Symbolic-numeric estimation of parameters in biochemical models by quantifier elimination

The sequencing of complete genomes allows analyses of the interactions between various biological molecules on a genomic scale, which prompted us to simulate the global behaviors of biological phenomena on the molecular level. One of the basic mathematical problems in the simulation is the parameter optimization in the kinetic model for complex dynamics, and many estimation methods have been designed. We introduce a new approach to estimate the parameters in biological kinetic models by quantifier elimination (QE), in combination with numerical simulation methods. The estimation method was applied to a model for the inhibition kinetics of HIV proteinase with ten parameters and nine variables, and attained the goodness of fit to 300 points of observed data with the same magnitude as that obtained by the previous estimation methods, remarkably by using only one or two points of data. Furthermore, the utilization of QE demonstrated the feasibility of the present method for elucidating the behavior of the parameters and the variables in the analyzed model. Therefore, the present symbolic-numeric method is a powerful approach to reveal the fundamental mechanisms of kinetic models, in addition to being a computational engine.