Parameter Optimization in Network Dynamics Including Unmeasured Variables by the Symbolic-numeric Approach∗

In this report, we propose a new symbolic-numeric method of differential algebra and a numerical parameter optimization algorithm. First, we utilize differential elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system, to derive the constraints between the kinetic parameters from the original system. Second, we introduce these constraints to effectively optimize the parameters into a genetic algorithm, Real-Coded Genetic Algorithms (RCGAs), which is a numerical parameter optimizing method. To evaluate the ability of our method, we performed a simulation study for an artificial biological network including one measured and three unmeasured molecules. As a result, our method, the symbolic-numeric method of differential elimination and RCGAs, precisely estimated the kinetic parameters in the simulated network, while RCGAs failed. Thus, our method is useful for analyzing the dynamics of a biological network including unmeasured molecules.