An optimization model of apoptosis: determination of kinetic constants

Apoptosis is a distinct mechanism of cell death. The result of apoptosis is elimination of invalid cells. The apoptosis system is a set of cytoplasmic proteins. After apoptosis induction the cascade of enzyme reactions is triggered. Once activated procaspases form active enzymes ? caspases. Apoptosis targets are destructed by executioner caspases. Apoptosis is induced by various stimuli (death receptor ligands, granzyme B, and many others antineoplastic agents). Granzyme B activates procaspases and direct cleaves apoptotic targets. The main purpose of this work is to study dynamics of caspase activation and target cleavage in granzyme B-induced apoptosis. In particular, the effects of changing granzyme B concentrations on the dynamics of caspase activation are studied using mathematical modeling technique. A major difficulty in the problem solving is the fact that most of the kinetic constants for biochemical reactions are lacking. Therefore, the other purpose of this work is to determine unknown kinetic constant using optimization approach. The results of this study enable us to estimate unknown kinetic constants. In addition, the peculiarities of the apoptosis dynamics can be studied qualitatively. A prolonged lag time between apoptosis initiation and a significant increase in caspase concentrations is predicted. With increasing granzyme B concentrations, the lag time is shortened. This model provides a new insight into caspase activation process that is critical for immune cell-mediated lyses of immunological targets.