Symbolic-numeric Estimation of Parameters in Biochemical Models by Quantifier Elimination

We introduce a new approach to optimize the parameters in biological kinetic models by quantifier elimination (QE), in combination with numerical simulation methods. The optimization 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 optimization 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 in the analyzed model. The present symbolic-numeric method is therefore a powerful approach to reveal the fundamental mechanisms of kinetic models, in addition to being a computational engine.