Complexity analysis and optimal experimental design for parameter estimation of biological systems

A biological system describes the dynamics of a biological process and can be modeled by a group of nonlinear differential equations. The nonlinear terms in differential equations of a biological system result from the reaction rates which can not be measured and yet contain important parameters to be identified. In practice, not all states are measured because of the limitation of experimental conditions and cost. In this paper, we develop a methodology for complexity analysis and optimal experimental design to maximize the number of identifiable parameters in the reaction rates while minimizing the number of states which must be measured. We use the model of the programmed cell death or apoptosis as an instance to illustrate the proposed method. The analysis shows that the results from our proposed method are better than those from the existing methods.