Inference of S-system models of genetic networks by solving linear programming problems and sets of linear algebraic equations

For the inference of S-system models of genetic networks, this study proposes a new method, i.e., a two-phase estimation method. The two-phase estimation method is an extension of the decoupling approach proposed by Voit and Almeida. The decoupling approach defines the estimation of S-system parameters as a problem of solving sets of non-linear algebraic equations. Our method first transforms each set of non-linear algebraic equations, that is defined by the decoupling approach, into a set of linear ones. The transformation of the equations is easily accomplished by solving a linear programming problem. The proposed method then estimates S-system parameters by solving the transformed linear equations. As the proposed two-phase estimation method infers an S-system model only by solving linear programming problems and sets of linear algebraic equations, it always provides us with a unique solution. Moreover, its computational cost is very low. Finally, we confirm the effectiveness of the proposed method through numerical experiments.