzymes to enhance reaction rates without shifting equilibrium
states. This approach facilitates the efficient evaluation of the global
controllability of models. We demonstrate the utility of our framework using
its application to a toy metabolic model, where we delineate the life-death
boundary. The formulation of cell death through mathematical principles
provides a foundation for the theoretical study of cellular mortality.
