A Power-Law Based Model for Caspase Activated Apoptosis and Its Parameter Estimation

Based on Michaelis-Menten kinetics model, a group of nonlinear differential equation with the fractional (nonlinear) reaction rates has been derived to describe the dynamics of caspase activated apoptosis. The fractional reaction rates cannot be measured and yet contains important parameters to be estimated for modeling and analysis. Several methods have been proposed to estimate the parameters in nonlinear reaction rates. However, there are always some parameters in the model which cannot be estimated or have unsatisfactory estimation errors by any existing methods. Alternately, the power-law has been proposed to model the kinetic reaction rates. In this paper, I develop a power-law based model for caspase activated apoptosis and propose a parameter estimation method for estimate parameter in power-law based reaction rate. The simulation and analysis show that the power-law based model has the same quality as the Michealis-Menten kinetics based model to describe the dynamics of caspase activated apoptosis, and yet the parameters in the former model is easier to be estimated than those in latter one.