Analysis of network dynamics including hidden variables by symbolic-numeric approach

We propose a symbolic-numeric method for estimating the kinetic constants in a biological network including hidden variables which mean that the behaviors of corresponding molecules cannot be directly measured. In the present method, an algebraic manipulation of the differential equations over the Laplace domain, formulated based on the assumption of linear relationships between the variables, is combined with the numerical fitting of the sampling data. The performance of the method is illustared for a part of MAPK network with the data measured by the transfection cell array in combination of the gene interference by siRNAs.